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diff --git a/Build/source/texk/web2c/mplibdir/mp.w b/Build/source/texk/web2c/mplibdir/mp.w new file mode 100644 index 00000000000..1303cf6f9e4 --- /dev/null +++ b/Build/source/texk/web2c/mplibdir/mp.w @@ -0,0 +1,26427 @@ +% $Id: mp.w 873 2009-03-19 07:44:11Z taco $ +% +% Copyright 2008 Taco Hoekwater. +% +% This program is free software: you can redistribute it and/or modify +% it under the terms of the GNU Lesser General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public License +% along with this program. If not, see <http://www.gnu.org/licenses/>. +% +% TeX is a trademark of the American Mathematical Society. +% METAFONT is a trademark of Addison-Wesley Publishing Company. +% PostScript is a trademark of Adobe Systems Incorporated. + +% Here is TeX material that gets inserted after \input webmac +\def\hang{\hangindent 3em\noindent\ignorespaces} +\def\textindent#1{\hangindent2.5em\noindent\hbox to2.5em{\hss#1 }\ignorespaces} +\def\ps{PostScript} +\def\psqrt#1{\sqrt{\mathstrut#1}} +\def\k{_{k+1}} +\def\pct!{{\char`\%}} % percent sign in ordinary text +\font\tenlogo=logo10 % font used for the METAFONT logo +\font\logos=logosl10 +\def\MF{{\tenlogo META}\-{\tenlogo FONT}} +\def\MP{{\tenlogo META}\-{\tenlogo POST}} +\def\[#1]{\ignorespaces} % left over from pascal web +\def\<#1>{$\langle#1\rangle$} +\def\section{\mathhexbox278} +\let\swap=\leftrightarrow +\def\round{\mathop{\rm round}\nolimits} +\mathchardef\vbv="026A % synonym for `\|' +\def\vb{\relax\ifmmode\vbv\else$\vbv$\fi} + +\def\(#1){} % this is used to make section names sort themselves better +\def\9#1{} % this is used for sort keys in the index via @@:sort key}{entry@@> +\def\title{MetaPost} +\pdfoutput=1 +\pageno=3 + +@* \[1] Introduction. + +This is \MP\ by John Hobby, a graphics-language processor based on D. E. Knuth's \MF. + +Much of the original Pascal version of this program was copied with +permission from MF.web Version 1.9. It interprets a language very +similar to D.E. Knuth's METAFONT, but with changes designed to make it +more suitable for PostScript output. + +The main purpose of the following program is to explain the algorithms of \MP\ +as clearly as possible. However, the program has been written so that it +can be tuned to run efficiently in a wide variety of operating environments +by making comparatively few changes. Such flexibility is possible because +the documentation that follows is written in the \.{WEB} language, which is +at a higher level than C. + +A large piece of software like \MP\ has inherent complexity that cannot +be reduced below a certain level of difficulty, although each individual +part is fairly simple by itself. The \.{WEB} language is intended to make +the algorithms as readable as possible, by reflecting the way the +individual program pieces fit together and by providing the +cross-references that connect different parts. Detailed comments about +what is going on, and about why things were done in certain ways, have +been liberally sprinkled throughout the program. These comments explain +features of the implementation, but they rarely attempt to explain the +\MP\ language itself, since the reader is supposed to be familiar with +{\sl The {\logos METAFONT\/}book} as well as the manual +@.WEB@> +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> +{\sl A User's Manual for MetaPost}, Computing Science Technical Report 162, +AT\AM T Bell Laboratories. + +@ The present implementation is a preliminary version, but the possibilities +for new features are limited by the desire to remain as nearly compatible +with \MF\ as possible. + +On the other hand, the \.{WEB} description can be extended without changing +the core of the program, and it has been designed so that such +extensions are not extremely difficult to make. +The |banner| string defined here should be changed whenever \MP\ +undergoes any modifications, so that it will be clear which version of +\MP\ might be the guilty party when a problem arises. +@^extensions to \MP@> +@^system dependencies@> + +@d default_banner "This is MetaPost, Version 1.110" /* printed when \MP\ starts */ +@d true 1 +@d false 0 + +@(mpmp.h@>= +#define metapost_version "1.110" +#define metapost_magic (('M'*256) + 'P')*65536 + 1110 +#define metapost_old_magic (('M'*256) + 'P')*65536 + 1080 + +@ The external library header for \MP\ is |mplib.h|. It contains a +few typedefs and the header defintions for the externally used +fuctions. + +The most important of the typedefs is the definition of the structure +|MP_options|, that acts as a small, configurable front-end to the fairly +large |MP_instance| structure. + +@(mplib.h@>= +typedef struct MP_instance * MP; +@<Exported types@> +typedef struct MP_options { + @<Option variables@> +} MP_options; +@<Exported function headers@> + +@ The internal header file is much longer: it not only lists the complete +|MP_instance|, but also a lot of functions that have to be available to +the \ps\ backend, that is defined in a separate \.{WEB} file. + +The variables from |MP_options| are included inside the |MP_instance| +wholesale. + +@(mpmp.h@>= +#include <setjmp.h> +typedef struct psout_data_struct * psout_data; +typedef struct svgout_data_struct * svgout_data; +#ifndef HAVE_BOOLEAN +typedef int boolean; +#endif +#ifndef INTEGER_TYPE +typedef int integer; +#endif +@<Declare helpers@> +@<Types in the outer block@> +@<Constants in the outer block@> +typedef struct MP_instance { + @<Option variables@> + @<Global variables@> +} MP_instance; +@<Internal library declarations@> + +@ @c +#include "config.h" +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <stdarg.h> +#include <assert.h> +#ifdef HAVE_UNISTD_H +#include <unistd.h> /* for access() */ +#endif +#include <time.h> /* for struct tm \& co */ +#include "mplib.h" +#include "mplibps.h" /* external header */ +#include "mplibsvg.h" /* external header */ +#include "mpmp.h" /* internal header */ +#include "mppsout.h" /* internal header */ +#include "mpsvgout.h" /* internal header */ +extern font_number mp_read_font_info (MP mp, char *fname); /* tfmin.w */ +@h +@<Declarations@> +@<Basic printing procedures@> +@<Error handling procedures@> + +@ Here are the functions that set up the \MP\ instance. + +@<Declarations@> = +MP_options *mp_options (void); +MP mp_initialize (MP_options *opt); + +@ @c +MP_options *mp_options (void) { + MP_options *opt; + size_t l = sizeof(MP_options); + opt = malloc(l); + if (opt!=NULL) { + memset (opt,0,l); + opt->ini_version = true; + } + return opt; +} + +@ @<Internal library declarations@>= +@<Declare subroutines for parsing file names@> + +@ The whole instance structure is initialized with zeroes, +this greatly reduces the number of statements needed in +the |Allocate or initialize variables| block. + +@d set_callback_option(A) do { mp->A = mp_##A; + if (opt->A!=NULL) mp->A = opt->A; +} while (0) + +@c +static MP mp_do_new (jmp_buf *buf) { + MP mp = malloc(sizeof(MP_instance)); + if (mp==NULL) { + xfree(buf); + return NULL; + } + memset(mp,0,sizeof(MP_instance)); + mp->jump_buf = buf; + return mp; +} + +@ @c +static void mp_free (MP mp) { + int k; /* loop variable */ + @<Dealloc variables@> + if (mp->noninteractive) { + @<Finish non-interactive use@>; + } + xfree(mp->jump_buf); + xfree(mp); +} + +@ @c +static void mp_do_initialize ( MP mp) { + @<Local variables for initialization@> + @<Set initial values of key variables@> +} + +@ This procedure gets things started properly. +@c +MP mp_initialize (MP_options *opt) { + MP mp; + jmp_buf *buf = malloc(sizeof(jmp_buf)); + if (buf == NULL || setjmp(*buf) != 0) + return NULL; + mp = mp_do_new(buf); + if (mp == NULL) + return NULL; + mp->userdata=opt->userdata; + @<Set |ini_version|@>; + mp->noninteractive=opt->noninteractive; + set_callback_option(find_file); + set_callback_option(open_file); + set_callback_option(read_ascii_file); + set_callback_option(read_binary_file); + set_callback_option(close_file); + set_callback_option(eof_file); + set_callback_option(flush_file); + set_callback_option(write_ascii_file); + set_callback_option(write_binary_file); + set_callback_option(shipout_backend); + if (opt->banner && *(opt->banner)) { + mp->banner = xstrdup(opt->banner); + } else { + mp->banner = xstrdup(default_banner); + } + if (opt->command_line && *(opt->command_line)) + mp->command_line = xstrdup(opt->command_line); + if (mp->noninteractive) { + @<Prepare function pointers for non-interactive use@>; + } + /* open the terminal for output */ + t_open_out; + @<Find constant sizes@>; + @<Allocate or initialize variables@> + mp_reallocate_memory(mp,mp->mem_max); + mp_reallocate_paths(mp,1000); + mp_reallocate_fonts(mp,8); + mp->history=mp_fatal_error_stop; /* in case we quit during initialization */ + @<Check the ``constant'' values...@>; + if ( mp->bad>0 ) { + char ss[256]; + mp_snprintf(ss,256,"Ouch---my internal constants have been clobbered!\n" + "---case %i",(int)mp->bad); + do_fprintf(mp->err_out,(char *)ss); +@.Ouch...clobbered@> + return mp; + } + mp_do_initialize(mp); /* erase preloaded mem */ + if (mp->ini_version) { + @<Run inimpost commands@>; + } + if (!mp->noninteractive) { + @<Initialize the output routines@>; + @<Get the first line of input and prepare to start@>; + @<Initializations after first line is read@>; + } else { + mp->history=mp_spotless; + } + return mp; +} + +@ @<Initializations after first line is read@>= +mp_open_log_file(mp); +mp_set_job_id(mp); +mp_init_map_file(mp, mp->troff_mode); +mp->history=mp_spotless; /* ready to go! */ +if (mp->troff_mode) { + mp->internal[mp_gtroffmode]=unity; + mp->internal[mp_prologues]=unity; +} +if ( mp->start_sym>0 ) { /* insert the `\&{everyjob}' symbol */ + mp->cur_sym=mp->start_sym; mp_back_input(mp); +} + +@ @<Exported function headers@>= +extern MP_options *mp_options (void); +extern MP mp_initialize (MP_options *opt) ; +extern int mp_status(MP mp); +extern void *mp_userdata(MP mp); + +@ @c +int mp_status(MP mp) { return mp->history; } + +@ @c +void *mp_userdata(MP mp) { return mp->userdata; } + +@ The overall \MP\ program begins with the heading just shown, after which +comes a bunch of procedure declarations and function declarations. +Finally we will get to the main program, which begins with the +comment `|start_here|'. If you want to skip down to the +main program now, you can look up `|start_here|' in the index. +But the author suggests that the best way to understand this program +is to follow pretty much the order of \MP's components as they appear in the +\.{WEB} description you are now reading, since the present ordering is +intended to combine the advantages of the ``bottom up'' and ``top down'' +approaches to the problem of understanding a somewhat complicated system. + +@ Some of the code below is intended to be used only when diagnosing the +strange behavior that sometimes occurs when \MP\ is being installed or +when system wizards are fooling around with \MP\ without quite knowing +what they are doing. Such code will not normally be compiled; it is +delimited by the preprocessor test `|#ifdef DEBUG .. #endif|'. + +@ This program has two important variations: (1) There is a long and slow +version called \.{INIMP}, which does the extra calculations needed to +@.INIMP@> +initialize \MP's internal tables; and (2)~there is a shorter and faster +production version, which cuts the initialization to a bare minimum. + +Which is which is decided at runtime. + +@ The following parameters can be changed at compile time to extend or +reduce \MP's capacity. They may have different values in \.{INIMP} and +in production versions of \MP. +@.INIMP@> +@^system dependencies@> + +@<Constants...@>= +#define file_name_size 255 /* file names shouldn't be longer than this */ +#define bistack_size 1500 /* size of stack for bisection algorithms; + should probably be left at this value */ + +@ Like the preceding parameters, the following quantities can be changed +to extend or reduce \MP's capacity. But if they are changed, +it is necessary to rerun the initialization program \.{INIMP} +@.INIMP@> +to generate new tables for the production \MP\ program. +One can't simply make helter-skelter changes to the following constants, +since certain rather complex initialization +numbers are computed from them. + +@ @<Glob...@>= +int max_strings; /* maximum number of strings; must not exceed |max_halfword| */ +int pool_size; /* maximum number of characters in strings, including all + error messages and help texts, and the names of all identifiers */ +int old_pool_size; /* a helper used by |mp_cat| */ +int mem_max; /* greatest index in \MP's internal |mem| array; + must be strictly less than |max_halfword|; + must be equal to |mem_top| in \.{INIMP}, otherwise |>=mem_top| */ +int mem_top; /* largest index in the |mem| array dumped by \.{INIMP}; + must not be greater than |mem_max| */ +int hash_prime; /* a prime number equal to about 85\pct! of |hash_size| */ + +@ @<Option variables@>= +int error_line; /* width of context lines on terminal error messages */ +int half_error_line; /* width of first lines of contexts in terminal + error messages; should be between 30 and |error_line-15| */ +int halt_on_error; /* do we quit at the first error? */ +int max_print_line; /* width of longest text lines output; should be at least 60 */ +unsigned hash_size; /* maximum number of symbolic tokens, + must be less than |max_halfword-3*param_size| */ +int param_size; /* maximum number of simultaneous macro parameters */ +int max_in_open; /* maximum number of input files and error insertions that + can be going on simultaneously */ +int main_memory; /* only for options, to set up |mem_max| and |mem_top| */ +void *userdata; /* this allows the calling application to setup local */ +char *banner; /* the banner that is printed to the screen and log */ + +@ @<Dealloc variables@>= +xfree(mp->banner); + +@ +@d set_value(a,b,c) do { a=c; if (b>c) a=b; } while (0) + +@<Allocate or ...@>= +mp->max_strings=500; +mp->pool_size=10000; +mp->old_pool_size=10000; +set_value(mp->error_line,opt->error_line,79); +set_value(mp->half_error_line,opt->half_error_line,50); +if (mp->half_error_line>mp->error_line-15 ) + mp->half_error_line = mp->error_line-15; +mp->max_print_line=100; +set_value(mp->max_print_line,opt->max_print_line,79); +mp->halt_on_error = (opt->halt_on_error ? true : false); + +@ In case somebody has inadvertently made bad settings of the ``constants,'' +\MP\ checks them using a global variable called |bad|. + +This is the second of many sections of \MP\ where global variables are +defined. + +@<Glob...@>= +integer bad; /* is some ``constant'' wrong? */ + +@ Later on we will say `\ignorespaces|if (mem_max>=max_halfword) bad=10;|', +or something similar. (We can't do that until |max_halfword| has been defined.) + +In case you are wondering about the non-consequtive values of |bad|: some +of the things that used to be WEB constants are now runtime variables +with checking at assignment time. + +@<Check the ``constant'' values for consistency@>= +mp->bad=0; +if ( mp->mem_top<=1100 ) mp->bad=4; + +@ Some |goto| labels are used by the following definitions. The label +`|restart|' is occasionally used at the very beginning of a procedure; and +the label `|reswitch|' is occasionally used just prior to a |case| +statement in which some cases change the conditions and we wish to branch +to the newly applicable case. Loops that are set up with the |loop| +construction defined below are commonly exited by going to `|done|' or to +`|found|' or to `|not_found|', and they are sometimes repeated by going to +`|continue|'. If two or more parts of a subroutine start differently but +end up the same, the shared code may be gathered together at +`|common_ending|'. + +@ Here are some macros for common programming idioms. + +@d incr(A) (A)=(A)+1 /* increase a variable by unity */ +@d decr(A) (A)=(A)-1 /* decrease a variable by unity */ +@d negate(A) (A)=-(A) /* change the sign of a variable */ +@d double(A) (A)=(A)+(A) +@d odd(A) ((A)%2==1) +@d do_nothing /* empty statement */ + +@* \[2] The character set. +In order to make \MP\ readily portable to a wide variety of +computers, all of its input text is converted to an internal eight-bit +code that includes standard ASCII, the ``American Standard Code for +Information Interchange.'' This conversion is done immediately when each +character is read in. Conversely, characters are converted from ASCII to +the user's external representation just before they are output to a +text file. +@^ASCII code@> + +Such an internal code is relevant to users of \MP\ only with respect to +the \&{char} and \&{ASCII} operations, and the comparison of strings. + +@ Characters of text that have been converted to \MP's internal form +are said to be of type |ASCII_code|, which is a subrange of the integers. + +@<Types...@>= +typedef unsigned char ASCII_code; /* eight-bit numbers */ + +@ The present specification of \MP\ has been written under the assumption +that the character set contains at least the letters and symbols associated +with ASCII codes 040 through 0176; all of these characters are now +available on most computer terminals. + +@<Types...@>= +typedef unsigned char text_char; /* the data type of characters in text files */ + +@ @<Local variables for init...@>= +integer i; + +@ The \MP\ processor converts between ASCII code and +the user's external character set by means of arrays |xord| and |xchr| +that are analogous to Pascal's |ord| and |chr| functions. + +@(mpmp.h@>= +#define xchr(A) mp->xchr[(A)] +#define xord(A) mp->xord[(A)] + +@ @<Glob...@>= +ASCII_code xord[256]; /* specifies conversion of input characters */ +text_char xchr[256]; /* specifies conversion of output characters */ + +@ The core system assumes all 8-bit is acceptable. If it is not, +a change file has to alter the below section. +@^system dependencies@> + +Additionally, people with extended character sets can +assign codes arbitrarily, giving an |xchr| equivalent to whatever +characters the users of \MP\ are allowed to have in their input files. +Appropriate changes to \MP's |char_class| table should then be made. +(Unlike \TeX, each installation of \MP\ has a fixed assignment of category +codes, called the |char_class|.) Such changes make portability of programs +more difficult, so they should be introduced cautiously if at all. +@^character set dependencies@> +@^system dependencies@> + +@<Set initial ...@>= +for (i=0;i<=0377;i++) { xchr(i)=(text_char)i; } + +@ The following system-independent code makes the |xord| array contain a +suitable inverse to the information in |xchr|. Note that if |xchr[i]=xchr[j]| +where |i<j<0177|, the value of |xord[xchr[i]]| will turn out to be +|j| or more; hence, standard ASCII code numbers will be used instead of +codes below 040 in case there is a coincidence. + +@<Set initial ...@>= +for (i=0;i<=255;i++) { + xord(xchr(i))=0177; +} +for (i=0200;i<=0377;i++) { xord(xchr(i))=(ASCII_code)i;} +for (i=0;i<=0176;i++) { xord(xchr(i))=(ASCII_code)i;} + +@* \[3] Input and output. +The bane of portability is the fact that different operating systems treat +input and output quite differently, perhaps because computer scientists +have not given sufficient attention to this problem. People have felt somehow +that input and output are not part of ``real'' programming. Well, it is true +that some kinds of programming are more fun than others. With existing +input/output conventions being so diverse and so messy, the only sources of +joy in such parts of the code are the rare occasions when one can find a +way to make the program a little less bad than it might have been. We have +two choices, either to attack I/O now and get it over with, or to postpone +I/O until near the end. Neither prospect is very attractive, so let's +get it over with. + +The basic operations we need to do are (1)~inputting and outputting of +text, to or from a file or the user's terminal; (2)~inputting and +outputting of eight-bit bytes, to or from a file; (3)~instructing the +operating system to initiate (``open'') or to terminate (``close'') input or +output from a specified file; (4)~testing whether the end of an input +file has been reached; (5)~display of bits on the user's screen. +The bit-display operation will be discussed in a later section; we shall +deal here only with more traditional kinds of I/O. + +@ Finding files happens in a slightly roundabout fashion: the \MP\ +instance object contains a field that holds a function pointer that finds a +file, and returns its name, or NULL. For this, it receives three +parameters: the non-qualified name |fname|, the intended |fopen| +operation type |fmode|, and the type of the file |ftype|. + +The file types that are passed on in |ftype| can be used to +differentiate file searches if a library like kpathsea is used, +the fopen mode is passed along for the same reason. + +@<Types...@>= +typedef unsigned char eight_bits ; /* unsigned one-byte quantity */ + +@ @<Exported types@>= +enum mp_filetype { + mp_filetype_terminal = 0, /* the terminal */ + mp_filetype_error, /* the terminal */ + mp_filetype_program , /* \MP\ language input */ + mp_filetype_log, /* the log file */ + mp_filetype_postscript, /* the postscript output */ + mp_filetype_memfile, /* memory dumps */ + mp_filetype_metrics, /* TeX font metric files */ + mp_filetype_fontmap, /* PostScript font mapping files */ + mp_filetype_font, /* PostScript type1 font programs */ + mp_filetype_encoding, /* PostScript font encoding files */ + mp_filetype_text /* first text file for readfrom and writeto primitives */ +}; +typedef char *(*mp_file_finder)(MP, const char *, const char *, int); +typedef void *(*mp_file_opener)(MP, const char *, const char *, int); +typedef char *(*mp_file_reader)(MP, void *, size_t *); +typedef void (*mp_binfile_reader)(MP, void *, void **, size_t *); +typedef void (*mp_file_closer)(MP, void *); +typedef int (*mp_file_eoftest)(MP, void *); +typedef void (*mp_file_flush)(MP, void *); +typedef void (*mp_file_writer)(MP, void *, const char *); +typedef void (*mp_binfile_writer)(MP, void *, void *, size_t); + +@ @<Option variables@>= +mp_file_finder find_file; +mp_file_opener open_file; +mp_file_reader read_ascii_file; +mp_binfile_reader read_binary_file; +mp_file_closer close_file; +mp_file_eoftest eof_file; +mp_file_flush flush_file; +mp_file_writer write_ascii_file; +mp_binfile_writer write_binary_file; + +@ The default function for finding files is |mp_find_file|. It is +pretty stupid: it will only find files in the current directory. + +This function may disappear altogether, it is currently only +used for the default font map file. + +@c +static char *mp_find_file (MP mp, const char *fname, const char *fmode, int ftype) { + (void) mp; + if (fmode[0] != 'r' || (! access (fname,R_OK)) || ftype) { + return mp_strdup(fname); + } + return NULL; +} + +@ Because |mp_find_file| is used so early, it has to be in the helpers +section. + +@<Declarations@>= +static char *mp_find_file (MP mp, const char *fname, const char *fmode, int ftype) ; +static void *mp_open_file (MP mp , const char *fname, const char *fmode, int ftype) ; +static char *mp_read_ascii_file (MP mp, void *f, size_t *size) ; +static void mp_read_binary_file (MP mp, void *f, void **d, size_t *size) ; +static void mp_close_file (MP mp, void *f) ; +static int mp_eof_file (MP mp, void *f) ; +static void mp_flush_file (MP mp, void *f) ; +static void mp_write_ascii_file (MP mp, void *f, const char *s) ; +static void mp_write_binary_file (MP mp, void *f, void *s, size_t t) ; + +@ The function to open files can now be very short. + +@c +void *mp_open_file(MP mp, const char *fname, const char *fmode, int ftype) { + char realmode[3]; + (void) mp; + realmode[0] = *fmode; + realmode[1] = 'b'; + realmode[2] = 0; + if (ftype==mp_filetype_terminal) { + return (fmode[0] == 'r' ? stdin : stdout); + } else if (ftype==mp_filetype_error) { + return stderr; + } else if (fname != NULL && (fmode[0] != 'r' || (! access (fname,R_OK)))) { + return (void *)fopen(fname, realmode); + } + return NULL; +} + +@ This is a legacy interface: (almost) all file names pass through |name_of_file|. + +@<Glob...@>= +char name_of_file[file_name_size+1]; /* the name of a system file */ +int name_length;/* this many characters are actually + relevant in |name_of_file| (the rest are blank) */ + +@ If this parameter is true, the terminal and log will report the found +file names for input files instead of the requested ones. +It is off by default because it creates an extra filename lookup. + +@<Option variables@>= +int print_found_names; /* configuration parameter */ + +@ @<Allocate or initialize ...@>= +mp->print_found_names = (opt->print_found_names>0 ? true : false); + +@ The |file_line_error_style| parameter makes \MP\ use a more +standard compiler error message format instead of the Knuthian +exclamation mark. It needs the actual version of the current input +file name, that will be saved by |a_open_in| in the global +|mp->long_name|. + +@<Glob...@>= +char *long_name; + +@ @<Option variables@>= +int file_line_error_style; /* configuration parameter */ + +@ @<Allocate or initialize ...@>= +mp->file_line_error_style = (opt->file_line_error_style>0 ? true : false); +mp->long_name = NULL; + +@ \MP's file-opening procedures return |false| if no file identified by +|name_of_file| could be opened. + +The |OPEN_FILE| macro takes care of the |print_found_names| parameter. +It is not used for opening a mem file for read, because that file name +is never printed. + +@d OPEN_FILE(A) do { + if (mp->print_found_names || mp->file_line_error_style) { + char *s = (mp->find_file)(mp,mp->name_of_file,A,ftype); + if (s!=NULL) { + *f = (mp->open_file)(mp,mp->name_of_file,A, ftype); + if (mp->print_found_names) { + strncpy(mp->name_of_file,s,file_name_size); + } + if ((*(A) == 'r') && (ftype == mp_filetype_program)) { + xfree(mp->long_name); + mp->long_name = xstrdup(s); + } + xfree(s); + } else { + *f = NULL; + } + } else { + *f = (mp->open_file)(mp,mp->name_of_file,A, ftype); + } +} while (0); +return (*f ? true : false) + +@c +static boolean mp_a_open_in (MP mp, void **f, int ftype) { + /* open a text file for input */ + OPEN_FILE("r"); +} +@# +boolean mp_w_open_in (MP mp, void **f) { + /* open a word file for input */ + *f = (mp->open_file)(mp,mp->name_of_file,"r",mp_filetype_memfile); + return (*f ? true : false); +} +@# +static boolean mp_a_open_out (MP mp, void **f, int ftype) { + /* open a text file for output */ + OPEN_FILE("w"); +} +@# +static boolean mp_b_open_out (MP mp, void **f, int ftype) { + /* open a binary file for output */ + OPEN_FILE("w"); +} +@# +boolean mp_w_open_out (MP mp, void **f) { + /* open a word file for output */ + int ftype = mp_filetype_memfile; + OPEN_FILE("w"); +} + +@ @<Internal library ...@>= +boolean mp_w_open_out (MP mp, void **f); + +@ @c +static char *mp_read_ascii_file (MP mp, void *ff, size_t *size) { + int c; + size_t len = 0, lim = 128; + char *s = NULL; + FILE *f = (FILE *)ff; + *size = 0; + (void) mp; /* for -Wunused */ + if (f==NULL) + return NULL; + c = fgetc(f); + if (c==EOF) + return NULL; + s = malloc(lim); + if (s==NULL) return NULL; + while (c!=EOF && c!='\n' && c!='\r') { + if ((len+1)==lim) { + s =realloc(s, (lim+(lim>>2))); + if (s==NULL) return NULL; + lim+=(lim>>2); + } + s[len++] = c; + c =fgetc(f); + } + if (c=='\r') { + c = fgetc(f); + if (c!=EOF && c!='\n') + ungetc(c,f); + } + s[len] = 0; + *size = len; + return s; +} + +@ @c +void mp_write_ascii_file (MP mp, void *f, const char *s) { + (void) mp; + if (f!=NULL) { + fputs(s,(FILE *)f); + } +} + +@ @c +void mp_read_binary_file (MP mp, void *f, void **data, size_t *size) { + size_t len = 0; + (void) mp; + if (f!=NULL) + len = fread(*data,1,*size,(FILE *)f); + *size = len; +} + +@ @c +void mp_write_binary_file (MP mp, void *f, void *s, size_t size) { + (void) mp; + if (f!=NULL) + (void)fwrite(s,size,1,(FILE *)f); +} + + +@ @c +void mp_close_file (MP mp, void *f) { + (void) mp; + if (f!=NULL) + fclose((FILE *)f); +} + +@ @c +int mp_eof_file (MP mp, void *f) { + (void) mp; + if (f!=NULL) + return feof((FILE *)f); + else + return 1; +} + +@ @c +void mp_flush_file (MP mp, void *f) { + (void) mp; + if (f!=NULL) + fflush((FILE *)f); +} + +@ Input from text files is read one line at a time, using a routine called +|input_ln|. This function is defined in terms of global variables called +|buffer|, |first|, and |last| that will be described in detail later; for +now, it suffices for us to know that |buffer| is an array of |ASCII_code| +values, and that |first| and |last| are indices into this array +representing the beginning and ending of a line of text. + +@<Glob...@>= +size_t buf_size; /* maximum number of characters simultaneously present in + current lines of open files */ +ASCII_code *buffer; /* lines of characters being read */ +size_t first; /* the first unused position in |buffer| */ +size_t last; /* end of the line just input to |buffer| */ +size_t max_buf_stack; /* largest index used in |buffer| */ + +@ @<Allocate or initialize ...@>= +mp->buf_size = 200; +mp->buffer = xmalloc((mp->buf_size+1),sizeof(ASCII_code)); + +@ @<Dealloc variables@>= +xfree(mp->buffer); + +@ @c +static void mp_reallocate_buffer(MP mp, size_t l) { + ASCII_code *buffer; + if (l>max_halfword) { + mp_confusion(mp,"buffer size"); /* can't happen (I hope) */ + } + buffer = xmalloc((l+1),sizeof(ASCII_code)); + memcpy(buffer,mp->buffer,(mp->buf_size+1)); + xfree(mp->buffer); + mp->buffer = buffer ; + mp->buf_size = l; +} + +@ The |input_ln| function brings the next line of input from the specified +field into available positions of the buffer array and returns the value +|true|, unless the file has already been entirely read, in which case it +returns |false| and sets |last:=first|. In general, the |ASCII_code| +numbers that represent the next line of the file are input into +|buffer[first]|, |buffer[first+1]|, \dots, |buffer[last-1]|; and the +global variable |last| is set equal to |first| plus the length of the +line. Trailing blanks are removed from the line; thus, either |last=first| +(in which case the line was entirely blank) or |buffer[last-1]<>" "|. +@^inner loop@> + +The variable |max_buf_stack|, which is used to keep track of how large +the |buf_size| parameter must be to accommodate the present job, is +also kept up to date by |input_ln|. + +@c +static boolean mp_input_ln (MP mp, void *f ) { + /* inputs the next line or returns |false| */ + char *s; + size_t size = 0; + mp->last=mp->first; /* cf.\ Matthew 19\thinspace:\thinspace30 */ + s = (mp->read_ascii_file)(mp,f, &size); + if (s==NULL) + return false; + if (size>0) { + mp->last = mp->first+size; + if ( mp->last>=mp->max_buf_stack ) { + mp->max_buf_stack=mp->last+1; + while ( mp->max_buf_stack>mp->buf_size ) { + mp_reallocate_buffer(mp,(mp->buf_size+(mp->buf_size>>2))); + } + } + memcpy((mp->buffer+mp->first),s,size); + /* while ( mp->buffer[mp->last]==' ' ) mp->last--; */ + } + free(s); + return true; +} + +@ The user's terminal acts essentially like other files of text, except +that it is used both for input and for output. When the terminal is +considered an input file, the file variable is called |term_in|, and when it +is considered an output file the file variable is |term_out|. +@^system dependencies@> + +@<Glob...@>= +void * term_in; /* the terminal as an input file */ +void * term_out; /* the terminal as an output file */ +void * err_out; /* the terminal as an output file */ + +@ Here is how to open the terminal files. In the default configuration, +nothing happens except that the command line (if there is one) is copied +to the input buffer. The variable |command_line| will be filled by the +|main| procedure. The copying can not be done earlier in the program +logic because in the |INI| version, the |buffer| is also used for primitive +initialization. + +@d t_open_out do {/* open the terminal for text output */ + mp->term_out = (mp->open_file)(mp,"terminal", "w", mp_filetype_terminal); + mp->err_out = (mp->open_file)(mp,"error", "w", mp_filetype_error); +} while (0) +@d t_open_in do { /* open the terminal for text input */ + mp->term_in = (mp->open_file)(mp,"terminal", "r", mp_filetype_terminal); + if (mp->command_line!=NULL) { + mp->last = strlen(mp->command_line); + strncpy((char *)mp->buffer,mp->command_line,mp->last); + xfree(mp->command_line); + } else { + mp->last = 0; + } +} while (0) + +@<Option variables@>= +char *command_line; + +@ Sometimes it is necessary to synchronize the input/output mixture that +happens on the user's terminal, and three system-dependent +procedures are used for this +purpose. The first of these, |update_terminal|, is called when we want +to make sure that everything we have output to the terminal so far has +actually left the computer's internal buffers and been sent. +The second, |clear_terminal|, is called when we wish to cancel any +input that the user may have typed ahead (since we are about to +issue an unexpected error message). The third, |wake_up_terminal|, +is supposed to revive the terminal if the user has disabled it by +some instruction to the operating system. The following macros show how +these operations can be specified: +@^system dependencies@> + +@(mpmp.h@>= +#define update_terminal (mp->flush_file)(mp,mp->term_out) /* empty the terminal output buffer */ +#define clear_terminal do_nothing /* clear the terminal input buffer */ +#define wake_up_terminal (mp->flush_file)(mp,mp->term_out) + /* cancel the user's cancellation of output */ + +@ We need a special routine to read the first line of \MP\ input from +the user's terminal. This line is different because it is read before we +have opened the transcript file; there is sort of a ``chicken and +egg'' problem here. If the user types `\.{input cmr10}' on the first +line, or if some macro invoked by that line does such an \.{input}, +the transcript file will be named `\.{cmr10.log}'; but if no \.{input} +commands are performed during the first line of terminal input, the transcript +file will acquire its default name `\.{mpout.log}'. (The transcript file +will not contain error messages generated by the first line before the +first \.{input} command.) + +The first line is even more special. It's nice to let the user start +running a \MP\ job by typing a command line like `\.{MP cmr10}'; in +such a case, \MP\ will operate as if the first line of input were +`\.{cmr10}', i.e., the first line will consist of the remainder of the +command line, after the part that invoked \MP. + +@ Different systems have different ways to get started. But regardless of +what conventions are adopted, the routine that initializes the terminal +should satisfy the following specifications: + +\yskip\textindent{1)}It should open file |term_in| for input from the + terminal. (The file |term_out| will already be open for output to the + terminal.) + +\textindent{2)}If the user has given a command line, this line should be + considered the first line of terminal input. Otherwise the + user should be prompted with `\.{**}', and the first line of input + should be whatever is typed in response. + +\textindent{3)}The first line of input, which might or might not be a + command line, should appear in locations |first| to |last-1| of the + |buffer| array. + +\textindent{4)}The global variable |loc| should be set so that the + character to be read next by \MP\ is in |buffer[loc]|. This + character should not be blank, and we should have |loc<last|. + +\yskip\noindent(It may be necessary to prompt the user several times +before a non-blank line comes in. The prompt is `\.{**}' instead of the +later `\.*' because the meaning is slightly different: `\.{input}' need +not be typed immediately after~`\.{**}'.) + +@d loc mp->cur_input.loc_field /* location of first unread character in |buffer| */ + +@c +boolean mp_init_terminal (MP mp) { /* gets the terminal input started */ + t_open_in; + if (mp->last!=0) { + loc = 0; mp->first = 0; + return true; + } + while (1) { + if (!mp->noninteractive) { + wake_up_terminal; do_fprintf(mp->term_out,"**"); update_terminal; +@.**@> + } + if ( ! mp_input_ln(mp, mp->term_in ) ) { /* this shouldn't happen */ + do_fprintf(mp->term_out,"\n! End of file on the terminal... why?"); +@.End of file on the terminal@> + return false; + } + loc=(halfword)mp->first; + while ( (loc<(int)mp->last)&&(mp->buffer[loc]==' ') ) + incr(loc); + if ( loc<(int)mp->last ) { + return true; /* return unless the line was all blank */ + } + if (!mp->noninteractive) { + do_fprintf(mp->term_out,"Please type the name of your input file.\n"); + } + } +} + +@ @<Declarations@>= +static boolean mp_init_terminal (MP mp) ; + + +@* \[4] String handling. +Symbolic token names and diagnostic messages are variable-length strings +of eight-bit characters. Many strings \MP\ uses are simply literals +in the compiled source, like the error messages and the names of the +internal parameters. Other strings are used or defined from the \MP\ input +language, and these have to be interned. + +\MP\ uses strings more extensively than \MF\ does, but the necessary +operations can still be handled with a fairly simple data structure. +The array |str_pool| contains all of the (eight-bit) ASCII codes in all +of the strings, and the array |str_start| contains indices of the starting +points of each string. Strings are referred to by integer numbers, so that +string number |s| comprises the characters |str_pool[j]| for +|str_start[s]<=j<str_start[ss]| where |ss=next_str[s]|. The string pool +is allocated sequentially and |str_pool[pool_ptr]| is the next unused +location. The first string number not currently in use is |str_ptr| +and |next_str[str_ptr]| begins a list of free string numbers. String +pool entries |str_start[str_ptr]| up to |pool_ptr| are reserved for a +string currently being constructed. + +String numbers 0 to 255 are reserved for strings that correspond to single +ASCII characters. This is in accordance with the conventions of \.{WEB}, +@.WEB@> +which converts single-character strings into the ASCII code number of the +single character involved, while it converts other strings into integers +and builds a string pool file. Thus, when the string constant \.{"."} appears +in the program below, \.{WEB} converts it into the integer 46, which is the +ASCII code for a period, while \.{WEB} will convert a string like \.{"hello"} +into some integer greater than~255. String number 46 will presumably be the +single character `\..'\thinspace; but some ASCII codes have no standard visible +representation, and \MP\ may need to be able to print an arbitrary +ASCII character, so the first 256 strings are used to specify exactly what +should be printed for each of the 256 possibilities. + +@<Types...@>= +typedef int pool_pointer; /* for variables that point into |str_pool| */ +typedef int str_number; /* for variables that point into |str_start| */ + +@ @<Glob...@>= +ASCII_code *str_pool; /* the characters */ +pool_pointer *str_start; /* the starting pointers */ +str_number *next_str; /* for linking strings in order */ +pool_pointer pool_ptr; /* first unused position in |str_pool| */ +str_number str_ptr; /* number of the current string being created */ +pool_pointer init_pool_ptr; /* the starting value of |pool_ptr| */ +str_number init_str_use; /* the initial number of strings in use */ +pool_pointer max_pool_ptr; /* the maximum so far of |pool_ptr| */ +str_number max_str_ptr; /* the maximum so far of |str_ptr| */ + +@ @<Allocate or initialize ...@>= +mp->str_pool = xmalloc ((mp->pool_size +1),sizeof(ASCII_code)); +mp->str_start = xmalloc ((mp->max_strings+1),sizeof(pool_pointer)); +mp->next_str = xmalloc ((mp->max_strings+1),sizeof(str_number)); + +@ @<Dealloc variables@>= +xfree(mp->str_pool); +xfree(mp->str_start); +xfree(mp->next_str); + +@ Most printing is done from |char *|s, but sometimes not. Here are +functions that convert an internal string into a |char *| for use +by the printing routines, and vice versa. + +@d str(A) mp_str(mp,A) +@d rts(A) mp_rts(mp,A) +@d null_str rts("") + +@<Internal ...@>= +int mp_xstrcmp (const char *a, const char *b); +char * mp_str (MP mp, str_number s); + +@ @<Declarations@>= +static str_number mp_rts (MP mp, const char *s); +static str_number mp_make_string (MP mp); + +@ @c +int mp_xstrcmp (const char *a, const char *b) { + if (a==NULL && b==NULL) + return 0; + if (a==NULL) + return -1; + if (b==NULL) + return 1; + return strcmp(a,b); +} + +@ The attempt to catch interrupted strings that is in |mp_rts|, is not +very good: it does not handle nesting over more than one level. + +@c +char * mp_str (MP mp, str_number ss) { + char *s; + size_t len; + if (ss==mp->str_ptr) { + return NULL; + } else { + len = (size_t)length(ss); + s = xmalloc(len+1,sizeof(char)); + strncpy(s,(char *)(mp->str_pool+(mp->str_start[ss])),len); + s[len] = 0; + return (char *)s; + } +} +str_number mp_rts (MP mp, const char *s) { + int r; /* the new string */ + int old; /* a possible string in progress */ + int i=0; + if (strlen(s)==0) { + return 256; + } else if (strlen(s)==1) { + return s[0]; + } else { + old=0; + str_room((integer)strlen(s)); + if (mp->str_start[mp->str_ptr]<mp->pool_ptr) + old = mp_make_string(mp); + while (*s) { + append_char(*s); + s++; + } + r = mp_make_string(mp); + if (old!=0) { + str_room(length(old)); + while (i<length(old)) { + append_char((mp->str_start[old]+i)); + } + mp_flush_string(mp,old); + } + return r; + } +} + +@ Except for |strs_used_up|, the following string statistics are only +maintained when code between |stat| $\ldots$ |tats| delimiters is not +commented out: + +@<Glob...@>= +integer strs_used_up; /* strings in use or unused but not reclaimed */ +integer pool_in_use; /* total number of cells of |str_pool| actually in use */ +integer strs_in_use; /* total number of strings actually in use */ +integer max_pl_used; /* maximum |pool_in_use| so far */ +integer max_strs_used; /* maximum |strs_in_use| so far */ + +@ Several of the elementary string operations are performed using \.{WEB} +macros instead of functions, because many of the +operations are done quite frequently and we want to avoid the +overhead of procedure calls. For example, here is +a simple macro that computes the length of a string. +@.WEB@> + +@d str_stop(A) mp->str_start[mp->next_str[(A)]] /* one cell past the end of string \# */ +@d length(A) (str_stop((A))-mp->str_start[(A)]) /* the number of characters in string \# */ + +@ The length of the current string is called |cur_length|. If we decide that +the current string is not needed, |flush_cur_string| resets |pool_ptr| so that +|cur_length| becomes zero. + +@d cur_length (mp->pool_ptr - mp->str_start[mp->str_ptr]) +@d flush_cur_string mp->pool_ptr=mp->str_start[mp->str_ptr] + +@ Strings are created by appending character codes to |str_pool|. +The |append_char| macro, defined here, does not check to see if the +value of |pool_ptr| has gotten too high; this test is supposed to be +made before |append_char| is used. + +To test if there is room to append |l| more characters to |str_pool|, +we shall write |str_room(l)|, which tries to make sure there is enough room +by compacting the string pool if necessary. If this does not work, +|do_compaction| aborts \MP\ and gives an apologetic error message. + +@d append_char(A) /* put |ASCII_code| \# at the end of |str_pool| */ +{ mp->str_pool[mp->pool_ptr]=(ASCII_code)(A); incr(mp->pool_ptr); +} +@d str_room(A) /* make sure that the pool hasn't overflowed */ + { if ( mp->pool_ptr+(A) > mp->max_pool_ptr ) { + if ( mp->pool_ptr+(A) > mp->pool_size ) mp_do_compaction(mp, (A)); + else mp->max_pool_ptr=mp->pool_ptr+(A); } + } + +@ The following routine is similar to |str_room(1)| but it uses the +argument |mp->pool_size| to prevent |do_compaction| from aborting when +string space is exhausted. + +@<Declarations@>= +static void mp_unit_str_room (MP mp); + +@ @c +void mp_unit_str_room (MP mp) { + if ( mp->pool_ptr>=mp->pool_size ) mp_do_compaction(mp, mp->pool_size); + if ( mp->pool_ptr>=mp->max_pool_ptr ) mp->max_pool_ptr=mp->pool_ptr+1; +} + +@ \MP's string expressions are implemented in a brute-force way: Every +new string or substring that is needed is simply copied into the string pool. +Space is eventually reclaimed by a procedure called |do_compaction| with +the aid of a simple system system of reference counts. +@^reference counts@> + +The number of references to string number |s| will be |str_ref[s]|. The +special value |str_ref[s]=max_str_ref=127| is used to denote an unknown +positive number of references; such strings will never be recycled. If +a string is ever referred to more than 126 times, simultaneously, we +put it in this category. Hence a single byte suffices to store each |str_ref|. + +@d max_str_ref 127 /* ``infinite'' number of references */ +@d add_str_ref(A) { if ( mp->str_ref[(A)]<max_str_ref ) incr(mp->str_ref[(A)]); } + +@<Glob...@>= +int *str_ref; + +@ @<Allocate or initialize ...@>= +mp->str_ref = xmalloc ((mp->max_strings+1),sizeof(int)); + +@ @<Dealloc variables@>= +xfree(mp->str_ref); + +@ Here's what we do when a string reference disappears: + +@d delete_str_ref(A) { + if ( mp->str_ref[(A)]<max_str_ref ) { + if ( mp->str_ref[(A)]>1 ) decr(mp->str_ref[(A)]); + else mp_flush_string(mp, (A)); + } + } + +@<Declarations@>= +static void mp_flush_string (MP mp,str_number s) ; + +@ We can't flush the first set of static strings at all, so there +is no point in trying + +@c +void mp_flush_string (MP mp,str_number s) { + if (length(s)>1) { + mp->pool_in_use=mp->pool_in_use-length(s); + decr(mp->strs_in_use); + if ( mp->next_str[s]!=mp->str_ptr ) { + mp->str_ref[s]=0; + } else { + mp->str_ptr=s; + decr(mp->strs_used_up); + } + mp->pool_ptr=mp->str_start[mp->str_ptr]; + } +} + +@ C literals cannot be simply added, they need to be set so they can't +be flushed. + +@d intern(A) mp_intern(mp,(A)) + +@c +str_number mp_intern (MP mp, const char *s) { + str_number r ; + r = rts(s); + mp->str_ref[r] = max_str_ref; + return r; +} + +@ @<Declarations@>= +static str_number mp_intern (MP mp, const char *s); + + +@ Once a sequence of characters has been appended to |str_pool|, it +officially becomes a string when the function |make_string| is called. +This function returns the identification number of the new string as its +value. + +When getting the next unused string number from the linked list, we pretend +that +$$ \hbox{|max_str_ptr+1|, |max_str_ptr+2|, $\ldots$, |mp->max_strings|} $$ +are linked sequentially even though the |next_str| entries have not been +initialized yet. We never allow |str_ptr| to reach |mp->max_strings|; +|do_compaction| is responsible for making sure of this. + +@<Declarations@>= +static str_number mp_make_string (MP mp); + +@ @c +str_number mp_make_string (MP mp) { /* current string enters the pool */ + str_number s; /* the new string */ +RESTART: + s=mp->str_ptr; + mp->str_ptr=mp->next_str[s]; + if ( mp->str_ptr>mp->max_str_ptr ) { + if ( mp->str_ptr==mp->max_strings ) { + mp->str_ptr=s; + mp_do_compaction(mp, 0); + goto RESTART; + } else { + mp->max_str_ptr=mp->str_ptr; + mp->next_str[mp->str_ptr]=mp->max_str_ptr+1; + } + } + mp->str_ref[s]=1; + mp->str_start[mp->str_ptr]=mp->pool_ptr; + incr(mp->strs_used_up); + incr(mp->strs_in_use); + mp->pool_in_use=mp->pool_in_use+length(s); + if ( mp->pool_in_use>mp->max_pl_used ) + mp->max_pl_used=mp->pool_in_use; + if ( mp->strs_in_use>mp->max_strs_used ) + mp->max_strs_used=mp->strs_in_use; + return s; +} + +@ The most interesting string operation is string pool compaction. The idea +is to recover unused space in the |str_pool| array by recopying the strings +to close the gaps created when some strings become unused. All string +numbers~$k$ where |str_ref[k]=0| are to be linked into the list of free string +numbers after |str_ptr|. If this fails to free enough pool space we issue an +|overflow| error unless |needed=mp->pool_size|. Calling |do_compaction| +with |needed=mp->pool_size| supresses all overflow tests. + +The compaction process starts with |last_fixed_str| because all lower numbered +strings are permanently allocated with |max_str_ref| in their |str_ref| entries. + +@<Glob...@>= +str_number last_fixed_str; /* last permanently allocated string */ +str_number fixed_str_use; /* number of permanently allocated strings */ + +@ @<Internal library ...@>= +void mp_do_compaction (MP mp, pool_pointer needed) ; + +@ @c +void mp_do_compaction (MP mp, pool_pointer needed) { + str_number str_use; /* a count of strings in use */ + str_number r,s,t; /* strings being manipulated */ + pool_pointer p,q; /* destination and source for copying string characters */ + @<Advance |last_fixed_str| as far as possible and set |str_use|@>; + r=mp->last_fixed_str; + s=mp->next_str[r]; + p=mp->str_start[s]; + while ( s!=mp->str_ptr ) { + while ( mp->str_ref[s]==0 ) { + @<Advance |s| and add the old |s| to the list of free string numbers; + then |break| if |s=str_ptr|@>; + } + r=s; s=mp->next_str[s]; + incr(str_use); + @<Move string |r| back so that |str_start[r]=p|; make |p| the location + after the end of the string@>; + } +DONE: + @<Move the current string back so that it starts at |p|@>; + if ( needed<mp->pool_size ) { + @<Make sure that there is room for another string with |needed| characters@>; + } + @<Account for the compaction and make sure the statistics agree with the + global versions@>; + mp->strs_used_up=str_use; +} + +@ @<Advance |last_fixed_str| as far as possible and set |str_use|@>= +t=mp->next_str[mp->last_fixed_str]; +while (t!=mp->str_ptr && mp->str_ref[t]==max_str_ref) { + incr(mp->fixed_str_use); + mp->last_fixed_str=t; + t=mp->next_str[t]; +} +str_use=mp->fixed_str_use + +@ Because of the way |flush_string| has been written, it should never be +necessary to |break| here. The extra line of code seems worthwhile to +preserve the generality of |do_compaction|. + +@<Advance |s| and add the old |s| to the list of free string numbers;...@>= +{ +t=s; +s=mp->next_str[s]; +mp->next_str[r]=s; +mp->next_str[t]=mp->next_str[mp->str_ptr]; +mp->next_str[mp->str_ptr]=t; +if ( s==mp->str_ptr ) goto DONE; +} + +@ The string currently starts at |str_start[r]| and ends just before +|str_start[s]|. We don't change |str_start[s]| because it might be needed +to locate the next string. + +@<Move string |r| back so that |str_start[r]=p|; make |p| the location...@>= +q=mp->str_start[r]; +mp->str_start[r]=p; +while ( q<mp->str_start[s] ) { + mp->str_pool[p]=mp->str_pool[q]; + incr(p); incr(q); +} + +@ Pointers |str_start[str_ptr]| and |pool_ptr| have not been updated. When +we do this, anything between them should be moved. + +@ @<Move the current string back so that it starts at |p|@>= +q=mp->str_start[mp->str_ptr]; +mp->str_start[mp->str_ptr]=p; +while ( q<mp->pool_ptr ) { + mp->str_pool[p]=mp->str_pool[q]; + incr(p); incr(q); +} +mp->pool_ptr=p + +@ We must remember that |str_ptr| is not allowed to reach |mp->max_strings|. + +@<Make sure that there is room for another string with |needed| char...@>= +if ( str_use>=mp->max_strings-1 ) + mp_reallocate_strings (mp,str_use); +if ( mp->pool_ptr+needed>mp->max_pool_ptr ) { + mp_reallocate_pool(mp, mp->pool_ptr+needed); + mp->max_pool_ptr=mp->pool_ptr+needed; +} + +@ @<Internal library ...@>= +void mp_reallocate_strings (MP mp, str_number str_use) ; +void mp_reallocate_pool(MP mp, pool_pointer needed) ; + +@ @c +void mp_reallocate_strings (MP mp, str_number str_use) { + while ( str_use>=mp->max_strings-1 ) { + int l = mp->max_strings + (mp->max_strings/4); + XREALLOC (mp->str_ref, l, int); + XREALLOC (mp->str_start, l, pool_pointer); + XREALLOC (mp->next_str, l, str_number); + mp->max_strings = l; + } +} +void mp_reallocate_pool(MP mp, pool_pointer needed) { + while ( needed>mp->pool_size ) { + int l = mp->pool_size + (mp->pool_size/4); + XREALLOC (mp->str_pool, l, ASCII_code); + mp->pool_size = l; + } +} + +@ @<Account for the compaction and make sure the statistics agree with...@>= +if ( (mp->str_start[mp->str_ptr]!=mp->pool_in_use)||(str_use!=mp->strs_in_use) ) + mp_confusion(mp, "string"); +@:this can't happen string}{\quad string@> +incr(mp->pact_count); +mp->pact_chars=mp->pact_chars+mp->pool_ptr-str_stop(mp->last_fixed_str); +mp->pact_strs=mp->pact_strs+str_use-mp->fixed_str_use; + +@ A few more global variables are needed to keep track of statistics when +|stat| $\ldots$ |tats| blocks are not commented out. + +@<Glob...@>= +integer pact_count; /* number of string pool compactions so far */ +integer pact_chars; /* total number of characters moved during compactions */ +integer pact_strs; /* total number of strings moved during compactions */ + +@ @<Initialize compaction statistics@>= +mp->pact_count=0; +mp->pact_chars=0; +mp->pact_strs=0; + +@ The following subroutine compares string |s| with another string of the +same length that appears in |buffer| starting at position |k|; +the result is |true| if and only if the strings are equal. + +@c +static boolean mp_str_eq_buf (MP mp,str_number s, integer k) { + /* test equality of strings */ + pool_pointer j; /* running index */ + j=mp->str_start[s]; + while ( j<str_stop(s) ) { + if ( mp->str_pool[j++]!=mp->buffer[k++] ) + return false; + } + return true; +} + +@ Here is a similar routine, but it compares two strings in the string pool, +and it does not assume that they have the same length. If the first string +is lexicographically greater than, less than, or equal to the second, +the result is respectively positive, negative, or zero. + +@c +static integer mp_str_vs_str (MP mp, str_number s, str_number t) { + /* test equality of strings */ + pool_pointer j,k; /* running indices */ + integer ls,lt; /* lengths */ + integer l; /* length remaining to test */ + ls=length(s); lt=length(t); + if ( ls<=lt ) l=ls; else l=lt; + j=mp->str_start[s]; k=mp->str_start[t]; + while ( l-->0 ) { + if ( mp->str_pool[j]!=mp->str_pool[k] ) { + return (mp->str_pool[j]-mp->str_pool[k]); + } + j++; k++; + } + return (ls-lt); +} + +@ The initial values of |str_pool|, |str_start|, |pool_ptr|, +and |str_ptr| are computed by the \.{INIMP} program, based in part +on the information that \.{WEB} has output while processing \MP. +@.INIMP@> +@^string pool@> + +@c +void mp_get_strings_started (MP mp) { + /* initializes the string pool, + but returns |false| if something goes wrong */ + int k; /* small indices or counters */ + str_number g; /* a new string */ + mp->pool_ptr=0; mp->str_ptr=0; mp->max_pool_ptr=0; mp->max_str_ptr=0; + mp->str_start[0]=0; + mp->next_str[0]=1; + mp->pool_in_use=0; mp->strs_in_use=0; + mp->max_pl_used=0; mp->max_strs_used=0; + @<Initialize compaction statistics@>; + mp->strs_used_up=0; + @<Make the first 256 strings@>; + g=mp_make_string(mp); /* string 256 == "" */ + mp->str_ref[g]=max_str_ref; + mp->last_fixed_str=mp->str_ptr-1; + mp->fixed_str_use=mp->str_ptr; + return; +} + +@ @<Declarations@>= +static void mp_get_strings_started (MP mp); + +@ The first 256 strings will consist of a single character only. + +@<Make the first 256...@>= +for (k=0;k<=255;k++) { + append_char(k); + g=mp_make_string(mp); + mp->str_ref[g]=max_str_ref; +} + +@ The first 128 strings will contain 95 standard ASCII characters, and the +other 33 characters will be printed in three-symbol form like `\.{\^\^A}' +unless a system-dependent change is made here. Installations that have +an extended character set, where for example |xchr[032]=@t\.{'^^Z'}@>|, +would like string 032 to be printed as the single character 032 instead +of the three characters 0136, 0136, 0132 (\.{\^\^Z}). On the other hand, +even people with an extended character set will want to represent string +015 by \.{\^\^M}, since 015 is ASCII's ``carriage return'' code; the idea is +to produce visible strings instead of tabs or line-feeds or carriage-returns +or bell-rings or characters that are treated anomalously in text files. + +The boolean expression defined here should be |true| unless \MP\ internal +code number~|k| corresponds to a non-troublesome visible symbol in the +local character set. +If character |k| cannot be printed, and |k<0200|, then character |k+0100| or +|k-0100| must be printable; moreover, ASCII codes |[060..071, 0141..0146]| +must be printable. +@^character set dependencies@> +@^system dependencies@> + +@<Character |k| cannot be printed@>= + (k<' ')||(k==127) + +@* \[5] On-line and off-line printing. +Messages that are sent to a user's terminal and to the transcript-log file +are produced by several `|print|' procedures. These procedures will +direct their output to a variety of places, based on the setting of +the global variable |selector|, which has the following possible +values: + +\yskip +\hang |term_and_log|, the normal setting, prints on the terminal and on the + transcript file. + +\hang |log_only|, prints only on the transcript file. + +\hang |term_only|, prints only on the terminal. + +\hang |no_print|, doesn't print at all. This is used only in rare cases + before the transcript file is open. + +\hang |pseudo|, puts output into a cyclic buffer that is used + by the |show_context| routine; when we get to that routine we shall discuss + the reasoning behind this curious mode. + +\hang |new_string|, appends the output to the current string in the + string pool. + +\hang |>=write_file| prints on one of the files used for the \&{write} +@:write_}{\&{write} primitive@> + command. + +\yskip +\noindent The symbolic names `|term_and_log|', etc., have been assigned +numeric codes that satisfy the convenient relations |no_print+1=term_only|, +|no_print+2=log_only|, |term_only+2=log_only+1=term_and_log|. These +relations are not used when |selector| could be |pseudo|, or |new_string|. +We need not check for unprintable characters when |selector<pseudo|. + +Three additional global variables, |tally|, |term_offset| and |file_offset| +record the number of characters that have been printed +since they were most recently cleared to zero. We use |tally| to record +the length of (possibly very long) stretches of printing; |term_offset|, +and |file_offset|, on the other hand, keep track of how many +characters have appeared so far on the current line that has been output +to the terminal, the transcript file, or the \ps\ output file, respectively. + +@d new_string 0 /* printing is deflected to the string pool */ +@d pseudo 2 /* special |selector| setting for |show_context| */ +@d no_print 3 /* |selector| setting that makes data disappear */ +@d term_only 4 /* printing is destined for the terminal only */ +@d log_only 5 /* printing is destined for the transcript file only */ +@d term_and_log 6 /* normal |selector| setting */ +@d write_file 7 /* first write file selector */ + +@<Glob...@>= +void * log_file; /* transcript of \MP\ session */ +void * output_file; /* the generic font output goes here */ +unsigned int selector; /* where to print a message */ +unsigned char dig[23]; /* digits in a number, for rounding */ +integer tally; /* the number of characters recently printed */ +unsigned int term_offset; + /* the number of characters on the current terminal line */ +unsigned int file_offset; + /* the number of characters on the current file line */ +ASCII_code *trick_buf; /* circular buffer for pseudoprinting */ +integer trick_count; /* threshold for pseudoprinting, explained later */ +integer first_count; /* another variable for pseudoprinting */ + +@ @<Allocate or initialize ...@>= +mp->trick_buf = xmalloc((mp->error_line+1),sizeof(ASCII_code)); + +@ @<Dealloc variables@>= +xfree(mp->trick_buf); + +@ @<Initialize the output routines@>= +mp->selector=term_only; mp->tally=0; mp->term_offset=0; mp->file_offset=0; + +@ Macro abbreviations for output to the terminal and to the log file are +defined here for convenience. Some systems need special conventions +for terminal output, and it is possible to adhere to those conventions +by changing |wterm|, |wterm_ln|, and |wterm_cr| here. +@^system dependencies@> + +@(mpmp.h@>= +#define do_fprintf(f,b) (mp->write_ascii_file)(mp,f,b) +#define wterm(A) do_fprintf(mp->term_out,(A)) +#define wterm_chr(A) { unsigned char ss[2]; ss[0]=(A); ss[1]='\0'; wterm((char *)ss);} +#define wterm_cr do_fprintf(mp->term_out,"\n") +#define wterm_ln(A) { wterm_cr; do_fprintf(mp->term_out,(A)); } +#define wlog(A) do_fprintf(mp->log_file,(A)) +#define wlog_chr(A) { unsigned char ss[2]; ss[0]=(A); ss[1]='\0'; wlog((char *)ss);} +#define wlog_cr do_fprintf(mp->log_file, "\n") +#define wlog_ln(A) { wlog_cr; do_fprintf(mp->log_file,(A)); } + + +@ To end a line of text output, we call |print_ln|. Cases |0..max_write_files| +use an array |wr_file| that will be declared later. + +@d mp_print_text(A) mp_print_str(mp,text((A))) + +@<Internal library ...@>= +void mp_print (MP mp, const char *s); +void mp_print_ln (MP mp); +void mp_print_visible_char (MP mp, ASCII_code s); +void mp_print_char (MP mp, ASCII_code k); +void mp_print_str (MP mp, str_number s); +void mp_print_nl (MP mp, const char *s); +void mp_print_two (MP mp,scaled x, scaled y) ; +void mp_print_scaled (MP mp,scaled s); + +@ @<Basic print...@>= +void mp_print_ln (MP mp) { /* prints an end-of-line */ + switch (mp->selector) { + case term_and_log: + wterm_cr; wlog_cr; + mp->term_offset=0; mp->file_offset=0; + break; + case log_only: + wlog_cr; mp->file_offset=0; + break; + case term_only: + wterm_cr; mp->term_offset=0; + break; + case no_print: + case pseudo: + case new_string: + break; + default: + do_fprintf(mp->wr_file[(mp->selector-write_file)],"\n"); + } +} /* note that |tally| is not affected */ + +@ The |print_visible_char| procedure sends one character to the desired +destination, using the |xchr| array to map it into an external character +compatible with |input_ln|. (It assumes that it is always called with +a visible ASCII character.) All printing comes through |print_ln| or +|print_char|, which ultimately calls |print_visible_char|, hence these +routines are the ones that limit lines to at most |max_print_line| characters. +But we must make an exception for the \ps\ output file since it is not safe +to cut up lines arbitrarily in \ps. + +Procedure |unit_str_room| needs to be declared |forward| here because it calls +|do_compaction| and |do_compaction| can call the error routines. Actually, +|unit_str_room| avoids |overflow| errors but it can call |confusion|. + +@<Basic printing...@>= +void mp_print_visible_char (MP mp, ASCII_code s) { /* prints a single character */ + switch (mp->selector) { + case term_and_log: + wterm_chr(xchr(s)); wlog_chr(xchr(s)); + incr(mp->term_offset); incr(mp->file_offset); + if ( mp->term_offset==(unsigned)mp->max_print_line ) { + wterm_cr; mp->term_offset=0; + }; + if ( mp->file_offset==(unsigned)mp->max_print_line ) { + wlog_cr; mp->file_offset=0; + }; + break; + case log_only: + wlog_chr(xchr(s)); incr(mp->file_offset); + if ( mp->file_offset==(unsigned)mp->max_print_line ) mp_print_ln(mp); + break; + case term_only: + wterm_chr(xchr(s)); incr(mp->term_offset); + if ( mp->term_offset==(unsigned)mp->max_print_line ) mp_print_ln(mp); + break; + case no_print: + break; + case pseudo: + if ( mp->tally<mp->trick_count ) + mp->trick_buf[mp->tally % mp->error_line]=s; + break; + case new_string: + if (mp->pool_ptr>=mp->pool_size || mp->pool_ptr>=mp->max_pool_ptr ) { + mp_unit_str_room(mp); + if ( mp->pool_ptr>=mp->pool_size ) + goto DONE; /* drop characters if string space is full */ + }; + append_char(s); + break; + default: + { text_char ss[2]; ss[0] = xchr(s); ss[1]=0; + do_fprintf(mp->wr_file[(mp->selector-write_file)],(char *)ss); + } + } +DONE: + incr(mp->tally); +} + +@ The |print_char| procedure sends one character to the desired destination. +File names and string expressions might contain |ASCII_code| values that +can't be printed using |print_visible_char|. These characters will be +printed in three- or four-symbol form like `\.{\^\^A}' or `\.{\^\^e4}'. +(This procedure assumes that it is safe to bypass all checks for unprintable +characters when |selector| is in the range |0..max_write_files-1|. +The user might want to write unprintable characters. + +@<Basic printing...@>= +void mp_print_char (MP mp, ASCII_code k) { /* prints a single character */ + if ( mp->selector<pseudo || mp->selector>=write_file) { + mp_print_visible_char(mp, k); + } else if ( @<Character |k| cannot be printed@> ) { + mp_print(mp, "^^"); + if ( k<0100 ) { + mp_print_visible_char(mp, k+0100); + } else if ( k<0200 ) { + mp_print_visible_char(mp, k-0100); + } else { + int l; /* small index or counter */ + l = (k / 16); + mp_print_visible_char(mp, xord(l<10 ? l+'0' : l-10+'a')); + l = (k % 16); + mp_print_visible_char(mp, xord(l<10 ? l+'0' : l-10+'a')); + } + } else { + mp_print_visible_char(mp, k); + } +} + +@ An entire string is output by calling |print|. Note that if we are outputting +the single standard ASCII character \.c, we could call |print("c")|, since +|"c"=99| is the number of a single-character string, as explained above. But +|print_char("c")| is quicker, so \MP\ goes directly to the |print_char| +routine when it knows that this is safe. (The present implementation +assumes that it is always safe to print a visible ASCII character.) +@^system dependencies@> + +@<Basic print...@>= +static void mp_do_print (MP mp, const char *ss, size_t len) { /* prints string |s| */ + size_t j = 0; + if (mp->selector == new_string) { + str_room((integer)(len*4)); + } + while ( j<len ){ + /* this was |xord((int)ss[j])| but that doesnt work */ + mp_print_char(mp, (ASCII_code)ss[j]); j++; + } +} + +@ +@<Basic print...@>= +void mp_print (MP mp, const char *ss) { + if (ss==NULL) return; + mp_do_print(mp, ss,strlen(ss)); +} +void mp_print_str (MP mp, str_number s) { + pool_pointer j; /* current character code position */ + if ( (s<0)||(s>mp->max_str_ptr) ) { + mp_do_print(mp,"???",3); /* this can't happen */ +@.???@> + } + j=mp->str_start[s]; + mp_do_print(mp, (char *)(mp->str_pool+j), (size_t)(str_stop(s)-j)); +} + + +@ Here is the very first thing that \MP\ prints: a headline that identifies +the version number and base name. The |term_offset| variable is temporarily +incorrect, but the discrepancy is not serious since we assume that the banner +and mem identifier together will occupy at most |max_print_line| +character positions. + +@<Initialize the output...@>= +wterm (mp->banner); +if (mp->mem_ident!=NULL) + mp_print(mp,mp->mem_ident); +mp_print_ln(mp); +update_terminal; + +@ The procedure |print_nl| is like |print|, but it makes sure that the +string appears at the beginning of a new line. + +@<Basic print...@>= +void mp_print_nl (MP mp, const char *s) { /* prints string |s| at beginning of line */ + switch(mp->selector) { + case term_and_log: + if ( (mp->term_offset>0)||(mp->file_offset>0) ) mp_print_ln(mp); + break; + case log_only: + if ( mp->file_offset>0 ) mp_print_ln(mp); + break; + case term_only: + if ( mp->term_offset>0 ) mp_print_ln(mp); + break; + case no_print: + case pseudo: + case new_string: + break; + } /* there are no other cases */ + mp_print(mp, s); +} + +@ The following procedure, which prints out the decimal representation of a +given integer |n|, assumes that all integers fit nicely into a |int|. +@^system dependencies@> + +@<Basic print...@>= +void mp_print_int (MP mp,integer n) { /* prints an integer in decimal form */ + char s[12]; + mp_snprintf(s,12,"%d", (int)n); + mp_print(mp,s); +} + +@ @<Internal library ...@>= +void mp_print_int (MP mp,integer n); + +@ \MP\ also makes use of a trivial procedure to print two digits. The +following subroutine is usually called with a parameter in the range |0<=n<=99|. + +@c +static void mp_print_dd (MP mp,integer n) { /* prints two least significant digits */ + n=abs(n) % 100; + mp_print_char(mp, xord('0'+(n / 10))); + mp_print_char(mp, xord('0'+(n % 10))); +} + + +@ @<Declarations@>= +static void mp_print_dd (MP mp,integer n); + +@ Here is a procedure that asks the user to type a line of input, +assuming that the |selector| setting is either |term_only| or |term_and_log|. +The input is placed into locations |first| through |last-1| of the +|buffer| array, and echoed on the transcript file if appropriate. + +This procedure is never called when |interaction<mp_scroll_mode|. + +@d prompt_input(A) do { + if (!mp->noninteractive) { + wake_up_terminal; mp_print(mp, (A)); + } + mp_term_input(mp); + } while (0) /* prints a string and gets a line of input */ + +@c +void mp_term_input (MP mp) { /* gets a line from the terminal */ + size_t k; /* index into |buffer| */ + if (mp->noninteractive) { + if (!mp_input_ln(mp, mp->term_in )) + longjmp(*(mp->jump_buf),1); /* chunk finished */ + mp->buffer[mp->last]=xord('%'); + } else { + update_terminal; /* Now the user sees the prompt for sure */ + if (!mp_input_ln(mp, mp->term_in )) { + mp_fatal_error(mp, "End of file on the terminal!"); +@.End of file on the terminal@> + } + mp->term_offset=0; /* the user's line ended with \<\rm return> */ + decr(mp->selector); /* prepare to echo the input */ + if ( mp->last!=mp->first ) { + for (k=mp->first;k<mp->last;k++) { + mp_print_char(mp, mp->buffer[k]); + } + } + mp_print_ln(mp); + mp->buffer[mp->last]=xord('%'); + incr(mp->selector); /* restore previous status */ + } +} + +@* \[6] Reporting errors. +When something anomalous is detected, \MP\ typically does something like this: +$$\vbox{\halign{#\hfil\cr +|print_err("Something anomalous has been detected");|\cr +|help3("This is the first line of my offer to help.")|\cr +|("This is the second line. I'm trying to")|\cr +|("explain the best way for you to proceed.");|\cr +|error;|\cr}}$$ +A two-line help message would be given using |help2|, etc.; these informal +helps should use simple vocabulary that complements the words used in the +official error message that was printed. (Outside the U.S.A., the help +messages should preferably be translated into the local vernacular. Each +line of help is at most 60 characters long, in the present implementation, +so that |max_print_line| will not be exceeded.) + +The |print_err| procedure supplies a `\.!' before the official message, +and makes sure that the terminal is awake if a stop is going to occur. +The |error| procedure supplies a `\..' after the official message, then it +shows the location of the error; and if |interaction=error_stop_mode|, +it also enters into a dialog with the user, during which time the help +message may be printed. +@^system dependencies@> + +@ The global variable |interaction| has four settings, representing increasing +amounts of user interaction: + +@<Exported types@>= +enum mp_interaction_mode { + mp_unspecified_mode=0, /* extra value for command-line switch */ + mp_batch_mode, /* omits all stops and omits terminal output */ + mp_nonstop_mode, /* omits all stops */ + mp_scroll_mode, /* omits error stops */ + mp_error_stop_mode /* stops at every opportunity to interact */ +}; + +@ @<Option variables@>= +int interaction; /* current level of interaction */ +int noninteractive; /* do we have a terminal? */ + +@ Set it here so it can be overwritten by the commandline + +@<Allocate or initialize ...@>= +mp->interaction=opt->interaction; +if (mp->interaction==mp_unspecified_mode || mp->interaction>mp_error_stop_mode) + mp->interaction=mp_error_stop_mode; +if (mp->interaction<mp_unspecified_mode) + mp->interaction=mp_batch_mode; + +@ + +@d print_err(A) mp_print_err(mp,(A)) + +@<Internal ...@>= +void mp_print_err(MP mp, const char * A); + +@ @c +void mp_print_err(MP mp, const char * A) { + if ( mp->interaction==mp_error_stop_mode ) + wake_up_terminal; + if (mp->file_line_error_style && file_state && !terminal_input) { + mp_print_nl(mp, ""); + if (mp->long_name != NULL) { + mp_print(mp, mp->long_name); + } else { + mp_print(mp, mp_str(mp,name)); + } + mp_print(mp, ":"); + mp_print_int(mp, line); + mp_print(mp, ": "); + } else{ + mp_print_nl(mp, "! "); + } + mp_print(mp, A); +@.!\relax@> +} + + +@ \MP\ is careful not to call |error| when the print |selector| setting +might be unusual. The only possible values of |selector| at the time of +error messages are + +\yskip\hang|no_print| (when |interaction=mp_batch_mode| + and |log_file| not yet open); + +\hang|term_only| (when |interaction>mp_batch_mode| and |log_file| not yet open); + +\hang|log_only| (when |interaction=mp_batch_mode| and |log_file| is open); + +\hang|term_and_log| (when |interaction>mp_batch_mode| and |log_file| is open). + +@<Initialize the print |selector| based on |interaction|@>= +if ( mp->interaction==mp_batch_mode ) mp->selector=no_print; else mp->selector=term_only + +@ A global variable |deletions_allowed| is set |false| if the |get_next| +routine is active when |error| is called; this ensures that |get_next| +will never be called recursively. +@^recursion@> + +The global variable |history| records the worst level of error that +has been detected. It has four possible values: |spotless|, |warning_issued|, +|error_message_issued|, and |fatal_error_stop|. + +Another global variable, |error_count|, is increased by one when an +|error| occurs without an interactive dialog, and it is reset to zero at +the end of every statement. If |error_count| reaches 100, \MP\ decides +that there is no point in continuing further. + +@<Exported types@>= +enum mp_history_state { + mp_spotless=0, /* |history| value when nothing has been amiss yet */ + mp_warning_issued, /* |history| value when |begin_diagnostic| has been called */ + mp_error_message_issued, /* |history| value when |error| has been called */ + mp_fatal_error_stop, /* |history| value when termination was premature */ + mp_system_error_stop /* |history| value when termination was due to disaster */ +}; + +@ @<Glob...@>= +boolean deletions_allowed; /* is it safe for |error| to call |get_next|? */ +int history; /* has the source input been clean so far? */ +int error_count; /* the number of scrolled errors since the last statement ended */ + +@ The value of |history| is initially |fatal_error_stop|, but it will +be changed to |spotless| if \MP\ survives the initialization process. + +@<Allocate or ...@>= +mp->deletions_allowed=true; /* |history| is initialized elsewhere */ + +@ Since errors can be detected almost anywhere in \MP, we want to declare the +error procedures near the beginning of the program. But the error procedures +in turn use some other procedures, which need to be declared |forward| +before we get to |error| itself. + +It is possible for |error| to be called recursively if some error arises +when |get_next| is being used to delete a token, and/or if some fatal error +occurs while \MP\ is trying to fix a non-fatal one. But such recursion +@^recursion@> +is never more than two levels deep. + +@<Declarations@>= +static void mp_get_next (MP mp); +static void mp_term_input (MP mp); +static void mp_show_context (MP mp); +static void mp_begin_file_reading (MP mp); +static void mp_open_log_file (MP mp); +static void mp_clear_for_error_prompt (MP mp); + +@ @<Internal ...@>= +void mp_normalize_selector (MP mp); + +@ Individual lines of help are recorded in the array |help_line|, which +contains entries in positions |0..(help_ptr-1)|. They should be printed +in reverse order, i.e., with |help_line[0]| appearing last. + +@d hlp1(A) mp->help_line[0]=A; } +@d hlp2(A,B) mp->help_line[1]=A; hlp1(B) +@d hlp3(A,B,C) mp->help_line[2]=A; hlp2(B,C) +@d hlp4(A,B,C,D) mp->help_line[3]=A; hlp3(B,C,D) +@d hlp5(A,B,C,D,E) mp->help_line[4]=A; hlp4(B,C,D,E) +@d hlp6(A,B,C,D,E,F) mp->help_line[5]=A; hlp5(B,C,D,E,F) +@d help0 mp->help_ptr=0 /* sometimes there might be no help */ +@d help1 { mp->help_ptr=1; hlp1 /* use this with one help line */ +@d help2 { mp->help_ptr=2; hlp2 /* use this with two help lines */ +@d help3 { mp->help_ptr=3; hlp3 /* use this with three help lines */ +@d help4 { mp->help_ptr=4; hlp4 /* use this with four help lines */ +@d help5 { mp->help_ptr=5; hlp5 /* use this with five help lines */ +@d help6 { mp->help_ptr=6; hlp6 /* use this with six help lines */ + +@<Glob...@>= +const char * help_line[6]; /* helps for the next |error| */ +unsigned int help_ptr; /* the number of help lines present */ +boolean use_err_help; /* should the |err_help| string be shown? */ +str_number err_help; /* a string set up by \&{errhelp} */ + +@ @<Allocate or ...@>= +mp->use_err_help=false; + +@ The |jump_out| procedure just cuts across all active procedure levels and +goes to |end_of_MP|. This is the only nonlocal |goto| statement in the +whole program. It is used when there is no recovery from a particular error. + +The program uses a |jump_buf| to handle this, this is initialized at three +spots: the start of |mp_new|, the start of |mp_initialize|, and the start +of |mp_run|. Those are the only library enty points. + +@^system dependencies@> + +@<Glob...@>= +jmp_buf *jump_buf; + +@ If the array of internals is still |NULL| when |jump_out| is called, a +crash occured during initialization, and it is not safe to run the normal +cleanup routine. + +@<Error hand...@>= +static void mp_jump_out (MP mp) { + if (mp->internal!=NULL && mp->history < mp_system_error_stop) + mp_close_files_and_terminate(mp); + longjmp(*(mp->jump_buf),1); +} + +@ Here now is the general |error| routine. + +@<Error hand...@>= +void mp_error (MP mp) { /* completes the job of error reporting */ + ASCII_code c; /* what the user types */ + integer s1,s2,s3; /* used to save global variables when deleting tokens */ + pool_pointer j; /* character position being printed */ + if ( mp->history<mp_error_message_issued ) + mp->history=mp_error_message_issued; + mp_print_char(mp, xord('.')); mp_show_context(mp); + if (mp->halt_on_error) { + mp->history=mp_fatal_error_stop; mp_jump_out(mp); + } + if ((!mp->noninteractive) && (mp->interaction==mp_error_stop_mode )) { + @<Get user's advice and |return|@>; + } + incr(mp->error_count); + if ( mp->error_count==100 ) { + mp_print_nl(mp,"(That makes 100 errors; please try again.)"); +@.That makes 100 errors...@> + mp->history=mp_fatal_error_stop; mp_jump_out(mp); + } + @<Put help message on the transcript file@>; +} +void mp_warn (MP mp, const char *msg) { + unsigned saved_selector = mp->selector; + mp_normalize_selector(mp); + mp_print_nl(mp,"Warning: "); + mp_print(mp,msg); + mp_print_ln(mp); + mp->selector = saved_selector; +} + +@ @<Exported function ...@>= +extern void mp_error (MP mp); +extern void mp_warn (MP mp, const char *msg); + + +@ @<Get user's advice...@>= +while (true) { +CONTINUE: + mp_clear_for_error_prompt(mp); prompt_input("? "); +@.?\relax@> + if ( mp->last==mp->first ) return; + c=mp->buffer[mp->first]; + if ( c>='a' ) c=c+'A'-'a'; /* convert to uppercase */ + @<Interpret code |c| and |return| if done@>; +} + +@ It is desirable to provide an `\.E' option here that gives the user +an easy way to return from \MP\ to the system editor, with the offending +line ready to be edited. But such an extension requires some system +wizardry, so the present implementation simply types out the name of the +file that should be +edited and the relevant line number. +@^system dependencies@> + +@<Exported types@>= +typedef void (*mp_editor_cmd)(MP, char *, int); + +@ @<Option variables@>= +mp_editor_cmd run_editor; + +@ @<Allocate or initialize ...@>= +set_callback_option(run_editor); + +@ @<Declarations@>= +static void mp_run_editor (MP mp, char *fname, int fline); + +@ @c +void mp_run_editor (MP mp, char *fname, int fline) { + char *s = xmalloc(256,1); + mp_snprintf(s, 256,"You want to edit file %s at line %d\n", fname, fline); + wterm_ln(s); +@.You want to edit file x@> +} + +@ +There is a secret `\.D' option available when the debugging routines haven't +been commented~out. +@^debugging@> + +@<Interpret code |c| and |return| if done@>= +switch (c) { +case '0': case '1': case '2': case '3': case '4': +case '5': case '6': case '7': case '8': case '9': + if ( mp->deletions_allowed ) { + @<Delete |c-"0"| tokens and |continue|@>; + } + break; +case 'E': + if ( mp->file_ptr>0 ){ + mp->interaction=mp_scroll_mode; + mp_close_files_and_terminate(mp); + (mp->run_editor)(mp, + str(mp->input_stack[mp->file_ptr].name_field), + mp_true_line(mp)); + mp_jump_out(mp); + } + break; +case 'H': + @<Print the help information and |continue|@>; + /* |break;| */ +case 'I': + @<Introduce new material from the terminal and |return|@>; + /* |break;| */ +case 'Q': case 'R': case 'S': + @<Change the interaction level and |return|@>; + /* |break;| */ +case 'X': + mp->interaction=mp_scroll_mode; mp_jump_out(mp); + break; +default: + break; +} +@<Print the menu of available options@> + +@ @<Print the menu...@>= +{ + mp_print(mp, "Type <return> to proceed, S to scroll future error messages,"); +@.Type <return> to proceed...@> + mp_print_nl(mp, "R to run without stopping, Q to run quietly,"); + mp_print_nl(mp, "I to insert something, "); + if ( mp->file_ptr>0 ) + mp_print(mp, "E to edit your file,"); + if ( mp->deletions_allowed ) + mp_print_nl(mp, "1 or ... or 9 to ignore the next 1 to 9 tokens of input,"); + mp_print_nl(mp, "H for help, X to quit."); +} + +@ Here the author of \MP\ apologizes for making use of the numerical +relation between |"Q"|, |"R"|, |"S"|, and the desired interaction settings +|mp_batch_mode|, |mp_nonstop_mode|, |mp_scroll_mode|. +@^Knuth, Donald Ervin@> + +@<Change the interaction...@>= +{ + mp->error_count=0; mp->interaction=mp_batch_mode+c-'Q'; + mp_print(mp, "OK, entering "); + switch (c) { + case 'Q': mp_print(mp, "batchmode"); decr(mp->selector); break; + case 'R': mp_print(mp, "nonstopmode"); break; + case 'S': mp_print(mp, "scrollmode"); break; + } /* there are no other cases */ + mp_print(mp, "..."); mp_print_ln(mp); update_terminal; return; +} + +@ When the following code is executed, |buffer[(first+1)..(last-1)]| may +contain the material inserted by the user; otherwise another prompt will +be given. In order to understand this part of the program fully, you need +to be familiar with \MP's input stacks. + +@<Introduce new material...@>= +{ + mp_begin_file_reading(mp); /* enter a new syntactic level for terminal input */ + if ( mp->last>mp->first+1 ) { + loc=(halfword)(mp->first+1); mp->buffer[mp->first]=xord(' '); + } else { + prompt_input("insert>"); loc=(halfword)mp->first; +@.insert>@> + }; + mp->first=mp->last+1; mp->cur_input.limit_field=(halfword)mp->last; return; +} + +@ We allow deletion of up to 99 tokens at a time. + +@<Delete |c-"0"| tokens...@>= +{ + s1=mp->cur_cmd; s2=mp->cur_mod; s3=mp->cur_sym; mp->OK_to_interrupt=false; + if ( (mp->last>mp->first+1) && (mp->buffer[mp->first+1]>='0')&&(mp->buffer[mp->first+1]<='9') ) + c=xord(c*10+mp->buffer[mp->first+1]-'0'*11); + else + c=c-'0'; + while ( c>0 ) { + mp_get_next(mp); /* one-level recursive call of |error| is possible */ + @<Decrease the string reference count, if the current token is a string@>; + decr(c); + }; + mp->cur_cmd=s1; mp->cur_mod=s2; mp->cur_sym=s3; mp->OK_to_interrupt=true; + help2("I have just deleted some text, as you asked.", + "You can now delete more, or insert, or whatever."); + mp_show_context(mp); + goto CONTINUE; +} + +@ @<Print the help info...@>= +{ + if ( mp->use_err_help ) { + @<Print the string |err_help|, possibly on several lines@>; + mp->use_err_help=false; + } else { + if ( mp->help_ptr==0 ) { + help2("Sorry, I don't know how to help in this situation.", + "Maybe you should try asking a human?"); + } + do { + decr(mp->help_ptr); mp_print(mp, mp->help_line[mp->help_ptr]); mp_print_ln(mp); + } while (mp->help_ptr!=0); + }; + help4("Sorry, I already gave what help I could...", + "Maybe you should try asking a human?", + "An error might have occurred before I noticed any problems.", + "``If all else fails, read the instructions.''"); + goto CONTINUE; +} + +@ @<Print the string |err_help|, possibly on several lines@>= +j=mp->str_start[mp->err_help]; +while ( j<str_stop(mp->err_help) ) { + if ( mp->str_pool[j]!='%' ) mp_print_str(mp, mp->str_pool[j]); + else if ( j+1==str_stop(mp->err_help) ) mp_print_ln(mp); + else if ( mp->str_pool[j+1]!='%' ) mp_print_ln(mp); + else { j++; mp_print_char(mp, xord('%')); }; + j++; +} + +@ @<Put help message on the transcript file@>= +if ( mp->interaction>mp_batch_mode ) decr(mp->selector); /* avoid terminal output */ +if ( mp->use_err_help ) { + mp_print_nl(mp, ""); + @<Print the string |err_help|, possibly on several lines@>; +} else { + while ( mp->help_ptr>0 ){ + decr(mp->help_ptr); mp_print_nl(mp, mp->help_line[mp->help_ptr]); + }; +} +mp_print_ln(mp); +if ( mp->interaction>mp_batch_mode ) incr(mp->selector); /* re-enable terminal output */ +mp_print_ln(mp) + +@ In anomalous cases, the print selector might be in an unknown state; +the following subroutine is called to fix things just enough to keep +running a bit longer. + +@c +void mp_normalize_selector (MP mp) { + if ( mp->log_opened ) mp->selector=term_and_log; + else mp->selector=term_only; + if ( mp->job_name==NULL) mp_open_log_file(mp); + if ( mp->interaction==mp_batch_mode ) decr(mp->selector); +} + +@ The following procedure prints \MP's last words before dying. + +@d succumb { if ( mp->interaction==mp_error_stop_mode ) + mp->interaction=mp_scroll_mode; /* no more interaction */ + if ( mp->log_opened ) mp_error(mp); + mp->history=mp_fatal_error_stop; mp_jump_out(mp); /* irrecoverable error */ + } + +@<Error hand...@>= +void mp_fatal_error (MP mp, const char *s) { /* prints |s|, and that's it */ + mp_normalize_selector(mp); + print_err("Emergency stop"); help1(s); succumb; +@.Emergency stop@> +} + +@ @<Exported function ...@>= +extern void mp_fatal_error (MP mp, const char *s); + + +@ Here is the most dreaded error message. + +@<Error hand...@>= +void mp_overflow (MP mp, const char *s, integer n) { /* stop due to finiteness */ + char msg[256]; + mp_normalize_selector(mp); + mp_snprintf(msg, 256, "MetaPost capacity exceeded, sorry [%s=%d]",s,(int)n); +@.MetaPost capacity exceeded ...@> + print_err(msg); + help2("If you really absolutely need more capacity,", + "you can ask a wizard to enlarge me."); + succumb; +} + +@ @<Internal library declarations@>= +void mp_overflow (MP mp, const char *s, integer n); + +@ The program might sometime run completely amok, at which point there is +no choice but to stop. If no previous error has been detected, that's bad +news; a message is printed that is really intended for the \MP\ +maintenance person instead of the user (unless the user has been +particularly diabolical). The index entries for `this can't happen' may +help to pinpoint the problem. +@^dry rot@> + +@<Internal library ...@>= +void mp_confusion (MP mp, const char *s); + +@ Consistency check violated; |s| tells where. +@<Error hand...@>= +void mp_confusion (MP mp, const char *s) { + char msg[256]; + mp_normalize_selector(mp); + if ( mp->history<mp_error_message_issued ) { + mp_snprintf(msg, 256, "This can't happen (%s)",s); +@.This can't happen@> + print_err(msg); + help1("I'm broken. Please show this to someone who can fix can fix"); + } else { + print_err("I can\'t go on meeting you like this"); +@.I can't go on...@> + help2("One of your faux pas seems to have wounded me deeply...", + "in fact, I'm barely conscious. Please fix it and try again."); + } + succumb; +} + +@ Users occasionally want to interrupt \MP\ while it's running. +If the runtime system allows this, one can implement +a routine that sets the global variable |interrupt| to some nonzero value +when such an interrupt is signaled. Otherwise there is probably at least +a way to make |interrupt| nonzero using the C debugger. +@^system dependencies@> +@^debugging@> + +@d check_interrupt { if ( mp->interrupt!=0 ) + mp_pause_for_instructions(mp); } + +@<Global...@>= +integer interrupt; /* should \MP\ pause for instructions? */ +boolean OK_to_interrupt; /* should interrupts be observed? */ +integer run_state; /* are we processing input ?*/ +boolean finished; /* set true by |close_files_and_terminate| */ + +@ @<Allocate or ...@>= +mp->OK_to_interrupt=true; +mp->finished=false; + +@ When an interrupt has been detected, the program goes into its +highest interaction level and lets the user have the full flexibility of +the |error| routine. \MP\ checks for interrupts only at times when it is +safe to do this. + +@c +static void mp_pause_for_instructions (MP mp) { + if ( mp->OK_to_interrupt ) { + mp->interaction=mp_error_stop_mode; + if ( (mp->selector==log_only)||(mp->selector==no_print) ) + incr(mp->selector); + print_err("Interruption"); +@.Interruption@> + help3("You rang?", + "Try to insert some instructions for me (e.g.,`I show x'),", + "unless you just want to quit by typing `X'."); + mp->deletions_allowed=false; mp_error(mp); mp->deletions_allowed=true; + mp->interrupt=0; + } +} + +@ Many of \MP's error messages state that a missing token has been +inserted behind the scenes. We can save string space and program space +by putting this common code into a subroutine. + +@c +static void mp_missing_err (MP mp, const char *s) { + char msg[256]; + mp_snprintf(msg, 256, "Missing `%s' has been inserted", s); +@.Missing...inserted@> + print_err(msg); +} + +@* \[7] Arithmetic with scaled numbers. +The principal computations performed by \MP\ are done entirely in terms of +integers less than $2^{31}$ in magnitude; thus, the arithmetic specified in this +program can be carried out in exactly the same way on a wide variety of +computers, including some small ones. +@^small computers@> + +But C does not rigidly define the |/| operation in the case of negative +dividends; for example, the result of |(-2*n-1) / 2| is |-(n+1)| on some +computers and |-n| on others (is this true ?). There are two principal +types of arithmetic: ``translation-preserving,'' in which the identity +|(a+q*b)/b=(a/b)+q| is valid; and ``negation-preserving,'' in which +|(-a)/b=-(a/b)|. This leads to two \MP s, which can produce +different results, although the differences should be negligible when the +language is being used properly. The \TeX\ processor has been defined +carefully so that both varieties of arithmetic will produce identical +output, but it would be too inefficient to constrain \MP\ in a similar way. + +@d el_gordo 0x7fffffff /* $2^{31}-1$, the largest value that \MP\ likes */ + + +@ One of \MP's most common operations is the calculation of +$\lfloor{a+b\over2}\rfloor$, +the midpoint of two given integers |a| and~|b|. The most decent way to do +this is to write `|(a+b)/2|'; but on many machines it is more efficient +to calculate `|(a+b)>>1|'. + +Therefore the midpoint operation will always be denoted by `|half(a+b)|' +in this program. If \MP\ is being implemented with languages that permit +binary shifting, the |half| macro should be changed to make this operation +as efficient as possible. Since some systems have shift operators that can +only be trusted to work on positive numbers, there is also a macro |halfp| +that is used only when the quantity being halved is known to be positive +or zero. + +@d half(A) ((A) / 2) +@d halfp(A) (integer)((unsigned)(A) >> 1) + +@ A single computation might use several subroutine calls, and it is +desirable to avoid producing multiple error messages in case of arithmetic +overflow. So the routines below set the global variable |arith_error| to |true| +instead of reporting errors directly to the user. +@^overflow in arithmetic@> + +@<Glob...@>= +boolean arith_error; /* has arithmetic overflow occurred recently? */ + +@ @<Allocate or ...@>= +mp->arith_error=false; + +@ At crucial points the program will say |check_arith|, to test if +an arithmetic error has been detected. + +@d check_arith { if ( mp->arith_error ) mp_clear_arith(mp); } + +@c +static void mp_clear_arith (MP mp) { + print_err("Arithmetic overflow"); +@.Arithmetic overflow@> + help4("Uh, oh. A little while ago one of the quantities that I was", + "computing got too large, so I'm afraid your answers will be", + "somewhat askew. You'll probably have to adopt different", + "tactics next time. But I shall try to carry on anyway."); + mp_error(mp); + mp->arith_error=false; +} + +@ Addition is not always checked to make sure that it doesn't overflow, +but in places where overflow isn't too unlikely the |slow_add| routine +is used. + +@c static integer mp_slow_add (MP mp,integer x, integer y) { + if ( x>=0 ) { + if ( y<=el_gordo-x ) { + return x+y; + } else { + mp->arith_error=true; + return el_gordo; + } + } else if ( -y<=el_gordo+x ) { + return x+y; + } else { + mp->arith_error=true; + return -el_gordo; + } +} + +@ Fixed-point arithmetic is done on {\sl scaled integers\/} that are multiples +of $2^{-16}$. In other words, a binary point is assumed to be sixteen bit +positions from the right end of a binary computer word. + +@d quarter_unit 040000 /* $2^{14}$, represents 0.250000 */ +@d half_unit 0100000 /* $2^{15}$, represents 0.50000 */ +@d three_quarter_unit 0140000 /* $3\cdot2^{14}$, represents 0.75000 */ +@d unity 0200000 /* $2^{16}$, represents 1.00000 */ +@d two 0400000 /* $2^{17}$, represents 2.00000 */ +@d three 0600000 /* $2^{17}+2^{16}$, represents 3.00000 */ + +@<Types...@>= +typedef integer scaled; /* this type is used for scaled integers */ + +@ The following function is used to create a scaled integer from a given decimal +fraction $(.d_0d_1\ldots d_{k-1})$, where |0<=k<=17|. The digit $d_i$ is +given in |dig[i]|, and the calculation produces a correctly rounded result. + +@c +static scaled mp_round_decimals (MP mp,quarterword k) { + /* converts a decimal fraction */ + unsigned a = 0; /* the accumulator */ + while ( k-->0 ) { + a=(a+mp->dig[k]*two) / 10; + } + return (scaled)halfp(a+1); +} + +@ Conversely, here is a procedure analogous to |print_int|. If the output +of this procedure is subsequently read by \MP\ and converted by the +|round_decimals| routine above, it turns out that the original value will +be reproduced exactly. A decimal point is printed only if the value is +not an integer. If there is more than one way to print the result with +the optimum number of digits following the decimal point, the closest +possible value is given. + +The invariant relation in the \&{repeat} loop is that a sequence of +decimal digits yet to be printed will yield the original number if and only if +they form a fraction~$f$ in the range $s-\delta\L10\cdot2^{16}f<s$. +We can stop if and only if $f=0$ satisfies this condition; the loop will +terminate before $s$ can possibly become zero. + +@<Basic printing...@>= +void mp_print_scaled (MP mp,scaled s) { /* prints scaled real, rounded to five digits */ + scaled delta; /* amount of allowable inaccuracy */ + if ( s<0 ) { + mp_print_char(mp, xord('-')); + negate(s); /* print the sign, if negative */ + } + mp_print_int(mp, s / unity); /* print the integer part */ + s=10*(s % unity)+5; + if ( s!=5 ) { + delta=10; + mp_print_char(mp, xord('.')); + do { + if ( delta>unity ) + s=s+0100000-(delta / 2); /* round the final digit */ + mp_print_char(mp, xord('0'+(s / unity))); + s=10*(s % unity); + delta=delta*10; + } while (s>delta); + } +} + +@ We often want to print two scaled quantities in parentheses, +separated by a comma. + +@<Basic printing...@>= +void mp_print_two (MP mp,scaled x, scaled y) { /* prints `|(x,y)|' */ + mp_print_char(mp, xord('(')); + mp_print_scaled(mp, x); + mp_print_char(mp, xord(',')); + mp_print_scaled(mp, y); + mp_print_char(mp, xord(')')); +} + +@ The |scaled| quantities in \MP\ programs are generally supposed to be +less than $2^{12}$ in absolute value, so \MP\ does much of its internal +arithmetic with 28~significant bits of precision. A |fraction| denotes +a scaled integer whose binary point is assumed to be 28 bit positions +from the right. + +@d fraction_half 01000000000 /* $2^{27}$, represents 0.50000000 */ +@d fraction_one 02000000000 /* $2^{28}$, represents 1.00000000 */ +@d fraction_two 04000000000 /* $2^{29}$, represents 2.00000000 */ +@d fraction_three 06000000000 /* $3\cdot2^{28}$, represents 3.00000000 */ +@d fraction_four 010000000000 /* $2^{30}$, represents 4.00000000 */ + +@<Types...@>= +typedef integer fraction; /* this type is used for scaled fractions */ + +@ In fact, the two sorts of scaling discussed above aren't quite +sufficient; \MP\ has yet another, used internally to keep track of angles +in units of $2^{-20}$ degrees. + +@d forty_five_deg 0264000000 /* $45\cdot2^{20}$, represents $45^\circ$ */ +@d ninety_deg 0550000000 /* $90\cdot2^{20}$, represents $90^\circ$ */ +@d one_eighty_deg 01320000000 /* $180\cdot2^{20}$, represents $180^\circ$ */ +@d three_sixty_deg 02640000000 /* $360\cdot2^{20}$, represents $360^\circ$ */ + +@<Types...@>= +typedef integer angle; /* this type is used for scaled angles */ + +@ The |make_fraction| routine produces the |fraction| equivalent of +|p/q|, given integers |p| and~|q|; it computes the integer +$f=\lfloor2^{28}p/q+{1\over2}\rfloor$, when $p$ and $q$ are +positive. If |p| and |q| are both of the same scaled type |t|, +the ``type relation'' |make_fraction(t,t)=fraction| is valid; +and it's also possible to use the subroutine ``backwards,'' using +the relation |make_fraction(t,fraction)=t| between scaled types. + +If the result would have magnitude $2^{31}$ or more, |make_fraction| +sets |arith_error:=true|. Most of \MP's internal computations have +been designed to avoid this sort of error. + +If this subroutine were programmed in assembly language on a typical +machine, we could simply compute |(@t$2^{28}$@>*p)div q|, since a +double-precision product can often be input to a fixed-point division +instruction. But when we are restricted to int-eger arithmetic it +is necessary either to resort to multiple-precision maneuvering +or to use a simple but slow iteration. The multiple-precision technique +would be about three times faster than the code adopted here, but it +would be comparatively long and tricky, involving about sixteen +additional multiplications and divisions. + +This operation is part of \MP's ``inner loop''; indeed, it will +consume nearly 10\pct! of the running time (exclusive of input and output) +if the code below is left unchanged. A machine-dependent recoding +will therefore make \MP\ run faster. The present implementation +is highly portable, but slow; it avoids multiplication and division +except in the initial stage. System wizards should be careful to +replace it with a routine that is guaranteed to produce identical +results in all cases. +@^system dependencies@> + +As noted below, a few more routines should also be replaced by machine-dependent +code, for efficiency. But when a procedure is not part of the ``inner loop,'' +such changes aren't advisable; simplicity and robustness are +preferable to trickery, unless the cost is too high. +@^inner loop@> + +@<Internal library declarations@>= +integer mp_take_scaled (MP mp,integer q, scaled f) ; + +@ @<Declarations@>= +static fraction mp_make_fraction (MP mp,integer p, integer q); + +@ If FIXPT is not defined, we need these preprocessor values + +@d TWEXP31 2147483648.0 +@d TWEXP28 268435456.0 +@d TWEXP16 65536.0 +@d TWEXP_16 (1.0/65536.0) +@d TWEXP_28 (1.0/268435456.0) + + +@c +fraction mp_make_fraction (MP mp,integer p, integer q) { + fraction i; + if ( q==0 ) mp_confusion(mp, "/"); +@:this can't happen /}{\quad \./@> +#ifdef FIXPT +{ + integer f; /* the fraction bits, with a leading 1 bit */ + integer n; /* the integer part of $\vert p/q\vert$ */ + boolean negative = false; /* should the result be negated? */ + if ( p<0 ) { + negate(p); negative=true; + } + if ( q<0 ) { + negate(q); negative = ! negative; + } + n=p / q; p=p % q; + if ( n>=8 ){ + mp->arith_error=true; + i= ( negative ? -el_gordo : el_gordo); + } else { + n=(n-1)*fraction_one; + @<Compute $f=\lfloor 2^{28}(1+p/q)+{1\over2}\rfloor$@>; + i = (negative ? (-(f+n)) : (f+n)); + } +} +#else /* FIXPT */ + { + register double d; + d = TWEXP28 * (double)p /(double)q; + if ((p^q) >= 0) { + d += 0.5; + if (d>=TWEXP31) {mp->arith_error=true; return el_gordo;} + i = (integer) d; + if (d==(double)i && ( ((q>0 ? -q : q)&077777) + * (((i&037777)<<1)-1) & 04000)!=0) --i; + } else { + d -= 0.5; + if (d<= -TWEXP31) {mp->arith_error=true; return -el_gordo;} + i = (integer) d; + if (d==(double)i && ( ((q>0 ? q : -q)&077777) + * (((i&037777)<<1)+1) & 04000)!=0) ++i; + } + } +#endif /* FIXPT */ + return i; +} + +@ The |repeat| loop here preserves the following invariant relations +between |f|, |p|, and~|q|: +(i)~|0<=p<q|; (ii)~$fq+p=2^k(q+p_0)$, where $k$ is an integer and +$p_0$ is the original value of~$p$. + +Notice that the computation specifies +|(p-q)+p| instead of |(p+p)-q|, because the latter could overflow. +Let us hope that optimizing compilers do not miss this point; a +special variable |be_careful| is used to emphasize the necessary +order of computation. Optimizing compilers should keep |be_careful| +in a register, not store it in memory. +@^inner loop@> + +@<Compute $f=\lfloor 2^{28}(1+p/q)+{1\over2}\rfloor$@>= +{ + integer be_careful; /* disables certain compiler optimizations */ + f=1; + do { + be_careful=p-q; p=be_careful+p; + if ( p>=0 ) { + f=f+f+1; + } else { + f+=f; p=p+q; + } + } while (f<fraction_one); + be_careful=p-q; + if ( be_careful+p>=0 ) incr(f); +} + +@ The dual of |make_fraction| is |take_fraction|, which multiplies a +given integer~|q| by a fraction~|f|. When the operands are positive, it +computes $p=\lfloor qf/2^{28}+{1\over2}\rfloor$, a symmetric function +of |q| and~|f|. + +This routine is even more ``inner loopy'' than |make_fraction|; +the present implementation consumes almost 20\pct! of \MP's computation +time during typical jobs, so a machine-language substitute is advisable. +@^inner loop@> @^system dependencies@> + +@<Internal library declarations@>= +integer mp_take_fraction (MP mp,integer q, fraction f) ; + +@ @c +#ifdef FIXPT +integer mp_take_fraction (MP mp,integer q, fraction f) { + integer p; /* the fraction so far */ + boolean negative; /* should the result be negated? */ + integer n; /* additional multiple of $q$ */ + integer be_careful; /* disables certain compiler optimizations */ + @<Reduce to the case that |f>=0| and |q>=0|@>; + if ( f<fraction_one ) { + n=0; + } else { + n=f / fraction_one; f=f % fraction_one; + if ( q<=el_gordo / n ) { + n=n*q ; + } else { + mp->arith_error=true; n=el_gordo; + } + } + f=f+fraction_one; + @<Compute $p=\lfloor qf/2^{28}+{1\over2}\rfloor-q$@>; + be_careful=n-el_gordo; + if ( be_careful+p>0 ){ + mp->arith_error=true; n=el_gordo-p; + } + if ( negative ) + return (-(n+p)); + else + return (n+p); +#else /* FIXPT */ +integer mp_take_fraction (MP mp,integer p, fraction q) { + register double d; + register integer i; + d = (double)p * (double)q * TWEXP_28; + if ((p^q) >= 0) { + d += 0.5; + if (d>=TWEXP31) { + if (d!=TWEXP31 || (((p&077777)*(q&077777))&040000)==0) + mp->arith_error = true; + return el_gordo; + } + i = (integer) d; + if (d==(double)i && (((p&077777)*(q&077777))&040000)!=0) --i; + } else { + d -= 0.5; + if (d<= -TWEXP31) { + if (d!= -TWEXP31 || ((-(p&077777)*(q&077777))&040000)==0) + mp->arith_error = true; + return -el_gordo; + } + i = (integer) d; + if (d==(double)i && ((-(p&077777)*(q&077777))&040000)!=0) ++i; + } + return i; +#endif /* FIXPT */ +} + +@ @<Reduce to the case that |f>=0| and |q>=0|@>= +if ( f>=0 ) { + negative=false; +} else { + negate( f); negative=true; +} +if ( q<0 ) { + negate(q); negative=! negative; +} + +@ The invariant relations in this case are (i)~$\lfloor(qf+p)/2^k\rfloor +=\lfloor qf_0/2^{28}+{1\over2}\rfloor$, where $k$ is an integer and +$f_0$ is the original value of~$f$; (ii)~$2^k\L f<2^{k+1}$. +@^inner loop@> + +@<Compute $p=\lfloor qf/2^{28}+{1\over2}\rfloor-q$@>= +p=fraction_half; /* that's $2^{27}$; the invariants hold now with $k=28$ */ +if ( q<fraction_four ) { + do { + if ( odd(f) ) p=halfp(p+q); else p=halfp(p); + f=halfp(f); + } while (f!=1); +} else { + do { + if ( odd(f) ) p=p+halfp(q-p); else p=halfp(p); + f=halfp(f); + } while (f!=1); +} + + +@ When we want to multiply something by a |scaled| quantity, we use a scheme +analogous to |take_fraction| but with a different scaling. +Given positive operands, |take_scaled| +computes the quantity $p=\lfloor qf/2^{16}+{1\over2}\rfloor$. + +Once again it is a good idea to use a machine-language replacement if +possible; otherwise |take_scaled| will use more than 2\pct! of the running time +when the Computer Modern fonts are being generated. +@^inner loop@> + +@c +#ifdef FIXPT +integer mp_take_scaled (MP mp,integer q, scaled f) { + integer p; /* the fraction so far */ + boolean negative; /* should the result be negated? */ + integer n; /* additional multiple of $q$ */ + integer be_careful; /* disables certain compiler optimizations */ + @<Reduce to the case that |f>=0| and |q>=0|@>; + if ( f<unity ) { + n=0; + } else { + n=f / unity; f=f % unity; + if ( q<=el_gordo / n ) { + n=n*q; + } else { + mp->arith_error=true; n=el_gordo; + } + } + f=f+unity; + @<Compute $p=\lfloor qf/2^{16}+{1\over2}\rfloor-q$@>; + be_careful=n-el_gordo; + if ( be_careful+p>0 ) { + mp->arith_error=true; n=el_gordo-p; + } + return ( negative ?(-(n+p)) :(n+p)); +#else /* FIXPT */ +integer mp_take_scaled (MP mp,integer p, scaled q) { + register double d; + register integer i; + d = (double)p * (double)q * TWEXP_16; + if ((p^q) >= 0) { + d += 0.5; + if (d>=TWEXP31) { + if (d!=TWEXP31 || (((p&077777)*(q&077777))&040000)==0) + mp->arith_error = true; + return el_gordo; + } + i = (integer) d; + if (d==(double)i && (((p&077777)*(q&077777))&040000)!=0) --i; + } else { + d -= 0.5; + if (d<= -TWEXP31) { + if (d!= -TWEXP31 || ((-(p&077777)*(q&077777))&040000)==0) + mp->arith_error = true; + return -el_gordo; + } + i = (integer) d; + if (d==(double)i && ((-(p&077777)*(q&077777))&040000)!=0) ++i; + } + return i; +#endif /* FIXPT */ +} + +@ @<Compute $p=\lfloor qf/2^{16}+{1\over2}\rfloor-q$@>= +p=half_unit; /* that's $2^{15}$; the invariants hold now with $k=16$ */ +@^inner loop@> +if ( q<fraction_four ) { + do { + p = (odd(f) ? halfp(p+q) : halfp(p)); + f=halfp(f); + } while (f!=1); +} else { + do { + p = (odd(f) ? p+halfp(q-p) : halfp(p)); + f=halfp(f); + } while (f!=1); +} + +@ For completeness, there's also |make_scaled|, which computes a +quotient as a |scaled| number instead of as a |fraction|. +In other words, the result is $\lfloor2^{16}p/q+{1\over2}\rfloor$, if the +operands are positive. \ (This procedure is not used especially often, +so it is not part of \MP's inner loop.) + +@<Internal library ...@>= +scaled mp_make_scaled (MP mp,integer p, integer q) ; + +@ @c +scaled mp_make_scaled (MP mp,integer p, integer q) { + register integer i; + if ( q==0 ) mp_confusion(mp, "/"); +@:this can't happen /}{\quad \./@> + { +#ifdef FIXPT + integer f; /* the fraction bits, with a leading 1 bit */ + integer n; /* the integer part of $\vert p/q\vert$ */ + boolean negative; /* should the result be negated? */ + integer be_careful; /* disables certain compiler optimizations */ + if ( p>=0 ) negative=false; + else { negate(p); negative=true; }; + if ( q<0 ) { + negate(q); negative=! negative; + } + n=p / q; p=p % q; + if ( n>=0100000 ) { + mp->arith_error=true; + return (negative ? (-el_gordo) : el_gordo); + } else { + n=(n-1)*unity; + @<Compute $f=\lfloor 2^{16}(1+p/q)+{1\over2}\rfloor$@>; + i = (negative ? (-(f+n)) :(f+n)); + } +#else /* FIXPT */ + register double d; + d = TWEXP16 * (double)p /(double)q; + if ((p^q) >= 0) { + d += 0.5; + if (d>=TWEXP31) {mp->arith_error=true; return el_gordo;} + i = (integer) d; + if (d==(double)i && ( ((q>0 ? -q : q)&077777) + * (((i&037777)<<1)-1) & 04000)!=0) --i; + } else { + d -= 0.5; + if (d<= -TWEXP31) {mp->arith_error=true; return -el_gordo;} + i = (integer) d; + if (d==(double)i && ( ((q>0 ? q : -q)&077777) + * (((i&037777)<<1)+1) & 04000)!=0) ++i; + } +#endif /* FIXPT */ + } + return i; +} + +@ @<Compute $f=\lfloor 2^{16}(1+p/q)+{1\over2}\rfloor$@>= +f=1; +do { + be_careful=p-q; p=be_careful+p; + if ( p>=0 ) f=f+f+1; + else { f+=f; p=p+q; }; +} while (f<unity); +be_careful=p-q; +if ( be_careful+p>=0 ) incr(f) + +@ Here is a typical example of how the routines above can be used. +It computes the function +$${1\over3\tau}f(\theta,\phi)= +{\tau^{-1}\bigl(2+\sqrt2\,(\sin\theta-{1\over16}\sin\phi) + (\sin\phi-{1\over16}\sin\theta)(\cos\theta-\cos\phi)\bigr)\over +3\,\bigl(1+{1\over2}(\sqrt5-1)\cos\theta+{1\over2}(3-\sqrt5\,)\cos\phi\bigr)},$$ +where $\tau$ is a |scaled| ``tension'' parameter. This is \MP's magic +fudge factor for placing the first control point of a curve that starts +at an angle $\theta$ and ends at an angle $\phi$ from the straight path. +(Actually, if the stated quantity exceeds 4, \MP\ reduces it to~4.) + +The trigonometric quantity to be multiplied by $\sqrt2$ is less than $\sqrt2$. +(It's a sum of eight terms whose absolute values can be bounded using +relations such as $\sin\theta\cos\theta\L{1\over2}$.) Thus the numerator +is positive; and since the tension $\tau$ is constrained to be at least +$3\over4$, the numerator is less than $16\over3$. The denominator is +nonnegative and at most~6. Hence the fixed-point calculations below +are guaranteed to stay within the bounds of a 32-bit computer word. + +The angles $\theta$ and $\phi$ are given implicitly in terms of |fraction| +arguments |st|, |ct|, |sf|, and |cf|, representing $\sin\theta$, $\cos\theta$, +$\sin\phi$, and $\cos\phi$, respectively. + +@c +static fraction mp_velocity (MP mp,fraction st, fraction ct, fraction sf, + fraction cf, scaled t) { + integer acc,num,denom; /* registers for intermediate calculations */ + acc=mp_take_fraction(mp, st-(sf / 16), sf-(st / 16)); + acc=mp_take_fraction(mp, acc,ct-cf); + num=fraction_two+mp_take_fraction(mp, acc,379625062); + /* $2^{28}\sqrt2\approx379625062.497$ */ + denom=fraction_three+mp_take_fraction(mp, ct,497706707)+mp_take_fraction(mp, cf,307599661); + /* $3\cdot2^{27}\cdot(\sqrt5-1)\approx497706706.78$ and + $3\cdot2^{27}\cdot(3-\sqrt5\,)\approx307599661.22$ */ + if ( t!=unity ) num=mp_make_scaled(mp, num,t); + /* |make_scaled(fraction,scaled)=fraction| */ + if ( num / 4>=denom ) + return fraction_four; + else + return mp_make_fraction(mp, num, denom); +} + +@ The following somewhat different subroutine tests rigorously if $ab$ is +greater than, equal to, or less than~$cd$, +given integers $(a,b,c,d)$. In most cases a quick decision is reached. +The result is $+1$, 0, or~$-1$ in the three respective cases. + +@d mp_ab_vs_cd(M,A,B,C,D) mp_do_ab_vs_cd(A,B,C,D) + +@c +static integer mp_do_ab_vs_cd (integer a,integer b, integer c, integer d) { + integer q,r; /* temporary registers */ + @<Reduce to the case that |a,c>=0|, |b,d>0|@>; + while (1) { + q = a / d; r = c / b; + if ( q!=r ) + return ( q>r ? 1 : -1); + q = a % d; r = c % b; + if ( r==0 ) + return (q ? 1 : 0); + if ( q==0 ) return -1; + a=b; b=q; c=d; d=r; + } /* now |a>d>0| and |c>b>0| */ +} + +@ @<Reduce to the case that |a...@>= +if ( a<0 ) { negate(a); negate(b); }; +if ( c<0 ) { negate(c); negate(d); }; +if ( d<=0 ) { + if ( b>=0 ) { + if ( (a==0||b==0)&&(c==0||d==0) ) return 0; + else return 1; + } + if ( d==0 ) + return ( a==0 ? 0 : -1); + q=a; a=c; c=q; q=-b; b=-d; d=q; +} else if ( b<=0 ) { + if ( b<0 ) if ( a>0 ) return -1; + return (c==0 ? 0 : -1); +} + +@ We conclude this set of elementary routines with some simple rounding +and truncation operations. + +@<Internal library declarations@>= +#define mp_floor_scaled(M,i) ((i)&(-65536)) +#define mp_round_unscaled(M,i) (i>0 ? (((i/32768)+1)/2) : (((i/32768)-1)/2)) +#define mp_round_fraction(M,i) (i>0 ? (((i/2048)+1)/2) : (((i/2048)-1)/2)) + + +@* \[8] Algebraic and transcendental functions. +\MP\ computes all of the necessary special functions from scratch, without +relying on |real| arithmetic or system subroutines for sines, cosines, etc. + +@ To get the square root of a |scaled| number |x|, we want to calculate +$s=\lfloor 2^8\!\sqrt x +{1\over2}\rfloor$. If $x>0$, this is the unique +integer such that $2^{16}x-s\L s^2<2^{16}x+s$. The following subroutine +determines $s$ by an iterative method that maintains the invariant +relations $x=2^{46-2k}x_0\bmod 2^{30}$, $0<y=\lfloor 2^{16-2k}x_0\rfloor +-s^2+s\L q=2s$, where $x_0$ is the initial value of $x$. The value of~$y$ +might, however, be zero at the start of the first iteration. + +@<Declarations@>= +static scaled mp_square_rt (MP mp,scaled x) ; + +@ @c +scaled mp_square_rt (MP mp,scaled x) { + quarterword k; /* iteration control counter */ + integer y; /* register for intermediate calculations */ + unsigned q; /* register for intermediate calculations */ + if ( x<=0 ) { + @<Handle square root of zero or negative argument@>; + } else { + k=23; q=2; + while ( x<fraction_two ) { /* i.e., |while x<@t$2^{29}$@>|\unskip */ + decr(k); x=x+x+x+x; + } + if ( x<fraction_four ) y=0; + else { x=x-fraction_four; y=1; }; + do { + @<Decrease |k| by 1, maintaining the invariant + relations between |x|, |y|, and~|q|@>; + } while (k!=0); + return (scaled)(halfp(q)); + } +} + +@ @<Handle square root of zero...@>= +{ + if ( x<0 ) { + print_err("Square root of "); +@.Square root...replaced by 0@> + mp_print_scaled(mp, x); mp_print(mp, " has been replaced by 0"); + help2("Since I don't take square roots of negative numbers,", + "I'm zeroing this one. Proceed, with fingers crossed."); + mp_error(mp); + }; + return 0; +} + +@ @<Decrease |k| by 1, maintaining...@>= +x+=x; y+=y; +if ( x>=fraction_four ) { /* note that |fraction_four=@t$2^{30}$@>| */ + x=x-fraction_four; y++; +}; +x+=x; y=y+y-q; q+=q; +if ( x>=fraction_four ) { x=x-fraction_four; y++; }; +if ( y>(int)q ){ y=y-q; q=q+2; } +else if ( y<=0 ) { q=q-2; y=y+q; }; +decr(k) + +@ Pythagorean addition $\psqrt{a^2+b^2}$ is implemented by an elegant +iterative scheme due to Cleve Moler and Donald Morrison [{\sl IBM Journal +@^Moler, Cleve Barry@> +@^Morrison, Donald Ross@> +of Research and Development\/ \bf27} (1983), 577--581]. It modifies |a| and~|b| +in such a way that their Pythagorean sum remains invariant, while the +smaller argument decreases. + +@<Internal library ...@>= +integer mp_pyth_add (MP mp,integer a, integer b); + + +@ @c +integer mp_pyth_add (MP mp,integer a, integer b) { + fraction r; /* register used to transform |a| and |b| */ + boolean big; /* is the result dangerously near $2^{31}$? */ + a=abs(a); b=abs(b); + if ( a<b ) { r=b; b=a; a=r; }; /* now |0<=b<=a| */ + if ( b>0 ) { + if ( a<fraction_two ) { + big=false; + } else { + a=a / 4; b=b / 4; big=true; + }; /* we reduced the precision to avoid arithmetic overflow */ + @<Replace |a| by an approximation to $\psqrt{a^2+b^2}$@>; + if ( big ) { + if ( a<fraction_two ) { + a=a+a+a+a; + } else { + mp->arith_error=true; a=el_gordo; + }; + } + } + return a; +} + +@ The key idea here is to reflect the vector $(a,b)$ about the +line through $(a,b/2)$. + +@<Replace |a| by an approximation to $\psqrt{a^2+b^2}$@>= +while (1) { + r=mp_make_fraction(mp, b,a); + r=mp_take_fraction(mp, r,r); /* now $r\approx b^2/a^2$ */ + if ( r==0 ) break; + r=mp_make_fraction(mp, r,fraction_four+r); + a=a+mp_take_fraction(mp, a+a,r); b=mp_take_fraction(mp, b,r); +} + + +@ Here is a similar algorithm for $\psqrt{a^2-b^2}$. +It converges slowly when $b$ is near $a$, but otherwise it works fine. + +@c +static integer mp_pyth_sub (MP mp,integer a, integer b) { + fraction r; /* register used to transform |a| and |b| */ + boolean big; /* is the input dangerously near $2^{31}$? */ + a=abs(a); b=abs(b); + if ( a<=b ) { + @<Handle erroneous |pyth_sub| and set |a:=0|@>; + } else { + if ( a<fraction_four ) { + big=false; + } else { + a=(integer)halfp(a); b=(integer)halfp(b); big=true; + } + @<Replace |a| by an approximation to $\psqrt{a^2-b^2}$@>; + if ( big ) double(a); + } + return a; +} + +@ @<Replace |a| by an approximation to $\psqrt{a^2-b^2}$@>= +while (1) { + r=mp_make_fraction(mp, b,a); + r=mp_take_fraction(mp, r,r); /* now $r\approx b^2/a^2$ */ + if ( r==0 ) break; + r=mp_make_fraction(mp, r,fraction_four-r); + a=a-mp_take_fraction(mp, a+a,r); b=mp_take_fraction(mp, b,r); +} + +@ @<Handle erroneous |pyth_sub| and set |a:=0|@>= +{ + if ( a<b ){ + print_err("Pythagorean subtraction "); mp_print_scaled(mp, a); + mp_print(mp, "+-+"); mp_print_scaled(mp, b); + mp_print(mp, " has been replaced by 0"); +@.Pythagorean...@> + help2("Since I don't take square roots of negative numbers,", + "I'm zeroing this one. Proceed, with fingers crossed."); + mp_error(mp); + } + a=0; +} + +@ The subroutines for logarithm and exponential involve two tables. +The first is simple: |two_to_the[k]| equals $2^k$. The second involves +a bit more calculation, which the author claims to have done correctly: +|spec_log[k]| is $2^{27}$ times $\ln\bigl(1/(1-2^{-k})\bigr)= +2^{-k}+{1\over2}2^{-2k}+{1\over3}2^{-3k}+\cdots\,$, rounded to the +nearest integer. + +@d two_to_the(A) (1<<(unsigned)(A)) + +@<Declarations@>= +static const integer spec_log[29] = { 0, /* special logarithms */ +93032640, 38612034, 17922280, 8662214, 4261238, 2113709, +1052693, 525315, 262400, 131136, 65552, 32772, 16385, +8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 1 }; + +@ @<Local variables for initialization@>= +integer k; /* all-purpose loop index */ + + +@ Here is the routine that calculates $2^8$ times the natural logarithm +of a |scaled| quantity; it is an integer approximation to $2^{24}\ln(x/2^{16})$, +when |x| is a given positive integer. + +The method is based on exercise 1.2.2--25 in {\sl The Art of Computer +Programming\/}: During the main iteration we have $1\L 2^{-30}x<1/(1-2^{1-k})$, +and the logarithm of $2^{30}x$ remains to be added to an accumulator +register called~$y$. Three auxiliary bits of accuracy are retained in~$y$ +during the calculation, and sixteen auxiliary bits to extend |y| are +kept in~|z| during the initial argument reduction. (We add +$100\cdot2^{16}=6553600$ to~|z| and subtract 100 from~|y| so that |z| will +not become negative; also, the actual amount subtracted from~|y| is~96, +not~100, because we want to add~4 for rounding before the final division by~8.) + +@c +static scaled mp_m_log (MP mp,scaled x) { + integer y,z; /* auxiliary registers */ + integer k; /* iteration counter */ + if ( x<=0 ) { + @<Handle non-positive logarithm@>; + } else { + y=1302456956+4-100; /* $14\times2^{27}\ln2\approx1302456956.421063$ */ + z=27595+6553600; /* and $2^{16}\times .421063\approx 27595$ */ + while ( x<fraction_four ) { + double(x); y-=93032639; z-=48782; + } /* $2^{27}\ln2\approx 93032639.74436163$ and $2^{16}\times.74436163\approx 48782$ */ + y=y+(z / unity); k=2; + while ( x>fraction_four+4 ) { + @<Increase |k| until |x| can be multiplied by a + factor of $2^{-k}$, and adjust $y$ accordingly@>; + } + return (y / 8); + } +} + +@ @<Increase |k| until |x| can...@>= +{ + z=((x-1) / two_to_the(k))+1; /* $z=\lceil x/2^k\rceil$ */ + while ( x<fraction_four+z ) { z=halfp(z+1); k++; }; + y+=spec_log[k]; x-=z; +} + +@ @<Handle non-positive logarithm@>= +{ + print_err("Logarithm of "); +@.Logarithm...replaced by 0@> + mp_print_scaled(mp, x); mp_print(mp, " has been replaced by 0"); + help2("Since I don't take logs of non-positive numbers,", + "I'm zeroing this one. Proceed, with fingers crossed."); + mp_error(mp); + return 0; +} + +@ Conversely, the exponential routine calculates $\exp(x/2^8)$, +when |x| is |scaled|. The result is an integer approximation to +$2^{16}\exp(x/2^{24})$, when |x| is regarded as an integer. + +@c +static scaled mp_m_exp (MP mp,scaled x) { + quarterword k; /* loop control index */ + integer y,z; /* auxiliary registers */ + if ( x>174436200 ) { + /* $2^{24}\ln((2^{31}-1)/2^{16})\approx 174436199.51$ */ + mp->arith_error=true; + return el_gordo; + } else if ( x<-197694359 ) { + /* $2^{24}\ln(2^{-1}/2^{16})\approx-197694359.45$ */ + return 0; + } else { + if ( x<=0 ) { + z=-8*x; y=04000000; /* $y=2^{20}$ */ + } else { + if ( x<=127919879 ) { + z=1023359037-8*x; + /* $2^{27}\ln((2^{31}-1)/2^{20})\approx 1023359037.125$ */ + } else { + z=8*(174436200-x); /* |z| is always nonnegative */ + } + y=el_gordo; + }; + @<Multiply |y| by $\exp(-z/2^{27})$@>; + if ( x<=127919879 ) + return ((y+8) / 16); + else + return y; + } +} + +@ The idea here is that subtracting |spec_log[k]| from |z| corresponds +to multiplying |y| by $1-2^{-k}$. + +A subtle point (which had to be checked) was that if $x=127919879$, the +value of~|y| will decrease so that |y+8| doesn't overflow. In fact, +$z$ will be 5 in this case, and |y| will decrease by~64 when |k=25| +and by~16 when |k=27|. + +@<Multiply |y| by...@>= +k=1; +while ( z>0 ) { + while ( z>=spec_log[k] ) { + z-=spec_log[k]; + y=y-1-((y-two_to_the(k-1)) / two_to_the(k)); + } + k++; +} + +@ The trigonometric subroutines use an auxiliary table such that +|spec_atan[k]| contains an approximation to the |angle| whose tangent +is~$1/2^k$. $\arctan2^{-k}$ times $2^{20}\cdot180/\pi$ + +@<Declarations@>= +static const angle spec_atan[27] = { 0, 27855475, 14718068, 7471121, 3750058, +1876857, 938658, 469357, 234682, 117342, 58671, 29335, 14668, 7334, 3667, +1833, 917, 458, 229, 115, 57, 29, 14, 7, 4, 2, 1 }; + +@ Given integers |x| and |y|, not both zero, the |n_arg| function +returns the |angle| whose tangent points in the direction $(x,y)$. +This subroutine first determines the correct octant, then solves the +problem for |0<=y<=x|, then converts the result appropriately to +return an answer in the range |-one_eighty_deg<=@t$\theta$@><=one_eighty_deg|. +(The answer is |+one_eighty_deg| if |y=0| and |x<0|, but an answer of +|-one_eighty_deg| is possible if, for example, |y=-1| and $x=-2^{30}$.) + +The octants are represented in a ``Gray code,'' since that turns out +to be computationally simplest. + +@d negate_x 1 +@d negate_y 2 +@d switch_x_and_y 4 +@d first_octant 1 +@d second_octant (first_octant+switch_x_and_y) +@d third_octant (first_octant+switch_x_and_y+negate_x) +@d fourth_octant (first_octant+negate_x) +@d fifth_octant (first_octant+negate_x+negate_y) +@d sixth_octant (first_octant+switch_x_and_y+negate_x+negate_y) +@d seventh_octant (first_octant+switch_x_and_y+negate_y) +@d eighth_octant (first_octant+negate_y) + +@c +static angle mp_n_arg (MP mp,integer x, integer y) { + angle z; /* auxiliary register */ + integer t; /* temporary storage */ + quarterword k; /* loop counter */ + int octant; /* octant code */ + if ( x>=0 ) { + octant=first_octant; + } else { + negate(x); octant=first_octant+negate_x; + } + if ( y<0 ) { + negate(y); octant=octant+negate_y; + } + if ( x<y ) { + t=y; y=x; x=t; octant=octant+switch_x_and_y; + } + if ( x==0 ) { + @<Handle undefined arg@>; + } else { + @<Set variable |z| to the arg of $(x,y)$@>; + @<Return an appropriate answer based on |z| and |octant|@>; + } +} + +@ @<Handle undefined arg@>= +{ + print_err("angle(0,0) is taken as zero"); +@.angle(0,0)...zero@> + help2("The `angle' between two identical points is undefined.", + "I'm zeroing this one. Proceed, with fingers crossed."); + mp_error(mp); + return 0; +} + +@ @<Return an appropriate answer...@>= +switch (octant) { +case first_octant: return z; +case second_octant: return (ninety_deg-z); +case third_octant: return (ninety_deg+z); +case fourth_octant: return (one_eighty_deg-z); +case fifth_octant: return (z-one_eighty_deg); +case sixth_octant: return (-z-ninety_deg); +case seventh_octant: return (z-ninety_deg); +case eighth_octant: return (-z); +}; /* there are no other cases */ +return 0 + +@ At this point we have |x>=y>=0|, and |x>0|. The numbers are scaled up +or down until $2^{28}\L x<2^{29}$, so that accurate fixed-point calculations +will be made. + +@<Set variable |z| to the arg...@>= +while ( x>=fraction_two ) { + x=halfp(x); y=halfp(y); +} +z=0; +if ( y>0 ) { + while ( x<fraction_one ) { + x+=x; y+=y; + }; + @<Increase |z| to the arg of $(x,y)$@>; +} + +@ During the calculations of this section, variables |x| and~|y| +represent actual coordinates $(x,2^{-k}y)$. We will maintain the +condition |x>=y|, so that the tangent will be at most $2^{-k}$. +If $x<2y$, the tangent is greater than $2^{-k-1}$. The transformation +$(a,b)\mapsto(a+b\tan\phi,b-a\tan\phi)$ replaces $(a,b)$ by +coordinates whose angle has decreased by~$\phi$; in the special case +$a=x$, $b=2^{-k}y$, and $\tan\phi=2^{-k-1}$, this operation reduces +to the particularly simple iteration shown here. [Cf.~John E. Meggitt, +@^Meggitt, John E.@> +{\sl IBM Journal of Research and Development\/ \bf6} (1962), 210--226.] + +The initial value of |x| will be multiplied by at most +$(1+{1\over2})(1+{1\over8})(1+{1\over32})\cdots\approx 1.7584$; hence +there is no chance of integer overflow. + +@<Increase |z|...@>= +k=0; +do { + y+=y; k++; + if ( y>x ){ + z=z+spec_atan[k]; t=x; x=x+(y / two_to_the(k+k)); y=y-t; + }; +} while (k!=15); +do { + y+=y; k++; + if ( y>x ) { z=z+spec_atan[k]; y=y-x; }; +} while (k!=26) + +@ Conversely, the |n_sin_cos| routine takes an |angle| and produces the sine +and cosine of that angle. The results of this routine are +stored in global integer variables |n_sin| and |n_cos|. + +@<Glob...@>= +fraction n_sin;fraction n_cos; /* results computed by |n_sin_cos| */ + +@ Given an integer |z| that is $2^{20}$ times an angle $\theta$ in degrees, +the purpose of |n_sin_cos(z)| is to set +|x=@t$r\cos\theta$@>| and |y=@t$r\sin\theta$@>| (approximately), +for some rather large number~|r|. The maximum of |x| and |y| +will be between $2^{28}$ and $2^{30}$, so that there will be hardly +any loss of accuracy. Then |x| and~|y| are divided by~|r|. + +@c +static void mp_n_sin_cos (MP mp,angle z) { /* computes a multiple of the sine + and cosine */ + quarterword k; /* loop control variable */ + int q; /* specifies the quadrant */ + fraction r; /* magnitude of |(x,y)| */ + integer x,y,t; /* temporary registers */ + while ( z<0 ) z=z+three_sixty_deg; + z=z % three_sixty_deg; /* now |0<=z<three_sixty_deg| */ + q=z / forty_five_deg; z=z % forty_five_deg; + x=fraction_one; y=x; + if ( ! odd(q) ) z=forty_five_deg-z; + @<Subtract angle |z| from |(x,y)|@>; + @<Convert |(x,y)| to the octant determined by~|q|@>; + r=mp_pyth_add(mp, x,y); + mp->n_cos=mp_make_fraction(mp, x,r); + mp->n_sin=mp_make_fraction(mp, y,r); +} + +@ In this case the octants are numbered sequentially. + +@<Convert |(x,...@>= +switch (q) { +case 0: break; +case 1: t=x; x=y; y=t; break; +case 2: t=x; x=-y; y=t; break; +case 3: negate(x); break; +case 4: negate(x); negate(y); break; +case 5: t=x; x=-y; y=-t; break; +case 6: t=x; x=y; y=-t; break; +case 7: negate(y); break; +} /* there are no other cases */ + +@ The main iteration of |n_sin_cos| is similar to that of |n_arg| but +applied in reverse. The values of |spec_atan[k]| decrease slowly enough +that this loop is guaranteed to terminate before the (nonexistent) value +|spec_atan[27]| would be required. + +@<Subtract angle |z|...@>= +k=1; +while ( z>0 ){ + if ( z>=spec_atan[k] ) { + z=z-spec_atan[k]; t=x; + x=t+y / two_to_the(k); + y=y-t / two_to_the(k); + } + k++; +} +if ( y<0 ) y=0 /* this precaution may never be needed */ + +@ And now let's complete our collection of numeric utility routines +by considering random number generation. +\MP\ generates pseudo-random numbers with the additive scheme recommended +in Section 3.6 of {\sl The Art of Computer Programming}; however, the +results are random fractions between 0 and |fraction_one-1|, inclusive. + +There's an auxiliary array |randoms| that contains 55 pseudo-random +fractions. Using the recurrence $x_n=(x_{n-55}-x_{n-31})\bmod 2^{28}$, +we generate batches of 55 new $x_n$'s at a time by calling |new_randoms|. +The global variable |j_random| tells which element has most recently +been consumed. +The global variable |random_seed| was introduced in version 0.9, +for the sole reason of stressing the fact that the initial value of the +random seed is system-dependant. The initialization code below will initialize +this variable to |(internal[mp_time] div unity)+internal[mp_day]|, but this +is not good enough on modern fast machines that are capable of running +multiple MetaPost processes within the same second. +@^system dependencies@> + +@<Glob...@>= +fraction randoms[55]; /* the last 55 random values generated */ +int j_random; /* the number of unused |randoms| */ + +@ @<Option variables@>= +int random_seed; /* the default random seed */ + +@ @<Allocate or initialize ...@>= +mp->random_seed = (scaled)opt->random_seed; + +@ To consume a random fraction, the program below will say `|next_random|' +and then it will fetch |randoms[j_random]|. + +@d next_random { if ( mp->j_random==0 ) mp_new_randoms(mp); + else decr(mp->j_random); } + +@c +static void mp_new_randoms (MP mp) { + int k; /* index into |randoms| */ + fraction x; /* accumulator */ + for (k=0;k<=23;k++) { + x=mp->randoms[k]-mp->randoms[k+31]; + if ( x<0 ) x=x+fraction_one; + mp->randoms[k]=x; + } + for (k=24;k<= 54;k++){ + x=mp->randoms[k]-mp->randoms[k-24]; + if ( x<0 ) x=x+fraction_one; + mp->randoms[k]=x; + } + mp->j_random=54; +} + +@ @<Declarations@>= +static void mp_init_randoms (MP mp,scaled seed); + +@ To initialize the |randoms| table, we call the following routine. + +@c +void mp_init_randoms (MP mp,scaled seed) { + fraction j,jj,k; /* more or less random integers */ + int i; /* index into |randoms| */ + j=abs(seed); + while ( j>=fraction_one ) j=halfp(j); + k=1; + for (i=0;i<=54;i++ ){ + jj=k; k=j-k; j=jj; + if ( k<0 ) k=k+fraction_one; + mp->randoms[(i*21)% 55]=j; + } + mp_new_randoms(mp); + mp_new_randoms(mp); + mp_new_randoms(mp); /* ``warm up'' the array */ +} + +@ To produce a uniform random number in the range |0<=u<x| or |0>=u>x| +or |0=u=x|, given a |scaled| value~|x|, we proceed as shown here. + +Note that the call of |take_fraction| will produce the values 0 and~|x| +with about half the probability that it will produce any other particular +values between 0 and~|x|, because it rounds its answers. + +@c +static scaled mp_unif_rand (MP mp,scaled x) { + scaled y; /* trial value */ + next_random; y=mp_take_fraction(mp, abs(x),mp->randoms[mp->j_random]); + if ( y==abs(x) ) return 0; + else if ( x>0 ) return y; + else return (-y); +} + +@ Finally, a normal deviate with mean zero and unit standard deviation +can readily be obtained with the ratio method (Algorithm 3.4.1R in +{\sl The Art of Computer Programming\/}). + +@c +static scaled mp_norm_rand (MP mp) { + integer x,u,l; /* what the book would call $2^{16}X$, $2^{28}U$, and $-2^{24}\ln U$ */ + do { + do { + next_random; + x=mp_take_fraction(mp, 112429,mp->randoms[mp->j_random]-fraction_half); + /* $2^{16}\sqrt{8/e}\approx 112428.82793$ */ + next_random; u=mp->randoms[mp->j_random]; + } while (abs(x)>=u); + x=mp_make_fraction(mp, x,u); + l=139548960-mp_m_log(mp, u); /* $2^{24}\cdot12\ln2\approx139548959.6165$ */ + } while (mp_ab_vs_cd(mp, 1024,l,x,x)<0); + return x; +} + +@* \[9] Packed data. +In order to make efficient use of storage space, \MP\ bases its major data +structures on a |memory_word|, which contains either a (signed) integer, +possibly scaled, or a small number of fields that are one half or one +quarter of the size used for storing integers. + +If |x| is a variable of type |memory_word|, it contains up to four +fields that can be referred to as follows: +$$\vbox{\halign{\hfil#&#\hfil&#\hfil\cr +|x|&.|int|&(an |integer|)\cr +|x|&.|sc|\qquad&(a |scaled| integer)\cr +|x.hh.lh|, |x.hh|&.|rh|&(two halfword fields)\cr +|x.hh.b0|, |x.hh.b1|, |x.hh|&.|rh|&(two quarterword fields, one halfword + field)\cr +|x.qqqq.b0|, |x.qqqq.b1|, |x.qqqq|&.|b2|, |x.qqqq.b3|\hskip-100pt + &\qquad\qquad\qquad(four quarterword fields)\cr}}$$ +This is somewhat cumbersome to write, and not very readable either, but +macros will be used to make the notation shorter and more transparent. +The code below gives a formal definition of |memory_word| and +its subsidiary types, using packed variant records. \MP\ makes no +assumptions about the relative positions of the fields within a word. + +@d max_quarterword 0x3FFF /* largest allowable value in a |quarterword| */ +@d max_halfword 0xFFFFFFF /* largest allowable value in a |halfword| */ + +@ Here are the inequalities that the quarterword and halfword values +must satisfy (or rather, the inequalities that they mustn't satisfy): + +@<Check the ``constant''...@>= +if (mp->ini_version) { + if ( mp->mem_max!=mp->mem_top ) mp->bad=8; +} else { + if ( mp->mem_max<mp->mem_top ) mp->bad=8; +} +if ( mp->mem_max>=max_halfword ) mp->bad=12; +if ( mp->max_strings>max_halfword ) mp->bad=13; + +@ The macros |qi| and |qo| are used for input to and output +from quarterwords. These are legacy macros. +@^system dependencies@> + +@d qo(A) (A) /* to read eight bits from a quarterword */ +@d qi(A) (quarterword)(A) /* to store eight bits in a quarterword */ + +@ The reader should study the following definitions closely: +@^system dependencies@> + +@d sc cint /* |scaled| data is equivalent to |integer| */ + +@<Types...@>= +typedef short quarterword; /* 1/4 of a word */ +typedef int halfword; /* 1/2 of a word */ +typedef union { + struct { + halfword RH, LH; + } v; + struct { /* Make B0,B1 overlap the most significant bytes of LH. */ + halfword junk; + quarterword B0, B1; + } u; +} two_halves; +typedef struct { + struct { + quarterword B2, B3, B0, B1; + } u; +} four_quarters; +typedef union { + two_halves hh; + integer cint; + four_quarters qqqq; +} memory_word; +#define b0 u.B0 +#define b1 u.B1 +#define b2 u.B2 +#define b3 u.B3 +#define rh v.RH +#define lh v.LH + +@ When debugging, we may want to print a |memory_word| without knowing +what type it is; so we print it in all modes. +@^debugging@> + +@c +void mp_print_word (MP mp,memory_word w) { + /* prints |w| in all ways */ + mp_print_int(mp, w.cint); mp_print_char(mp, xord(' ')); + mp_print_scaled(mp, w.sc); mp_print_char(mp, xord(' ')); + mp_print_scaled(mp, w.sc / 010000); mp_print_ln(mp); + mp_print_int(mp, w.hh.lh); mp_print_char(mp, xord('=')); + mp_print_int(mp, w.hh.b0); mp_print_char(mp, xord(':')); + mp_print_int(mp, w.hh.b1); mp_print_char(mp, xord(';')); + mp_print_int(mp, w.hh.rh); mp_print_char(mp, xord(' ')); + mp_print_int(mp, w.qqqq.b0); mp_print_char(mp, xord(':')); + mp_print_int(mp, w.qqqq.b1); mp_print_char(mp, xord(':')); + mp_print_int(mp, w.qqqq.b2); mp_print_char(mp, xord(':')); + mp_print_int(mp, w.qqqq.b3); +} + + +@* \[10] Dynamic memory allocation. + +The \MP\ system does nearly all of its own memory allocation, so that it +can readily be transported into environments that do not have automatic +facilities for strings, garbage collection, etc., and so that it can be in +control of what error messages the user receives. The dynamic storage +requirements of \MP\ are handled by providing a large array |mem| in +which consecutive blocks of words are used as nodes by the \MP\ routines. + +Pointer variables are indices into this array, or into another array +called |eqtb| that will be explained later. A pointer variable might +also be a special flag that lies outside the bounds of |mem|, so we +allow pointers to assume any |halfword| value. The minimum memory +index represents a null pointer. + +@d null 0 /* the null pointer */ +@d mp_void (null+1) /* a null pointer different from |null| */ + + +@<Types...@>= +typedef halfword pointer; /* a flag or a location in |mem| or |eqtb| */ + +@ The |mem| array is divided into two regions that are allocated separately, +but the dividing line between these two regions is not fixed; they grow +together until finding their ``natural'' size in a particular job. +Locations less than or equal to |lo_mem_max| are used for storing +variable-length records consisting of two or more words each. This region +is maintained using an algorithm similar to the one described in exercise +2.5--19 of {\sl The Art of Computer Programming}. However, no size field +appears in the allocated nodes; the program is responsible for knowing the +relevant size when a node is freed. Locations greater than or equal to +|hi_mem_min| are used for storing one-word records; a conventional +\.{AVAIL} stack is used for allocation in this region. + +Locations of |mem| between |0| and |mem_top| may be dumped as part +of preloaded mem files, by the \.{INIMP} preprocessor. +@.INIMP@> +Production versions of \MP\ may extend the memory at the top end in order to +provide more space; these locations, between |mem_top| and |mem_max|, +are always used for single-word nodes. + +The key pointers that govern |mem| allocation have a prescribed order: +$$\hbox{|null=0<lo_mem_max<hi_mem_min<mem_top<=mem_end<=mem_max|.}$$ + +@<Glob...@>= +memory_word *mem; /* the big dynamic storage area */ +pointer lo_mem_max; /* the largest location of variable-size memory in use */ +pointer hi_mem_min; /* the smallest location of one-word memory in use */ + + +@ +@d xfree(A) do { mp_xfree(A); A=NULL; } while (0) +@d xrealloc(P,A,B) mp_xrealloc(mp,P,(size_t)A,B) +@d xmalloc(A,B) mp_xmalloc(mp,(size_t)A,B) +@d xstrdup(A) mp_xstrdup(mp,A) +@d XREALLOC(a,b,c) a = xrealloc(a,(b+1),sizeof(c)); + +@<Declare helpers@>= +extern char *mp_strdup(const char *p) ; +extern char *mp_strldup(const char *p, size_t l) ; +extern void mp_xfree ( @= /*@@only@@*/ /*@@out@@*/ /*@@null@@*/ @> void *x); +extern @= /*@@only@@*/ @> void *mp_xrealloc (MP mp, void *p, size_t nmem, size_t size) ; +extern @= /*@@only@@*/ @> void *mp_xmalloc (MP mp, size_t nmem, size_t size) ; +extern @= /*@@only@@*/ @> char *mp_xstrdup(MP mp, const char *s); +extern @= /*@@only@@*/ @> char *mp_xstrldup(MP mp, const char *s, size_t l); +extern void mp_do_snprintf(char *str, int size, const char *fmt, ...); + +@ The |max_size_test| guards against overflow, on the assumption that +|size_t| is at least 31bits wide. + +@d max_size_test 0x7FFFFFFF + +@c +char *mp_strldup(const char *p, size_t l) { + char *r; + if (p==NULL) return NULL; + r = malloc ((size_t)(l*sizeof(char)+1)); + if (r==NULL) + return NULL; + return memcpy (r,p,(size_t)(l+1)); +} +char *mp_strdup(const char *p) { + if (p==NULL) return NULL; + return mp_strldup(p, strlen(p)); +} +void mp_xfree (void *x) { + if (x!=NULL) free(x); +} +void *mp_xrealloc (MP mp, void *p, size_t nmem, size_t size) { + void *w ; + if ((max_size_test/size)<nmem) { + do_fprintf(mp->err_out,"Memory size overflow!\n"); + mp->history =mp_fatal_error_stop; mp_jump_out(mp); + } + w = realloc (p,(nmem*size)); + if (w==NULL) { + do_fprintf(mp->err_out,"Out of memory!\n"); + mp->history =mp_system_error_stop; mp_jump_out(mp); + } + return w; +} +void *mp_xmalloc (MP mp, size_t nmem, size_t size) { + void *w; + if ((max_size_test/size)<nmem) { + do_fprintf(mp->err_out,"Memory size overflow!\n"); + mp->history =mp_fatal_error_stop; mp_jump_out(mp); + } + w = malloc (nmem*size); + if (w==NULL) { + do_fprintf(mp->err_out,"Out of memory!\n"); + mp->history =mp_system_error_stop; mp_jump_out(mp); + } + return w; +} +char *mp_xstrldup(MP mp, const char *s, size_t l) { + char *w; + if (s==NULL) + return NULL; + w = mp_strldup(s, l); + if (w==NULL) { + do_fprintf(mp->err_out,"Out of memory!\n"); + mp->history =mp_system_error_stop; mp_jump_out(mp); + } + return w; +} +char *mp_xstrdup(MP mp, const char *s) { + if (s==NULL) return NULL; + return mp_xstrldup(mp,s,strlen(s)); +} + + +@ @<Internal library declarations@>= +#ifdef HAVE_SNPRINTF +#define mp_snprintf (void)snprintf +#else +#define mp_snprintf mp_do_snprintf +#endif + +@ This internal version is rather stupid, but good enough for its purpose. + +@c +static char *mp_itoa (int i) { + char res[32] ; + unsigned idx = 30; + unsigned v = (unsigned)abs(i); + memset(res,0,32*sizeof(char)); + while (v>=10) { + char d = (char)(v % 10); + v = v / 10; + res[idx--] = (char)d + '0'; + } + res[idx--] = (char)v + '0'; + if (i<0) { + res[idx--] = '-'; + } + return mp_strdup((res+idx+1)); +} +static char *mp_utoa (unsigned v) { + char res[32] ; + unsigned idx = 30; + memset(res,0,32*sizeof(char)); + while (v>=10) { + char d = (char)(v % 10); + v = v / 10; + res[idx--] = d + '0'; + } + res[idx--] = (char)v + '0'; + return mp_strdup((res+idx+1)); +} +void mp_do_snprintf (char *str, int size, const char *format, ...) { + const char *fmt; + char *res; + int fw, pad; + va_list ap; + va_start(ap, format); + res = str; + for (fmt=format;*fmt!='\0';fmt++) { + if (*fmt=='%') { + fw=0; + pad=0; + fmt++; + switch(*fmt) { + case '0': + pad=1; + break; + case '1': + case '2': + case '3': + case '4': + case '5': + case '6': + case '7': + case '8': + case '9': + assert(fw==0); + fw = *fmt-'0'; + break; + case 's': + { + char *s = va_arg(ap, char *); + while (*s) { + *res = *s++; + if (size-->0) res++; + } + } + break; + case 'i': + case 'd': + { + char *s = mp_itoa(va_arg(ap, int)); + if (fw) { + int ffw = fw-strlen(s); + while (ffw-->0) { + *res = (pad ? '0' : ' '); + if (size-->0) res++; + } + } + if (s != NULL) { + while (*s) { + *res = *s++; + if (size-->0) res++; + } + } + } + break; + case 'u': + { + char *s = mp_utoa(va_arg(ap, unsigned)); + if (fw) { + int ffw = fw-strlen(s); + while (ffw-->0) { + *res = (pad ? '0' : ' '); + if (size-->0) res++; + } + } + if (s != NULL) { + while (*s) { + *res = *s++; + if (size-->0) res++; + } + } + } + break; + case '%': + *res = '%'; + if (size-->0) res++; + break; + default: + *res = '%'; + if (size-->0) res++; + *res = *fmt; + if (size-->0) res++; + break; + } + } else { + *res = *fmt; + if (size-->0) res++; + } + } + *res = '\0'; + va_end(ap); +} + +@ +@<Allocate or initialize ...@>= +mp->mem = xmalloc ((mp->mem_max+1),sizeof (memory_word)); +memset(mp->mem,0,(mp->mem_max+1)*sizeof (memory_word)); + +@ @<Dealloc variables@>= +xfree(mp->mem); + +@ Users who wish to study the memory requirements of particular applications can +can use optional special features that keep track of current and +maximum memory usage. When code between the delimiters |stat| $\ldots$ +|tats| is not ``commented out,'' \MP\ will run a bit slower but it will +report these statistics when |mp_tracing_stats| is positive. + +@<Glob...@>= +integer var_used; integer dyn_used; /* how much memory is in use */ + +@ Let's consider the one-word memory region first, since it's the +simplest. The pointer variable |mem_end| holds the highest-numbered location +of |mem| that has ever been used. The free locations of |mem| that +occur between |hi_mem_min| and |mem_end|, inclusive, are of type +|two_halves|, and we write |info(p)| and |mp_link(p)| for the |lh| +and |rh| fields of |mem[p]| when it is of this type. The single-word +free locations form a linked list +$$|avail|,\;\hbox{|mp_link(avail)|},\;\hbox{|mp_link(mp_link(avail))|},\;\ldots$$ +terminated by |null|. + +@(mpmp.h@>= +#define mp_link(A) mp->mem[(A)].hh.rh /* the |link| field of a memory word */ +#define mp_info(A) mp->mem[(A)].hh.lh /* the |info| field of a memory word */ + +@ @<Glob...@>= +pointer avail; /* head of the list of available one-word nodes */ +pointer mem_end; /* the last one-word node used in |mem| */ + +@ If one-word memory is exhausted, it might mean that the user has forgotten +a token like `\&{enddef}' or `\&{endfor}'. We will define some procedures +later that try to help pinpoint the trouble. + +@ The function |get_avail| returns a pointer to a new one-word node whose +|link| field is null. However, \MP\ will halt if there is no more room left. +@^inner loop@> + +@c +static pointer mp_get_avail (MP mp) { /* single-word node allocation */ + pointer p; /* the new node being got */ + p=mp->avail; /* get top location in the |avail| stack */ + if ( p!=null ) { + mp->avail=mp_link(mp->avail); /* and pop it off */ + } else if ( mp->mem_end<mp->mem_max ) { /* or go into virgin territory */ + incr(mp->mem_end); p=mp->mem_end; + } else { + decr(mp->hi_mem_min); p=mp->hi_mem_min; + if ( mp->hi_mem_min<=mp->lo_mem_max ) { + mp_runaway(mp); /* if memory is exhausted, display possible runaway text */ + mp_overflow(mp, "main memory size",mp->mem_max); + /* quit; all one-word nodes are busy */ +@:MetaPost capacity exceeded main memory size}{\quad main memory size@> + } + } + mp_link(p)=null; /* provide an oft-desired initialization of the new node */ + incr(mp->dyn_used);/* maintain statistics */ + return p; +} + +@ Conversely, a one-word node is recycled by calling |free_avail|. + +@d free_avail(A) /* single-word node liberation */ + { mp_link((A))=mp->avail; mp->avail=(A); decr(mp->dyn_used); } + +@ There's also a |fast_get_avail| routine, which saves the procedure-call +overhead at the expense of extra programming. This macro is used in +the places that would otherwise account for the most calls of |get_avail|. +@^inner loop@> + +@d fast_get_avail(A) { + (A)=mp->avail; /* avoid |get_avail| if possible, to save time */ + if ( (A)==null ) { (A)=mp_get_avail(mp); } + else { mp->avail=mp_link((A)); mp_link((A))=null; incr(mp->dyn_used); } + } + +@ The available-space list that keeps track of the variable-size portion +of |mem| is a nonempty, doubly-linked circular list of empty nodes, +pointed to by the roving pointer |rover|. + +Each empty node has size 2 or more; the first word contains the special +value |max_halfword| in its |link| field and the size in its |info| field; +the second word contains the two pointers for double linking. + +Each nonempty node also has size 2 or more. Its first word is of type +|two_halves|\kern-1pt, and its |link| field is never equal to |max_halfword|. +Otherwise there is complete flexibility with respect to the contents +of its other fields and its other words. + +(We require |mem_max<max_halfword| because terrible things can happen +when |max_halfword| appears in the |link| field of a nonempty node.) + +@d empty_flag max_halfword /* the |link| of an empty variable-size node */ +@d is_empty(A) (mp_link((A))==empty_flag) /* tests for empty node */ + +@(mpmp.h@>= +#define node_size mp_info /* the size field in empty variable-size nodes */ +#define lmp_link(A) mp_info((A)+1) /* left link in doubly-linked list of empty nodes */ +#define rmp_link(A) mp_link((A)+1) /* right link in doubly-linked list of empty nodes */ + +@ @<Glob...@>= +pointer rover; /* points to some node in the list of empties */ + +@ A call to |get_node| with argument |s| returns a pointer to a new node +of size~|s|, which must be 2~or more. The |link| field of the first word +of this new node is set to null. An overflow stop occurs if no suitable +space exists. + +If |get_node| is called with $s=2^{30}$, it simply merges adjacent free +areas and returns the value |max_halfword|. + +@<Internal library declarations@>= +pointer mp_get_node (MP mp,integer s) ; + +@ @c +pointer mp_get_node (MP mp,integer s) { /* variable-size node allocation */ + pointer p; /* the node currently under inspection */ + pointer q; /* the node physically after node |p| */ + integer r; /* the newly allocated node, or a candidate for this honor */ + integer t,tt; /* temporary registers */ +@^inner loop@> + RESTART: + p=mp->rover; /* start at some free node in the ring */ + do { + @<Try to allocate within node |p| and its physical successors, + and |goto found| if allocation was possible@>; + if (rmp_link(p)==null || (rmp_link(p)==p && p!=mp->rover)) { + print_err("Free list garbled"); + help3("I found an entry in the list of free nodes that links", + "badly. I will try to ignore the broken link, but something", + "is seriously amiss. It is wise to warn the maintainers.") + mp_error(mp); + rmp_link(p)=mp->rover; + } + p=rmp_link(p); /* move to the next node in the ring */ + } while (p!=mp->rover); /* repeat until the whole list has been traversed */ + if ( s==010000000000 ) { + return max_halfword; + }; + if ( mp->lo_mem_max+2<mp->hi_mem_min ) { + if ( mp->lo_mem_max+2<=max_halfword ) { + @<Grow more variable-size memory and |goto restart|@>; + } + } + mp_overflow(mp, "main memory size",mp->mem_max); + /* sorry, nothing satisfactory is left */ +@:MetaPost capacity exceeded main memory size}{\quad main memory size@> +FOUND: + mp_link(r)=null; /* this node is now nonempty */ + mp->var_used+=s; /* maintain usage statistics */ + return r; +} + +@ The lower part of |mem| grows by 1000 words at a time, unless +we are very close to going under. When it grows, we simply link +a new node into the available-space list. This method of controlled +growth helps to keep the |mem| usage consecutive when \MP\ is +implemented on ``virtual memory'' systems. +@^virtual memory@> + +@<Grow more variable-size memory and |goto restart|@>= +{ + if ( mp->hi_mem_min-mp->lo_mem_max>=1998 ) { + t=mp->lo_mem_max+1000; + } else { + t=mp->lo_mem_max+1+(mp->hi_mem_min-mp->lo_mem_max) / 2; + /* |lo_mem_max+2<=t<hi_mem_min| */ + } + if ( t>max_halfword ) t=max_halfword; + p=lmp_link(mp->rover); q=mp->lo_mem_max; rmp_link(p)=q; lmp_link(mp->rover)=q; + rmp_link(q)=mp->rover; lmp_link(q)=p; mp_link(q)=empty_flag; + node_size(q)=t-mp->lo_mem_max; + mp->lo_mem_max=t; mp_link(mp->lo_mem_max)=null; mp_info(mp->lo_mem_max)=null; + mp->rover=q; + goto RESTART; +} + +@ @<Try to allocate...@>= +q=p+node_size(p); /* find the physical successor */ +while ( is_empty(q) ) { /* merge node |p| with node |q| */ + t=rmp_link(q); tt=lmp_link(q); +@^inner loop@> + if ( q==mp->rover ) mp->rover=t; + lmp_link(t)=tt; rmp_link(tt)=t; + q=q+node_size(q); +} +r=q-s; +if ( r>p+1 ) { + @<Allocate from the top of node |p| and |goto found|@>; +} +if ( r==p ) { + if ( rmp_link(p)!=p ) { + @<Allocate entire node |p| and |goto found|@>; + } +} +node_size(p)=q-p /* reset the size in case it grew */ + +@ @<Allocate from the top...@>= +{ + node_size(p)=r-p; /* store the remaining size */ + mp->rover=p; /* start searching here next time */ + goto FOUND; +} + +@ Here we delete node |p| from the ring, and let |rover| rove around. + +@<Allocate entire...@>= +{ + mp->rover=rmp_link(p); t=lmp_link(p); + lmp_link(mp->rover)=t; rmp_link(t)=mp->rover; + goto FOUND; +} + +@ Conversely, when some variable-size node |p| of size |s| is no longer needed, +the operation |free_node(p,s)| will make its words available, by inserting +|p| as a new empty node just before where |rover| now points. + +@<Internal library declarations@>= +void mp_free_node (MP mp, pointer p, halfword s) ; + +@ @c +void mp_free_node (MP mp, pointer p, halfword s) { /* variable-size node + liberation */ + pointer q; /* |lmp_link(rover)| */ + node_size(p)=s; mp_link(p)=empty_flag; +@^inner loop@> + q=lmp_link(mp->rover); lmp_link(p)=q; rmp_link(p)=mp->rover; /* set both links */ + lmp_link(mp->rover)=p; rmp_link(q)=p; /* insert |p| into the ring */ + mp->var_used-=s; /* maintain statistics */ +} + +@* \[11] Memory layout. +Some areas of |mem| are dedicated to fixed usage, since static allocation is +more efficient than dynamic allocation when we can get away with it. For +example, locations |0| to |1| are always used to store a +two-word dummy token whose second word is zero. +The following macro definitions accomplish the static allocation by giving +symbolic names to the fixed positions. Static variable-size nodes appear +in locations |0| through |lo_mem_stat_max|, and static single-word nodes +appear in locations |hi_mem_stat_min| through |mem_top|, inclusive. + +@d sentinel mp->mem_top /* end of sorted lists */ +@d temp_head (mp->mem_top-1) /* head of a temporary list of some kind */ +@d hold_head (mp->mem_top-2) /* head of a temporary list of another kind */ + +@(mpmp.h@>= +#define spec_head (mp->mem_top-3) /* head of a list of unprocessed \&{special} items */ +#define null_dash (2) /* the first two words are reserved for a null value */ +#define dep_head (null_dash+3) /* we will define |dash_node_size=3| */ +#define zero_val (dep_head+2) /* two words for a permanently zero value */ +#define temp_val (zero_val+2) /* two words for a temporary value node */ +#define end_attr temp_val /* we use |end_attr+2| only */ +#define inf_val (end_attr+2) /* and |inf_val+1| only */ +#define bad_vardef (inf_val+2) /* two words for \&{vardef} error recovery */ +#define lo_mem_stat_max (bad_vardef+1) /* largest statically + allocated word in the variable-size |mem| */ +#define hi_mem_stat_min (mp->mem_top-3) /* smallest statically allocated word in + the one-word |mem| */ + +@ The following code gets the dynamic part of |mem| off to a good start, +when \MP\ is initializing itself the slow way. + +@<Initialize table entries (done by \.{INIMP} only)@>= +mp->rover=lo_mem_stat_max+1; /* initialize the dynamic memory */ +mp_link(mp->rover)=empty_flag; +node_size(mp->rover)=1000; /* which is a 1000-word available node */ +lmp_link(mp->rover)=mp->rover; rmp_link(mp->rover)=mp->rover; +mp->lo_mem_max=mp->rover+1000; +mp_link(mp->lo_mem_max)=null; mp_info(mp->lo_mem_max)=null; +for (k=hi_mem_stat_min;k<=(int)mp->mem_top;k++) { + mp->mem[k]=mp->mem[mp->lo_mem_max]; /* clear list heads */ +} +mp->avail=null; mp->mem_end=mp->mem_top; +mp->hi_mem_min=hi_mem_stat_min; /* initialize the one-word memory */ +mp->var_used=lo_mem_stat_max+1; +mp->dyn_used=mp->mem_top+1-(hi_mem_stat_min); /* initialize statistics */ + +@ The procedure |flush_list(p)| frees an entire linked list of one-word +nodes that starts at a given position, until coming to |sentinel| or a +pointer that is not in the one-word region. Another procedure, +|flush_node_list|, frees an entire linked list of one-word and two-word +nodes, until coming to a |null| pointer. +@^inner loop@> + +@c +static void mp_flush_list (MP mp,pointer p) { /* makes list of single-word nodes available */ + pointer q,r; /* list traversers */ + if ( p>=mp->hi_mem_min ) if ( p!=sentinel ) { + r=p; + do { + q=r; r=mp_link(r); + decr(mp->dyn_used); + if ( r<mp->hi_mem_min ) break; + } while (r!=sentinel); + /* now |q| is the last node on the list */ + mp_link(q)=mp->avail; mp->avail=p; + } +} +@# +static void mp_flush_node_list (MP mp,pointer p) { + pointer q; /* the node being recycled */ + while ( p!=null ){ + q=p; p=mp_link(p); + if ( q<mp->hi_mem_min ) + mp_free_node(mp, q,2); + else + free_avail(q); + } +} + +@ If \MP\ is extended improperly, the |mem| array might get screwed up. +For example, some pointers might be wrong, or some ``dead'' nodes might not +have been freed when the last reference to them disappeared. Procedures +|check_mem| and |search_mem| are available to help diagnose such +problems. These procedures make use of two arrays called |free| and +|was_free| that are present only if \MP's debugging routines have +been included. (You may want to decrease the size of |mem| while you +@^debugging@> +are debugging.) + +Because |boolean|s are typedef-d as ints, it is better to use +unsigned chars here. + +@<Glob...@>= +unsigned char *free; /* free cells */ +unsigned char *was_free; /* previously free cells */ +pointer was_mem_end; pointer was_lo_max; pointer was_hi_min; + /* previous |mem_end|, |lo_mem_max|,and |hi_mem_min| */ +boolean panicking; /* do we want to check memory constantly? */ + +@ @<Allocate or initialize ...@>= +mp->free = xmalloc ((mp->mem_max+1),sizeof (unsigned char)); +mp->was_free = xmalloc ((mp->mem_max+1), sizeof (unsigned char)); + +@ @<Dealloc variables@>= +xfree(mp->free); +xfree(mp->was_free); + +@ @<Allocate or ...@>= +mp->was_hi_min=mp->mem_max; +mp->panicking=false; + +@ @<Declarations@>= +static void mp_reallocate_memory(MP mp, int l) ; + +@ @c +static void mp_reallocate_memory(MP mp, int l) { + XREALLOC(mp->free, l, unsigned char); + XREALLOC(mp->was_free, l, unsigned char); + if (mp->mem) { + int newarea = l-mp->mem_max; + XREALLOC(mp->mem, l, memory_word); + memset (mp->mem+(mp->mem_max+1),0,sizeof(memory_word)*(newarea)); + } else { + XREALLOC(mp->mem, l, memory_word); + memset(mp->mem,0,sizeof(memory_word)*(l+1)); + } + mp->mem_max = l; + if (mp->ini_version) + mp->mem_top = l; +} + + + +@ Procedure |check_mem| makes sure that the available space lists of +|mem| are well formed, and it optionally prints out all locations +that are reserved now but were free the last time this procedure was called. + +@c +void mp_check_mem (MP mp,boolean print_locs ) { + pointer p,q,r; /* current locations of interest in |mem| */ + boolean clobbered; /* is something amiss? */ + for (p=0;p<=mp->lo_mem_max;p++) { + mp->free[p]=false; /* you can probably do this faster */ + } + for (p=mp->hi_mem_min;p<= mp->mem_end;p++) { + mp->free[p]=false; /* ditto */ + } + @<Check single-word |avail| list@>; + @<Check variable-size |avail| list@>; + @<Check flags of unavailable nodes@>; + @<Check the list of linear dependencies@>; + if ( print_locs ) { + @<Print newly busy locations@>; + } + memcpy(mp->was_free,mp->free, sizeof(char)*(mp->mem_end+1)); + mp->was_mem_end=mp->mem_end; + mp->was_lo_max=mp->lo_mem_max; + mp->was_hi_min=mp->hi_mem_min; +} + +@ @<Check single-word...@>= +p=mp->avail; q=null; clobbered=false; +while ( p!=null ) { + if ( (p>mp->mem_end)||(p<mp->hi_mem_min) ) clobbered=true; + else if ( mp->free[p] ) clobbered=true; + if ( clobbered ) { + mp_print_nl(mp, "AVAIL list clobbered at "); +@.AVAIL list clobbered...@> + mp_print_int(mp, q); break; + } + mp->free[p]=true; q=p; p=mp_link(q); +} + +@ @<Check variable-size...@>= +p=mp->rover; q=null; clobbered=false; +do { + if ( (p>=mp->lo_mem_max)||(p<0) ) clobbered=true; + else if ( (rmp_link(p)>=mp->lo_mem_max)||(rmp_link(p)<0) ) clobbered=true; + else if ( !(is_empty(p))||(node_size(p)<2)|| + (p+node_size(p)>mp->lo_mem_max)|| (lmp_link(rmp_link(p))!=p) ) clobbered=true; + if ( clobbered ) { + mp_print_nl(mp, "Double-AVAIL list clobbered at "); +@.Double-AVAIL list clobbered...@> + mp_print_int(mp, q); break; + } + for (q=p;q<=p+node_size(p)-1;q++) { /* mark all locations free */ + if ( mp->free[q] ) { + mp_print_nl(mp, "Doubly free location at "); +@.Doubly free location...@> + mp_print_int(mp, q); break; + } + mp->free[q]=true; + } + q=p; p=rmp_link(p); +} while (p!=mp->rover) + + +@ @<Check flags...@>= +p=0; +while ( p<=mp->lo_mem_max ) { /* node |p| should not be empty */ + if ( is_empty(p) ) { + mp_print_nl(mp, "Bad flag at "); mp_print_int(mp, p); +@.Bad flag...@> + } + while ( (p<=mp->lo_mem_max) && ! mp->free[p] ) p++; + while ( (p<=mp->lo_mem_max) && mp->free[p] ) p++; +} + +@ @<Print newly busy...@>= +{ + @<Do intialization required before printing new busy locations@>; + mp_print_nl(mp, "New busy locs:"); +@.New busy locs@> + for (p=0;p<= mp->lo_mem_max;p++ ) { + if ( ! mp->free[p] && ((p>mp->was_lo_max) || mp->was_free[p]) ) { + @<Indicate that |p| is a new busy location@>; + } + } + for (p=mp->hi_mem_min;p<=mp->mem_end;p++ ) { + if ( ! mp->free[p] && + ((p<mp->was_hi_min) || (p>mp->was_mem_end) || mp->was_free[p]) ) { + @<Indicate that |p| is a new busy location@>; + } + } + @<Finish printing new busy locations@>; +} + +@ There might be many new busy locations so we are careful to print contiguous +blocks compactly. During this operation |q| is the last new busy location and +|r| is the start of the block containing |q|. + +@<Indicate that |p| is a new busy location@>= +{ + if ( p>q+1 ) { + if ( q>r ) { + mp_print(mp, ".."); mp_print_int(mp, q); + } + mp_print_char(mp, xord(' ')); mp_print_int(mp, p); + r=p; + } + q=p; +} + +@ @<Do intialization required before printing new busy locations@>= +q=mp->mem_max; r=mp->mem_max + +@ @<Finish printing new busy locations@>= +if ( q>r ) { + mp_print(mp, ".."); mp_print_int(mp, q); +} + +@ The |search_mem| procedure attempts to answer the question ``Who points +to node~|p|?'' In doing so, it fetches |link| and |info| fields of |mem| +that might not be of type |two_halves|. Strictly speaking, this is +undefined, and it can lead to ``false drops'' (words that seem to +point to |p| purely by coincidence). But for debugging purposes, we want +to rule out the places that do {\sl not\/} point to |p|, so a few false +drops are tolerable. + +@c +void mp_search_mem (MP mp, pointer p) { /* look for pointers to |p| */ + integer q; /* current position being searched */ + for (q=0;q<=mp->lo_mem_max;q++) { + if ( mp_link(q)==p ){ + mp_print_nl(mp, "LINK("); mp_print_int(mp, q); mp_print_char(mp, xord(')')); + } + if ( mp_info(q)==p ) { + mp_print_nl(mp, "INFO("); mp_print_int(mp, q); mp_print_char(mp, xord(')')); + } + } + for (q=mp->hi_mem_min;q<=mp->mem_end;q++) { + if ( mp_link(q)==p ) { + mp_print_nl(mp, "LINK("); mp_print_int(mp, q); mp_print_char(mp, xord(')')); + } + if ( mp_info(q)==p ) { + mp_print_nl(mp, "INFO("); mp_print_int(mp, q); mp_print_char(mp, xord(')')); + } + } + @<Search |eqtb| for equivalents equal to |p|@>; +} + +@ Just before \.{INIMP} writes out the memory, it sorts the doubly linked +available space list. The list is probably very short at such times, so a +simple insertion sort is used. The smallest available location will be +pointed to by |rover|, the next-smallest by |rmp_link(rover)|, etc. + +@<Internal library ...@>= +void mp_sort_avail (MP mp); + +@ @c +void mp_sort_avail (MP mp) { /* sorts the available variable-size nodes + by location */ + pointer p,q,r; /* indices into |mem| */ + pointer old_rover; /* initial |rover| setting */ + p=mp_get_node(mp, 010000000000); /* merge adjacent free areas */ + p=rmp_link(mp->rover); rmp_link(mp->rover)=max_halfword; old_rover=mp->rover; + while ( p!=old_rover ) { + @<Sort |p| into the list starting at |rover| + and advance |p| to |rmp_link(p)|@>; + } + p=mp->rover; + while ( rmp_link(p)!=max_halfword ) { + lmp_link(rmp_link(p))=p; p=rmp_link(p); + }; + rmp_link(p)=mp->rover; lmp_link(mp->rover)=p; +} + +@ The following |while| loop is guaranteed to +terminate, since the list that starts at +|rover| ends with |max_halfword| during the sorting procedure. + +@<Sort |p|...@>= +if ( p<mp->rover ) { + q=p; p=rmp_link(q); rmp_link(q)=mp->rover; mp->rover=q; +} else { + q=mp->rover; + while ( rmp_link(q)<p ) q=rmp_link(q); + r=rmp_link(p); rmp_link(p)=rmp_link(q); rmp_link(q)=p; p=r; +} + + +@* \[12] The command codes. +Before we can go much further, we need to define symbolic names for the internal +code numbers that represent the various commands obeyed by \MP. These codes +are somewhat arbitrary, but not completely so. For example, +some codes have been made adjacent so that |case| statements in the +program need not consider cases that are widely spaced, or so that |case| +statements can be replaced by |if| statements. A command can begin an +expression if and only if its code lies between |min_primary_command| and +|max_primary_command|, inclusive. The first token of a statement that doesn't +begin with an expression has a command code between |min_command| and +|max_statement_command|, inclusive. Anything less than |min_command| is +eliminated during macro expansions, and anything no more than |max_pre_command| +is eliminated when expanding \TeX\ material. Ranges such as +|min_secondary_command..max_secondary_command| are used when parsing +expressions, but the relative ordering within such a range is generally not +critical. + +The ordering of the highest-numbered commands +(|comma<semicolon<end_group<stop|) is crucial for the parsing and +error-recovery methods of this program as is the ordering |if_test<fi_or_else| +for the smallest two commands. The ordering is also important in the ranges +|numeric_token..plus_or_minus| and |left_brace..ampersand|. + +At any rate, here is the list, for future reference. + +@d start_tex 1 /* begin \TeX\ material (\&{btex}, \&{verbatimtex}) */ +@d etex_marker 2 /* end \TeX\ material (\&{etex}) */ +@d mpx_break 3 /* stop reading an \.{MPX} file (\&{mpxbreak}) */ +@d max_pre_command mpx_break +@d if_test 4 /* conditional text (\&{if}) */ +@d fi_or_else 5 /* delimiters for conditionals (\&{elseif}, \&{else}, \&{fi}) */ +@d input 6 /* input a source file (\&{input}, \&{endinput}) */ +@d iteration 7 /* iterate (\&{for}, \&{forsuffixes}, \&{forever}, \&{endfor}) */ +@d repeat_loop 8 /* special command substituted for \&{endfor} */ +@d exit_test 9 /* premature exit from a loop (\&{exitif}) */ +@d relax 10 /* do nothing (\.{\char`\\}) */ +@d scan_tokens 11 /* put a string into the input buffer */ +@d expand_after 12 /* look ahead one token */ +@d defined_macro 13 /* a macro defined by the user */ +@d min_command (defined_macro+1) +@d save_command 14 /* save a list of tokens (\&{save}) */ +@d interim_command 15 /* save an internal quantity (\&{interim}) */ +@d let_command 16 /* redefine a symbolic token (\&{let}) */ +@d new_internal 17 /* define a new internal quantity (\&{newinternal}) */ +@d macro_def 18 /* define a macro (\&{def}, \&{vardef}, etc.) */ +@d ship_out_command 19 /* output a character (\&{shipout}) */ +@d add_to_command 20 /* add to edges (\&{addto}) */ +@d bounds_command 21 /* add bounding path to edges (\&{setbounds}, \&{clip}) */ +@d tfm_command 22 /* command for font metric info (\&{ligtable}, etc.) */ +@d protection_command 23 /* set protection flag (\&{outer}, \&{inner}) */ +@d show_command 24 /* diagnostic output (\&{show}, \&{showvariable}, etc.) */ +@d mode_command 25 /* set interaction level (\&{batchmode}, etc.) */ +@d mp_random_seed 26 /* initialize random number generator (\&{randomseed}) */ +@d message_command 27 /* communicate to user (\&{message}, \&{errmessage}) */ +@d every_job_command 28 /* designate a starting token (\&{everyjob}) */ +@d delimiters 29 /* define a pair of delimiters (\&{delimiters}) */ +@d special_command 30 /* output special info (\&{special}) + or font map info (\&{fontmapfile}, \&{fontmapline}) */ +@d write_command 31 /* write text to a file (\&{write}) */ +@d type_name 32 /* declare a type (\&{numeric}, \&{pair}, etc.) */ +@d max_statement_command type_name +@d min_primary_command type_name +@d left_delimiter 33 /* the left delimiter of a matching pair */ +@d begin_group 34 /* beginning of a group (\&{begingroup}) */ +@d nullary 35 /* an operator without arguments (e.g., \&{normaldeviate}) */ +@d unary 36 /* an operator with one argument (e.g., \&{sqrt}) */ +@d str_op 37 /* convert a suffix to a string (\&{str}) */ +@d cycle 38 /* close a cyclic path (\&{cycle}) */ +@d primary_binary 39 /* binary operation taking `\&{of}' (e.g., \&{point}) */ +@d capsule_token 40 /* a value that has been put into a token list */ +@d string_token 41 /* a string constant (e.g., |"hello"|) */ +@d internal_quantity 42 /* internal numeric parameter (e.g., \&{pausing}) */ +@d min_suffix_token internal_quantity +@d tag_token 43 /* a symbolic token without a primitive meaning */ +@d numeric_token 44 /* a numeric constant (e.g., \.{3.14159}) */ +@d max_suffix_token numeric_token +@d plus_or_minus 45 /* either `\.+' or `\.-' */ +@d max_primary_command plus_or_minus /* should also be |numeric_token+1| */ +@d min_tertiary_command plus_or_minus +@d tertiary_secondary_macro 46 /* a macro defined by \&{secondarydef} */ +@d tertiary_binary 47 /* an operator at the tertiary level (e.g., `\.{++}') */ +@d max_tertiary_command tertiary_binary +@d left_brace 48 /* the operator `\.{\char`\{}' */ +@d min_expression_command left_brace +@d path_join 49 /* the operator `\.{..}' */ +@d ampersand 50 /* the operator `\.\&' */ +@d expression_tertiary_macro 51 /* a macro defined by \&{tertiarydef} */ +@d expression_binary 52 /* an operator at the expression level (e.g., `\.<') */ +@d equals 53 /* the operator `\.=' */ +@d max_expression_command equals +@d and_command 54 /* the operator `\&{and}' */ +@d min_secondary_command and_command +@d secondary_primary_macro 55 /* a macro defined by \&{primarydef} */ +@d slash 56 /* the operator `\./' */ +@d secondary_binary 57 /* an operator at the binary level (e.g., \&{shifted}) */ +@d max_secondary_command secondary_binary +@d param_type 58 /* type of parameter (\&{primary}, \&{expr}, \&{suffix}, etc.) */ +@d controls 59 /* specify control points explicitly (\&{controls}) */ +@d tension 60 /* specify tension between knots (\&{tension}) */ +@d at_least 61 /* bounded tension value (\&{atleast}) */ +@d curl_command 62 /* specify curl at an end knot (\&{curl}) */ +@d macro_special 63 /* special macro operators (\&{quote}, \.{\#\AT!}, etc.) */ +@d right_delimiter 64 /* the right delimiter of a matching pair */ +@d left_bracket 65 /* the operator `\.[' */ +@d right_bracket 66 /* the operator `\.]' */ +@d right_brace 67 /* the operator `\.{\char`\}}' */ +@d with_option 68 /* option for filling (\&{withpen}, \&{withweight}, etc.) */ +@d thing_to_add 69 + /* variant of \&{addto} (\&{contour}, \&{doublepath}, \&{also}) */ +@d of_token 70 /* the operator `\&{of}' */ +@d to_token 71 /* the operator `\&{to}' */ +@d step_token 72 /* the operator `\&{step}' */ +@d until_token 73 /* the operator `\&{until}' */ +@d within_token 74 /* the operator `\&{within}' */ +@d lig_kern_token 75 + /* the operators `\&{kern}' and `\.{=:}' and `\.{=:\char'174}', etc. */ +@d assignment 76 /* the operator `\.{:=}' */ +@d skip_to 77 /* the operation `\&{skipto}' */ +@d bchar_label 78 /* the operator `\.{\char'174\char'174:}' */ +@d double_colon 79 /* the operator `\.{::}' */ +@d colon 80 /* the operator `\.:' */ +@# +@d comma 81 /* the operator `\.,', must be |colon+1| */ +@d end_of_statement (mp->cur_cmd>comma) +@d semicolon 82 /* the operator `\.;', must be |comma+1| */ +@d end_group 83 /* end a group (\&{endgroup}), must be |semicolon+1| */ +@d stop 84 /* end a job (\&{end}, \&{dump}), must be |end_group+1| */ +@d max_command_code stop +@d outer_tag (max_command_code+1) /* protection code added to command code */ + +@<Types...@>= +typedef int command_code; + +@ Variables and capsules in \MP\ have a variety of ``types,'' +distinguished by the code numbers defined here. These numbers are also +not completely arbitrary. Things that get expanded must have types +|>mp_independent|; a type remaining after expansion is numeric if and only if +its code number is at least |numeric_type|; objects containing numeric +parts must have types between |transform_type| and |pair_type|; +all other types must be smaller than |transform_type|; and among the types +that are not unknown or vacuous, the smallest two must be |boolean_type| +and |string_type| in that order. + +@d undefined 0 /* no type has been declared */ +@d unknown_tag 1 /* this constant is added to certain type codes below */ +@d unknown_types mp_unknown_boolean: case mp_unknown_string: + case mp_unknown_pen: case mp_unknown_picture: case mp_unknown_path + +@<Types...@>= +enum mp_variable_type { +mp_vacuous=1, /* no expression was present */ +mp_boolean_type, /* \&{boolean} with a known value */ +mp_unknown_boolean, +mp_string_type, /* \&{string} with a known value */ +mp_unknown_string, +mp_pen_type, /* \&{pen} with a known value */ +mp_unknown_pen, +mp_path_type, /* \&{path} with a known value */ +mp_unknown_path, +mp_picture_type, /* \&{picture} with a known value */ +mp_unknown_picture, +mp_transform_type, /* \&{transform} variable or capsule */ +mp_color_type, /* \&{color} variable or capsule */ +mp_cmykcolor_type, /* \&{cmykcolor} variable or capsule */ +mp_pair_type, /* \&{pair} variable or capsule */ +mp_numeric_type, /* variable that has been declared \&{numeric} but not used */ +mp_known, /* \&{numeric} with a known value */ +mp_dependent, /* a linear combination with |fraction| coefficients */ +mp_proto_dependent, /* a linear combination with |scaled| coefficients */ +mp_independent, /* \&{numeric} with unknown value */ +mp_token_list, /* variable name or suffix argument or text argument */ +mp_structured, /* variable with subscripts and attributes */ +mp_unsuffixed_macro, /* variable defined with \&{vardef} but no \.{\AT!\#} */ +mp_suffixed_macro /* variable defined with \&{vardef} and \.{\AT!\#} */ +} ; + +@ @<Declarations@>= +static void mp_print_type (MP mp,quarterword t) ; + +@ @<Basic printing procedures@>= +void mp_print_type (MP mp,quarterword t) { + switch (t) { + case mp_vacuous:mp_print(mp, "mp_vacuous"); break; + case mp_boolean_type:mp_print(mp, "boolean"); break; + case mp_unknown_boolean:mp_print(mp, "unknown boolean"); break; + case mp_string_type:mp_print(mp, "string"); break; + case mp_unknown_string:mp_print(mp, "unknown string"); break; + case mp_pen_type:mp_print(mp, "pen"); break; + case mp_unknown_pen:mp_print(mp, "unknown pen"); break; + case mp_path_type:mp_print(mp, "path"); break; + case mp_unknown_path:mp_print(mp, "unknown path"); break; + case mp_picture_type:mp_print(mp, "picture"); break; + case mp_unknown_picture:mp_print(mp, "unknown picture"); break; + case mp_transform_type:mp_print(mp, "transform"); break; + case mp_color_type:mp_print(mp, "color"); break; + case mp_cmykcolor_type:mp_print(mp, "cmykcolor"); break; + case mp_pair_type:mp_print(mp, "pair"); break; + case mp_known:mp_print(mp, "known numeric"); break; + case mp_dependent:mp_print(mp, "dependent"); break; + case mp_proto_dependent:mp_print(mp, "proto-dependent"); break; + case mp_numeric_type:mp_print(mp, "numeric"); break; + case mp_independent:mp_print(mp, "independent"); break; + case mp_token_list:mp_print(mp, "token list"); break; + case mp_structured:mp_print(mp, "mp_structured"); break; + case mp_unsuffixed_macro:mp_print(mp, "unsuffixed macro"); break; + case mp_suffixed_macro:mp_print(mp, "suffixed macro"); break; + default: mp_print(mp, "undefined"); break; + } +} + +@ Values inside \MP\ are stored in two-word nodes that have a |name_type| +as well as a |type|. The possibilities for |name_type| are defined +here; they will be explained in more detail later. + +@<Types...@>= +enum mp_name_types { + mp_root=0, /* |name_type| at the top level of a variable */ + mp_saved_root, /* same, when the variable has been saved */ + mp_structured_root, /* |name_type| where a |mp_structured| branch occurs */ + mp_subscr, /* |name_type| in a subscript node */ + mp_attr, /* |name_type| in an attribute node */ + mp_x_part_sector, /* |name_type| in the \&{xpart} of a node */ + mp_y_part_sector, /* |name_type| in the \&{ypart} of a node */ + mp_xx_part_sector, /* |name_type| in the \&{xxpart} of a node */ + mp_xy_part_sector, /* |name_type| in the \&{xypart} of a node */ + mp_yx_part_sector, /* |name_type| in the \&{yxpart} of a node */ + mp_yy_part_sector, /* |name_type| in the \&{yypart} of a node */ + mp_red_part_sector, /* |name_type| in the \&{redpart} of a node */ + mp_green_part_sector, /* |name_type| in the \&{greenpart} of a node */ + mp_blue_part_sector, /* |name_type| in the \&{bluepart} of a node */ + mp_cyan_part_sector, /* |name_type| in the \&{redpart} of a node */ + mp_magenta_part_sector, /* |name_type| in the \&{greenpart} of a node */ + mp_yellow_part_sector, /* |name_type| in the \&{bluepart} of a node */ + mp_black_part_sector, /* |name_type| in the \&{greenpart} of a node */ + mp_grey_part_sector, /* |name_type| in the \&{bluepart} of a node */ + mp_capsule, /* |name_type| in stashed-away subexpressions */ + mp_token /* |name_type| in a numeric token or string token */ +}; + +@ Primitive operations that produce values have a secondary identification +code in addition to their command code; it's something like genera and species. +For example, `\.*' has the command code |primary_binary|, and its +secondary identification is |times|. The secondary codes start at 30 so that +they don't overlap with the type codes; some type codes (e.g., |mp_string_type|) +are used as operators as well as type identifications. The relative values +are not critical, except for |true_code..false_code|, |or_op..and_op|, +and |filled_op..bounded_op|. The restrictions are that +|and_op-false_code=or_op-true_code|, that the ordering of +|x_part...blue_part| must match that of |x_part_sector..mp_blue_part_sector|, +and the ordering of |filled_op..bounded_op| must match that of the code +values they test for. + +@d true_code 30 /* operation code for \.{true} */ +@d false_code 31 /* operation code for \.{false} */ +@d null_picture_code 32 /* operation code for \.{nullpicture} */ +@d null_pen_code 33 /* operation code for \.{nullpen} */ +@d job_name_op 34 /* operation code for \.{jobname} */ +@d read_string_op 35 /* operation code for \.{readstring} */ +@d pen_circle 36 /* operation code for \.{pencircle} */ +@d normal_deviate 37 /* operation code for \.{normaldeviate} */ +@d read_from_op 38 /* operation code for \.{readfrom} */ +@d close_from_op 39 /* operation code for \.{closefrom} */ +@d odd_op 40 /* operation code for \.{odd} */ +@d known_op 41 /* operation code for \.{known} */ +@d unknown_op 42 /* operation code for \.{unknown} */ +@d not_op 43 /* operation code for \.{not} */ +@d decimal 44 /* operation code for \.{decimal} */ +@d reverse 45 /* operation code for \.{reverse} */ +@d make_path_op 46 /* operation code for \.{makepath} */ +@d make_pen_op 47 /* operation code for \.{makepen} */ +@d oct_op 48 /* operation code for \.{oct} */ +@d hex_op 49 /* operation code for \.{hex} */ +@d ASCII_op 50 /* operation code for \.{ASCII} */ +@d char_op 51 /* operation code for \.{char} */ +@d length_op 52 /* operation code for \.{length} */ +@d turning_op 53 /* operation code for \.{turningnumber} */ +@d color_model_part 54 /* operation code for \.{colormodel} */ +@d x_part 55 /* operation code for \.{xpart} */ +@d y_part 56 /* operation code for \.{ypart} */ +@d xx_part 57 /* operation code for \.{xxpart} */ +@d xy_part 58 /* operation code for \.{xypart} */ +@d yx_part 59 /* operation code for \.{yxpart} */ +@d yy_part 60 /* operation code for \.{yypart} */ +@d red_part 61 /* operation code for \.{redpart} */ +@d green_part 62 /* operation code for \.{greenpart} */ +@d blue_part 63 /* operation code for \.{bluepart} */ +@d cyan_part 64 /* operation code for \.{cyanpart} */ +@d magenta_part 65 /* operation code for \.{magentapart} */ +@d yellow_part 66 /* operation code for \.{yellowpart} */ +@d black_part 67 /* operation code for \.{blackpart} */ +@d grey_part 68 /* operation code for \.{greypart} */ +@d font_part 69 /* operation code for \.{fontpart} */ +@d text_part 70 /* operation code for \.{textpart} */ +@d path_part 71 /* operation code for \.{pathpart} */ +@d pen_part 72 /* operation code for \.{penpart} */ +@d dash_part 73 /* operation code for \.{dashpart} */ +@d sqrt_op 74 /* operation code for \.{sqrt} */ +@d mp_m_exp_op 75 /* operation code for \.{mexp} */ +@d mp_m_log_op 76 /* operation code for \.{mlog} */ +@d sin_d_op 77 /* operation code for \.{sind} */ +@d cos_d_op 78 /* operation code for \.{cosd} */ +@d floor_op 79 /* operation code for \.{floor} */ +@d uniform_deviate 80 /* operation code for \.{uniformdeviate} */ +@d char_exists_op 81 /* operation code for \.{charexists} */ +@d font_size 82 /* operation code for \.{fontsize} */ +@d ll_corner_op 83 /* operation code for \.{llcorner} */ +@d lr_corner_op 84 /* operation code for \.{lrcorner} */ +@d ul_corner_op 85 /* operation code for \.{ulcorner} */ +@d ur_corner_op 86 /* operation code for \.{urcorner} */ +@d arc_length 87 /* operation code for \.{arclength} */ +@d angle_op 88 /* operation code for \.{angle} */ +@d cycle_op 89 /* operation code for \.{cycle} */ +@d filled_op 90 /* operation code for \.{filled} */ +@d stroked_op 91 /* operation code for \.{stroked} */ +@d textual_op 92 /* operation code for \.{textual} */ +@d clipped_op 93 /* operation code for \.{clipped} */ +@d bounded_op 94 /* operation code for \.{bounded} */ +@d plus 95 /* operation code for \.+ */ +@d minus 96 /* operation code for \.- */ +@d times 97 /* operation code for \.* */ +@d over 98 /* operation code for \./ */ +@d pythag_add 99 /* operation code for \.{++} */ +@d pythag_sub 100 /* operation code for \.{+-+} */ +@d or_op 101 /* operation code for \.{or} */ +@d and_op 102 /* operation code for \.{and} */ +@d less_than 103 /* operation code for \.< */ +@d less_or_equal 104 /* operation code for \.{<=} */ +@d greater_than 105 /* operation code for \.> */ +@d greater_or_equal 106 /* operation code for \.{>=} */ +@d equal_to 107 /* operation code for \.= */ +@d unequal_to 108 /* operation code for \.{<>} */ +@d concatenate 109 /* operation code for \.\& */ +@d rotated_by 110 /* operation code for \.{rotated} */ +@d slanted_by 111 /* operation code for \.{slanted} */ +@d scaled_by 112 /* operation code for \.{scaled} */ +@d shifted_by 113 /* operation code for \.{shifted} */ +@d transformed_by 114 /* operation code for \.{transformed} */ +@d x_scaled 115 /* operation code for \.{xscaled} */ +@d y_scaled 116 /* operation code for \.{yscaled} */ +@d z_scaled 117 /* operation code for \.{zscaled} */ +@d in_font 118 /* operation code for \.{infont} */ +@d intersect 119 /* operation code for \.{intersectiontimes} */ +@d double_dot 120 /* operation code for improper \.{..} */ +@d substring_of 121 /* operation code for \.{substring} */ +@d min_of substring_of +@d subpath_of 122 /* operation code for \.{subpath} */ +@d direction_time_of 123 /* operation code for \.{directiontime} */ +@d point_of 124 /* operation code for \.{point} */ +@d precontrol_of 125 /* operation code for \.{precontrol} */ +@d postcontrol_of 126 /* operation code for \.{postcontrol} */ +@d pen_offset_of 127 /* operation code for \.{penoffset} */ +@d arc_time_of 128 /* operation code for \.{arctime} */ +@d mp_version 129 /* operation code for \.{mpversion} */ +@d envelope_of 130 /* operation code for \.{envelope} */ + +@c static void mp_print_op (MP mp,quarterword c) { + if (c<=mp_numeric_type ) { + mp_print_type(mp, c); + } else { + switch (c) { + case true_code:mp_print(mp, "true"); break; + case false_code:mp_print(mp, "false"); break; + case null_picture_code:mp_print(mp, "nullpicture"); break; + case null_pen_code:mp_print(mp, "nullpen"); break; + case job_name_op:mp_print(mp, "jobname"); break; + case read_string_op:mp_print(mp, "readstring"); break; + case pen_circle:mp_print(mp, "pencircle"); break; + case normal_deviate:mp_print(mp, "normaldeviate"); break; + case read_from_op:mp_print(mp, "readfrom"); break; + case close_from_op:mp_print(mp, "closefrom"); break; + case odd_op:mp_print(mp, "odd"); break; + case known_op:mp_print(mp, "known"); break; + case unknown_op:mp_print(mp, "unknown"); break; + case not_op:mp_print(mp, "not"); break; + case decimal:mp_print(mp, "decimal"); break; + case reverse:mp_print(mp, "reverse"); break; + case make_path_op:mp_print(mp, "makepath"); break; + case make_pen_op:mp_print(mp, "makepen"); break; + case oct_op:mp_print(mp, "oct"); break; + case hex_op:mp_print(mp, "hex"); break; + case ASCII_op:mp_print(mp, "ASCII"); break; + case char_op:mp_print(mp, "char"); break; + case length_op:mp_print(mp, "length"); break; + case turning_op:mp_print(mp, "turningnumber"); break; + case x_part:mp_print(mp, "xpart"); break; + case y_part:mp_print(mp, "ypart"); break; + case xx_part:mp_print(mp, "xxpart"); break; + case xy_part:mp_print(mp, "xypart"); break; + case yx_part:mp_print(mp, "yxpart"); break; + case yy_part:mp_print(mp, "yypart"); break; + case red_part:mp_print(mp, "redpart"); break; + case green_part:mp_print(mp, "greenpart"); break; + case blue_part:mp_print(mp, "bluepart"); break; + case cyan_part:mp_print(mp, "cyanpart"); break; + case magenta_part:mp_print(mp, "magentapart"); break; + case yellow_part:mp_print(mp, "yellowpart"); break; + case black_part:mp_print(mp, "blackpart"); break; + case grey_part:mp_print(mp, "greypart"); break; + case color_model_part:mp_print(mp, "colormodel"); break; + case font_part:mp_print(mp, "fontpart"); break; + case text_part:mp_print(mp, "textpart"); break; + case path_part:mp_print(mp, "pathpart"); break; + case pen_part:mp_print(mp, "penpart"); break; + case dash_part:mp_print(mp, "dashpart"); break; + case sqrt_op:mp_print(mp, "sqrt"); break; + case mp_m_exp_op:mp_print(mp, "mexp"); break; + case mp_m_log_op:mp_print(mp, "mlog"); break; + case sin_d_op:mp_print(mp, "sind"); break; + case cos_d_op:mp_print(mp, "cosd"); break; + case floor_op:mp_print(mp, "floor"); break; + case uniform_deviate:mp_print(mp, "uniformdeviate"); break; + case char_exists_op:mp_print(mp, "charexists"); break; + case font_size:mp_print(mp, "fontsize"); break; + case ll_corner_op:mp_print(mp, "llcorner"); break; + case lr_corner_op:mp_print(mp, "lrcorner"); break; + case ul_corner_op:mp_print(mp, "ulcorner"); break; + case ur_corner_op:mp_print(mp, "urcorner"); break; + case arc_length:mp_print(mp, "arclength"); break; + case angle_op:mp_print(mp, "angle"); break; + case cycle_op:mp_print(mp, "cycle"); break; + case filled_op:mp_print(mp, "filled"); break; + case stroked_op:mp_print(mp, "stroked"); break; + case textual_op:mp_print(mp, "textual"); break; + case clipped_op:mp_print(mp, "clipped"); break; + case bounded_op:mp_print(mp, "bounded"); break; + case plus:mp_print_char(mp, xord('+')); break; + case minus:mp_print_char(mp, xord('-')); break; + case times:mp_print_char(mp, xord('*')); break; + case over:mp_print_char(mp, xord('/')); break; + case pythag_add:mp_print(mp, "++"); break; + case pythag_sub:mp_print(mp, "+-+"); break; + case or_op:mp_print(mp, "or"); break; + case and_op:mp_print(mp, "and"); break; + case less_than:mp_print_char(mp, xord('<')); break; + case less_or_equal:mp_print(mp, "<="); break; + case greater_than:mp_print_char(mp, xord('>')); break; + case greater_or_equal:mp_print(mp, ">="); break; + case equal_to:mp_print_char(mp, xord('=')); break; + case unequal_to:mp_print(mp, "<>"); break; + case concatenate:mp_print(mp, "&"); break; + case rotated_by:mp_print(mp, "rotated"); break; + case slanted_by:mp_print(mp, "slanted"); break; + case scaled_by:mp_print(mp, "scaled"); break; + case shifted_by:mp_print(mp, "shifted"); break; + case transformed_by:mp_print(mp, "transformed"); break; + case x_scaled:mp_print(mp, "xscaled"); break; + case y_scaled:mp_print(mp, "yscaled"); break; + case z_scaled:mp_print(mp, "zscaled"); break; + case in_font:mp_print(mp, "infont"); break; + case intersect:mp_print(mp, "intersectiontimes"); break; + case substring_of:mp_print(mp, "substring"); break; + case subpath_of:mp_print(mp, "subpath"); break; + case direction_time_of:mp_print(mp, "directiontime"); break; + case point_of:mp_print(mp, "point"); break; + case precontrol_of:mp_print(mp, "precontrol"); break; + case postcontrol_of:mp_print(mp, "postcontrol"); break; + case pen_offset_of:mp_print(mp, "penoffset"); break; + case arc_time_of:mp_print(mp, "arctime"); break; + case mp_version:mp_print(mp, "mpversion"); break; + case envelope_of:mp_print(mp, "envelope"); break; + default: mp_print(mp, ".."); break; + } + } +} + +@ \MP\ also has a bunch of internal parameters that a user might want to +fuss with. Every such parameter has an identifying code number, defined here. + +@<Types...@>= +enum mp_given_internal { + mp_output_template=1, /* a string set up by \&{outputtemplate} */ + mp_output_format, /* the output format set up by \&{outputformat} */ + mp_tracing_titles, /* show titles online when they appear */ + mp_tracing_equations, /* show each variable when it becomes known */ + mp_tracing_capsules, /* show capsules too */ + mp_tracing_choices, /* show the control points chosen for paths */ + mp_tracing_specs, /* show path subdivision prior to filling with polygonal a pen */ + mp_tracing_commands, /* show commands and operations before they are performed */ + mp_tracing_restores, /* show when a variable or internal is restored */ + mp_tracing_macros, /* show macros before they are expanded */ + mp_tracing_output, /* show digitized edges as they are output */ + mp_tracing_stats, /* show memory usage at end of job */ + mp_tracing_lost_chars, /* show characters that aren't \&{infont} */ + mp_tracing_online, /* show long diagnostics on terminal and in the log file */ + mp_year, /* the current year (e.g., 1984) */ + mp_month, /* the current month (e.g., 3 $\equiv$ March) */ + mp_day, /* the current day of the month */ + mp_time, /* the number of minutes past midnight when this job started */ + mp_char_code, /* the number of the next character to be output */ + mp_char_ext, /* the extension code of the next character to be output */ + mp_char_wd, /* the width of the next character to be output */ + mp_char_ht, /* the height of the next character to be output */ + mp_char_dp, /* the depth of the next character to be output */ + mp_char_ic, /* the italic correction of the next character to be output */ + mp_design_size, /* the unit of measure used for |mp_char_wd..mp_char_ic|, in points */ + mp_pausing, /* positive to display lines on the terminal before they are read */ + mp_showstopping, /* positive to stop after each \&{show} command */ + mp_fontmaking, /* positive if font metric output is to be produced */ + mp_linejoin, /* as in \ps: 0 for mitered, 1 for round, 2 for beveled */ + mp_linecap, /* as in \ps: 0 for butt, 1 for round, 2 for square */ + mp_miterlimit, /* controls miter length as in \ps */ + mp_warning_check, /* controls error message when variable value is large */ + mp_boundary_char, /* the right boundary character for ligatures */ + mp_prologues, /* positive to output conforming PostScript using built-in fonts */ + mp_true_corners, /* positive to make \&{llcorner} etc. ignore \&{setbounds} */ + mp_default_color_model, /* the default color model for unspecified items */ + mp_restore_clip_color, + mp_procset, /* wether or not create PostScript command shortcuts */ + mp_gtroffmode /* whether the user specified |-troff| on the command line */ +}; + +@ + +@d max_given_internal mp_gtroffmode + +@<Glob...@>= +scaled *internal; /* the values of internal quantities */ +char **int_name; /* their names */ +int int_ptr; /* the maximum internal quantity defined so far */ +int max_internal; /* current maximum number of internal quantities */ + +@ @<Option variables@>= +int troff_mode; + +@ @<Allocate or initialize ...@>= +mp->max_internal=2*max_given_internal; +mp->internal = xmalloc ((mp->max_internal+1), sizeof(scaled)); +memset(mp->internal,0,(mp->max_internal+1)* sizeof(scaled)); +mp->int_name = xmalloc ((mp->max_internal+1), sizeof(char *)); +memset(mp->int_name,0,(mp->max_internal+1) * sizeof(char *)); +mp->troff_mode=(opt->troff_mode>0 ? true : false); + +@ @<Exported function ...@>= +int mp_troff_mode(MP mp); + +@ @c +int mp_troff_mode(MP mp) { return mp->troff_mode; } + +@ @<Set initial ...@>= +mp->int_ptr=max_given_internal; + +@ The symbolic names for internal quantities are put into \MP's hash table +by using a routine called |primitive|, which will be defined later. Let us +enter them now, so that we don't have to list all those names again +anywhere else. + +@<Put each of \MP's primitives into the hash table@>= +mp_primitive(mp, "tracingtitles",internal_quantity,mp_tracing_titles); +@:tracingtitles_}{\&{tracingtitles} primitive@> +mp_primitive(mp, "tracingequations",internal_quantity,mp_tracing_equations); +@:mp_tracing_equations_}{\&{tracingequations} primitive@> +mp_primitive(mp, "tracingcapsules",internal_quantity,mp_tracing_capsules); +@:mp_tracing_capsules_}{\&{tracingcapsules} primitive@> +mp_primitive(mp, "tracingchoices",internal_quantity,mp_tracing_choices); +@:mp_tracing_choices_}{\&{tracingchoices} primitive@> +mp_primitive(mp, "tracingspecs",internal_quantity,mp_tracing_specs); +@:mp_tracing_specs_}{\&{tracingspecs} primitive@> +mp_primitive(mp, "tracingcommands",internal_quantity,mp_tracing_commands); +@:mp_tracing_commands_}{\&{tracingcommands} primitive@> +mp_primitive(mp, "tracingrestores",internal_quantity,mp_tracing_restores); +@:mp_tracing_restores_}{\&{tracingrestores} primitive@> +mp_primitive(mp, "tracingmacros",internal_quantity,mp_tracing_macros); +@:mp_tracing_macros_}{\&{tracingmacros} primitive@> +mp_primitive(mp, "tracingoutput",internal_quantity,mp_tracing_output); +@:mp_tracing_output_}{\&{tracingoutput} primitive@> +mp_primitive(mp, "tracingstats",internal_quantity,mp_tracing_stats); +@:mp_tracing_stats_}{\&{tracingstats} primitive@> +mp_primitive(mp, "tracinglostchars",internal_quantity,mp_tracing_lost_chars); +@:mp_tracing_lost_chars_}{\&{tracinglostchars} primitive@> +mp_primitive(mp, "tracingonline",internal_quantity,mp_tracing_online); +@:mp_tracing_online_}{\&{tracingonline} primitive@> +mp_primitive(mp, "year",internal_quantity,mp_year); +@:mp_year_}{\&{year} primitive@> +mp_primitive(mp, "month",internal_quantity,mp_month); +@:mp_month_}{\&{month} primitive@> +mp_primitive(mp, "day",internal_quantity,mp_day); +@:mp_day_}{\&{day} primitive@> +mp_primitive(mp, "time",internal_quantity,mp_time); +@:time_}{\&{time} primitive@> +mp_primitive(mp, "charcode",internal_quantity,mp_char_code); +@:mp_char_code_}{\&{charcode} primitive@> +mp_primitive(mp, "charext",internal_quantity,mp_char_ext); +@:mp_char_ext_}{\&{charext} primitive@> +mp_primitive(mp, "charwd",internal_quantity,mp_char_wd); +@:mp_char_wd_}{\&{charwd} primitive@> +mp_primitive(mp, "charht",internal_quantity,mp_char_ht); +@:mp_char_ht_}{\&{charht} primitive@> +mp_primitive(mp, "chardp",internal_quantity,mp_char_dp); +@:mp_char_dp_}{\&{chardp} primitive@> +mp_primitive(mp, "charic",internal_quantity,mp_char_ic); +@:mp_char_ic_}{\&{charic} primitive@> +mp_primitive(mp, "designsize",internal_quantity,mp_design_size); +@:mp_design_size_}{\&{designsize} primitive@> +mp_primitive(mp, "pausing",internal_quantity,mp_pausing); +@:mp_pausing_}{\&{pausing} primitive@> +mp_primitive(mp, "showstopping",internal_quantity,mp_showstopping); +@:mp_showstopping_}{\&{showstopping} primitive@> +mp_primitive(mp, "fontmaking",internal_quantity,mp_fontmaking); +@:mp_fontmaking_}{\&{fontmaking} primitive@> +mp_primitive(mp, "linejoin",internal_quantity,mp_linejoin); +@:mp_linejoin_}{\&{linejoin} primitive@> +mp_primitive(mp, "linecap",internal_quantity,mp_linecap); +@:mp_linecap_}{\&{linecap} primitive@> +mp_primitive(mp, "miterlimit",internal_quantity,mp_miterlimit); +@:mp_miterlimit_}{\&{miterlimit} primitive@> +mp_primitive(mp, "warningcheck",internal_quantity,mp_warning_check); +@:mp_warning_check_}{\&{warningcheck} primitive@> +mp_primitive(mp, "boundarychar",internal_quantity,mp_boundary_char); +@:mp_boundary_char_}{\&{boundarychar} primitive@> +mp_primitive(mp, "prologues",internal_quantity,mp_prologues); +@:mp_prologues_}{\&{prologues} primitive@> +mp_primitive(mp, "truecorners",internal_quantity,mp_true_corners); +@:mp_true_corners_}{\&{truecorners} primitive@> +mp_primitive(mp, "mpprocset",internal_quantity,mp_procset); +@:mp_procset_}{\&{mpprocset} primitive@> +mp_primitive(mp, "troffmode",internal_quantity,mp_gtroffmode); +@:troffmode_}{\&{troffmode} primitive@> +mp_primitive(mp, "defaultcolormodel",internal_quantity,mp_default_color_model); +@:mp_default_color_model_}{\&{defaultcolormodel} primitive@> +mp_primitive(mp, "restoreclipcolor",internal_quantity,mp_restore_clip_color); +@:mp_restore_clip_color_}{\&{restoreclipcolor} primitive@> +mp_primitive(mp, "outputtemplate",internal_quantity,mp_output_template); +@:mp_output_template_}{\&{outputtemplate} primitive@> +mp_primitive(mp, "outputformat",internal_quantity,mp_output_format); +@:mp_output_format_}{\&{outputformat} primitive@> + +@ Colors can be specified in four color models. In the special +case of |no_model|, MetaPost does not output any color operator to +the postscript output. + +Note: these values are passed directly on to |with_option|. This only +works because the other possible values passed to |with_option| are +8 and 10 respectively (from |with_pen| and |with_picture|). + +There is a first state, that is only used for |gs_colormodel|. It flags +the fact that there has not been any kind of color specification by +the user so far in the game. + +@(mplib.h@>= +enum mp_color_model { + mp_no_model=1, + mp_grey_model=3, + mp_rgb_model=5, + mp_cmyk_model=7, + mp_uninitialized_model=9 +}; + + +@ @<Initialize table entries (done by \.{INIMP} only)@>= +mp->internal[mp_default_color_model]=(mp_rgb_model*unity); +mp->internal[mp_restore_clip_color]=unity; +mp->internal[mp_output_template]=intern("%j.%c"); +mp->internal[mp_output_format]=intern("eps"); + +@ Well, we do have to list the names one more time, for use in symbolic +printouts. + +@<Initialize table...@>= +mp->int_name[mp_tracing_titles]=xstrdup("tracingtitles"); +mp->int_name[mp_tracing_equations]=xstrdup("tracingequations"); +mp->int_name[mp_tracing_capsules]=xstrdup("tracingcapsules"); +mp->int_name[mp_tracing_choices]=xstrdup("tracingchoices"); +mp->int_name[mp_tracing_specs]=xstrdup("tracingspecs"); +mp->int_name[mp_tracing_commands]=xstrdup("tracingcommands"); +mp->int_name[mp_tracing_restores]=xstrdup("tracingrestores"); +mp->int_name[mp_tracing_macros]=xstrdup("tracingmacros"); +mp->int_name[mp_tracing_output]=xstrdup("tracingoutput"); +mp->int_name[mp_tracing_stats]=xstrdup("tracingstats"); +mp->int_name[mp_tracing_lost_chars]=xstrdup("tracinglostchars"); +mp->int_name[mp_tracing_online]=xstrdup("tracingonline"); +mp->int_name[mp_year]=xstrdup("year"); +mp->int_name[mp_month]=xstrdup("month"); +mp->int_name[mp_day]=xstrdup("day"); +mp->int_name[mp_time]=xstrdup("time"); +mp->int_name[mp_char_code]=xstrdup("charcode"); +mp->int_name[mp_char_ext]=xstrdup("charext"); +mp->int_name[mp_char_wd]=xstrdup("charwd"); +mp->int_name[mp_char_ht]=xstrdup("charht"); +mp->int_name[mp_char_dp]=xstrdup("chardp"); +mp->int_name[mp_char_ic]=xstrdup("charic"); +mp->int_name[mp_design_size]=xstrdup("designsize"); +mp->int_name[mp_pausing]=xstrdup("pausing"); +mp->int_name[mp_showstopping]=xstrdup("showstopping"); +mp->int_name[mp_fontmaking]=xstrdup("fontmaking"); +mp->int_name[mp_linejoin]=xstrdup("linejoin"); +mp->int_name[mp_linecap]=xstrdup("linecap"); +mp->int_name[mp_miterlimit]=xstrdup("miterlimit"); +mp->int_name[mp_warning_check]=xstrdup("warningcheck"); +mp->int_name[mp_boundary_char]=xstrdup("boundarychar"); +mp->int_name[mp_prologues]=xstrdup("prologues"); +mp->int_name[mp_true_corners]=xstrdup("truecorners"); +mp->int_name[mp_default_color_model]=xstrdup("defaultcolormodel"); +mp->int_name[mp_procset]=xstrdup("mpprocset"); +mp->int_name[mp_gtroffmode]=xstrdup("troffmode"); +mp->int_name[mp_restore_clip_color]=xstrdup("restoreclipcolor"); +mp->int_name[mp_output_template]=xstrdup("outputtemplate"); +mp->int_name[mp_output_format]=xstrdup("outputformat"); + +@ The following procedure, which is called just before \MP\ initializes its +input and output, establishes the initial values of the date and time. +@^system dependencies@> + +Note that the values are |scaled| integers. Hence \MP\ can no longer +be used after the year 32767. + +@c +static void mp_fix_date_and_time (MP mp) { + time_t aclock = time ((time_t *) 0); + struct tm *tmptr = localtime (&aclock); + mp->internal[mp_time]= + (tmptr->tm_hour*60+tmptr->tm_min)*unity; /* minutes since midnight */ + mp->internal[mp_day]=(tmptr->tm_mday)*unity; /* fourth day of the month */ + mp->internal[mp_month]=(tmptr->tm_mon+1)*unity; /* seventh month of the year */ + mp->internal[mp_year]=(tmptr->tm_year+1900)*unity; /* Anno Domini */ +} + +@ @<Declarations@>= +static void mp_fix_date_and_time (MP mp) ; + +@ \MP\ is occasionally supposed to print diagnostic information that +goes only into the transcript file, unless |mp_tracing_online| is positive. +Now that we have defined |mp_tracing_online| we can define +two routines that adjust the destination of print commands: + +@<Declarations@>= +static void mp_begin_diagnostic (MP mp) ; +static void mp_end_diagnostic (MP mp,boolean blank_line); +static void mp_print_diagnostic (MP mp, const char *s, const char *t, boolean nuline) ; + +@ @<Basic printing...@>= +void mp_begin_diagnostic (MP mp) { /* prepare to do some tracing */ + mp->old_setting=mp->selector; + if ((mp->internal[mp_tracing_online]<=0)&&(mp->selector==term_and_log)){ + decr(mp->selector); + if ( mp->history==mp_spotless ) mp->history=mp_warning_issued; + } +} +@# +void mp_end_diagnostic (MP mp,boolean blank_line) { + /* restore proper conditions after tracing */ + mp_print_nl(mp, ""); + if ( blank_line ) mp_print_ln(mp); + mp->selector=mp->old_setting; +} + +@ + +@<Glob...@>= +unsigned int old_setting; + +@ We will occasionally use |begin_diagnostic| in connection with line-number +printing, as follows. (The parameter |s| is typically |"Path"| or +|"Cycle spec"|, etc.) + +@<Basic printing...@>= +void mp_print_diagnostic (MP mp, const char *s, const char *t, boolean nuline) { + mp_begin_diagnostic(mp); + if ( nuline ) mp_print_nl(mp, s); else mp_print(mp, s); + mp_print(mp, " at line "); + mp_print_int(mp, mp_true_line(mp)); + mp_print(mp, t); mp_print_char(mp, xord(':')); +} + +@ The 256 |ASCII_code| characters are grouped into classes by means of +the |char_class| table. Individual class numbers have no semantic +or syntactic significance, except in a few instances defined here. +There's also |max_class|, which can be used as a basis for additional +class numbers in nonstandard extensions of \MP. + +@d digit_class 0 /* the class number of \.{0123456789} */ +@d period_class 1 /* the class number of `\..' */ +@d space_class 2 /* the class number of spaces and nonstandard characters */ +@d percent_class 3 /* the class number of `\.\%' */ +@d string_class 4 /* the class number of `\."' */ +@d right_paren_class 8 /* the class number of `\.)' */ +@d isolated_classes 5: case 6: case 7: case 8 /* characters that make length-one tokens only */ +@d letter_class 9 /* letters and the underline character */ +@d left_bracket_class 17 /* `\.[' */ +@d right_bracket_class 18 /* `\.]' */ +@d invalid_class 20 /* bad character in the input */ +@d max_class 20 /* the largest class number */ + +@<Glob...@>= +int char_class[256]; /* the class numbers */ + +@ If changes are made to accommodate non-ASCII character sets, they should +follow the guidelines in Appendix~C of {\sl The {\logos METAFONT\/}book}. +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> +@^system dependencies@> + +@<Set initial ...@>= +for (k='0';k<='9';k++) + mp->char_class[k]=digit_class; +mp->char_class['.']=period_class; +mp->char_class[' ']=space_class; +mp->char_class['%']=percent_class; +mp->char_class['"']=string_class; +mp->char_class[',']=5; +mp->char_class[';']=6; +mp->char_class['(']=7; +mp->char_class[')']=right_paren_class; +for (k='A';k<= 'Z';k++ ) + mp->char_class[k]=letter_class; +for (k='a';k<='z';k++) + mp->char_class[k]=letter_class; +mp->char_class['_']=letter_class; +mp->char_class['<']=10; +mp->char_class['=']=10; +mp->char_class['>']=10; +mp->char_class[':']=10; +mp->char_class['|']=10; +mp->char_class['`']=11; +mp->char_class['\'']=11; +mp->char_class['+']=12; +mp->char_class['-']=12; +mp->char_class['/']=13; +mp->char_class['*']=13; +mp->char_class['\\']=13; +mp->char_class['!']=14; +mp->char_class['?']=14; +mp->char_class['#']=15; +mp->char_class['&']=15; +mp->char_class['@@']=15; +mp->char_class['$']=15; +mp->char_class['^']=16; +mp->char_class['~']=16; +mp->char_class['[']=left_bracket_class; +mp->char_class[']']=right_bracket_class; +mp->char_class['{']=19; +mp->char_class['}']=19; +for (k=0;k<' ';k++) + mp->char_class[k]=invalid_class; +mp->char_class['\t']=space_class; +mp->char_class['\f']=space_class; +for (k=127;k<=255;k++) + mp->char_class[k]=invalid_class; + +@* \[13] The hash table. +Symbolic tokens are stored and retrieved by means of a fairly standard hash +table algorithm called the method of ``coalescing lists'' (cf.\ Algorithm 6.4C +in {\sl The Art of Computer Programming\/}). Once a symbolic token enters the +table, it is never removed. + +The actual sequence of characters forming a symbolic token is +stored in the |str_pool| array together with all the other strings. An +auxiliary array |hash| consists of items with two halfword fields per +word. The first of these, called |mp_next(p)|, points to the next identifier +belonging to the same coalesced list as the identifier corresponding to~|p|; +and the other, called |text(p)|, points to the |str_start| entry for +|p|'s identifier. If position~|p| of the hash table is empty, we have +|text(p)=0|; if position |p| is either empty or the end of a coalesced +hash list, we have |mp_next(p)=0|. + +An auxiliary pointer variable called |hash_used| is maintained in such a +way that all locations |p>=hash_used| are nonempty. The global variable +|st_count| tells how many symbolic tokens have been defined, if statistics +are being kept. + +The first 256 locations of |hash| are reserved for symbols of length one. + +There's a parallel array called |eqtb| that contains the current equivalent +values of each symbolic token. The entries of this array consist of +two halfwords called |eq_type| (a command code) and |equiv| (a secondary +piece of information that qualifies the |eq_type|). + +@d eq_type(A) mp->eqtb[(A)].lh /* the current ``meaning'' of a symbolic token */ +@d equiv(A) mp->eqtb[(A)].rh /* parametric part of a token's meaning */ +@d hash_is_full (mp->hash_used==hash_base) /* are all positions occupied? */ + +@(mpmp.h@>= +#define mp_next(A) mp->hash[(A)].lh /* link for coalesced lists */ +#define text(A) mp->hash[(A)].rh /* string number for symbolic token name */ +#define hash_base 257 /* hashing actually starts here */ + +@ @<Glob...@>= +pointer hash_used; /* allocation pointer for |hash| */ +integer st_count; /* total number of known identifiers */ + +@ Certain entries in the hash table are ``frozen'' and not redefinable, +since they are used in error recovery. + +@(mpmp.h@>= +#define hash_top (integer)(hash_base+mp->hash_size) /* the first location of the frozen area */ +#define frozen_inaccessible hash_top /* |hash| location to protect the frozen area */ +#define frozen_repeat_loop (hash_top+1) /* |hash| location of a loop-repeat token */ +#define frozen_right_delimiter (hash_top+2) /* |hash| location of a permanent `\.)' */ +#define frozen_left_bracket (hash_top+3) /* |hash| location of a permanent `\.[' */ +#define frozen_slash (hash_top+4) /* |hash| location of a permanent `\./' */ +#define frozen_colon (hash_top+5) /* |hash| location of a permanent `\.:' */ +#define frozen_semicolon (hash_top+6) /* |hash| location of a permanent `\.;' */ +#define frozen_end_for (hash_top+7) /* |hash| location of a permanent \&{endfor} */ +#define frozen_end_def (hash_top+8) /* |hash| location of a permanent \&{enddef} */ +#define frozen_fi (hash_top+9) /* |hash| location of a permanent \&{fi} */ +#define frozen_end_group (hash_top+10) /* |hash| location of a permanent `\.{endgroup}' */ +#define frozen_etex (hash_top+11) /* |hash| location of a permanent \&{etex} */ +#define frozen_mpx_break (hash_top+12) /* |hash| location of a permanent \&{mpxbreak} */ +#define frozen_bad_vardef (hash_top+13) /* |hash| location of `\.{a bad variable}' */ +#define frozen_undefined (hash_top+14) /* |hash| location that never gets defined */ +#define hash_end (integer)(hash_top+14) /* the actual size of the |hash| and |eqtb| arrays */ + + +@ @<Glob...@>= +two_halves *hash; /* the hash table */ +two_halves *eqtb; /* the equivalents */ + +@ @<Allocate or initialize ...@>= +mp->hash = xmalloc((hash_end+1),sizeof(two_halves)); +mp->eqtb = xmalloc((hash_end+1),sizeof(two_halves)); + +@ @<Dealloc variables@>= +xfree(mp->hash); +xfree(mp->eqtb); + +@ @<Set init...@>= +mp_next(1)=0; text(1)=0; eq_type(1)=tag_token; equiv(1)=null; +for (k=2;k<=hash_end;k++) { + mp->hash[k]=mp->hash[1]; mp->eqtb[k]=mp->eqtb[1]; +} + +@ @<Initialize table entries...@>= +mp->hash_used=frozen_inaccessible; /* nothing is used */ +mp->st_count=0; +text(frozen_bad_vardef)=intern("a bad variable"); +text(frozen_etex)=intern("etex"); +text(frozen_mpx_break)=intern("mpxbreak"); +text(frozen_fi)=intern("fi"); +text(frozen_end_group)=intern("endgroup"); +text(frozen_end_def)=intern("enddef"); +text(frozen_end_for)=intern("endfor"); +text(frozen_semicolon)=intern(";"); +text(frozen_colon)=intern(":"); +text(frozen_slash)=intern("/"); +text(frozen_left_bracket)=intern("["); +text(frozen_right_delimiter)=intern(")"); +text(frozen_inaccessible)=intern(" INACCESSIBLE"); +eq_type(frozen_right_delimiter)=right_delimiter; + +@ @<Check the ``constant'' values...@>= +if ( hash_end+mp->max_internal>max_halfword ) mp->bad=17; + +@ Here is the subroutine that searches the hash table for an identifier +that matches a given string of length~|l| appearing in |buffer[j.. +(j+l-1)]|. If the identifier is not found, it is inserted; hence it +will always be found, and the corresponding hash table address +will be returned. + +@c +static pointer mp_id_lookup (MP mp,integer j, integer l) { /* search the hash table */ + integer h; /* hash code */ + pointer p; /* index in |hash| array */ + pointer k; /* index in |buffer| array */ + if (l==1) { + @<Treat special case of length 1 and |break|@>; + } + @<Compute the hash code |h|@>; + p=h+hash_base; /* we start searching here; note that |0<=h<hash_prime| */ + while (true) { + if (text(p)>0 && length(text(p))==l && mp_str_eq_buf(mp, text(p),j)) + break; + if ( mp_next(p)==0 ) { + @<Insert a new symbolic token after |p|, then + make |p| point to it and |break|@>; + } + p=mp_next(p); + } + return p; +} + +@ @<Treat special case of length 1...@>= + p=mp->buffer[j]+1; text(p)=p-1; return p; + + +@ @<Insert a new symbolic...@>= +{ +if ( text(p)>0 ) { + do { + if ( hash_is_full ) + mp_overflow(mp, "hash size",(integer)mp->hash_size); +@:MetaPost capacity exceeded hash size}{\quad hash size@> + decr(mp->hash_used); + } while (text(mp->hash_used)!=0); /* search for an empty location in |hash| */ + mp_next(p)=mp->hash_used; + p=mp->hash_used; +} +str_room(l); +for (k=j;k<j+l;k++) { + append_char(mp->buffer[k]); +} +text(p)=mp_make_string(mp); +mp->str_ref[text(p)]=max_str_ref; +incr(mp->st_count); +break; +} + + +@ The value of |hash_prime| should be roughly 85\pct! of |hash_size|, and it +should be a prime number. The theory of hashing tells us to expect fewer +than two table probes, on the average, when the search is successful. +[See J.~S. Vitter, {\sl Journal of the ACM\/ \bf30} (1983), 231--258.] +@^Vitter, Jeffrey Scott@> + +@<Compute the hash code |h|@>= +h=mp->buffer[j]; +for (k=j+1;k<j+l;k++){ + h=h+h+mp->buffer[k]; + while ( h>=mp->hash_prime ) h=h-mp->hash_prime; +} + +@ @<Search |eqtb| for equivalents equal to |p|@>= +for (q=1;q<=hash_end;q++) { + if ( equiv(q)==p ) { + mp_print_nl(mp, "EQUIV("); + mp_print_int(mp, q); + mp_print_char(mp, xord(')')); + } +} + +@ We need to put \MP's ``primitive'' symbolic tokens into the hash +table, together with their command code (which will be the |eq_type|) +and an operand (which will be the |equiv|). The |primitive| procedure +does this, in a way that no \MP\ user can. The global value |cur_sym| +contains the new |eqtb| pointer after |primitive| has acted. + +@c +static void mp_primitive (MP mp, const char *ss, halfword c, halfword o) { + pool_pointer k; /* index into |str_pool| */ + quarterword j; /* index into |buffer| */ + quarterword l; /* length of the string */ + str_number s; + s = intern(ss); + k=mp->str_start[s]; l=str_stop(s)-k; + /* we will move |s| into the (empty) |buffer| */ + for (j=0;j<=l-1;j++) { + mp->buffer[j]=mp->str_pool[k+j]; + } + mp->cur_sym=mp_id_lookup(mp, 0,l); + if ( s>=256 ) { /* we don't want to have the string twice */ + mp_flush_string(mp, text(mp->cur_sym)); text(mp->cur_sym)=s; + }; + eq_type(mp->cur_sym)=c; + equiv(mp->cur_sym)=o; +} + + +@ Many of \MP's primitives need no |equiv|, since they are identifiable +by their |eq_type| alone. These primitives are loaded into the hash table +as follows: + +@<Put each of \MP's primitives into the hash table@>= +mp_primitive(mp, "..",path_join,0); +@:.._}{\.{..} primitive@> +mp_primitive(mp, "[",left_bracket,0); mp->eqtb[frozen_left_bracket]=mp->eqtb[mp->cur_sym]; +@:[ }{\.{[} primitive@> +mp_primitive(mp, "]",right_bracket,0); +@:] }{\.{]} primitive@> +mp_primitive(mp, "}",right_brace,0); +@:]]}{\.{\char`\}} primitive@> +mp_primitive(mp, "{",left_brace,0); +@:][}{\.{\char`\{} primitive@> +mp_primitive(mp, ":",colon,0); mp->eqtb[frozen_colon]=mp->eqtb[mp->cur_sym]; +@:: }{\.{:} primitive@> +mp_primitive(mp, "::",double_colon,0); +@::: }{\.{::} primitive@> +mp_primitive(mp, "||:",bchar_label,0); +@:::: }{\.{\char'174\char'174:} primitive@> +mp_primitive(mp, ":=",assignment,0); +@::=_}{\.{:=} primitive@> +mp_primitive(mp, ",",comma,0); +@:, }{\., primitive@> +mp_primitive(mp, ";",semicolon,0); mp->eqtb[frozen_semicolon]=mp->eqtb[mp->cur_sym]; +@:; }{\.; primitive@> +mp_primitive(mp, "\\",relax,0); +@:]]\\}{\.{\char`\\} primitive@> +@# +mp_primitive(mp, "addto",add_to_command,0); +@:add_to_}{\&{addto} primitive@> +mp_primitive(mp, "atleast",at_least,0); +@:at_least_}{\&{atleast} primitive@> +mp_primitive(mp, "begingroup",begin_group,0); mp->bg_loc=mp->cur_sym; +@:begin_group_}{\&{begingroup} primitive@> +mp_primitive(mp, "controls",controls,0); +@:controls_}{\&{controls} primitive@> +mp_primitive(mp, "curl",curl_command,0); +@:curl_}{\&{curl} primitive@> +mp_primitive(mp, "delimiters",delimiters,0); +@:delimiters_}{\&{delimiters} primitive@> +mp_primitive(mp, "endgroup",end_group,0); + mp->eqtb[frozen_end_group]=mp->eqtb[mp->cur_sym]; mp->eg_loc=mp->cur_sym; +@:endgroup_}{\&{endgroup} primitive@> +mp_primitive(mp, "everyjob",every_job_command,0); +@:every_job_}{\&{everyjob} primitive@> +mp_primitive(mp, "exitif",exit_test,0); +@:exit_if_}{\&{exitif} primitive@> +mp_primitive(mp, "expandafter",expand_after,0); +@:expand_after_}{\&{expandafter} primitive@> +mp_primitive(mp, "interim",interim_command,0); +@:interim_}{\&{interim} primitive@> +mp_primitive(mp, "let",let_command,0); +@:let_}{\&{let} primitive@> +mp_primitive(mp, "newinternal",new_internal,0); +@:new_internal_}{\&{newinternal} primitive@> +mp_primitive(mp, "of",of_token,0); +@:of_}{\&{of} primitive@> +mp_primitive(mp, "randomseed",mp_random_seed,0); +@:mp_random_seed_}{\&{randomseed} primitive@> +mp_primitive(mp, "save",save_command,0); +@:save_}{\&{save} primitive@> +mp_primitive(mp, "scantokens",scan_tokens,0); +@:scan_tokens_}{\&{scantokens} primitive@> +mp_primitive(mp, "shipout",ship_out_command,0); +@:ship_out_}{\&{shipout} primitive@> +mp_primitive(mp, "skipto",skip_to,0); +@:skip_to_}{\&{skipto} primitive@> +mp_primitive(mp, "special",special_command,0); +@:special}{\&{special} primitive@> +mp_primitive(mp, "fontmapfile",special_command,1); +@:fontmapfile}{\&{fontmapfile} primitive@> +mp_primitive(mp, "fontmapline",special_command,2); +@:fontmapline}{\&{fontmapline} primitive@> +mp_primitive(mp, "step",step_token,0); +@:step_}{\&{step} primitive@> +mp_primitive(mp, "str",str_op,0); +@:str_}{\&{str} primitive@> +mp_primitive(mp, "tension",tension,0); +@:tension_}{\&{tension} primitive@> +mp_primitive(mp, "to",to_token,0); +@:to_}{\&{to} primitive@> +mp_primitive(mp, "until",until_token,0); +@:until_}{\&{until} primitive@> +mp_primitive(mp, "within",within_token,0); +@:within_}{\&{within} primitive@> +mp_primitive(mp, "write",write_command,0); +@:write_}{\&{write} primitive@> + +@ Each primitive has a corresponding inverse, so that it is possible to +display the cryptic numeric contents of |eqtb| in symbolic form. +Every call of |primitive| in this program is therefore accompanied by some +straightforward code that forms part of the |print_cmd_mod| routine +explained below. + +@<Cases of |print_cmd_mod| for symbolic printing of primitives@>= +case add_to_command:mp_print(mp, "addto"); break; +case assignment:mp_print(mp, ":="); break; +case at_least:mp_print(mp, "atleast"); break; +case bchar_label:mp_print(mp, "||:"); break; +case begin_group:mp_print(mp, "begingroup"); break; +case colon:mp_print(mp, ":"); break; +case comma:mp_print(mp, ","); break; +case controls:mp_print(mp, "controls"); break; +case curl_command:mp_print(mp, "curl"); break; +case delimiters:mp_print(mp, "delimiters"); break; +case double_colon:mp_print(mp, "::"); break; +case end_group:mp_print(mp, "endgroup"); break; +case every_job_command:mp_print(mp, "everyjob"); break; +case exit_test:mp_print(mp, "exitif"); break; +case expand_after:mp_print(mp, "expandafter"); break; +case interim_command:mp_print(mp, "interim"); break; +case left_brace:mp_print(mp, "{"); break; +case left_bracket:mp_print(mp, "["); break; +case let_command:mp_print(mp, "let"); break; +case new_internal:mp_print(mp, "newinternal"); break; +case of_token:mp_print(mp, "of"); break; +case path_join:mp_print(mp, ".."); break; +case mp_random_seed:mp_print(mp, "randomseed"); break; +case relax:mp_print_char(mp, xord('\\')); break; +case right_brace:mp_print_char(mp, xord('}')); break; +case right_bracket:mp_print_char(mp, xord(']')); break; +case save_command:mp_print(mp, "save"); break; +case scan_tokens:mp_print(mp, "scantokens"); break; +case semicolon:mp_print_char(mp, xord(';')); break; +case ship_out_command:mp_print(mp, "shipout"); break; +case skip_to:mp_print(mp, "skipto"); break; +case special_command: if ( m==2 ) mp_print(mp, "fontmapline"); else + if ( m==1 ) mp_print(mp, "fontmapfile"); else + mp_print(mp, "special"); break; +case step_token:mp_print(mp, "step"); break; +case str_op:mp_print(mp, "str"); break; +case tension:mp_print(mp, "tension"); break; +case to_token:mp_print(mp, "to"); break; +case until_token:mp_print(mp, "until"); break; +case within_token:mp_print(mp, "within"); break; +case write_command:mp_print(mp, "write"); break; + +@ We will deal with the other primitives later, at some point in the program +where their |eq_type| and |equiv| values are more meaningful. For example, +the primitives for macro definitions will be loaded when we consider the +routines that define macros. +It is easy to find where each particular +primitive was treated by looking in the index at the end; for example, the +section where |"def"| entered |eqtb| is listed under `\&{def} primitive'. + +@* \[14] Token lists. +A \MP\ token is either symbolic or numeric or a string, or it denotes +a macro parameter or capsule; so there are five corresponding ways to encode it +@^token@> +internally: (1)~A symbolic token whose hash code is~|p| +is represented by the number |p|, in the |info| field of a single-word +node in~|mem|. (2)~A numeric token whose |scaled| value is~|v| is +represented in a two-word node of~|mem|; the |type| field is |known|, +the |name_type| field is |token|, and the |value| field holds~|v|. +The fact that this token appears in a two-word node rather than a +one-word node is, of course, clear from the node address. +(3)~A string token is also represented in a two-word node; the |type| +field is |mp_string_type|, the |name_type| field is |token|, and the +|value| field holds the corresponding |str_number|. (4)~Capsules have +|name_type=capsule|, and their |type| and |value| fields represent +arbitrary values (in ways to be explained later). (5)~Macro parameters +are like symbolic tokens in that they appear in |info| fields of +one-word nodes. The $k$th parameter is represented by |expr_base+k| if it +is of type \&{expr}, or by |suffix_base+k| if it is of type \&{suffix}, or +by |text_base+k| if it is of type \&{text}. (Here |0<=k<param_size|.) +Actual values of these parameters are kept in a separate stack, as we will +see later. The constants |expr_base|, |suffix_base|, and |text_base| are, +of course, chosen so that there will be no confusion between symbolic +tokens and parameters of various types. + +Note that +the `\\{type}' field of a node has nothing to do with ``type'' in a +printer's sense. It's curious that the same word is used in such different ways. + +@d mp_type(A) mp->mem[(A)].hh.b0 /* identifies what kind of value this is */ +@d mp_name_type(A) mp->mem[(A)].hh.b1 /* a clue to the name of this value */ +@d token_node_size 2 /* the number of words in a large token node */ +@d value_loc(A) ((A)+1) /* the word that contains the |value| field */ +@d value(A) mp->mem[value_loc((A))].cint /* the value stored in a large token node */ +@d expr_base (hash_end+1) /* code for the zeroth \&{expr} parameter */ +@d suffix_base (expr_base+mp->param_size) /* code for the zeroth \&{suffix} parameter */ +@d text_base (suffix_base+mp->param_size) /* code for the zeroth \&{text} parameter */ + +@<Check the ``constant''...@>= +if ( text_base+mp->param_size>max_halfword ) mp->bad=18; + +@ We have set aside a two word node beginning at |null| so that we can have +|value(null)=0|. We will make use of this coincidence later. + +@<Initialize table entries...@>= +mp_link(null)=null; value(null)=0; + +@ A numeric token is created by the following trivial routine. + +@c +static pointer mp_new_num_tok (MP mp,scaled v) { + pointer p; /* the new node */ + p=mp_get_node(mp, token_node_size); value(p)=v; + mp_type(p)=mp_known; mp_name_type(p)=mp_token; + return p; +} + +@ A token list is a singly linked list of nodes in |mem|, where +each node contains a token and a link. Here's a subroutine that gets rid +of a token list when it is no longer needed. + +@c static void mp_flush_token_list (MP mp,pointer p) { + pointer q; /* the node being recycled */ + while ( p!=null ) { + q=p; p=mp_link(p); + if ( q>=mp->hi_mem_min ) { + free_avail(q); + } else { + switch (mp_type(q)) { + case mp_vacuous: case mp_boolean_type: case mp_known: + break; + case mp_string_type: + delete_str_ref(value(q)); + break; + case unknown_types: case mp_pen_type: case mp_path_type: + case mp_picture_type: case mp_pair_type: case mp_color_type: + case mp_cmykcolor_type: case mp_transform_type: case mp_dependent: + case mp_proto_dependent: case mp_independent: + mp_recycle_value(mp,q); + break; + default: mp_confusion(mp, "token"); +@:this can't happen token}{\quad token@> + } + mp_free_node(mp, q,token_node_size); + } + } +} + +@ The procedure |show_token_list|, which prints a symbolic form of +the token list that starts at a given node |p|, illustrates these +conventions. The token list being displayed should not begin with a reference +count. However, the procedure is intended to be fairly robust, so that if the +memory links are awry or if |p| is not really a pointer to a token list, +almost nothing catastrophic can happen. + +An additional parameter |q| is also given; this parameter is either null +or it points to a node in the token list where a certain magic computation +takes place that will be explained later. (Basically, |q| is non-null when +we are printing the two-line context information at the time of an error +message; |q| marks the place corresponding to where the second line +should begin.) + +The generation will stop, and `\.{\char`\ ETC.}' will be printed, if the length +of printing exceeds a given limit~|l|; the length of printing upon entry is +assumed to be a given amount called |null_tally|. (Note that +|show_token_list| sometimes uses itself recursively to print +variable names within a capsule.) +@^recursion@> + +Unusual entries are printed in the form of all-caps tokens +preceded by a space, e.g., `\.{\char`\ BAD}'. + +@<Declarations@>= +static void mp_show_token_list (MP mp, integer p, integer q, integer l, + integer null_tally) ; + +@ @c +void mp_show_token_list (MP mp, integer p, integer q, integer l, + integer null_tally) { + quarterword class,c; /* the |char_class| of previous and new tokens */ + integer r,v; /* temporary registers */ + class=percent_class; + mp->tally=null_tally; + while ( (p!=null) && (mp->tally<l) ) { + if ( p==q ) + @<Do magic computation@>; + @<Display token |p| and set |c| to its class; + but |return| if there are problems@>; + class=c; p=mp_link(p); + } + if ( p!=null ) + mp_print(mp, " ETC."); +@.ETC@> + return; +} + +@ @<Display token |p| and set |c| to its class...@>= +c=letter_class; /* the default */ +if ( (p<0)||(p>mp->mem_end) ) { + mp_print(mp, " CLOBBERED"); return; +@.CLOBBERED@> +} +if ( p<mp->hi_mem_min ) { + @<Display two-word token@>; +} else { + r=mp_info(p); + if ( r>=expr_base ) { + @<Display a parameter token@>; + } else { + if ( r<1 ) { + if ( r==0 ) { + @<Display a collective subscript@> + } else { + mp_print(mp, " IMPOSSIBLE"); +@.IMPOSSIBLE@> + } + } else { + r=text(r); + if ( (r<0)||(r>mp->max_str_ptr) ) { + mp_print(mp, " NONEXISTENT"); +@.NONEXISTENT@> + } else { + @<Print string |r| as a symbolic token + and set |c| to its class@>; + } + } + } +} + +@ @<Display two-word token@>= +if ( mp_name_type(p)==mp_token ) { + if ( mp_type(p)==mp_known ) { + @<Display a numeric token@>; + } else if ( mp_type(p)!=mp_string_type ) { + mp_print(mp, " BAD"); +@.BAD@> + } else { + mp_print_char(mp, xord('"')); mp_print_str(mp, value(p)); mp_print_char(mp, xord('"')); + c=string_class; + } +} else if ((mp_name_type(p)!=mp_capsule)||(mp_type(p)<mp_vacuous)||(mp_type(p)>mp_independent) ) { + mp_print(mp, " BAD"); +} else { + mp_print_capsule(mp,p); c=right_paren_class; +} + +@ @<Display a numeric token@>= +if ( class==digit_class ) + mp_print_char(mp, xord(' ')); +v=value(p); +if ( v<0 ){ + if ( class==left_bracket_class ) + mp_print_char(mp, xord(' ')); + mp_print_char(mp, xord('[')); mp_print_scaled(mp, v); mp_print_char(mp, xord(']')); + c=right_bracket_class; +} else { + mp_print_scaled(mp, v); c=digit_class; +} + + +@ Strictly speaking, a genuine token will never have |mp_info(p)=0|. +But we will see later (in the |print_variable_name| routine) that +it is convenient to let |mp_info(p)=0| stand for `\.{[]}'. + +@<Display a collective subscript@>= +{ +if ( class==left_bracket_class ) + mp_print_char(mp, xord(' ')); +mp_print(mp, "[]"); c=right_bracket_class; +} + +@ @<Display a parameter token@>= +{ +if ( r<suffix_base ) { + mp_print(mp, "(EXPR"); r=r-(expr_base); +@.EXPR@> +} else if ( r<text_base ) { + mp_print(mp, "(SUFFIX"); r=r-(suffix_base); +@.SUFFIX@> +} else { + mp_print(mp, "(TEXT"); r=r-(text_base); +@.TEXT@> +} +mp_print_int(mp, r); mp_print_char(mp, xord(')')); c=right_paren_class; +} + + +@ @<Print string |r| as a symbolic token...@>= +{ +c=mp->char_class[mp->str_pool[mp->str_start[r]]]; +if ( c==class ) { + switch (c) { + case letter_class:mp_print_char(mp, xord('.')); break; + case isolated_classes: break; + default: mp_print_char(mp, xord(' ')); break; + } +} +mp_print_str(mp, r); +} + +@ @<Declarations@>= +static void mp_print_capsule (MP mp, pointer p); + +@ @<Declare miscellaneous procedures that were declared |forward|@>= +void mp_print_capsule (MP mp, pointer p) { + mp_print_char(mp, xord('(')); mp_print_exp(mp,p,0); mp_print_char(mp, xord(')')); +} + +@ Macro definitions are kept in \MP's memory in the form of token lists +that have a few extra one-word nodes at the beginning. + +The first node contains a reference count that is used to tell when the +list is no longer needed. To emphasize the fact that a reference count is +present, we shall refer to the |info| field of this special node as the +|ref_count| field. +@^reference counts@> + +The next node or nodes after the reference count serve to describe the +formal parameters. They consist of zero or more parameter tokens followed +by a code for the type of macro. + +@d ref_count mp_info + /* reference count preceding a macro definition or picture header */ +@d add_mac_ref(A) incr(ref_count((A))) /* make a new reference to a macro list */ +@d general_macro 0 /* preface to a macro defined with a parameter list */ +@d primary_macro 1 /* preface to a macro with a \&{primary} parameter */ +@d secondary_macro 2 /* preface to a macro with a \&{secondary} parameter */ +@d tertiary_macro 3 /* preface to a macro with a \&{tertiary} parameter */ +@d expr_macro 4 /* preface to a macro with an undelimited \&{expr} parameter */ +@d of_macro 5 /* preface to a macro with + undelimited `\&{expr} |x| \&{of}~|y|' parameters */ +@d suffix_macro 6 /* preface to a macro with an undelimited \&{suffix} parameter */ +@d text_macro 7 /* preface to a macro with an undelimited \&{text} parameter */ + +@c +static void mp_delete_mac_ref (MP mp,pointer p) { + /* |p| points to the reference count of a macro list that is + losing one reference */ + if ( ref_count(p)==null ) mp_flush_token_list(mp, p); + else decr(ref_count(p)); +} + +@ The following subroutine displays a macro, given a pointer to its +reference count. + +@c +static void mp_show_macro (MP mp, pointer p, integer q, integer l) { + pointer r; /* temporary storage */ + p=mp_link(p); /* bypass the reference count */ + while ( mp_info(p)>text_macro ){ + r=mp_link(p); mp_link(p)=null; + mp_show_token_list(mp, p,null,l,0); mp_link(p)=r; p=r; + if ( l>0 ) l=l-mp->tally; else return; + } /* control printing of `\.{ETC.}' */ +@.ETC@> + mp->tally=0; + switch(mp_info(p)) { + case general_macro:mp_print(mp, "->"); break; +@.->@> + case primary_macro: case secondary_macro: case tertiary_macro: + mp_print_char(mp, xord('<')); + mp_print_cmd_mod(mp, param_type,mp_info(p)); + mp_print(mp, ">->"); + break; + case expr_macro:mp_print(mp, "<expr>->"); break; + case of_macro:mp_print(mp, "<expr>of<primary>->"); break; + case suffix_macro:mp_print(mp, "<suffix>->"); break; + case text_macro:mp_print(mp, "<text>->"); break; + } /* there are no other cases */ + mp_show_token_list(mp, mp_link(p),q,l-mp->tally,0); +} + +@* \[15] Data structures for variables. +The variables of \MP\ programs can be simple, like `\.x', or they can +combine the structural properties of arrays and records, like `\.{x20a.b}'. +A \MP\ user assigns a type to a variable like \.{x20a.b} by saying, for +example, `\.{boolean} \.{x[]a.b}'. It's time for us to study how such +things are represented inside of the computer. + +Each variable value occupies two consecutive words, either in a two-word +node called a value node, or as a two-word subfield of a larger node. One +of those two words is called the |value| field; it is an integer, +containing either a |scaled| numeric value or the representation of some +other type of quantity. (It might also be subdivided into halfwords, in +which case it is referred to by other names instead of |value|.) The other +word is broken into subfields called |type|, |name_type|, and |link|. The +|type| field is a quarterword that specifies the variable's type, and +|name_type| is a quarterword from which \MP\ can reconstruct the +variable's name (sometimes by using the |link| field as well). Thus, only +1.25 words are actually devoted to the value itself; the other +three-quarters of a word are overhead, but they aren't wasted because they +allow \MP\ to deal with sparse arrays and to provide meaningful diagnostics. + +In this section we shall be concerned only with the structural aspects of +variables, not their values. Later parts of the program will change the +|type| and |value| fields, but we shall treat those fields as black boxes +whose contents should not be touched. + +However, if the |type| field is |mp_structured|, there is no |value| field, +and the second word is broken into two pointer fields called |attr_head| +and |subscr_head|. Those fields point to additional nodes that +contain structural information, as we shall see. + +@d subscr_head_loc(A) (A)+1 /* where |value|, |subscr_head| and |attr_head| are */ +@d attr_head(A) mp_info(subscr_head_loc((A))) /* pointer to attribute info */ +@d subscr_head(A) mp_link(subscr_head_loc((A))) /* pointer to subscript info */ +@d value_node_size 2 /* the number of words in a value node */ + +@ An attribute node is three words long. Two of these words contain |type| +and |value| fields as described above, and the third word contains +additional information: There is an |attr_loc| field, which contains the +hash address of the token that names this attribute; and there's also a +|parent| field, which points to the value node of |mp_structured| type at the +next higher level (i.e., at the level to which this attribute is +subsidiary). The |name_type| in an attribute node is `|attr|'. The +|link| field points to the next attribute with the same parent; these are +arranged in increasing order, so that |attr_loc(mp_link(p))>attr_loc(p)|. The +final attribute node links to the constant |end_attr|, whose |attr_loc| +field is greater than any legal hash address. The |attr_head| in the +parent points to a node whose |name_type| is |mp_structured_root|; this +node represents the null attribute, i.e., the variable that is relevant +when no attributes are attached to the parent. The |attr_head| node +has the fields of either +a value node, a subscript node, or an attribute node, depending on what +the parent would be if it were not structured; but the subscript and +attribute fields are ignored, so it effectively contains only the data of +a value node. The |link| field in this special node points to an attribute +node whose |attr_loc| field is zero; the latter node represents a collective +subscript `\.{[]}' attached to the parent, and its |link| field points to +the first non-special attribute node (or to |end_attr| if there are none). + +A subscript node likewise occupies three words, with |type| and |value| fields +plus extra information; its |name_type| is |subscr|. In this case the +third word is called the |subscript| field, which is a |scaled| integer. +The |link| field points to the subscript node with the next larger +subscript, if any; otherwise the |link| points to the attribute node +for collective subscripts at this level. We have seen that the latter node +contains an upward pointer, so that the parent can be deduced. + +The |name_type| in a parent-less value node is |root|, and the |link| +is the hash address of the token that names this value. + +In other words, variables have a hierarchical structure that includes +enough threads running around so that the program is able to move easily +between siblings, parents, and children. An example should be helpful: +(The reader is advised to draw a picture while reading the following +description, since that will help to firm up the ideas.) +Suppose that `\.x' and `\.{x.a}' and `\.{x[]b}' and `\.{x5}' +and `\.{x20b}' have been mentioned in a user's program, where +\.{x[]b} has been declared to be of \&{boolean} type. Let |h(x)|, |h(a)|, +and |h(b)| be the hash addresses of \.x, \.a, and~\.b. Then +|eq_type(h(x))=name| and |equiv(h(x))=p|, where |p|~is a two-word value +node with |mp_name_type(p)=root| and |mp_link(p)=h(x)|. We have |type(p)=mp_structured|, +|attr_head(p)=q|, and |subscr_head(p)=r|, where |q| points to a value +node and |r| to a subscript node. (Are you still following this? Use +a pencil to draw a diagram.) The lone variable `\.x' is represented by +|type(q)| and |value(q)|; furthermore +|mp_name_type(q)=mp_structured_root| and |mp_link(q)=q1|, where |q1| points +to an attribute node representing `\.{x[]}'. Thus |mp_name_type(q1)=attr|, +|attr_loc(q1)=collective_subscript=0|, |parent(q1)=p|, +|type(q1)=mp_structured|, |attr_head(q1)=qq|, and |subscr_head(q1)=qq1|; +|qq| is a three-word ``attribute-as-value'' node with |type(qq)=numeric_type| +(assuming that \.{x5} is numeric, because |qq| represents `\.{x[]}' +with no further attributes), |mp_name_type(qq)=structured_root|, +|attr_loc(qq)=0|, |parent(qq)=p|, and +|mp_link(qq)=qq1|. (Now pay attention to the next part.) Node |qq1| is +an attribute node representing `\.{x[][]}', which has never yet +occurred; its |type| field is |undefined|, and its |value| field is +undefined. We have |mp_name_type(qq1)=attr|, |attr_loc(qq1)=collective_subscript|, +|parent(qq1)=q1|, and |mp_link(qq1)=qq2|. Since |qq2| represents +`\.{x[]b}', |type(qq2)=mp_unknown_boolean|; also |attr_loc(qq2)=h(b)|, +|parent(qq2)=q1|, |mp_name_type(qq2)=attr|, |mp_link(qq2)=end_attr|. +(Maybe colored lines will help untangle your picture.) + Node |r| is a subscript node with |type| and |value| +representing `\.{x5}'; |mp_name_type(r)=subscr|, |subscript(r)=5.0|, +and |mp_link(r)=r1| is another subscript node. To complete the picture, +see if you can guess what |mp_link(r1)| is; give up? It's~|q1|. +Furthermore |subscript(r1)=20.0|, |mp_name_type(r1)=subscr|, +|type(r1)=mp_structured|, |attr_head(r1)=qqq|, |subscr_head(r1)=qqq1|, +and we finish things off with three more nodes +|qqq|, |qqq1|, and |qqq2| hung onto~|r1|. (Perhaps you should start again +with a larger sheet of paper.) The value of variable \.{x20b} +appears in node~|qqq2|, as you can well imagine. + +If the example in the previous paragraph doesn't make things crystal +clear, a glance at some of the simpler subroutines below will reveal how +things work out in practice. + +The only really unusual thing about these conventions is the use of +collective subscript attributes. The idea is to avoid repeating a lot of +type information when many elements of an array are identical macros +(for which distinct values need not be stored) or when they don't have +all of the possible attributes. Branches of the structure below collective +subscript attributes do not carry actual values except for macro identifiers; +branches of the structure below subscript nodes do not carry significant +information in their collective subscript attributes. + +@d attr_loc_loc(A) ((A)+2) /* where the |attr_loc| and |parent| fields are */ +@d attr_loc(A) mp_info(attr_loc_loc((A))) /* hash address of this attribute */ +@d parent(A) mp_link(attr_loc_loc((A))) /* pointer to |mp_structured| variable */ +@d subscript_loc(A) ((A)+2) /* where the |subscript| field lives */ +@d subscript(A) mp->mem[subscript_loc((A))].sc /* subscript of this variable */ +@d attr_node_size 3 /* the number of words in an attribute node */ +@d subscr_node_size 3 /* the number of words in a subscript node */ +@d collective_subscript 0 /* code for the attribute `\.{[]}' */ + +@<Initialize table...@>= +attr_loc(end_attr)=hash_end+1; parent(end_attr)=null; + +@ Variables of type \&{pair} will have values that point to four-word +nodes containing two numeric values. The first of these values has +|name_type=mp_x_part_sector| and the second has |name_type=mp_y_part_sector|; +the |link| in the first points back to the node whose |value| points +to this four-word node. + +Variables of type \&{transform} are similar, but in this case their +|value| points to a 12-word node containing six values, identified by +|x_part_sector|, |y_part_sector|, |mp_xx_part_sector|, |mp_xy_part_sector|, +|mp_yx_part_sector|, and |mp_yy_part_sector|. +Finally, variables of type \&{color} have 3~values in 6~words +identified by |mp_red_part_sector|, |mp_green_part_sector|, and |mp_blue_part_sector|. + +When an entire structured variable is saved, the |root| indication +is temporarily replaced by |saved_root|. + +Some variables have no name; they just are used for temporary storage +while expressions are being evaluated. We call them {\sl capsules}. + +@d x_part_loc(A) (A) /* where the \&{xpart} is found in a pair or transform node */ +@d y_part_loc(A) ((A)+2) /* where the \&{ypart} is found in a pair or transform node */ +@d xx_part_loc(A) ((A)+4) /* where the \&{xxpart} is found in a transform node */ +@d xy_part_loc(A) ((A)+6) /* where the \&{xypart} is found in a transform node */ +@d yx_part_loc(A) ((A)+8) /* where the \&{yxpart} is found in a transform node */ +@d yy_part_loc(A) ((A)+10) /* where the \&{yypart} is found in a transform node */ +@d red_part_loc(A) (A) /* where the \&{redpart} is found in a color node */ +@d green_part_loc(A) ((A)+2) /* where the \&{greenpart} is found in a color node */ +@d blue_part_loc(A) ((A)+4) /* where the \&{bluepart} is found in a color node */ +@d cyan_part_loc(A) (A) /* where the \&{cyanpart} is found in a color node */ +@d magenta_part_loc(A) ((A)+2) /* where the \&{magentapart} is found in a color node */ +@d yellow_part_loc(A) ((A)+4) /* where the \&{yellowpart} is found in a color node */ +@d black_part_loc(A) ((A)+6) /* where the \&{blackpart} is found in a color node */ +@d grey_part_loc(A) (A) /* where the \&{greypart} is found in a color node */ +@# +@d pair_node_size 4 /* the number of words in a pair node */ +@d transform_node_size 12 /* the number of words in a transform node */ +@d color_node_size 6 /* the number of words in a color node */ +@d cmykcolor_node_size 8 /* the number of words in a color node */ + +@<Glob...@>= +quarterword big_node_size[mp_pair_type+1]; +quarterword sector0[mp_pair_type+1]; +quarterword sector_offset[mp_black_part_sector+1]; + +@ The |sector0| array gives for each big node type, |name_type| values +for its first subfield; the |sector_offset| array gives for each +|name_type| value, the offset from the first subfield in words; +and the |big_node_size| array gives the size in words for each type of +big node. + +@<Set init...@>= +mp->big_node_size[mp_transform_type]=transform_node_size; +mp->big_node_size[mp_pair_type]=pair_node_size; +mp->big_node_size[mp_color_type]=color_node_size; +mp->big_node_size[mp_cmykcolor_type]=cmykcolor_node_size; +mp->sector0[mp_transform_type]=mp_x_part_sector; +mp->sector0[mp_pair_type]=mp_x_part_sector; +mp->sector0[mp_color_type]=mp_red_part_sector; +mp->sector0[mp_cmykcolor_type]=mp_cyan_part_sector; +for (k=mp_x_part_sector;k<= mp_yy_part_sector;k++ ) { + mp->sector_offset[k]=2*(k-mp_x_part_sector); +} +for (k=mp_red_part_sector;k<= mp_blue_part_sector ; k++) { + mp->sector_offset[k]=2*(k-mp_red_part_sector); +} +for (k=mp_cyan_part_sector;k<= mp_black_part_sector;k++ ) { + mp->sector_offset[k]=2*(k-mp_cyan_part_sector); +} + +@ If |type(p)=mp_pair_type| or |mp_transform_type| and if |value(p)=null|, the +procedure call |init_big_node(p)| will allocate a pair or transform node +for~|p|. The individual parts of such nodes are initially of type +|mp_independent|. + +@c +static void mp_init_big_node (MP mp,pointer p) { + pointer q; /* the new node */ + quarterword s; /* its size */ + s=mp->big_node_size[mp_type(p)]; q=mp_get_node(mp, s); + do { + s=s-2; + @<Make variable |q+s| newly independent@>; + mp_name_type(q+s)=halfp(s)+mp->sector0[mp_type(p)]; + mp_link(q+s)=null; + } while (s!=0); + mp_link(q)=p; value(p)=q; +} + +@ The |id_transform| function creates a capsule for the +identity transformation. + +@c +static pointer mp_id_transform (MP mp) { + pointer p,q,r; /* list manipulation registers */ + p=mp_get_node(mp, value_node_size); mp_type(p)=mp_transform_type; + mp_name_type(p)=mp_capsule; value(p)=null; mp_init_big_node(mp, p); q=value(p); + r=q+transform_node_size; + do { + r=r-2; + mp_type(r)=mp_known; value(r)=0; + } while (r!=q); + value(xx_part_loc(q))=unity; + value(yy_part_loc(q))=unity; + return p; +} + +@ Tokens are of type |tag_token| when they first appear, but they point +to |null| until they are first used as the root of a variable. +The following subroutine establishes the root node on such grand occasions. + +@c +static void mp_new_root (MP mp,pointer x) { + pointer p; /* the new node */ + p=mp_get_node(mp, value_node_size); mp_type(p)=undefined; mp_name_type(p)=mp_root; + mp_link(p)=x; equiv(x)=p; +} + +@ These conventions for variable representation are illustrated by the +|print_variable_name| routine, which displays the full name of a +variable given only a pointer to its two-word value packet. + +@<Declarations@>= +static void mp_print_variable_name (MP mp, pointer p); + +@ @c +void mp_print_variable_name (MP mp, pointer p) { + pointer q; /* a token list that will name the variable's suffix */ + pointer r; /* temporary for token list creation */ + while ( mp_name_type(p)>=mp_x_part_sector ) { + @<Preface the output with a part specifier; |return| in the + case of a capsule@>; + } + q=null; + while ( mp_name_type(p)>mp_saved_root ) { + @<Ascend one level, pushing a token onto list |q| + and replacing |p| by its parent@>; + } + r=mp_get_avail(mp); mp_info(r)=mp_link(p); mp_link(r)=q; + if ( mp_name_type(p)==mp_saved_root ) mp_print(mp, "(SAVED)"); +@.SAVED@> + mp_show_token_list(mp, r,null,el_gordo,mp->tally); + mp_flush_token_list(mp, r); +} + +@ @<Ascend one level, pushing a token onto list |q|...@>= +{ + if ( mp_name_type(p)==mp_subscr ) { + r=mp_new_num_tok(mp, subscript(p)); + do { + p=mp_link(p); + } while (mp_name_type(p)!=mp_attr); + } else if ( mp_name_type(p)==mp_structured_root ) { + p=mp_link(p); goto FOUND; + } else { + if ( mp_name_type(p)!=mp_attr ) mp_confusion(mp, "var"); +@:this can't happen var}{\quad var@> + r=mp_get_avail(mp); mp_info(r)=attr_loc(p); + } + mp_link(r)=q; q=r; +FOUND: + p=parent(p); +} + +@ @<Preface the output with a part specifier...@>= +{ switch (mp_name_type(p)) { + case mp_x_part_sector: mp_print_char(mp, xord('x')); break; + case mp_y_part_sector: mp_print_char(mp, xord('y')); break; + case mp_xx_part_sector: mp_print(mp, "xx"); break; + case mp_xy_part_sector: mp_print(mp, "xy"); break; + case mp_yx_part_sector: mp_print(mp, "yx"); break; + case mp_yy_part_sector: mp_print(mp, "yy"); break; + case mp_red_part_sector: mp_print(mp, "red"); break; + case mp_green_part_sector: mp_print(mp, "green"); break; + case mp_blue_part_sector: mp_print(mp, "blue"); break; + case mp_cyan_part_sector: mp_print(mp, "cyan"); break; + case mp_magenta_part_sector: mp_print(mp, "magenta"); break; + case mp_yellow_part_sector: mp_print(mp, "yellow"); break; + case mp_black_part_sector: mp_print(mp, "black"); break; + case mp_grey_part_sector: mp_print(mp, "grey"); break; + case mp_capsule: + mp_print(mp, "%CAPSULE"); mp_print_int(mp, p-null); return; + break; +@.CAPSULE@> + } /* there are no other cases */ + mp_print(mp, "part "); + p=mp_link(p-mp->sector_offset[mp_name_type(p)]); +} + +@ The |interesting| function returns |true| if a given variable is not +in a capsule, or if the user wants to trace capsules. + +@c +static boolean mp_interesting (MP mp,pointer p) { + quarterword t; /* a |name_type| */ + if ( mp->internal[mp_tracing_capsules]>0 ) { + return true; + } else { + t=mp_name_type(p); + if ( t>=mp_x_part_sector ) if ( t!=mp_capsule ) + t=mp_name_type(mp_link(p-mp->sector_offset[t])); + return (t!=mp_capsule); + } +} + +@ Now here is a subroutine that converts an unstructured type into an +equivalent structured type, by inserting a |mp_structured| node that is +capable of growing. This operation is done only when |mp_name_type(p)=root|, +|subscr|, or |attr|. + +The procedure returns a pointer to the new node that has taken node~|p|'s +place in the structure. Node~|p| itself does not move, nor are its +|value| or |type| fields changed in any way. + +@c +static pointer mp_new_structure (MP mp,pointer p) { + pointer q,r=0; /* list manipulation registers */ + switch (mp_name_type(p)) { + case mp_root: + q=mp_link(p); r=mp_get_node(mp, value_node_size); equiv(q)=r; + break; + case mp_subscr: + @<Link a new subscript node |r| in place of node |p|@>; + break; + case mp_attr: + @<Link a new attribute node |r| in place of node |p|@>; + break; + default: + mp_confusion(mp, "struct"); +@:this can't happen struct}{\quad struct@> + break; + } + mp_link(r)=mp_link(p); mp_type(r)=mp_structured; mp_name_type(r)=mp_name_type(p); + attr_head(r)=p; mp_name_type(p)=mp_structured_root; + q=mp_get_node(mp, attr_node_size); mp_link(p)=q; subscr_head(r)=q; + parent(q)=r; mp_type(q)=undefined; mp_name_type(q)=mp_attr; mp_link(q)=end_attr; + attr_loc(q)=collective_subscript; + return r; +} + +@ @<Link a new subscript node |r| in place of node |p|@>= +{ + q=p; + do { + q=mp_link(q); + } while (mp_name_type(q)!=mp_attr); + q=parent(q); r=subscr_head_loc(q); /* |mp_link(r)=subscr_head(q)| */ + do { + q=r; r=mp_link(r); + } while (r!=p); + r=mp_get_node(mp, subscr_node_size); + mp_link(q)=r; subscript(r)=subscript(p); +} + +@ If the attribute is |collective_subscript|, there are two pointers to +node~|p|, so we must change both of them. + +@<Link a new attribute node |r| in place of node |p|@>= +{ + q=parent(p); r=attr_head(q); + do { + q=r; r=mp_link(r); + } while (r!=p); + r=mp_get_node(mp, attr_node_size); mp_link(q)=r; + mp->mem[attr_loc_loc(r)]=mp->mem[attr_loc_loc(p)]; /* copy |attr_loc| and |parent| */ + if ( attr_loc(p)==collective_subscript ) { + q=subscr_head_loc(parent(p)); + while ( mp_link(q)!=p ) q=mp_link(q); + mp_link(q)=r; + } +} + +@ The |find_variable| routine is given a pointer~|t| to a nonempty token +list of suffixes; it returns a pointer to the corresponding two-word +value. For example, if |t| points to token \.x followed by a numeric +token containing the value~7, |find_variable| finds where the value of +\.{x7} is stored in memory. This may seem a simple task, and it +usually is, except when \.{x7} has never been referenced before. +Indeed, \.x may never have even been subscripted before; complexities +arise with respect to updating the collective subscript information. + +If a macro type is detected anywhere along path~|t|, or if the first +item on |t| isn't a |tag_token|, the value |null| is returned. +Otherwise |p| will be a non-null pointer to a node such that +|undefined<type(p)<mp_structured|. + +@d abort_find { return null; } + +@c +static pointer mp_find_variable (MP mp,pointer t) { + pointer p,q,r,s; /* nodes in the ``value'' line */ + pointer pp,qq,rr,ss; /* nodes in the ``collective'' line */ + integer n; /* subscript or attribute */ + memory_word save_word; /* temporary storage for a word of |mem| */ +@^inner loop@> + p=mp_info(t); t=mp_link(t); + if ( (eq_type(p) % outer_tag) != tag_token ) abort_find; + if ( equiv(p)==null ) mp_new_root(mp, p); + p=equiv(p); pp=p; + while ( t!=null ) { + @<Make sure that both nodes |p| and |pp| are of |mp_structured| type@>; + if ( t<mp->hi_mem_min ) { + @<Descend one level for the subscript |value(t)|@> + } else { + @<Descend one level for the attribute |mp_info(t)|@>; + } + t=mp_link(t); + } + if ( mp_type(pp)>=mp_structured ) { + if ( mp_type(pp)==mp_structured ) pp=attr_head(pp); else abort_find; + } + if ( mp_type(p)==mp_structured ) p=attr_head(p); + if ( mp_type(p)==undefined ) { + if ( mp_type(pp)==undefined ) { mp_type(pp)=mp_numeric_type; value(pp)=null; }; + mp_type(p)=mp_type(pp); value(p)=null; + }; + return p; +} + +@ Although |pp| and |p| begin together, they diverge when a subscript occurs; +|pp|~stays in the collective line while |p|~goes through actual subscript +values. + +@<Make sure that both nodes |p| and |pp|...@>= +if ( mp_type(pp)!=mp_structured ) { + if ( mp_type(pp)>mp_structured ) abort_find; + ss=mp_new_structure(mp, pp); + if ( p==pp ) p=ss; + pp=ss; +}; /* now |type(pp)=mp_structured| */ +if ( mp_type(p)!=mp_structured ) /* it cannot be |>mp_structured| */ + p=mp_new_structure(mp, p) /* now |type(p)=mp_structured| */ + +@ We want this part of the program to be reasonably fast, in case there are +@^inner loop@> +lots of subscripts at the same level of the data structure. Therefore +we store an ``infinite'' value in the word that appears at the end of the +subscript list, even though that word isn't part of a subscript node. + +@<Descend one level for the subscript |value(t)|@>= +{ + n=value(t); + pp=mp_link(attr_head(pp)); /* now |attr_loc(pp)=collective_subscript| */ + q=mp_link(attr_head(p)); save_word=mp->mem[subscript_loc(q)]; + subscript(q)=el_gordo; s=subscr_head_loc(p); /* |mp_link(s)=subscr_head(p)| */ + do { + r=s; s=mp_link(s); + } while (n>subscript(s)); + if ( n==subscript(s) ) { + p=s; + } else { + p=mp_get_node(mp, subscr_node_size); mp_link(r)=p; mp_link(p)=s; + subscript(p)=n; mp_name_type(p)=mp_subscr; mp_type(p)=undefined; + } + mp->mem[subscript_loc(q)]=save_word; +} + +@ @<Descend one level for the attribute |mp_info(t)|@>= +{ + n=mp_info(t); + ss=attr_head(pp); + do { + rr=ss; ss=mp_link(ss); + } while (n>attr_loc(ss)); + if ( n<attr_loc(ss) ) { + qq=mp_get_node(mp, attr_node_size); mp_link(rr)=qq; mp_link(qq)=ss; + attr_loc(qq)=n; mp_name_type(qq)=mp_attr; mp_type(qq)=undefined; + parent(qq)=pp; ss=qq; + } + if ( p==pp ) { + p=ss; pp=ss; + } else { + pp=ss; s=attr_head(p); + do { + r=s; s=mp_link(s); + } while (n>attr_loc(s)); + if ( n==attr_loc(s) ) { + p=s; + } else { + q=mp_get_node(mp, attr_node_size); mp_link(r)=q; mp_link(q)=s; + attr_loc(q)=n; mp_name_type(q)=mp_attr; mp_type(q)=undefined; + parent(q)=p; p=q; + } + } +} + +@ Variables lose their former values when they appear in a type declaration, +or when they are defined to be macros or \&{let} equal to something else. +A subroutine will be defined later that recycles the storage associated +with any particular |type| or |value|; our goal now is to study a higher +level process called |flush_variable|, which selectively frees parts of a +variable structure. + +This routine has some complexity because of examples such as +`\hbox{\tt numeric x[]a[]b}' +which recycles all variables of the form \.{x[i]a[j]b} (and no others), while +`\hbox{\tt vardef x[]a[]=...}' +discards all variables of the form \.{x[i]a[j]} followed by an arbitrary +suffix, except for the collective node \.{x[]a[]} itself. The obvious way +to handle such examples is to use recursion; so that's what we~do. +@^recursion@> + +Parameter |p| points to the root information of the variable; +parameter |t| points to a list of one-word nodes that represent +suffixes, with |info=collective_subscript| for subscripts. + +@<Declarations@>= +static void mp_flush_cur_exp (MP mp,scaled v) ; + +@ @c +static void mp_flush_variable (MP mp,pointer p, pointer t, boolean discard_suffixes) { + pointer q,r; /* list manipulation */ + halfword n; /* attribute to match */ + while ( t!=null ) { + if ( mp_type(p)!=mp_structured ) return; + n=mp_info(t); t=mp_link(t); + if ( n==collective_subscript ) { + r=subscr_head_loc(p); q=mp_link(r); /* |q=subscr_head(p)| */ + while ( mp_name_type(q)==mp_subscr ){ + mp_flush_variable(mp, q,t,discard_suffixes); + if ( t==null ) { + if ( mp_type(q)==mp_structured ) r=q; + else { mp_link(r)=mp_link(q); mp_free_node(mp, q,subscr_node_size); } + } else { + r=q; + } + q=mp_link(r); + } + } + p=attr_head(p); + do { + r=p; p=mp_link(p); + } while (attr_loc(p)<n); + if ( attr_loc(p)!=n ) return; + } + if ( discard_suffixes ) { + mp_flush_below_variable(mp, p); + } else { + if ( mp_type(p)==mp_structured ) p=attr_head(p); + mp_recycle_value(mp, p); + } +} + +@ The next procedure is simpler; it wipes out everything but |p| itself, +which becomes undefined. + +@<Declarations@>= +static void mp_flush_below_variable (MP mp, pointer p); + +@ @c +void mp_flush_below_variable (MP mp,pointer p) { + pointer q,r; /* list manipulation registers */ + if ( mp_type(p)!=mp_structured ) { + mp_recycle_value(mp, p); /* this sets |type(p)=undefined| */ + } else { + q=subscr_head(p); + while ( mp_name_type(q)==mp_subscr ) { + mp_flush_below_variable(mp, q); r=q; q=mp_link(q); + mp_free_node(mp, r,subscr_node_size); + } + r=attr_head(p); q=mp_link(r); mp_recycle_value(mp, r); + if ( mp_name_type(p)<=mp_saved_root ) mp_free_node(mp, r,value_node_size); + else mp_free_node(mp, r,subscr_node_size); + /* we assume that |subscr_node_size=attr_node_size| */ + do { + mp_flush_below_variable(mp, q); r=q; q=mp_link(q); mp_free_node(mp, r,attr_node_size); + } while (q!=end_attr); + mp_type(p)=undefined; + } +} + +@ Just before assigning a new value to a variable, we will recycle the +old value and make the old value undefined. The |und_type| routine +determines what type of undefined value should be given, based on +the current type before recycling. + +@c +static quarterword mp_und_type (MP mp,pointer p) { + switch (mp_type(p)) { + case undefined: case mp_vacuous: + return undefined; + case mp_boolean_type: case mp_unknown_boolean: + return mp_unknown_boolean; + case mp_string_type: case mp_unknown_string: + return mp_unknown_string; + case mp_pen_type: case mp_unknown_pen: + return mp_unknown_pen; + case mp_path_type: case mp_unknown_path: + return mp_unknown_path; + case mp_picture_type: case mp_unknown_picture: + return mp_unknown_picture; + case mp_transform_type: case mp_color_type: case mp_cmykcolor_type: + case mp_pair_type: case mp_numeric_type: + return mp_type(p); + case mp_known: case mp_dependent: case mp_proto_dependent: case mp_independent: + return mp_numeric_type; + } /* there are no other cases */ + return 0; +} + +@ The |clear_symbol| routine is used when we want to redefine the equivalent +of a symbolic token. It must remove any variable structure or macro +definition that is currently attached to that symbol. If the |saving| +parameter is true, a subsidiary structure is saved instead of destroyed. + +@c +static void mp_clear_symbol (MP mp,pointer p, boolean saving) { + pointer q; /* |equiv(p)| */ + q=equiv(p); + switch (eq_type(p) % outer_tag) { + case defined_macro: + case secondary_primary_macro: + case tertiary_secondary_macro: + case expression_tertiary_macro: + if ( ! saving ) mp_delete_mac_ref(mp, q); + break; + case tag_token: + if ( q!=null ) { + if ( saving ) { + mp_name_type(q)=mp_saved_root; + } else { + mp_flush_below_variable(mp, q); + mp_free_node(mp,q,value_node_size); + } + } + break; + default: + break; + } + mp->eqtb[p]=mp->eqtb[frozen_undefined]; +} + +@* \[16] Saving and restoring equivalents. +The nested structure given by \&{begingroup} and \&{endgroup} +allows |eqtb| entries to be saved and restored, so that temporary changes +can be made without difficulty. When the user requests a current value to +be saved, \MP\ puts that value into its ``save stack.'' An appearance of +\&{endgroup} ultimately causes the old values to be removed from the save +stack and put back in their former places. + +The save stack is a linked list containing three kinds of entries, +distinguished by their |info| fields. If |p| points to a saved item, +then + +\smallskip\hang +|mp_info(p)=0| stands for a group boundary; each \&{begingroup} contributes +such an item to the save stack and each \&{endgroup} cuts back the stack +until the most recent such entry has been removed. + +\smallskip\hang +|mp_info(p)=q|, where |1<=q<=hash_end|, means that |mem[p+1]| holds the former +contents of |eqtb[q]|. Such save stack entries are generated by \&{save} +commands. + +\smallskip\hang +|mp_info(p)=hash_end+q|, where |q>0|, means that |value(p)| is a |scaled| +integer to be restored to internal parameter number~|q|. Such entries +are generated by \&{interim} commands. + +\smallskip\noindent +The global variable |save_ptr| points to the top item on the save stack. + +@d save_node_size 2 /* number of words per non-boundary save-stack node */ +@d saved_equiv(A) mp->mem[(A)+1].hh /* where an |eqtb| entry gets saved */ +@d save_boundary_item(A) { (A)=mp_get_avail(mp); mp_info((A))=0; + mp_link((A))=mp->save_ptr; mp->save_ptr=(A); + } + +@<Glob...@>= +pointer save_ptr; /* the most recently saved item */ + +@ @<Set init...@>=mp->save_ptr=null; + +@ The |save_variable| routine is given a hash address |q|; it salts this +address in the save stack, together with its current equivalent, +then makes token~|q| behave as though it were brand new. + +Nothing is stacked when |save_ptr=null|, however; there's no way to remove +things from the stack when the program is not inside a group, so there's +no point in wasting the space. + +@c +static void mp_save_variable (MP mp,pointer q) { + pointer p; /* temporary register */ + if ( mp->save_ptr!=null ){ + p=mp_get_node(mp, save_node_size); mp_info(p)=q; mp_link(p)=mp->save_ptr; + saved_equiv(p)=mp->eqtb[q]; mp->save_ptr=p; + } + mp_clear_symbol(mp, q,(mp->save_ptr!=null)); +} + +@ Similarly, |save_internal| is given the location |q| of an internal +quantity like |mp_tracing_pens|. It creates a save stack entry of the +third kind. + +@c +static void mp_save_internal (MP mp,halfword q) { + pointer p; /* new item for the save stack */ + if ( mp->save_ptr!=null ){ + p=mp_get_node(mp, save_node_size); mp_info(p)=hash_end+q; + mp_link(p)=mp->save_ptr; value(p)=mp->internal[q]; mp->save_ptr=p; + } +} + +@ At the end of a group, the |unsave| routine restores all of the saved +equivalents in reverse order. This routine will be called only when there +is at least one boundary item on the save stack. + +@c +static void mp_unsave (MP mp) { + pointer q; /* index to saved item */ + pointer p; /* temporary register */ + while ( mp_info(mp->save_ptr)!=0 ) { + q=mp_info(mp->save_ptr); + if ( q>hash_end ) { + if ( mp->internal[mp_tracing_restores]>0 ) { + mp_begin_diagnostic(mp); mp_print_nl(mp, "{restoring "); + mp_print(mp, mp->int_name[q-(hash_end)]); mp_print_char(mp, xord('=')); + mp_print_scaled(mp, value(mp->save_ptr)); mp_print_char(mp, xord('}')); + mp_end_diagnostic(mp, false); + } + mp->internal[q-(hash_end)]=value(mp->save_ptr); + } else { + if ( mp->internal[mp_tracing_restores]>0 ) { + mp_begin_diagnostic(mp); mp_print_nl(mp, "{restoring "); + mp_print_text(q); mp_print_char(mp, xord('}')); + mp_end_diagnostic(mp, false); + } + mp_clear_symbol(mp, q,false); + mp->eqtb[q]=saved_equiv(mp->save_ptr); + if ( eq_type(q) % outer_tag==tag_token ) { + p=equiv(q); + if ( p!=null ) mp_name_type(p)=mp_root; + } + } + p=mp_link(mp->save_ptr); + mp_free_node(mp, mp->save_ptr,save_node_size); mp->save_ptr=p; + } + p=mp_link(mp->save_ptr); free_avail(mp->save_ptr); mp->save_ptr=p; +} + +@* \[17] Data structures for paths. +When a \MP\ user specifies a path, \MP\ will create a list of knots +and control points for the associated cubic spline curves. If the +knots are $z_0$, $z_1$, \dots, $z_n$, there are control points +$z_k^+$ and $z_{k+1}^-$ such that the cubic splines between knots +$z_k$ and $z_{k+1}$ are defined by B\'ezier's formula +@:Bezier}{B\'ezier, Pierre Etienne@> +$$\eqalign{z(t)&=B(z_k,z_k^+,z_{k+1}^-,z_{k+1};t)\cr +&=(1-t)^3z_k+3(1-t)^2tz_k^++3(1-t)t^2z_{k+1}^-+t^3z_{k+1}\cr}$$ +for |0<=t<=1|. + +There is a 8-word node for each knot $z_k$, containing one word of +control information and six words for the |x| and |y| coordinates of +$z_k^-$ and $z_k$ and~$z_k^+$. The control information appears in the +|mp_left_type| and |mp_right_type| fields, which each occupy a quarter of +the first word in the node; they specify properties of the curve as it +enters and leaves the knot. There's also a halfword |link| field, +which points to the following knot, and a final supplementary word (of +which only a quarter is used). + +If the path is a closed contour, knots 0 and |n| are identical; +i.e., the |link| in knot |n-1| points to knot~0. But if the path +is not closed, the |mp_left_type| of knot~0 and the |mp_right_type| of knot~|n| +are equal to |endpoint|. In the latter case the |link| in knot~|n| points +to knot~0, and the control points $z_0^-$ and $z_n^+$ are not used. + +@d mp_left_type(A) mp->mem[(A)].hh.b0 /* characterizes the path entering this knot */ +@d mp_right_type(A) mp->mem[(A)].hh.b1 /* characterizes the path leaving this knot */ +@d mp_x_coord(A) mp->mem[(A)+1].sc /* the |x| coordinate of this knot */ +@d mp_y_coord(A) mp->mem[(A)+2].sc /* the |y| coordinate of this knot */ +@d mp_left_x(A) mp->mem[(A)+3].sc /* the |x| coordinate of previous control point */ +@d mp_left_y(A) mp->mem[(A)+4].sc /* the |y| coordinate of previous control point */ +@d mp_right_x(A) mp->mem[(A)+5].sc /* the |x| coordinate of next control point */ +@d mp_right_y(A) mp->mem[(A)+6].sc /* the |y| coordinate of next control point */ +@d x_loc(A) ((A)+1) /* where the |x| coordinate is stored in a knot */ +@d y_loc(A) ((A)+2) /* where the |y| coordinate is stored in a knot */ +@d knot_coord(A) mp->mem[(A)].sc /* |x| or |y| coordinate given |x_loc| or |y_loc| */ +@d left_coord(A) mp->mem[(A)+2].sc + /* coordinate of previous control point given |x_loc| or |y_loc| */ +@d right_coord(A) mp->mem[(A)+4].sc + /* coordinate of next control point given |x_loc| or |y_loc| */ +@d knot_node_size 8 /* number of words in a knot node */ + +@(mplib.h@>= +enum mp_knot_type { + mp_endpoint=0, /* |mp_left_type| at path beginning and |mp_right_type| at path end */ + mp_explicit, /* |mp_left_type| or |mp_right_type| when control points are known */ + mp_given, /* |mp_left_type| or |mp_right_type| when a direction is given */ + mp_curl, /* |mp_left_type| or |mp_right_type| when a curl is desired */ + mp_open, /* |mp_left_type| or |mp_right_type| when \MP\ should choose the direction */ + mp_end_cycle +}; + +@ Before the B\'ezier control points have been calculated, the memory +space they will ultimately occupy is taken up by information that can be +used to compute them. There are four cases: + +\yskip +\textindent{$\bullet$} If |mp_right_type=mp_open|, the curve should leave +the knot in the same direction it entered; \MP\ will figure out a +suitable direction. + +\yskip +\textindent{$\bullet$} If |mp_right_type=mp_curl|, the curve should leave the +knot in a direction depending on the angle at which it enters the next +knot and on the curl parameter stored in |right_curl|. + +\yskip +\textindent{$\bullet$} If |mp_right_type=mp_given|, the curve should leave the +knot in a nonzero direction stored as an |angle| in |right_given|. + +\yskip +\textindent{$\bullet$} If |mp_right_type=mp_explicit|, the B\'ezier control +point for leaving this knot has already been computed; it is in the +|mp_right_x| and |mp_right_y| fields. + +\yskip\noindent +The rules for |mp_left_type| are similar, but they refer to the curve entering +the knot, and to \\{left} fields instead of \\{right} fields. + +Non-|explicit| control points will be chosen based on ``tension'' parameters +in the |left_tension| and |right_tension| fields. The +`\&{atleast}' option is represented by negative tension values. +@:at_least_}{\&{atleast} primitive@> + +For example, the \MP\ path specification +$$\.{z0..z1..tension atleast 1..\{curl 2\}z2..z3\{-1,-2\}..tension + 3 and 4..p},$$ +where \.p is the path `\.{z4..controls z45 and z54..z5}', will be represented +by the six knots +\def\lodash{\hbox to 1.1em{\thinspace\hrulefill\thinspace}} +$$\vbox{\halign{#\hfil&&\qquad#\hfil\cr +|mp_left_type|&\\{left} info&|mp_x_coord,mp_y_coord|&|mp_right_type|&\\{right} info\cr +\noalign{\yskip} +|endpoint|&\lodash$,\,$\lodash&$x_0,y_0$&|curl|&$1.0,1.0$\cr +|open|&\lodash$,1.0$&$x_1,y_1$&|open|&\lodash$,-1.0$\cr +|curl|&$2.0,-1.0$&$x_2,y_2$&|curl|&$2.0,1.0$\cr +|given|&$d,1.0$&$x_3,y_3$&|given|&$d,3.0$\cr +|open|&\lodash$,4.0$&$x_4,y_4$&|explicit|&$x_{45},y_{45}$\cr +|explicit|&$x_{54},y_{54}$&$x_5,y_5$&|endpoint|&\lodash$,\,$\lodash\cr}}$$ +Here |d| is the |angle| obtained by calling |n_arg(-unity,-two)|. +Of course, this example is more complicated than anything a normal user +would ever write. + +These types must satisfy certain restrictions because of the form of \MP's +path syntax: +(i)~|open| type never appears in the same node together with |endpoint|, +|given|, or |curl|. +(ii)~The |mp_right_type| of a node is |explicit| if and only if the +|mp_left_type| of the following node is |explicit|. +(iii)~|endpoint| types occur only at the ends, as mentioned above. + +@d left_curl mp_left_x /* curl information when entering this knot */ +@d left_given mp_left_x /* given direction when entering this knot */ +@d left_tension mp_left_y /* tension information when entering this knot */ +@d right_curl mp_right_x /* curl information when leaving this knot */ +@d right_given mp_right_x /* given direction when leaving this knot */ +@d right_tension mp_right_y /* tension information when leaving this knot */ + +@ Knots can be user-supplied, or they can be created by program code, +like the |split_cubic| function, or |copy_path|. The distinction is +needed for the cleanup routine that runs after |split_cubic|, because +it should only delete knots it has previously inserted, and never +anything that was user-supplied. In order to be able to differentiate +one knot from another, we will set |originator(p):=mp_metapost_user| when +it appeared in the actual metapost program, and +|originator(p):=mp_program_code| in all other cases. + +@d mp_originator(A) mp->mem[(A)+7].hh.b0 /* the creator of this knot */ + +@<Exported types@>= +enum mp_knot_originator { + mp_program_code=0, /* not created by a user */ + mp_metapost_user /* created by a user */ +}; + +@ Here is a routine that prints a given knot list +in symbolic form. It illustrates the conventions discussed above, +and checks for anomalies that might arise while \MP\ is being debugged. + +@<Declarations@>= +static void mp_pr_path (MP mp,pointer h); + +@ @c +void mp_pr_path (MP mp,pointer h) { + pointer p,q; /* for list traversal */ + p=h; + do { + q=mp_link(p); + if ( (p==null)||(q==null) ) { + mp_print_nl(mp, "???"); return; /* this won't happen */ +@.???@> + } + @<Print information for adjacent knots |p| and |q|@>; + DONE1: + p=q; + if ( (p!=h)||(mp_left_type(h)!=mp_endpoint) ) { + @<Print two dots, followed by |given| or |curl| if present@>; + } + } while (p!=h); + if ( mp_left_type(h)!=mp_endpoint ) + mp_print(mp, "cycle"); +} + +@ @<Print information for adjacent knots...@>= +mp_print_two(mp, mp_x_coord(p),mp_y_coord(p)); +switch (mp_right_type(p)) { +case mp_endpoint: + if ( mp_left_type(p)==mp_open ) mp_print(mp, "{open?}"); /* can't happen */ +@.open?@> + if ( (mp_left_type(q)!=mp_endpoint)||(q!=h) ) q=null; /* force an error */ + goto DONE1; + break; +case mp_explicit: + @<Print control points between |p| and |q|, then |goto done1|@>; + break; +case mp_open: + @<Print information for a curve that begins |open|@>; + break; +case mp_curl: +case mp_given: + @<Print information for a curve that begins |curl| or |given|@>; + break; +default: + mp_print(mp, "???"); /* can't happen */ +@.???@> + break; +} +if ( mp_left_type(q)<=mp_explicit ) { + mp_print(mp, "..control?"); /* can't happen */ +@.control?@> +} else if ( (right_tension(p)!=unity)||(left_tension(q)!=unity) ) { + @<Print tension between |p| and |q|@>; +} + +@ Since |n_sin_cos| produces |fraction| results, which we will print as if they +were |scaled|, the magnitude of a |given| direction vector will be~4096. + +@<Print two dots...@>= +{ + mp_print_nl(mp, " .."); + if ( mp_left_type(p)==mp_given ) { + mp_n_sin_cos(mp, left_given(p)); mp_print_char(mp, xord('{')); + mp_print_scaled(mp, mp->n_cos); mp_print_char(mp, xord(',')); + mp_print_scaled(mp, mp->n_sin); mp_print_char(mp, xord('}')); + } else if ( mp_left_type(p)==mp_curl ){ + mp_print(mp, "{curl "); + mp_print_scaled(mp, left_curl(p)); mp_print_char(mp, xord('}')); + } +} + +@ @<Print tension between |p| and |q|@>= +{ + mp_print(mp, "..tension "); + if ( right_tension(p)<0 ) mp_print(mp, "atleast"); + mp_print_scaled(mp, abs(right_tension(p))); + if ( right_tension(p)!=left_tension(q) ){ + mp_print(mp, " and "); + if ( left_tension(q)<0 ) mp_print(mp, "atleast"); + mp_print_scaled(mp, abs(left_tension(q))); + } +} + +@ @<Print control points between |p| and |q|, then |goto done1|@>= +{ + mp_print(mp, "..controls "); + mp_print_two(mp, mp_right_x(p),mp_right_y(p)); + mp_print(mp, " and "); + if ( mp_left_type(q)!=mp_explicit ) { + mp_print(mp, "??"); /* can't happen */ +@.??@> + } else { + mp_print_two(mp, mp_left_x(q),mp_left_y(q)); + } + goto DONE1; +} + +@ @<Print information for a curve that begins |open|@>= +if ( (mp_left_type(p)!=mp_explicit)&&(mp_left_type(p)!=mp_open) ) { + mp_print(mp, "{open?}"); /* can't happen */ +@.open?@> +} + +@ A curl of 1 is shown explicitly, so that the user sees clearly that +\MP's default curl is present. + +@<Print information for a curve that begins |curl|...@>= +{ + if ( mp_left_type(p)==mp_open ) + mp_print(mp, "??"); /* can't happen */ +@.??@> + if ( mp_right_type(p)==mp_curl ) { + mp_print(mp, "{curl "); mp_print_scaled(mp, right_curl(p)); + } else { + mp_n_sin_cos(mp, right_given(p)); mp_print_char(mp, xord('{')); + mp_print_scaled(mp, mp->n_cos); mp_print_char(mp, xord(',')); + mp_print_scaled(mp, mp->n_sin); + } + mp_print_char(mp, xord('}')); +} + +@ It is convenient to have another version of |pr_path| that prints the path +as a diagnostic message. + +@<Declarations@>= +static void mp_print_path (MP mp,pointer h, const char *s, boolean nuline) ; + +@ @c +void mp_print_path (MP mp,pointer h, const char *s, boolean nuline) { + mp_print_diagnostic(mp, "Path", s, nuline); mp_print_ln(mp); +@.Path at line...@> + mp_pr_path(mp, h); + mp_end_diagnostic(mp, true); +} + +@ If we want to duplicate a knot node, we can say |copy_knot|: + +@c +static pointer mp_copy_knot (MP mp,pointer p) { + pointer q; /* the copy */ + int k; /* runs through the words of a knot node */ + q=mp_get_node(mp, knot_node_size); + for (k=0;k<knot_node_size;k++) { + mp->mem[q+k]=mp->mem[p+k]; + } + mp_originator(q)=mp_originator(p); + return q; +} + +@ The |copy_path| routine makes a clone of a given path. + +@c +static pointer mp_copy_path (MP mp, pointer p) { + pointer q,pp,qq; /* for list manipulation */ + q=mp_copy_knot(mp, p); + qq=q; pp=mp_link(p); + while ( pp!=p ) { + mp_link(qq)=mp_copy_knot(mp, pp); + qq=mp_link(qq); + pp=mp_link(pp); + } + mp_link(qq)=q; + return q; +} + + +@ Just before |ship_out|, knot lists are exported for printing. + +The |gr_XXXX| macros are defined in |mppsout.h|. + +@c +static mp_knot *mp_export_knot (MP mp,pointer p) { + mp_knot *q; /* the copy */ + if (p==null) + return NULL; + q = xmalloc(1, sizeof (mp_knot)); + memset(q,0,sizeof (mp_knot)); + gr_left_type(q) = (unsigned short)mp_left_type(p); + gr_right_type(q) = (unsigned short)mp_right_type(p); + gr_x_coord(q) = mp_x_coord(p); + gr_y_coord(q) = mp_y_coord(p); + gr_left_x(q) = mp_left_x(p); + gr_left_y(q) = mp_left_y(p); + gr_right_x(q) = mp_right_x(p); + gr_right_y(q) = mp_right_y(p); + gr_originator(q) = (unsigned char)mp_originator(p); + return q; +} + +@ The |export_knot_list| routine therefore also makes a clone +of a given path. + +@c +static mp_knot *mp_export_knot_list (MP mp, pointer p) { + mp_knot *q, *qq; /* for list manipulation */ + pointer pp; /* for list manipulation */ + if (p==null) + return NULL; + q=mp_export_knot(mp, p); + qq=q; pp=mp_link(p); + while ( pp!=p ) { + gr_next_knot(qq)=mp_export_knot(mp, pp); + qq=gr_next_knot(qq); + pp=mp_link(pp); + } + gr_next_knot(qq)=q; + return q; +} + + +@ Similarly, there's a way to copy the {\sl reverse\/} of a path. This procedure +returns a pointer to the first node of the copy, if the path is a cycle, +but to the final node of a non-cyclic copy. The global +variable |path_tail| will point to the final node of the original path; +this trick makes it easier to implement `\&{doublepath}'. + +All node types are assumed to be |endpoint| or |explicit| only. + +@c +static pointer mp_htap_ypoc (MP mp,pointer p) { + pointer q,pp,qq,rr; /* for list manipulation */ + q=mp_get_node(mp, knot_node_size); /* this will correspond to |p| */ + qq=q; pp=p; + while (1) { + mp_right_type(qq)=mp_left_type(pp); mp_left_type(qq)=mp_right_type(pp); + mp_x_coord(qq)=mp_x_coord(pp); mp_y_coord(qq)=mp_y_coord(pp); + mp_right_x(qq)=mp_left_x(pp); mp_right_y(qq)=mp_left_y(pp); + mp_left_x(qq)=mp_right_x(pp); mp_left_y(qq)=mp_right_y(pp); + mp_originator(qq)=mp_originator(pp); + if ( mp_link(pp)==p ) { + mp_link(q)=qq; mp->path_tail=pp; return q; + } + rr=mp_get_node(mp, knot_node_size); mp_link(rr)=qq; qq=rr; pp=mp_link(pp); + } +} + +@ @<Glob...@>= +pointer path_tail; /* the node that links to the beginning of a path */ + +@ When a cyclic list of knot nodes is no longer needed, it can be recycled by +calling the following subroutine. + +@<Declarations@>= +static void mp_toss_knot_list (MP mp,pointer p) ; + +@ @c +void mp_toss_knot_list (MP mp,pointer p) { + pointer q; /* the node being freed */ + pointer r; /* the next node */ + q=p; + do { + r=mp_link(q); + mp_free_node(mp, q,knot_node_size); q=r; + } while (q!=p); +} + +@* \[18] Choosing control points. +Now we must actually delve into one of \MP's more difficult routines, +the |make_choices| procedure that chooses angles and control points for +the splines of a curve when the user has not specified them explicitly. +The parameter to |make_choices| points to a list of knots and +path information, as described above. + +A path decomposes into independent segments at ``breakpoint'' knots, +which are knots whose left and right angles are both prespecified in +some way (i.e., their |mp_left_type| and |mp_right_type| aren't both open). + +@c +static void mp_make_choices (MP mp,pointer knots) { + pointer h; /* the first breakpoint */ + pointer p,q; /* consecutive breakpoints being processed */ + @<Other local variables for |make_choices|@>; + check_arith; /* make sure that |arith_error=false| */ + if ( mp->internal[mp_tracing_choices]>0 ) + mp_print_path(mp, knots,", before choices",true); + @<If consecutive knots are equal, join them explicitly@>; + @<Find the first breakpoint, |h|, on the path; + insert an artificial breakpoint if the path is an unbroken cycle@>; + p=h; + do { + @<Fill in the control points between |p| and the next breakpoint, + then advance |p| to that breakpoint@>; + } while (p!=h); + if ( mp->internal[mp_tracing_choices]>0 ) + mp_print_path(mp, knots,", after choices",true); + if ( mp->arith_error ) { + @<Report an unexpected problem during the choice-making@>; + } +} + +@ @<Report an unexpected problem during the choice...@>= +{ + print_err("Some number got too big"); +@.Some number got too big@> + help2("The path that I just computed is out of range.", + "So it will probably look funny. Proceed, for a laugh."); + mp_put_get_error(mp); mp->arith_error=false; +} + +@ Two knots in a row with the same coordinates will always be joined +by an explicit ``curve'' whose control points are identical with the +knots. + +@<If consecutive knots are equal, join them explicitly@>= +p=knots; +do { + q=mp_link(p); + if ( mp_x_coord(p)==mp_x_coord(q) && + mp_y_coord(p)==mp_y_coord(q) && mp_right_type(p)>mp_explicit ) { + mp_right_type(p)=mp_explicit; + if ( mp_left_type(p)==mp_open ) { + mp_left_type(p)=mp_curl; left_curl(p)=unity; + } + mp_left_type(q)=mp_explicit; + if ( mp_right_type(q)==mp_open ) { + mp_right_type(q)=mp_curl; right_curl(q)=unity; + } + mp_right_x(p)=mp_x_coord(p); mp_left_x(q)=mp_x_coord(p); + mp_right_y(p)=mp_y_coord(p); mp_left_y(q)=mp_y_coord(p); + } + p=q; +} while (p!=knots) + +@ If there are no breakpoints, it is necessary to compute the direction +angles around an entire cycle. In this case the |mp_left_type| of the first +node is temporarily changed to |end_cycle|. + +@<Find the first breakpoint, |h|, on the path...@>= +h=knots; +while (1) { + if ( mp_left_type(h)!=mp_open ) break; + if ( mp_right_type(h)!=mp_open ) break; + h=mp_link(h); + if ( h==knots ) { + mp_left_type(h)=mp_end_cycle; break; + } +} + +@ If |mp_right_type(p)<given| and |q=mp_link(p)|, we must have +|mp_right_type(p)=mp_left_type(q)=mp_explicit| or |endpoint|. + +@<Fill in the control points between |p| and the next breakpoint...@>= +q=mp_link(p); +if ( mp_right_type(p)>=mp_given ) { + while ( (mp_left_type(q)==mp_open)&&(mp_right_type(q)==mp_open) ) q=mp_link(q); + @<Fill in the control information between + consecutive breakpoints |p| and |q|@>; +} else if ( mp_right_type(p)==mp_endpoint ) { + @<Give reasonable values for the unused control points between |p| and~|q|@>; +} +p=q + +@ This step makes it possible to transform an explicitly computed path without +checking the |mp_left_type| and |mp_right_type| fields. + +@<Give reasonable values for the unused control points between |p| and~|q|@>= +{ + mp_right_x(p)=mp_x_coord(p); mp_right_y(p)=mp_y_coord(p); + mp_left_x(q)=mp_x_coord(q); mp_left_y(q)=mp_y_coord(q); +} + +@ Before we can go further into the way choices are made, we need to +consider the underlying theory. The basic ideas implemented in |make_choices| +are due to John Hobby, who introduced the notion of ``mock curvature'' +@^Hobby, John Douglas@> +at a knot. Angles are chosen so that they preserve mock curvature when +a knot is passed, and this has been found to produce excellent results. + +It is convenient to introduce some notations that simplify the necessary +formulas. Let $d_{k,k+1}=\vert z\k-z_k\vert$ be the (nonzero) distance +between knots |k| and |k+1|; and let +$${z\k-z_k\over z_k-z_{k-1}}={d_{k,k+1}\over d_{k-1,k}}e^{i\psi_k}$$ +so that a polygonal line from $z_{k-1}$ to $z_k$ to $z\k$ turns left +through an angle of~$\psi_k$. We assume that $\vert\psi_k\vert\L180^\circ$. +The control points for the spline from $z_k$ to $z\k$ will be denoted by +$$\eqalign{z_k^+&=z_k+ + \textstyle{1\over3}\rho_k e^{i\theta_k}(z\k-z_k),\cr + z\k^-&=z\k- + \textstyle{1\over3}\sigma\k e^{-i\phi\k}(z\k-z_k),\cr}$$ +where $\rho_k$ and $\sigma\k$ are nonnegative ``velocity ratios'' at the +beginning and end of the curve, while $\theta_k$ and $\phi\k$ are the +corresponding ``offset angles.'' These angles satisfy the condition +$$\theta_k+\phi_k+\psi_k=0,\eqno(*)$$ +whenever the curve leaves an intermediate knot~|k| in the direction that +it enters. + +@ Let $\alpha_k$ and $\beta\k$ be the reciprocals of the ``tension'' of +the curve at its beginning and ending points. This means that +$\rho_k=\alpha_k f(\theta_k,\phi\k)$ and $\sigma\k=\beta\k f(\phi\k,\theta_k)$, +where $f(\theta,\phi)$ is \MP's standard velocity function defined in +the |velocity| subroutine. The cubic spline $B(z_k^{\phantom+},z_k^+, +z\k^-,z\k^{\phantom+};t)$ +has curvature +@^curvature@> +$${2\sigma\k\sin(\theta_k+\phi\k)-6\sin\theta_k\over\rho_k^2d_{k,k+1}} +\qquad{\rm and}\qquad +{2\rho_k\sin(\theta_k+\phi\k)-6\sin\phi\k\over\sigma\k^2d_{k,k+1}}$$ +at |t=0| and |t=1|, respectively. The mock curvature is the linear +@^mock curvature@> +approximation to this true curvature that arises in the limit for +small $\theta_k$ and~$\phi\k$, if second-order terms are discarded. +The standard velocity function satisfies +$$f(\theta,\phi)=1+O(\theta^2+\theta\phi+\phi^2);$$ +hence the mock curvatures are respectively +$${2\beta\k(\theta_k+\phi\k)-6\theta_k\over\alpha_k^2d_{k,k+1}} +\qquad{\rm and}\qquad +{2\alpha_k(\theta_k+\phi\k)-6\phi\k\over\beta\k^2d_{k,k+1}}.\eqno(**)$$ + +@ The turning angles $\psi_k$ are given, and equation $(*)$ above +determines $\phi_k$ when $\theta_k$ is known, so the task of +angle selection is essentially to choose appropriate values for each +$\theta_k$. When equation~$(*)$ is used to eliminate $\phi$~variables +from $(**)$, we obtain a system of linear equations of the form +$$A_k\theta_{k-1}+(B_k+C_k)\theta_k+D_k\theta\k=-B_k\psi_k-D_k\psi\k,$$ +where +$$A_k={\alpha_{k-1}\over\beta_k^2d_{k-1,k}}, +\qquad B_k={3-\alpha_{k-1}\over\beta_k^2d_{k-1,k}}, +\qquad C_k={3-\beta\k\over\alpha_k^2d_{k,k+1}}, +\qquad D_k={\beta\k\over\alpha_k^2d_{k,k+1}}.$$ +The tensions are always $3\over4$ or more, hence each $\alpha$ and~$\beta$ +will be at most $4\over3$. It follows that $B_k\G{5\over4}A_k$ and +$C_k\G{5\over4}D_k$; hence the equations are diagonally dominant; +hence they have a unique solution. Moreover, in most cases the tensions +are equal to~1, so that $B_k=2A_k$ and $C_k=2D_k$. This makes the +solution numerically stable, and there is an exponential damping +effect: The data at knot $k\pm j$ affects the angle at knot~$k$ by +a factor of~$O(2^{-j})$. + +@ However, we still must consider the angles at the starting and ending +knots of a non-cyclic path. These angles might be given explicitly, or +they might be specified implicitly in terms of an amount of ``curl.'' + +Let's assume that angles need to be determined for a non-cyclic path +starting at $z_0$ and ending at~$z_n$. Then equations of the form +$$A_k\theta_{k-1}+(B_k+C_k)\theta_k+D_k\theta_{k+1}=R_k$$ +have been given for $0<k<n$, and it will be convenient to introduce +equations of the same form for $k=0$ and $k=n$, where +$$A_0=B_0=C_n=D_n=0.$$ +If $\theta_0$ is supposed to have a given value $E_0$, we simply +define $C_0=1$, $D_0=0$, and $R_0=E_0$. Otherwise a curl +parameter, $\gamma_0$, has been specified at~$z_0$; this means +that the mock curvature at $z_0$ should be $\gamma_0$ times the +mock curvature at $z_1$; i.e., +$${2\beta_1(\theta_0+\phi_1)-6\theta_0\over\alpha_0^2d_{01}} +=\gamma_0{2\alpha_0(\theta_0+\phi_1)-6\phi_1\over\beta_1^2d_{01}}.$$ +This equation simplifies to +$$(\alpha_0\chi_0+3-\beta_1)\theta_0+ + \bigl((3-\alpha_0)\chi_0+\beta_1\bigr)\theta_1= + -\bigl((3-\alpha_0)\chi_0+\beta_1\bigr)\psi_1,$$ +where $\chi_0=\alpha_0^2\gamma_0/\beta_1^2$; so we can set $C_0= +\chi_0\alpha_0+3-\beta_1$, $D_0=(3-\alpha_0)\chi_0+\beta_1$, $R_0=-D_0\psi_1$. +It can be shown that $C_0>0$ and $C_0B_1-A_1D_0>0$ when $\gamma_0\G0$, +hence the linear equations remain nonsingular. + +Similar considerations apply at the right end, when the final angle $\phi_n$ +may or may not need to be determined. It is convenient to let $\psi_n=0$, +hence $\theta_n=-\phi_n$. We either have an explicit equation $\theta_n=E_n$, +or we have +$$\bigl((3-\beta_n)\chi_n+\alpha_{n-1}\bigr)\theta_{n-1}+ +(\beta_n\chi_n+3-\alpha_{n-1})\theta_n=0,\qquad + \chi_n={\beta_n^2\gamma_n\over\alpha_{n-1}^2}.$$ + +When |make_choices| chooses angles, it must compute the coefficients of +these linear equations, then solve the equations. To compute the coefficients, +it is necessary to compute arctangents of the given turning angles~$\psi_k$. +When the equations are solved, the chosen directions $\theta_k$ are put +back into the form of control points by essentially computing sines and +cosines. + +@ OK, we are ready to make the hard choices of |make_choices|. +Most of the work is relegated to an auxiliary procedure +called |solve_choices|, which has been introduced to keep +|make_choices| from being extremely long. + +@<Fill in the control information between...@>= +@<Calculate the turning angles $\psi_k$ and the distances $d_{k,k+1}$; + set $n$ to the length of the path@>; +@<Remove |open| types at the breakpoints@>; +mp_solve_choices(mp, p,q,n) + +@ It's convenient to precompute quantities that will be needed several +times later. The values of |delta_x[k]| and |delta_y[k]| will be the +coordinates of $z\k-z_k$, and the magnitude of this vector will be +|delta[k]=@t$d_{k,k+1}$@>|. The path angle $\psi_k$ between $z_k-z_{k-1}$ +and $z\k-z_k$ will be stored in |psi[k]|. + +@<Glob...@>= +int path_size; /* maximum number of knots between breakpoints of a path */ +scaled *delta_x; +scaled *delta_y; +scaled *delta; /* knot differences */ +angle *psi; /* turning angles */ + +@ @<Dealloc variables@>= +xfree(mp->delta_x); +xfree(mp->delta_y); +xfree(mp->delta); +xfree(mp->psi); + +@ @<Other local variables for |make_choices|@>= + int k,n; /* current and final knot numbers */ + pointer s,t; /* registers for list traversal */ + scaled delx,dely; /* directions where |open| meets |explicit| */ + fraction sine,cosine; /* trig functions of various angles */ + +@ @<Calculate the turning angles...@>= +{ +RESTART: + k=0; s=p; n=mp->path_size; + do { + t=mp_link(s); + mp->delta_x[k]=mp_x_coord(t)-mp_x_coord(s); + mp->delta_y[k]=mp_y_coord(t)-mp_y_coord(s); + mp->delta[k]=mp_pyth_add(mp, mp->delta_x[k],mp->delta_y[k]); + if ( k>0 ) { + sine=mp_make_fraction(mp, mp->delta_y[k-1],mp->delta[k-1]); + cosine=mp_make_fraction(mp, mp->delta_x[k-1],mp->delta[k-1]); + mp->psi[k]=mp_n_arg(mp, mp_take_fraction(mp, mp->delta_x[k],cosine)+ + mp_take_fraction(mp, mp->delta_y[k],sine), + mp_take_fraction(mp, mp->delta_y[k],cosine)- + mp_take_fraction(mp, mp->delta_x[k],sine)); + } + incr(k); s=t; + if ( k==mp->path_size ) { + mp_reallocate_paths(mp, mp->path_size+(mp->path_size/4)); + goto RESTART; /* retry, loop size has changed */ + } + if ( s==q ) n=k; + } while (!((k>=n)&&(mp_left_type(s)!=mp_end_cycle))); + if ( k==n ) mp->psi[n]=0; else mp->psi[k]=mp->psi[1]; +} + +@ When we get to this point of the code, |mp_right_type(p)| is either +|given| or |curl| or |open|. If it is |open|, we must have +|mp_left_type(p)=mp_end_cycle| or |mp_left_type(p)=mp_explicit|. In the latter +case, the |open| type is converted to |given|; however, if the +velocity coming into this knot is zero, the |open| type is +converted to a |curl|, since we don't know the incoming direction. + +Similarly, |mp_left_type(q)| is either |given| or |curl| or |open| or +|mp_end_cycle|. The |open| possibility is reduced either to |given| or to |curl|. + +@<Remove |open| types at the breakpoints@>= +if ( mp_left_type(q)==mp_open ) { + delx=mp_right_x(q)-mp_x_coord(q); dely=mp_right_y(q)-mp_y_coord(q); + if ( (delx==0)&&(dely==0) ) { + mp_left_type(q)=mp_curl; left_curl(q)=unity; + } else { + mp_left_type(q)=mp_given; left_given(q)=mp_n_arg(mp, delx,dely); + } +} +if ( (mp_right_type(p)==mp_open)&&(mp_left_type(p)==mp_explicit) ) { + delx=mp_x_coord(p)-mp_left_x(p); dely=mp_y_coord(p)-mp_left_y(p); + if ( (delx==0)&&(dely==0) ) { + mp_right_type(p)=mp_curl; right_curl(p)=unity; + } else { + mp_right_type(p)=mp_given; right_given(p)=mp_n_arg(mp, delx,dely); + } +} + +@ Linear equations need to be solved whenever |n>1|; and also when |n=1| +and exactly one of the breakpoints involves a curl. The simplest case occurs +when |n=1| and there is a curl at both breakpoints; then we simply draw +a straight line. + +But before coding up the simple cases, we might as well face the general case, +since we must deal with it sooner or later, and since the general case +is likely to give some insight into the way simple cases can be handled best. + +When there is no cycle, the linear equations to be solved form a tridiagonal +system, and we can apply the standard technique of Gaussian elimination +to convert that system to a sequence of equations of the form +$$\theta_0+u_0\theta_1=v_0,\quad +\theta_1+u_1\theta_2=v_1,\quad\ldots,\quad +\theta_{n-1}+u_{n-1}\theta_n=v_{n-1},\quad +\theta_n=v_n.$$ +It is possible to do this diagonalization while generating the equations. +Once $\theta_n$ is known, it is easy to determine $\theta_{n-1}$, \dots, +$\theta_1$, $\theta_0$; thus, the equations will be solved. + +The procedure is slightly more complex when there is a cycle, but the +basic idea will be nearly the same. In the cyclic case the right-hand +sides will be $v_k+w_k\theta_0$ instead of simply $v_k$, and we will start +the process off with $u_0=v_0=0$, $w_0=1$. The final equation will be not +$\theta_n=v_n$ but $\theta_n+u_n\theta_1=v_n+w_n\theta_0$; an appropriate +ending routine will take account of the fact that $\theta_n=\theta_0$ and +eliminate the $w$'s from the system, after which the solution can be +obtained as before. + +When $u_k$, $v_k$, and $w_k$ are being computed, the three pointer +variables |r|, |s|,~|t| will point respectively to knots |k-1|, |k|, +and~|k+1|. The $u$'s and $w$'s are scaled by $2^{28}$, i.e., they are +of type |fraction|; the $\theta$'s and $v$'s are of type |angle|. + +@<Glob...@>= +angle *theta; /* values of $\theta_k$ */ +fraction *uu; /* values of $u_k$ */ +angle *vv; /* values of $v_k$ */ +fraction *ww; /* values of $w_k$ */ + +@ @<Dealloc variables@>= +xfree(mp->theta); +xfree(mp->uu); +xfree(mp->vv); +xfree(mp->ww); + +@ @<Declarations@>= +static void mp_reallocate_paths (MP mp, int l); + +@ @c +void mp_reallocate_paths (MP mp, int l) { + XREALLOC (mp->delta_x, l, scaled); + XREALLOC (mp->delta_y, l, scaled); + XREALLOC (mp->delta, l, scaled); + XREALLOC (mp->psi, l, angle); + XREALLOC (mp->theta, l, angle); + XREALLOC (mp->uu, l, fraction); + XREALLOC (mp->vv, l, angle); + XREALLOC (mp->ww, l, fraction); + mp->path_size = l; +} + +@ Our immediate problem is to get the ball rolling by setting up the +first equation or by realizing that no equations are needed, and to fit +this initialization into a framework suitable for the overall computation. + +@<Declarations@>= +static void mp_solve_choices (MP mp,pointer p, pointer q, halfword n) ; + +@ @c +void mp_solve_choices (MP mp,pointer p, pointer q, halfword n) { + int k; /* current knot number */ + pointer r,s,t; /* registers for list traversal */ + @<Other local variables for |solve_choices|@>; + k=0; s=p; r=0; + while (1) { + t=mp_link(s); + if ( k==0 ) { + @<Get the linear equations started; or |return| + with the control points in place, if linear equations + needn't be solved@> + } else { + switch (mp_left_type(s)) { + case mp_end_cycle: case mp_open: + @<Set up equation to match mock curvatures + at $z_k$; then |goto found| with $\theta_n$ + adjusted to equal $\theta_0$, if a cycle has ended@>; + break; + case mp_curl: + @<Set up equation for a curl at $\theta_n$ + and |goto found|@>; + break; + case mp_given: + @<Calculate the given value of $\theta_n$ + and |goto found|@>; + break; + } /* there are no other cases */ + } + r=s; s=t; incr(k); + } +FOUND: + @<Finish choosing angles and assigning control points@>; +} + +@ On the first time through the loop, we have |k=0| and |r| is not yet +defined. The first linear equation, if any, will have $A_0=B_0=0$. + +@<Get the linear equations started...@>= +switch (mp_right_type(s)) { +case mp_given: + if ( mp_left_type(t)==mp_given ) { + @<Reduce to simple case of two givens and |return|@> + } else { + @<Set up the equation for a given value of $\theta_0$@>; + } + break; +case mp_curl: + if ( mp_left_type(t)==mp_curl ) { + @<Reduce to simple case of straight line and |return|@> + } else { + @<Set up the equation for a curl at $\theta_0$@>; + } + break; +case mp_open: + mp->uu[0]=0; mp->vv[0]=0; mp->ww[0]=fraction_one; + /* this begins a cycle */ + break; +} /* there are no other cases */ + +@ The general equation that specifies equality of mock curvature at $z_k$ is +$$A_k\theta_{k-1}+(B_k+C_k)\theta_k+D_k\theta\k=-B_k\psi_k-D_k\psi\k,$$ +as derived above. We want to combine this with the already-derived equation +$\theta_{k-1}+u_{k-1}\theta_k=v_{k-1}+w_{k-1}\theta_0$ in order to obtain +a new equation +$\theta_k+u_k\theta\k=v_k+w_k\theta_0$. This can be done by dividing the +equation +$$(B_k-u_{k-1}A_k+C_k)\theta_k+D_k\theta\k=-B_k\psi_k-D_k\psi\k-A_kv_{k-1} + -A_kw_{k-1}\theta_0$$ +by $B_k-u_{k-1}A_k+C_k$. The trick is to do this carefully with +fixed-point arithmetic, avoiding the chance of overflow while retaining +suitable precision. + +The calculations will be performed in several registers that +provide temporary storage for intermediate quantities. + +@<Other local variables for |solve_choices|@>= +fraction aa,bb,cc,ff,acc; /* temporary registers */ +scaled dd,ee; /* likewise, but |scaled| */ +scaled lt,rt; /* tension values */ + +@ @<Set up equation to match mock curvatures...@>= +{ @<Calculate the values $\\{aa}=A_k/B_k$, $\\{bb}=D_k/C_k$, + $\\{dd}=(3-\alpha_{k-1})d_{k,k+1}$, $\\{ee}=(3-\beta\k)d_{k-1,k}$, + and $\\{cc}=(B_k-u_{k-1}A_k)/B_k$@>; + @<Calculate the ratio $\\{ff}=C_k/(C_k+B_k-u_{k-1}A_k)$@>; + mp->uu[k]=mp_take_fraction(mp, ff,bb); + @<Calculate the values of $v_k$ and $w_k$@>; + if ( mp_left_type(s)==mp_end_cycle ) { + @<Adjust $\theta_n$ to equal $\theta_0$ and |goto found|@>; + } +} + +@ Since tension values are never less than 3/4, the values |aa| and +|bb| computed here are never more than 4/5. + +@<Calculate the values $\\{aa}=...@>= +if ( abs(right_tension(r))==unity) { + aa=fraction_half; dd=2*mp->delta[k]; +} else { + aa=mp_make_fraction(mp, unity,3*abs(right_tension(r))-unity); + dd=mp_take_fraction(mp, mp->delta[k], + fraction_three-mp_make_fraction(mp, unity,abs(right_tension(r)))); +} +if ( abs(left_tension(t))==unity ){ + bb=fraction_half; ee=2*mp->delta[k-1]; +} else { + bb=mp_make_fraction(mp, unity,3*abs(left_tension(t))-unity); + ee=mp_take_fraction(mp, mp->delta[k-1], + fraction_three-mp_make_fraction(mp, unity,abs(left_tension(t)))); +} +cc=fraction_one-mp_take_fraction(mp, mp->uu[k-1],aa) + +@ The ratio to be calculated in this step can be written in the form +$$\beta_k^2\cdot\\{ee}\over\beta_k^2\cdot\\{ee}+\alpha_k^2\cdot + \\{cc}\cdot\\{dd},$$ +because of the quantities just calculated. The values of |dd| and |ee| +will not be needed after this step has been performed. + +@<Calculate the ratio $\\{ff}=C_k/(C_k+B_k-u_{k-1}A_k)$@>= +dd=mp_take_fraction(mp, dd,cc); lt=abs(left_tension(s)); rt=abs(right_tension(s)); +if ( lt!=rt ) { /* $\beta_k^{-1}\ne\alpha_k^{-1}$ */ + if ( lt<rt ) { + ff=mp_make_fraction(mp, lt,rt); + ff=mp_take_fraction(mp, ff,ff); /* $\alpha_k^2/\beta_k^2$ */ + dd=mp_take_fraction(mp, dd,ff); + } else { + ff=mp_make_fraction(mp, rt,lt); + ff=mp_take_fraction(mp, ff,ff); /* $\beta_k^2/\alpha_k^2$ */ + ee=mp_take_fraction(mp, ee,ff); + } +} +ff=mp_make_fraction(mp, ee,ee+dd) + +@ The value of $u_{k-1}$ will be |<=1| except when $k=1$ and the previous +equation was specified by a curl. In that case we must use a special +method of computation to prevent overflow. + +Fortunately, the calculations turn out to be even simpler in this ``hard'' +case. The curl equation makes $w_0=0$ and $v_0=-u_0\psi_1$, hence +$-B_1\psi_1-A_1v_0=-(B_1-u_0A_1)\psi_1=-\\{cc}\cdot B_1\psi_1$. + +@<Calculate the values of $v_k$ and $w_k$@>= +acc=-mp_take_fraction(mp, mp->psi[k+1],mp->uu[k]); +if ( mp_right_type(r)==mp_curl ) { + mp->ww[k]=0; + mp->vv[k]=acc-mp_take_fraction(mp, mp->psi[1],fraction_one-ff); +} else { + ff=mp_make_fraction(mp, fraction_one-ff,cc); /* this is + $B_k/(C_k+B_k-u_{k-1}A_k)<5$ */ + acc=acc-mp_take_fraction(mp, mp->psi[k],ff); + ff=mp_take_fraction(mp, ff,aa); /* this is $A_k/(C_k+B_k-u_{k-1}A_k)$ */ + mp->vv[k]=acc-mp_take_fraction(mp, mp->vv[k-1],ff); + if ( mp->ww[k-1]==0 ) mp->ww[k]=0; + else mp->ww[k]=-mp_take_fraction(mp, mp->ww[k-1],ff); +} + +@ When a complete cycle has been traversed, we have $\theta_k+u_k\theta\k= +v_k+w_k\theta_0$, for |1<=k<=n|. We would like to determine the value of +$\theta_n$ and reduce the system to the form $\theta_k+u_k\theta\k=v_k$ +for |0<=k<n|, so that the cyclic case can be finished up just as if there +were no cycle. + +The idea in the following code is to observe that +$$\eqalign{\theta_n&=v_n+w_n\theta_0-u_n\theta_1=\cdots\cr +&=v_n+w_n\theta_0-u_n\bigl(v_1+w_1\theta_0-u_1(v_2+\cdots + -u_{n-2}(v_{n-1}+w_{n-1}\theta_0-u_{n-1}\theta_0))\bigr),\cr}$$ +so we can solve for $\theta_n=\theta_0$. + +@<Adjust $\theta_n$ to equal $\theta_0$ and |goto found|@>= +{ +aa=0; bb=fraction_one; /* we have |k=n| */ +do { decr(k); +if ( k==0 ) k=n; + aa=mp->vv[k]-mp_take_fraction(mp, aa,mp->uu[k]); + bb=mp->ww[k]-mp_take_fraction(mp, bb,mp->uu[k]); +} while (k!=n); /* now $\theta_n=\\{aa}+\\{bb}\cdot\theta_n$ */ +aa=mp_make_fraction(mp, aa,fraction_one-bb); +mp->theta[n]=aa; mp->vv[0]=aa; +for (k=1;k<n;k++) { + mp->vv[k]=mp->vv[k]+mp_take_fraction(mp, aa,mp->ww[k]); +} +goto FOUND; +} + +@ @d reduce_angle(A) if ( abs((A))>one_eighty_deg ) { + if ( (A)>0 ) (A)=(A)-three_sixty_deg; else (A)=(A)+three_sixty_deg; } + +@<Calculate the given value of $\theta_n$...@>= +{ + mp->theta[n]=left_given(s)-mp_n_arg(mp, mp->delta_x[n-1],mp->delta_y[n-1]); + reduce_angle(mp->theta[n]); + goto FOUND; +} + +@ @<Set up the equation for a given value of $\theta_0$@>= +{ + mp->vv[0]=right_given(s)-mp_n_arg(mp, mp->delta_x[0],mp->delta_y[0]); + reduce_angle(mp->vv[0]); + mp->uu[0]=0; mp->ww[0]=0; +} + +@ @<Set up the equation for a curl at $\theta_0$@>= +{ cc=right_curl(s); lt=abs(left_tension(t)); rt=abs(right_tension(s)); + if ( (rt==unity)&&(lt==unity) ) + mp->uu[0]=mp_make_fraction(mp, cc+cc+unity,cc+two); + else + mp->uu[0]=mp_curl_ratio(mp, cc,rt,lt); + mp->vv[0]=-mp_take_fraction(mp, mp->psi[1],mp->uu[0]); mp->ww[0]=0; +} + +@ @<Set up equation for a curl at $\theta_n$...@>= +{ cc=left_curl(s); lt=abs(left_tension(s)); rt=abs(right_tension(r)); + if ( (rt==unity)&&(lt==unity) ) + ff=mp_make_fraction(mp, cc+cc+unity,cc+two); + else + ff=mp_curl_ratio(mp, cc,lt,rt); + mp->theta[n]=-mp_make_fraction(mp, mp_take_fraction(mp, mp->vv[n-1],ff), + fraction_one-mp_take_fraction(mp, ff,mp->uu[n-1])); + goto FOUND; +} + +@ The |curl_ratio| subroutine has three arguments, which our previous notation +encourages us to call $\gamma$, $\alpha^{-1}$, and $\beta^{-1}$. It is +a somewhat tedious program to calculate +$${(3-\alpha)\alpha^2\gamma+\beta^3\over + \alpha^3\gamma+(3-\beta)\beta^2},$$ +with the result reduced to 4 if it exceeds 4. (This reduction of curl +is necessary only if the curl and tension are both large.) +The values of $\alpha$ and $\beta$ will be at most~4/3. + +@<Declarations@>= +static fraction mp_curl_ratio (MP mp,scaled gamma, scaled a_tension, + scaled b_tension) ; + +@ @c +fraction mp_curl_ratio (MP mp,scaled gamma, scaled a_tension, + scaled b_tension) { + fraction alpha,beta,num,denom,ff; /* registers */ + alpha=mp_make_fraction(mp, unity,a_tension); + beta=mp_make_fraction(mp, unity,b_tension); + if ( alpha<=beta ) { + ff=mp_make_fraction(mp, alpha,beta); ff=mp_take_fraction(mp, ff,ff); + gamma=mp_take_fraction(mp, gamma,ff); + beta=beta / 010000; /* convert |fraction| to |scaled| */ + denom=mp_take_fraction(mp, gamma,alpha)+three-beta; + num=mp_take_fraction(mp, gamma,fraction_three-alpha)+beta; + } else { + ff=mp_make_fraction(mp, beta,alpha); ff=mp_take_fraction(mp, ff,ff); + beta=mp_take_fraction(mp, beta,ff) / 010000; /* convert |fraction| to |scaled| */ + denom=mp_take_fraction(mp, gamma,alpha)+(ff / 1365)-beta; + /* $1365\approx 2^{12}/3$ */ + num=mp_take_fraction(mp, gamma,fraction_three-alpha)+beta; + } + if ( num>=denom+denom+denom+denom ) return fraction_four; + else return mp_make_fraction(mp, num,denom); +} + +@ We're in the home stretch now. + +@<Finish choosing angles and assigning control points@>= +for (k=n-1;k>=0;k--) { + mp->theta[k]=mp->vv[k]-mp_take_fraction(mp,mp->theta[k+1],mp->uu[k]); +} +s=p; k=0; +do { + t=mp_link(s); + mp_n_sin_cos(mp, mp->theta[k]); mp->st=mp->n_sin; mp->ct=mp->n_cos; + mp_n_sin_cos(mp, -mp->psi[k+1]-mp->theta[k+1]); mp->sf=mp->n_sin; mp->cf=mp->n_cos; + mp_set_controls(mp, s,t,k); + incr(k); s=t; +} while (k!=n) + +@ The |set_controls| routine actually puts the control points into +a pair of consecutive nodes |p| and~|q|. Global variables are used to +record the values of $\sin\theta$, $\cos\theta$, $\sin\phi$, and +$\cos\phi$ needed in this calculation. + +@<Glob...@>= +fraction st; +fraction ct; +fraction sf; +fraction cf; /* sines and cosines */ + +@ @<Declarations@>= +static void mp_set_controls (MP mp,pointer p, pointer q, integer k); + +@ @c +void mp_set_controls (MP mp,pointer p, pointer q, integer k) { + fraction rr,ss; /* velocities, divided by thrice the tension */ + scaled lt,rt; /* tensions */ + fraction sine; /* $\sin(\theta+\phi)$ */ + lt=abs(left_tension(q)); rt=abs(right_tension(p)); + rr=mp_velocity(mp, mp->st,mp->ct,mp->sf,mp->cf,rt); + ss=mp_velocity(mp, mp->sf,mp->cf,mp->st,mp->ct,lt); + if ( (right_tension(p)<0)||(left_tension(q)<0) ) { + @<Decrease the velocities, + if necessary, to stay inside the bounding triangle@>; + } + mp_right_x(p)=mp_x_coord(p)+mp_take_fraction(mp, + mp_take_fraction(mp, mp->delta_x[k],mp->ct)- + mp_take_fraction(mp, mp->delta_y[k],mp->st),rr); + mp_right_y(p)=mp_y_coord(p)+mp_take_fraction(mp, + mp_take_fraction(mp, mp->delta_y[k],mp->ct)+ + mp_take_fraction(mp, mp->delta_x[k],mp->st),rr); + mp_left_x(q)=mp_x_coord(q)-mp_take_fraction(mp, + mp_take_fraction(mp, mp->delta_x[k],mp->cf)+ + mp_take_fraction(mp, mp->delta_y[k],mp->sf),ss); + mp_left_y(q)=mp_y_coord(q)-mp_take_fraction(mp, + mp_take_fraction(mp, mp->delta_y[k],mp->cf)- + mp_take_fraction(mp, mp->delta_x[k],mp->sf),ss); + mp_right_type(p)=mp_explicit; mp_left_type(q)=mp_explicit; +} + +@ The boundedness conditions $\\{rr}\L\sin\phi\,/\sin(\theta+\phi)$ and +$\\{ss}\L\sin\theta\,/\sin(\theta+\phi)$ are to be enforced if $\sin\theta$, +$\sin\phi$, and $\sin(\theta+\phi)$ all have the same sign. Otherwise +there is no ``bounding triangle.'' + +@<Decrease the velocities, if necessary...@>= +if (((mp->st>=0)&&(mp->sf>=0))||((mp->st<=0)&&(mp->sf<=0)) ) { + sine=mp_take_fraction(mp, abs(mp->st),mp->cf)+ + mp_take_fraction(mp, abs(mp->sf),mp->ct); + if ( sine>0 ) { + sine=mp_take_fraction(mp, sine,fraction_one+unity); /* safety factor */ + if ( right_tension(p)<0 ) + if ( mp_ab_vs_cd(mp, abs(mp->sf),fraction_one,rr,sine)<0 ) + rr=mp_make_fraction(mp, abs(mp->sf),sine); + if ( left_tension(q)<0 ) + if ( mp_ab_vs_cd(mp, abs(mp->st),fraction_one,ss,sine)<0 ) + ss=mp_make_fraction(mp, abs(mp->st),sine); + } +} + +@ Only the simple cases remain to be handled. + +@<Reduce to simple case of two givens and |return|@>= +{ + aa=mp_n_arg(mp, mp->delta_x[0],mp->delta_y[0]); + mp_n_sin_cos(mp, right_given(p)-aa); mp->ct=mp->n_cos; mp->st=mp->n_sin; + mp_n_sin_cos(mp, left_given(q)-aa); mp->cf=mp->n_cos; mp->sf=-mp->n_sin; + mp_set_controls(mp, p,q,0); return; +} + +@ @<Reduce to simple case of straight line and |return|@>= +{ + mp_right_type(p)=mp_explicit; mp_left_type(q)=mp_explicit; + lt=abs(left_tension(q)); rt=abs(right_tension(p)); + if ( rt==unity ) { + if ( mp->delta_x[0]>=0 ) mp_right_x(p)=mp_x_coord(p)+((mp->delta_x[0]+1) / 3); + else mp_right_x(p)=mp_x_coord(p)+((mp->delta_x[0]-1) / 3); + if ( mp->delta_y[0]>=0 ) mp_right_y(p)=mp_y_coord(p)+((mp->delta_y[0]+1) / 3); + else mp_right_y(p)=mp_y_coord(p)+((mp->delta_y[0]-1) / 3); + } else { + ff=mp_make_fraction(mp, unity,3*rt); /* $\alpha/3$ */ + mp_right_x(p)=mp_x_coord(p)+mp_take_fraction(mp, mp->delta_x[0],ff); + mp_right_y(p)=mp_y_coord(p)+mp_take_fraction(mp, mp->delta_y[0],ff); + } + if ( lt==unity ) { + if ( mp->delta_x[0]>=0 ) mp_left_x(q)=mp_x_coord(q)-((mp->delta_x[0]+1) / 3); + else mp_left_x(q)=mp_x_coord(q)-((mp->delta_x[0]-1) / 3); + if ( mp->delta_y[0]>=0 ) mp_left_y(q)=mp_y_coord(q)-((mp->delta_y[0]+1) / 3); + else mp_left_y(q)=mp_y_coord(q)-((mp->delta_y[0]-1) / 3); + } else { + ff=mp_make_fraction(mp, unity,3*lt); /* $\beta/3$ */ + mp_left_x(q)=mp_x_coord(q)-mp_take_fraction(mp, mp->delta_x[0],ff); + mp_left_y(q)=mp_y_coord(q)-mp_take_fraction(mp, mp->delta_y[0],ff); + } + return; +} + +@* \[19] Measuring paths. +\MP's \&{llcorner}, \&{lrcorner}, \&{ulcorner}, and \&{urcorner} operators +allow the user to measure the bounding box of anything that can go into a +picture. It's easy to get rough bounds on the $x$ and $y$ extent of a path +by just finding the bounding box of the knots and the control points. We +need a more accurate version of the bounding box, but we can still use the +easy estimate to save time by focusing on the interesting parts of the path. + +@ Computing an accurate bounding box involves a theme that will come up again +and again. Given a Bernshte{\u\i}n polynomial +@^Bernshte{\u\i}n, Serge{\u\i} Natanovich@> +$$B(z_0,z_1,\ldots,z_n;t)=\sum_k{n\choose k}t^k(1-t)^{n-k}z_k,$$ +we can conveniently bisect its range as follows: + +\smallskip +\textindent{1)} Let $z_k^{(0)}=z_k$, for |0<=k<=n|. + +\smallskip +\textindent{2)} Let $z_k^{(j+1)}={1\over2}(z_k^{(j)}+z\k^{(j)})$, for +|0<=k<n-j|, for |0<=j<n|. + +\smallskip\noindent +Then +$$B(z_0,z_1,\ldots,z_n;t)=B(z_0^{(0)},z_0^{(1)},\ldots,z_0^{(n)};2t) + =B(z_0^{(n)},z_1^{(n-1)},\ldots,z_n^{(0)};2t-1).$$ +This formula gives us the coefficients of polynomials to use over the ranges +$0\L t\L{1\over2}$ and ${1\over2}\L t\L1$. + +@ Now here's a subroutine that's handy for all sorts of path computations: +Given a quadratic polynomial $B(a,b,c;t)$, the |crossing_point| function +returns the unique |fraction| value |t| between 0 and~1 at which +$B(a,b,c;t)$ changes from positive to negative, or returns +|t=fraction_one+1| if no such value exists. If |a<0| (so that $B(a,b,c;t)$ +is already negative at |t=0|), |crossing_point| returns the value zero. + +@d no_crossing { return (fraction_one+1); } +@d one_crossing { return fraction_one; } +@d zero_crossing { return 0; } +@d mp_crossing_point(M,A,B,C) mp_do_crossing_point(A,B,C) + +@c static fraction mp_do_crossing_point (integer a, integer b, integer c) { + integer d; /* recursive counter */ + integer x,xx,x0,x1,x2; /* temporary registers for bisection */ + if ( a<0 ) zero_crossing; + if ( c>=0 ) { + if ( b>=0 ) { + if ( c>0 ) { no_crossing; } + else if ( (a==0)&&(b==0) ) { no_crossing;} + else { one_crossing; } + } + if ( a==0 ) zero_crossing; + } else if ( a==0 ) { + if ( b<=0 ) zero_crossing; + } + @<Use bisection to find the crossing point, if one exists@>; +} + +@ The general bisection method is quite simple when $n=2$, hence +|crossing_point| does not take much time. At each stage in the +recursion we have a subinterval defined by |l| and~|j| such that +$B(a,b,c;2^{-l}(j+t))=B(x_0,x_1,x_2;t)$, and we want to ``zero in'' on +the subinterval where $x_0\G0$ and $\min(x_1,x_2)<0$. + +It is convenient for purposes of calculation to combine the values +of |l| and~|j| in a single variable $d=2^l+j$, because the operation +of bisection then corresponds simply to doubling $d$ and possibly +adding~1. Furthermore it proves to be convenient to modify +our previous conventions for bisection slightly, maintaining the +variables $X_0=2^lx_0$, $X_1=2^l(x_0-x_1)$, and $X_2=2^l(x_1-x_2)$. +With these variables the conditions $x_0\ge0$ and $\min(x_1,x_2)<0$ are +equivalent to $\max(X_1,X_1+X_2)>X_0\ge0$. + +The following code maintains the invariant relations +$0\L|x0|<\max(|x1|,|x1|+|x2|)$, +$\vert|x1|\vert<2^{30}$, $\vert|x2|\vert<2^{30}$; +it has been constructed in such a way that no arithmetic overflow +will occur if the inputs satisfy +$a<2^{30}$, $\vert a-b\vert<2^{30}$, and $\vert b-c\vert<2^{30}$. + +@<Use bisection to find the crossing point...@>= +d=1; x0=a; x1=a-b; x2=b-c; +do { + x=half(x1+x2); + if ( x1-x0>x0 ) { + x2=x; x0+=x0; d+=d; + } else { + xx=x1+x-x0; + if ( xx>x0 ) { + x2=x; x0+=x0; d+=d; + } else { + x0=x0-xx; + if ( x<=x0 ) { if ( x+x2<=x0 ) no_crossing; } + x1=x; d=d+d+1; + } + } +} while (d<fraction_one); +return (d-fraction_one) + +@ Here is a routine that computes the $x$ or $y$ coordinate of the point on +a cubic corresponding to the |fraction| value~|t|. + +It is convenient to define a \.{WEB} macro |t_of_the_way| such that +|t_of_the_way(a,b)| expands to |a-(a-b)*t|, i.e., to |t[a,b]|. + +@d t_of_the_way(A,B) ((A)-mp_take_fraction(mp,((A)-(B)),t)) + +@c static scaled mp_eval_cubic (MP mp,pointer p, pointer q, fraction t) { + scaled x1,x2,x3; /* intermediate values */ + x1=t_of_the_way(knot_coord(p),right_coord(p)); + x2=t_of_the_way(right_coord(p),left_coord(q)); + x3=t_of_the_way(left_coord(q),knot_coord(q)); + x1=t_of_the_way(x1,x2); + x2=t_of_the_way(x2,x3); + return t_of_the_way(x1,x2); +} + +@ The actual bounding box information is stored in global variables. +Since it is convenient to address the $x$ and $y$ information +separately, we define arrays indexed by |x_code..y_code| and use +macros to give them more convenient names. + +@<Types...@>= +enum mp_bb_code { + mp_x_code=0, /* index for |minx| and |maxx| */ + mp_y_code /* index for |miny| and |maxy| */ +} ; + +@ +@d mp_minx mp->bbmin[mp_x_code] +@d mp_maxx mp->bbmax[mp_x_code] +@d mp_miny mp->bbmin[mp_y_code] +@d mp_maxy mp->bbmax[mp_y_code] + +@<Glob...@>= +scaled bbmin[mp_y_code+1]; +scaled bbmax[mp_y_code+1]; +/* the result of procedures that compute bounding box information */ + +@ Now we're ready for the key part of the bounding box computation. +The |bound_cubic| procedure updates |bbmin[c]| and |bbmax[c]| based on +$$B(\hbox{|knot_coord(p)|}, \hbox{|right_coord(p)|}, + \hbox{|left_coord(q)|}, \hbox{|knot_coord(q)|};t) +$$ +for $0<t\le1$. In other words, the procedure adjusts the bounds to +accommodate |knot_coord(q)| and any extremes over the range $0<t<1$. +The |c| parameter is |x_code| or |y_code|. + +@c static void mp_bound_cubic (MP mp,pointer p, pointer q, quarterword c) { + boolean wavy; /* whether we need to look for extremes */ + scaled del1,del2,del3,del,dmax; /* proportional to the control + points of a quadratic derived from a cubic */ + fraction t,tt; /* where a quadratic crosses zero */ + scaled x; /* a value that |bbmin[c]| and |bbmax[c]| must accommodate */ + x=knot_coord(q); + @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>; + @<Check the control points against the bounding box and set |wavy:=true| + if any of them lie outside@>; + if ( wavy ) { + del1=right_coord(p)-knot_coord(p); + del2=left_coord(q)-right_coord(p); + del3=knot_coord(q)-left_coord(q); + @<Scale up |del1|, |del2|, and |del3| for greater accuracy; + also set |del| to the first nonzero element of |(del1,del2,del3)|@>; + if ( del<0 ) { + negate(del1); negate(del2); negate(del3); + }; + t=mp_crossing_point(mp, del1,del2,del3); + if ( t<fraction_one ) { + @<Test the extremes of the cubic against the bounding box@>; + } + } +} + +@ @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>= +if ( x<mp->bbmin[c] ) mp->bbmin[c]=x; +if ( x>mp->bbmax[c] ) mp->bbmax[c]=x + +@ @<Check the control points against the bounding box and set...@>= +wavy=true; +if ( mp->bbmin[c]<=right_coord(p) ) + if ( right_coord(p)<=mp->bbmax[c] ) + if ( mp->bbmin[c]<=left_coord(q) ) + if ( left_coord(q)<=mp->bbmax[c] ) + wavy=false + +@ If |del1=del2=del3=0|, it's impossible to obey the title of this +section. We just set |del=0| in that case. + +@<Scale up |del1|, |del2|, and |del3| for greater accuracy...@>= +if ( del1!=0 ) del=del1; +else if ( del2!=0 ) del=del2; +else del=del3; +if ( del!=0 ) { + dmax=abs(del1); + if ( abs(del2)>dmax ) dmax=abs(del2); + if ( abs(del3)>dmax ) dmax=abs(del3); + while ( dmax<fraction_half ) { + dmax+=dmax; del1+=del1; del2+=del2; del3+=del3; + } +} + +@ Since |crossing_point| has tried to choose |t| so that +$B(|del1|,|del2|,|del3|;\tau)$ crosses zero at $\tau=|t|$ with negative +slope, the value of |del2| computed below should not be positive. +But rounding error could make it slightly positive in which case we +must cut it to zero to avoid confusion. + +@<Test the extremes of the cubic against the bounding box@>= +{ + x=mp_eval_cubic(mp, p,q,t); + @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>; + del2=t_of_the_way(del2,del3); + /* now |0,del2,del3| represent the derivative on the remaining interval */ + if ( del2>0 ) del2=0; + tt=mp_crossing_point(mp, 0,-del2,-del3); + if ( tt<fraction_one ) { + @<Test the second extreme against the bounding box@>; + } +} + +@ @<Test the second extreme against the bounding box@>= +{ + x=mp_eval_cubic(mp, p,q,t_of_the_way(tt,fraction_one)); + @<Adjust |bbmin[c]| and |bbmax[c]| to accommodate |x|@>; +} + +@ Finding the bounding box of a path is basically a matter of applying +|bound_cubic| twice for each pair of adjacent knots. + +@c static void mp_path_bbox (MP mp,pointer h) { + pointer p,q; /* a pair of adjacent knots */ + mp_minx=mp_x_coord(h); mp_miny=mp_y_coord(h); + mp_maxx=mp_minx; mp_maxy=mp_miny; + p=h; + do { + if ( mp_right_type(p)==mp_endpoint ) return; + q=mp_link(p); + mp_bound_cubic(mp, x_loc(p),x_loc(q),mp_x_code); + mp_bound_cubic(mp, y_loc(p),y_loc(q),mp_y_code); + p=q; + } while (p!=h); +} + +@ Another important way to measure a path is to find its arc length. This +is best done by using the general bisection algorithm to subdivide the path +until obtaining ``well behaved'' subpaths whose arc lengths can be approximated +by simple means. + +Since the arc length is the integral with respect to time of the magnitude of +the velocity, it is natural to use Simpson's rule for the approximation. +@^Simpson's rule@> +If $\dot B(t)$ is the spline velocity, Simpson's rule gives +$$ \vb\dot B(0)\vb + 4\vb\dot B({1\over2})\vb + \vb\dot B(1)\vb \over 6 $$ +for the arc length of a path of length~1. For a cubic spline +$B(z_0,z_1,z_2,z_3;t)$, the time derivative $\dot B(t)$ is +$3B(dz_0,dz_1,dz_2;t)$, where $dz_i=z_{i+1}-z_i$. Hence the arc length +approximation is +$$ {\vb dz_0\vb \over 2} + 2\vb dz_{02}\vb + {\vb dz_2\vb \over 2}, $$ +where +$$ dz_{02}={1\over2}\left({dz_0+dz_1\over 2}+{dz_1+dz_2\over 2}\right)$$ +is the result of the bisection algorithm. + +@ The remaining problem is how to decide when a subpath is ``well behaved.'' +This could be done via the theoretical error bound for Simpson's rule, +@^Simpson's rule@> +but this is impractical because it requires an estimate of the fourth +derivative of the quantity being integrated. It is much easier to just perform +a bisection step and see how much the arc length estimate changes. Since the +error for Simpson's rule is proportional to the fourth power of the sample +spacing, the remaining error is typically about $1\over16$ of the amount of +the change. We say ``typically'' because the error has a pseudo-random behavior +that could cause the two estimates to agree when each contain large errors. + +To protect against disasters such as undetected cusps, the bisection process +should always continue until all the $dz_i$ vectors belong to a single +$90^\circ$ sector. This ensures that no point on the spline can have velocity +less than 70\% of the minimum of $\vb dz_0\vb$, $\vb dz_1\vb$ and $\vb dz_2\vb$. +If such a spline happens to produce an erroneous arc length estimate that +is little changed by bisection, the amount of the error is likely to be fairly +small. We will try to arrange things so that freak accidents of this type do +not destroy the inverse relationship between the \&{arclength} and +\&{arctime} operations. +@:arclength_}{\&{arclength} primitive@> +@:arctime_}{\&{arctime} primitive@> + +@ The \&{arclength} and \&{arctime} operations are both based on a recursive +@^recursion@> +function that finds the arc length of a cubic spline given $dz_0$, $dz_1$, +$dz_2$. This |arc_test| routine also takes an arc length goal |a_goal| and +returns the time when the arc length reaches |a_goal| if there is such a time. +Thus the return value is either an arc length less than |a_goal| or, if the +arc length would be at least |a_goal|, it returns a time value decreased by +|two|. This allows the caller to use the sign of the result to distinguish +between arc lengths and time values. On certain types of overflow, it is +possible for |a_goal| and the result of |arc_test| both to be |el_gordo|. +Otherwise, the result is always less than |a_goal|. + +Rather than halving the control point coordinates on each recursive call to +|arc_test|, it is better to keep them proportional to velocity on the original +curve and halve the results instead. This means that recursive calls can +potentially use larger error tolerances in their arc length estimates. How +much larger depends on to what extent the errors behave as though they are +independent of each other. To save computing time, we use optimistic assumptions +and increase the tolerance by a factor of about $\sqrt2$ for each recursive +call. + +In addition to the tolerance parameter, |arc_test| should also have parameters +for ${1\over3}\vb\dot B(0)\vb$, ${2\over3}\vb\dot B({1\over2})\vb$, and +${1\over3}\vb\dot B(1)\vb$. These quantities are relatively expensive to compute +and they are needed in different instances of |arc_test|. + +@c +static scaled mp_arc_test (MP mp, scaled dx0, scaled dy0, scaled dx1, scaled dy1, + scaled dx2, scaled dy2, scaled v0, scaled v02, + scaled v2, scaled a_goal, scaled tol) { + boolean simple; /* are the control points confined to a $90^\circ$ sector? */ + scaled dx01, dy01, dx12, dy12, dx02, dy02; /* bisection results */ + scaled v002, v022; + /* twice the velocity magnitudes at $t={1\over4}$ and $t={3\over4}$ */ + scaled arc; /* best arc length estimate before recursion */ + @<Other local variables in |arc_test|@>; + @<Bisect the B\'ezier quadratic given by |dx0|, |dy0|, |dx1|, |dy1|, + |dx2|, |dy2|@>; + @<Initialize |v002|, |v022|, and the arc length estimate |arc|; if it overflows + set |arc_test| and |return|@>; + @<Test if the control points are confined to one quadrant or rotating them + $45^\circ$ would put them in one quadrant. Then set |simple| appropriately@>; + if ( simple && (abs(arc-v02-halfp(v0+v2)) <= tol) ) { + if ( arc < a_goal ) { + return arc; + } else { + @<Estimate when the arc length reaches |a_goal| and set |arc_test| to + that time minus |two|@>; + } + } else { + @<Use one or two recursive calls to compute the |arc_test| function@>; + } +} + +@ The |tol| value should by multiplied by $\sqrt 2$ before making recursive +calls, but $1.5$ is an adequate approximation. It is best to avoid using +|make_fraction| in this inner loop. +@^inner loop@> + +@<Use one or two recursive calls to compute the |arc_test| function@>= +{ + @<Set |a_new| and |a_aux| so their sum is |2*a_goal| and |a_new| is as + large as possible@>; + tol = tol + halfp(tol); + a = mp_arc_test(mp, dx0,dy0, dx01,dy01, dx02,dy02, v0, v002, + halfp(v02), a_new, tol); + if ( a<0 ) { + return (-halfp(two-a)); + } else { + @<Update |a_new| to reduce |a_new+a_aux| by |a|@>; + b = mp_arc_test(mp, dx02,dy02, dx12,dy12, dx2,dy2, + halfp(v02), v022, v2, a_new, tol); + if ( b<0 ) + return (-halfp(-b) - half_unit); + else + return (a + half(b-a)); + } +} + +@ @<Other local variables in |arc_test|@>= +scaled a,b; /* results of recursive calls */ +scaled a_new,a_aux; /* the sum of these gives the |a_goal| */ + +@ @<Set |a_new| and |a_aux| so their sum is |2*a_goal| and |a_new| is...@>= +a_aux = el_gordo - a_goal; +if ( a_goal > a_aux ) { + a_aux = a_goal - a_aux; + a_new = el_gordo; +} else { + a_new = a_goal + a_goal; + a_aux = 0; +} + +@ There is no need to maintain |a_aux| at this point so we use it as a temporary +to force the additions and subtractions to be done in an order that avoids +overflow. + +@<Update |a_new| to reduce |a_new+a_aux| by |a|@>= +if ( a > a_aux ) { + a_aux = a_aux - a; + a_new = a_new + a_aux; +} + +@ This code assumes all {\it dx} and {\it dy} variables have magnitude less than +|fraction_four|. To simplify the rest of the |arc_test| routine, we strengthen +this assumption by requiring the norm of each $({\it dx},{\it dy})$ pair to obey +this bound. Note that recursive calls will maintain this invariant. + +@<Bisect the B\'ezier quadratic given by |dx0|, |dy0|, |dx1|, |dy1|,...@>= +dx01 = half(dx0 + dx1); +dx12 = half(dx1 + dx2); +dx02 = half(dx01 + dx12); +dy01 = half(dy0 + dy1); +dy12 = half(dy1 + dy2); +dy02 = half(dy01 + dy12) + +@ We should be careful to keep |arc<el_gordo| so that calling |arc_test| with +|a_goal=el_gordo| is guaranteed to yield the arc length. + +@<Initialize |v002|, |v022|, and the arc length estimate |arc|;...@>= +v002 = mp_pyth_add(mp, dx01+half(dx0+dx02), dy01+half(dy0+dy02)); +v022 = mp_pyth_add(mp, dx12+half(dx02+dx2), dy12+half(dy02+dy2)); +tmp = halfp(v02+2); +arc1 = v002 + half(halfp(v0+tmp) - v002); +arc = v022 + half(halfp(v2+tmp) - v022); +if ( (arc < el_gordo-arc1) ) { + arc = arc+arc1; +} else { + mp->arith_error = true; + if ( a_goal==el_gordo ) return (el_gordo); + else return (-two); +} + +@ @<Other local variables in |arc_test|@>= +scaled tmp, tmp2; /* all purpose temporary registers */ +scaled arc1; /* arc length estimate for the first half */ + +@ @<Test if the control points are confined to one quadrant or rotating...@>= +simple = ((dx0>=0) && (dx1>=0) && (dx2>=0)) || + ((dx0<=0) && (dx1<=0) && (dx2<=0)); +if ( simple ) + simple = ((dy0>=0) && (dy1>=0) && (dy2>=0)) || + ((dy0<=0) && (dy1<=0) && (dy2<=0)); +if ( ! simple ) { + simple = ((dx0>=dy0) && (dx1>=dy1) && (dx2>=dy2)) || + ((dx0<=dy0) && (dx1<=dy1) && (dx2<=dy2)); + if ( simple ) + simple = ((-dx0>=dy0) && (-dx1>=dy1) && (-dx2>=dy2)) || + ((-dx0<=dy0) && (-dx1<=dy1) && (-dx2<=dy2)); +} + +@ Since Simpson's rule is based on approximating the integrand by a parabola, +@^Simpson's rule@> +it is appropriate to use the same approximation to decide when the integral +reaches the intermediate value |a_goal|. At this point +$$\eqalign{ + {\vb\dot B(0)\vb\over 3} &= \hbox{|v0|}, \qquad + {\vb\dot B({1\over4})\vb\over 3} = {\hbox{|v002|}\over 2}, \qquad + {\vb\dot B({1\over2})\vb\over 3} = {\hbox{|v02|}\over 2}, \cr + {\vb\dot B({3\over4})\vb\over 3} &= {\hbox{|v022|}\over 2}, \qquad + {\vb\dot B(1)\vb\over 3} = \hbox{|v2|} \cr +} +$$ +and +$$ {\vb\dot B(t)\vb\over 3} \approx + \cases{B\left(\hbox{|v0|}, + \hbox{|v002|}-{1\over 2}\hbox{|v0|}-{1\over 4}\hbox{|v02|}, + {1\over 2}\hbox{|v02|}; 2t \right)& + if $t\le{1\over 2}$\cr + B\left({1\over 2}\hbox{|v02|}, + \hbox{|v022|}-{1\over 4}\hbox{|v02|}-{1\over 2}\hbox{|v2|}, + \hbox{|v2|}; 2t-1 \right)& + if $t\ge{1\over 2}$.\cr} + \eqno (*) +$$ +We can integrate $\vb\dot B(t)\vb$ by using +$$\int 3B(a,b,c;\tau)\,dt = + {B(0,a,a+b,a+b+c;\tau) + {\rm constant} \over {d\tau\over dt}}. +$$ + +This construction allows us to find the time when the arc length reaches +|a_goal| by solving a cubic equation of the form +$$ B(0,a,a+b,a+b+c;\tau) = x, $$ +where $\tau$ is $2t$ or $2t+1$, $x$ is |a_goal| or |a_goal-arc1|, and $a$, $b$, +and $c$ are the Bernshte{\u\i}n coefficients from $(*)$ divided by +@^Bernshte{\u\i}n, Serge{\u\i} Natanovich@> +$d\tau\over dt$. We shall define a function |solve_rising_cubic| that finds +$\tau$ given $a$, $b$, $c$, and $x$. + +@<Estimate when the arc length reaches |a_goal| and set |arc_test| to...@>= +{ + tmp = (v02 + 2) / 4; + if ( a_goal<=arc1 ) { + tmp2 = halfp(v0); + return + (halfp(mp_solve_rising_cubic(mp, tmp2, arc1-tmp2-tmp, tmp, a_goal))- two); + } else { + tmp2 = halfp(v2); + return ((half_unit - two) + + halfp(mp_solve_rising_cubic(mp, tmp, arc-arc1-tmp-tmp2, tmp2, a_goal-arc1))); + } +} + +@ Here is the |solve_rising_cubic| routine that finds the time~$t$ when +$$ B(0, a, a+b, a+b+c; t) = x. $$ +This routine is based on |crossing_point| but is simplified by the +assumptions that $B(a,b,c;t)\ge0$ for $0\le t\le1$ and that |0<=x<=a+b+c|. +If rounding error causes this condition to be violated slightly, we just ignore +it and proceed with binary search. This finds a time when the function value +reaches |x| and the slope is positive. + +@<Declarations@>= +static scaled mp_solve_rising_cubic (MP mp,scaled a, scaled b, scaled c, scaled x) ; + +@ @c +scaled mp_solve_rising_cubic (MP mp,scaled a, scaled b, scaled c, scaled x) { + scaled ab, bc, ac; /* bisection results */ + integer t; /* $2^k+q$ where unscaled answer is in $[q2^{-k},(q+1)2^{-k})$ */ + integer xx; /* temporary for updating |x| */ + if ( (a<0) || (c<0) ) mp_confusion(mp, "rising?"); +@:this can't happen rising?}{\quad rising?@> + if ( x<=0 ) { + return 0; + } else if ( x >= a+b+c ) { + return unity; + } else { + t = 1; + @<Rescale if necessary to make sure |a|, |b|, and |c| are all less than + |el_gordo div 3|@>; + do { + t+=t; + @<Subdivide the B\'ezier quadratic defined by |a|, |b|, |c|@>; + xx = x - a - ab - ac; + if ( xx < -x ) { x+=x; b=ab; c=ac; } + else { x = x + xx; a=ac; b=bc; t = t+1; }; + } while (t < unity); + return (t - unity); + } +} + +@ @<Subdivide the B\'ezier quadratic defined by |a|, |b|, |c|@>= +ab = half(a+b); +bc = half(b+c); +ac = half(ab+bc) + +@ @d one_third_el_gordo 05252525252 /* upper bound on |a|, |b|, and |c| */ + +@<Rescale if necessary to make sure |a|, |b|, and |c| are all less than...@>= +while ((a>one_third_el_gordo)||(b>one_third_el_gordo)||(c>one_third_el_gordo)) { + a = halfp(a); + b = half(b); + c = halfp(c); + x = halfp(x); +} + +@ It is convenient to have a simpler interface to |arc_test| that requires no +unnecessary arguments and ensures that each $({\it dx},{\it dy})$ pair has +length less than |fraction_four|. + +@d arc_tol 16 /* quit when change in arc length estimate reaches this */ + +@c static scaled mp_do_arc_test (MP mp,scaled dx0, scaled dy0, scaled dx1, + scaled dy1, scaled dx2, scaled dy2, scaled a_goal) { + scaled v0,v1,v2; /* length of each $({\it dx},{\it dy})$ pair */ + scaled v02; /* twice the norm of the quadratic at $t={1\over2}$ */ + v0 = mp_pyth_add(mp, dx0,dy0); + v1 = mp_pyth_add(mp, dx1,dy1); + v2 = mp_pyth_add(mp, dx2,dy2); + if ( (v0>=fraction_four) || (v1>=fraction_four) || (v2>=fraction_four) ) { + mp->arith_error = true; + if ( a_goal==el_gordo ) return el_gordo; + else return (-two); + } else { + v02 = mp_pyth_add(mp, dx1+half(dx0+dx2), dy1+half(dy0+dy2)); + return (mp_arc_test(mp, dx0,dy0, dx1,dy1, dx2,dy2, + v0, v02, v2, a_goal, arc_tol)); + } +} + +@ Now it is easy to find the arc length of an entire path. + +@c static scaled mp_get_arc_length (MP mp,pointer h) { + pointer p,q; /* for traversing the path */ + scaled a,a_tot; /* current and total arc lengths */ + a_tot = 0; + p = h; + while ( mp_right_type(p)!=mp_endpoint ){ + q = mp_link(p); + a = mp_do_arc_test(mp, mp_right_x(p)-mp_x_coord(p), mp_right_y(p)-mp_y_coord(p), + mp_left_x(q)-mp_right_x(p), mp_left_y(q)-mp_right_y(p), + mp_x_coord(q)-mp_left_x(q), mp_y_coord(q)-mp_left_y(q), el_gordo); + a_tot = mp_slow_add(mp, a, a_tot); + if ( q==h ) break; else p=q; + } + check_arith; + return a_tot; +} + +@ The inverse operation of finding the time on a path~|h| when the arc length +reaches some value |arc0| can also be accomplished via |do_arc_test|. Some care +is required to handle very large times or negative times on cyclic paths. For +non-cyclic paths, |arc0| values that are negative or too large cause +|get_arc_time| to return 0 or the length of path~|h|. + +If |arc0| is greater than the arc length of a cyclic path~|h|, the result is a +time value greater than the length of the path. Since it could be much greater, +we must be prepared to compute the arc length of path~|h| and divide this into +|arc0| to find how many multiples of the length of path~|h| to add. + +@c static scaled mp_get_arc_time (MP mp,pointer h, scaled arc0) { + pointer p,q; /* for traversing the path */ + scaled t_tot; /* accumulator for the result */ + scaled t; /* the result of |do_arc_test| */ + scaled arc; /* portion of |arc0| not used up so far */ + integer n; /* number of extra times to go around the cycle */ + if ( arc0<0 ) { + @<Deal with a negative |arc0| value and |return|@>; + } + if ( arc0==el_gordo ) decr(arc0); + t_tot = 0; + arc = arc0; + p = h; + while ( (mp_right_type(p)!=mp_endpoint) && (arc>0) ) { + q = mp_link(p); + t = mp_do_arc_test(mp, mp_right_x(p)-mp_x_coord(p), mp_right_y(p)-mp_y_coord(p), + mp_left_x(q)-mp_right_x(p), mp_left_y(q)-mp_right_y(p), + mp_x_coord(q)-mp_left_x(q), mp_y_coord(q)-mp_left_y(q), arc); + @<Update |arc| and |t_tot| after |do_arc_test| has just returned |t|@>; + if ( q==h ) { + @<Update |t_tot| and |arc| to avoid going around the cyclic + path too many times but set |arith_error:=true| and |goto done| on + overflow@>; + } + p = q; + } + check_arith; + return t_tot; +} + +@ @<Update |arc| and |t_tot| after |do_arc_test| has just returned |t|@>= +if ( t<0 ) { t_tot = t_tot + t + two; arc = 0; } +else { t_tot = t_tot + unity; arc = arc - t; } + +@ @<Deal with a negative |arc0| value and |return|@>= +{ + if ( mp_left_type(h)==mp_endpoint ) { + t_tot=0; + } else { + p = mp_htap_ypoc(mp, h); + t_tot = -mp_get_arc_time(mp, p, -arc0); + mp_toss_knot_list(mp, p); + } + check_arith; + return t_tot; +} + +@ @<Update |t_tot| and |arc| to avoid going around the cyclic...@>= +if ( arc>0 ) { + n = arc / (arc0 - arc); + arc = arc - n*(arc0 - arc); + if ( t_tot > (el_gordo / (n+1)) ) { + return el_gordo; + } + t_tot = (n + 1)*t_tot; +} + +@* \[20] Data structures for pens. +A Pen in \MP\ can be either elliptical or polygonal. Elliptical pens result +in \ps\ \&{stroke} commands, while anything drawn with a polygonal pen is +@:stroke}{\&{stroke} command@> +converted into an area fill as described in the next part of this program. +The mathematics behind this process is based on simple aspects of the theory +of tracings developed by Leo Guibas, Lyle Ramshaw, and Jorge Stolfi +[``A kinematic framework for computational geometry,'' Proc.\ IEEE Symp.\ +Foundations of Computer Science {\bf 24} (1983), 100--111]. + +Polygonal pens are created from paths via \MP's \&{makepen} primitive. +@:makepen_}{\&{makepen} primitive@> +This path representation is almost sufficient for our purposes except that +a pen path should always be a convex polygon with the vertices in +counter-clockwise order. +Since we will need to scan pen polygons both forward and backward, a pen +should be represented as a doubly linked ring of knot nodes. There is +room for the extra back pointer because we do not need the +|mp_left_type| or |mp_right_type| fields. In fact, we don't need the |mp_left_x|, +|mp_left_y|, |mp_right_x|, or |mp_right_y| fields either but we leave these alone +so that certain procedures can operate on both pens and paths. In particular, +pens can be copied using |copy_path| and recycled using |toss_knot_list|. + +@d knil mp_info + /* this replaces the |mp_left_type| and |mp_right_type| fields in a pen knot */ + +@ The |make_pen| procedure turns a path into a pen by initializing +the |knil| pointers and making sure the knots form a convex polygon. +Thus each cubic in the given path becomes a straight line and the control +points are ignored. If the path is not cyclic, the ends are connected by a +straight line. + +@d copy_pen(A) mp_make_pen(mp, mp_copy_path(mp, (A)),false) + +@c +static pointer mp_make_pen (MP mp,pointer h, boolean need_hull) { + pointer p,q; /* two consecutive knots */ + q=h; + do { + p=q; q=mp_link(q); + knil(q)=p; + } while (q!=h); + if ( need_hull ){ + h=mp_convex_hull(mp, h); + @<Make sure |h| isn't confused with an elliptical pen@>; + } + return h; +} + +@ The only information required about an elliptical pen is the overall +transformation that has been applied to the original \&{pencircle}. +@:pencircle_}{\&{pencircle} primitive@> +Since it suffices to keep track of how the three points $(0,0)$, $(1,0)$, +and $(0,1)$ are transformed, an elliptical pen can be stored in a single +knot node and transformed as if it were a path. + +@d pen_is_elliptical(A) ((A)==mp_link((A))) + +@c +static pointer mp_get_pen_circle (MP mp,scaled diam) { + pointer h; /* the knot node to return */ + h=mp_get_node(mp, knot_node_size); + mp_link(h)=h; knil(h)=h; + mp_originator(h)=mp_program_code; + mp_x_coord(h)=0; mp_y_coord(h)=0; + mp_left_x(h)=diam; mp_left_y(h)=0; + mp_right_x(h)=0; mp_right_y(h)=diam; + return h; +} + +@ If the polygon being returned by |make_pen| has only one vertex, it will +be interpreted as an elliptical pen. This is no problem since a degenerate +polygon can equally well be thought of as a degenerate ellipse. We need only +initialize the |mp_left_x|, |mp_left_y|, |mp_right_x|, and |mp_right_y| fields. + +@<Make sure |h| isn't confused with an elliptical pen@>= +if ( pen_is_elliptical( h) ){ + mp_left_x(h)=mp_x_coord(h); mp_left_y(h)=mp_y_coord(h); + mp_right_x(h)=mp_x_coord(h); mp_right_y(h)=mp_y_coord(h); +} + +@ Printing a polygonal pen is very much like printing a path + +@<Declarations@>= +static void mp_pr_pen (MP mp,pointer h) ; + +@ @c +void mp_pr_pen (MP mp,pointer h) { + pointer p,q; /* for list traversal */ + if ( pen_is_elliptical(h) ) { + @<Print the elliptical pen |h|@>; + } else { + p=h; + do { + mp_print_two(mp, mp_x_coord(p),mp_y_coord(p)); + mp_print_nl(mp, " .. "); + @<Advance |p| making sure the links are OK and |return| if there is + a problem@>; + } while (p!=h); + mp_print(mp, "cycle"); + } +} + +@ @<Advance |p| making sure the links are OK and |return| if there is...@>= +q=mp_link(p); +if ( (q==null) || (knil(q)!=p) ) { + mp_print_nl(mp, "???"); return; /* this won't happen */ +@.???@> +} +p=q + +@ @<Print the elliptical pen |h|@>= +{ +mp_print(mp, "pencircle transformed ("); +mp_print_scaled(mp, mp_x_coord(h)); +mp_print_char(mp, xord(',')); +mp_print_scaled(mp, mp_y_coord(h)); +mp_print_char(mp, xord(',')); +mp_print_scaled(mp, mp_left_x(h)-mp_x_coord(h)); +mp_print_char(mp, xord(',')); +mp_print_scaled(mp, mp_right_x(h)-mp_x_coord(h)); +mp_print_char(mp, xord(',')); +mp_print_scaled(mp, mp_left_y(h)-mp_y_coord(h)); +mp_print_char(mp, xord(',')); +mp_print_scaled(mp, mp_right_y(h)-mp_y_coord(h)); +mp_print_char(mp, xord(')')); +} + +@ Here us another version of |pr_pen| that prints the pen as a diagnostic +message. + +@<Declarations@>= +static void mp_print_pen (MP mp,pointer h, const char *s, boolean nuline) ; + +@ @c +void mp_print_pen (MP mp,pointer h, const char *s, boolean nuline) { + mp_print_diagnostic(mp, "Pen",s,nuline); mp_print_ln(mp); +@.Pen at line...@> + mp_pr_pen(mp, h); + mp_end_diagnostic(mp, true); +} + +@ Making a polygonal pen into a path involves restoring the |mp_left_type| and +|mp_right_type| fields and setting the control points so as to make a polygonal +path. + +@c +static void mp_make_path (MP mp,pointer h) { + pointer p; /* for traversing the knot list */ + quarterword k; /* a loop counter */ + @<Other local variables in |make_path|@>; + if ( pen_is_elliptical(h) ) { + @<Make the elliptical pen |h| into a path@>; + } else { + p=h; + do { + mp_left_type(p)=mp_explicit; + mp_right_type(p)=mp_explicit; + @<copy the coordinates of knot |p| into its control points@>; + p=mp_link(p); + } while (p!=h); + } +} + +@ @<copy the coordinates of knot |p| into its control points@>= +mp_left_x(p)=mp_x_coord(p); +mp_left_y(p)=mp_y_coord(p); +mp_right_x(p)=mp_x_coord(p); +mp_right_y(p)=mp_y_coord(p) + +@ We need an eight knot path to get a good approximation to an ellipse. + +@<Make the elliptical pen |h| into a path@>= +{ + @<Extract the transformation parameters from the elliptical pen~|h|@>; + p=h; + for (k=0;k<=7;k++ ) { + @<Initialize |p| as the |k|th knot of a circle of unit diameter, + transforming it appropriately@>; + if ( k==7 ) mp_link(p)=h; else mp_link(p)=mp_get_node(mp, knot_node_size); + p=mp_link(p); + } +} + +@ @<Extract the transformation parameters from the elliptical pen~|h|@>= +center_x=mp_x_coord(h); +center_y=mp_y_coord(h); +width_x=mp_left_x(h)-center_x; +width_y=mp_left_y(h)-center_y; +height_x=mp_right_x(h)-center_x; +height_y=mp_right_y(h)-center_y + +@ @<Other local variables in |make_path|@>= +scaled center_x,center_y; /* translation parameters for an elliptical pen */ +scaled width_x,width_y; /* the effect of a unit change in $x$ */ +scaled height_x,height_y; /* the effect of a unit change in $y$ */ +scaled dx,dy; /* the vector from knot |p| to its right control point */ +integer kk; + /* |k| advanced $270^\circ$ around the ring (cf. $\sin\theta=\cos(\theta+270)$) */ + +@ The only tricky thing here are the tables |half_cos| and |d_cos| used to +find the point $k/8$ of the way around the circle and the direction vector +to use there. + +@<Initialize |p| as the |k|th knot of a circle of unit diameter,...@>= +kk=(k+6)% 8; +mp_x_coord(p)=center_x+mp_take_fraction(mp, mp->half_cos[k],width_x) + +mp_take_fraction(mp, mp->half_cos[kk],height_x); +mp_y_coord(p)=center_y+mp_take_fraction(mp, mp->half_cos[k],width_y) + +mp_take_fraction(mp, mp->half_cos[kk],height_y); +dx=-mp_take_fraction(mp, mp->d_cos[kk],width_x) + +mp_take_fraction(mp, mp->d_cos[k],height_x); +dy=-mp_take_fraction(mp, mp->d_cos[kk],width_y) + +mp_take_fraction(mp, mp->d_cos[k],height_y); +mp_right_x(p)=mp_x_coord(p)+dx; +mp_right_y(p)=mp_y_coord(p)+dy; +mp_left_x(p)=mp_x_coord(p)-dx; +mp_left_y(p)=mp_y_coord(p)-dy; +mp_left_type(p)=mp_explicit; +mp_right_type(p)=mp_explicit; +mp_originator(p)=mp_program_code + +@ @<Glob...@>= +fraction half_cos[8]; /* ${1\over2}\cos(45k)$ */ +fraction d_cos[8]; /* a magic constant times $\cos(45k)$ */ + +@ The magic constant for |d_cos| is the distance between $({1\over2},0)$ and +$({1\over4}\sqrt2,{1\over4}\sqrt2)$ times the result of the |velocity| +function for $\theta=\phi=22.5^\circ$. This comes out to be +$$ d = {\sqrt{2-\sqrt2}\over 3+3\cos22.5^\circ} + \approx 0.132608244919772. +$$ + +@<Set init...@>= +mp->half_cos[0]=fraction_half; +mp->half_cos[1]=94906266; /* $2^{26}\sqrt2\approx94906265.62$ */ +mp->half_cos[2]=0; +mp->d_cos[0]=35596755; /* $2^{28}d\approx35596754.69$ */ +mp->d_cos[1]=25170707; /* $2^{27}\sqrt2\,d\approx25170706.63$ */ +mp->d_cos[2]=0; +for (k=3;k<= 4;k++ ) { + mp->half_cos[k]=-mp->half_cos[4-k]; + mp->d_cos[k]=-mp->d_cos[4-k]; +} +for (k=5;k<= 7;k++ ) { + mp->half_cos[k]=mp->half_cos[8-k]; + mp->d_cos[k]=mp->d_cos[8-k]; +} + +@ The |convex_hull| function forces a pen polygon to be convex when it is +returned by |make_pen| and after any subsequent transformation where rounding +error might allow the convexity to be lost. +The convex hull algorithm used here is described by F.~P. Preparata and +M.~I. Shamos [{\sl Computational Geometry}, Springer-Verlag, 1985]. + +@<Declarations@>= +static pointer mp_convex_hull (MP mp,pointer h); + +@ @c +pointer mp_convex_hull (MP mp,pointer h) { /* Make a polygonal pen convex */ + pointer l,r; /* the leftmost and rightmost knots */ + pointer p,q; /* knots being scanned */ + pointer s; /* the starting point for an upcoming scan */ + scaled dx,dy; /* a temporary pointer */ + if ( pen_is_elliptical(h) ) { + return h; + } else { + @<Set |l| to the leftmost knot in polygon~|h|@>; + @<Set |r| to the rightmost knot in polygon~|h|@>; + if ( l!=r ) { + s=mp_link(r); + @<Find any knots on the path from |l| to |r| above the |l|-|r| line and + move them past~|r|@>; + @<Find any knots on the path from |s| to |l| below the |l|-|r| line and + move them past~|l|@>; + @<Sort the path from |l| to |r| by increasing $x$@>; + @<Sort the path from |r| to |l| by decreasing $x$@>; + } + if ( l!=mp_link(l) ) { + @<Do a Gramm scan and remove vertices where there is no left turn@>; + } + return l; + } +} + +@ All comparisons are done primarily on $x$ and secondarily on $y$. + +@<Set |l| to the leftmost knot in polygon~|h|@>= +l=h; +p=mp_link(h); +while ( p!=h ) { + if ( mp_x_coord(p)<=mp_x_coord(l) ) + if ( (mp_x_coord(p)<mp_x_coord(l)) || (mp_y_coord(p)<mp_y_coord(l)) ) + l=p; + p=mp_link(p); +} + +@ @<Set |r| to the rightmost knot in polygon~|h|@>= +r=h; +p=mp_link(h); +while ( p!=h ) { + if ( mp_x_coord(p)>=mp_x_coord(r) ) + if ( (mp_x_coord(p)>mp_x_coord(r)) || (mp_y_coord(p)>mp_y_coord(r)) ) + r=p; + p=mp_link(p); +} + +@ @<Find any knots on the path from |l| to |r| above the |l|-|r| line...@>= +dx=mp_x_coord(r)-mp_x_coord(l); +dy=mp_y_coord(r)-mp_y_coord(l); +p=mp_link(l); +while ( p!=r ) { + q=mp_link(p); + if ( mp_ab_vs_cd(mp, dx,mp_y_coord(p)-mp_y_coord(l),dy,mp_x_coord(p)-mp_x_coord(l))>0 ) + mp_move_knot(mp, p, r); + p=q; +} + +@ The |move_knot| procedure removes |p| from a doubly linked list and inserts +it after |q|. + +@ @<Declarations@>= +static void mp_move_knot (MP mp,pointer p, pointer q) ; + +@ @c +void mp_move_knot (MP mp,pointer p, pointer q) { + mp_link(knil(p))=mp_link(p); + knil(mp_link(p))=knil(p); + knil(p)=q; + mp_link(p)=mp_link(q); + mp_link(q)=p; + knil(mp_link(p))=p; +} + +@ @<Find any knots on the path from |s| to |l| below the |l|-|r| line...@>= +p=s; +while ( p!=l ) { + q=mp_link(p); + if ( mp_ab_vs_cd(mp, dx,mp_y_coord(p)-mp_y_coord(l),dy,mp_x_coord(p)-mp_x_coord(l))<0 ) + mp_move_knot(mp, p,l); + p=q; +} + +@ The list is likely to be in order already so we just do linear insertions. +Secondary comparisons on $y$ ensure that the sort is consistent with the +choice of |l| and |r|. + +@<Sort the path from |l| to |r| by increasing $x$@>= +p=mp_link(l); +while ( p!=r ) { + q=knil(p); + while ( mp_x_coord(q)>mp_x_coord(p) ) q=knil(q); + while ( mp_x_coord(q)==mp_x_coord(p) ) { + if ( mp_y_coord(q)>mp_y_coord(p) ) q=knil(q); else break; + } + if ( q==knil(p) ) p=mp_link(p); + else { p=mp_link(p); mp_move_knot(mp, knil(p),q); }; +} + +@ @<Sort the path from |r| to |l| by decreasing $x$@>= +p=mp_link(r); +while ( p!=l ){ + q=knil(p); + while ( mp_x_coord(q)<mp_x_coord(p) ) q=knil(q); + while ( mp_x_coord(q)==mp_x_coord(p) ) { + if ( mp_y_coord(q)<mp_y_coord(p) ) q=knil(q); else break; + } + if ( q==knil(p) ) p=mp_link(p); + else { p=mp_link(p); mp_move_knot(mp, knil(p),q); }; +} + +@ The condition involving |ab_vs_cd| tests if there is not a left turn +at knot |q|. There usually will be a left turn so we streamline the case +where the |then| clause is not executed. + +@<Do a Gramm scan and remove vertices where there...@>= +{ +p=l; q=mp_link(l); +while (1) { + dx=mp_x_coord(q)-mp_x_coord(p); + dy=mp_y_coord(q)-mp_y_coord(p); + p=q; q=mp_link(q); + if ( p==l ) break; + if ( p!=r ) + if ( mp_ab_vs_cd(mp, dx,mp_y_coord(q)-mp_y_coord(p),dy,mp_x_coord(q)-mp_x_coord(p))<=0 ) { + @<Remove knot |p| and back up |p| and |q| but don't go past |l|@>; + } + } +} + +@ @<Remove knot |p| and back up |p| and |q| but don't go past |l|@>= +{ +s=knil(p); +mp_free_node(mp, p,knot_node_size); +mp_link(s)=q; knil(q)=s; +if ( s==l ) p=s; +else { p=knil(s); q=s; }; +} + +@ The |find_offset| procedure sets global variables |(cur_x,cur_y)| to the +offset associated with the given direction |(x,y)|. If two different offsets +apply, it chooses one of them. + +@c +static void mp_find_offset (MP mp,scaled x, scaled y, pointer h) { + pointer p,q; /* consecutive knots */ + scaled wx,wy,hx,hy; + /* the transformation matrix for an elliptical pen */ + fraction xx,yy; /* untransformed offset for an elliptical pen */ + fraction d; /* a temporary register */ + if ( pen_is_elliptical(h) ) { + @<Find the offset for |(x,y)| on the elliptical pen~|h|@> + } else { + q=h; + do { + p=q; q=mp_link(q); + } while (!(mp_ab_vs_cd(mp, mp_x_coord(q)-mp_x_coord(p),y, mp_y_coord(q)-mp_y_coord(p),x)>=0)); + do { + p=q; q=mp_link(q); + } while (!(mp_ab_vs_cd(mp, mp_x_coord(q)-mp_x_coord(p),y, mp_y_coord(q)-mp_y_coord(p),x)<=0)); + mp->cur_x=mp_x_coord(p); + mp->cur_y=mp_y_coord(p); + } +} + +@ @<Glob...@>= +scaled cur_x; +scaled cur_y; /* all-purpose return value registers */ + +@ @<Find the offset for |(x,y)| on the elliptical pen~|h|@>= +if ( (x==0) && (y==0) ) { + mp->cur_x=mp_x_coord(h); mp->cur_y=mp_y_coord(h); +} else { + @<Find the non-constant part of the transformation for |h|@>; + while ( (abs(x)<fraction_half) && (abs(y)<fraction_half) ){ + x+=x; y+=y; + }; + @<Make |(xx,yy)| the offset on the untransformed \&{pencircle} for the + untransformed version of |(x,y)|@>; + mp->cur_x=mp_x_coord(h)+mp_take_fraction(mp, xx,wx)+mp_take_fraction(mp, yy,hx); + mp->cur_y=mp_y_coord(h)+mp_take_fraction(mp, xx,wy)+mp_take_fraction(mp, yy,hy); +} + +@ @<Find the non-constant part of the transformation for |h|@>= +wx=mp_left_x(h)-mp_x_coord(h); +wy=mp_left_y(h)-mp_y_coord(h); +hx=mp_right_x(h)-mp_x_coord(h); +hy=mp_right_y(h)-mp_y_coord(h) + +@ @<Make |(xx,yy)| the offset on the untransformed \&{pencircle} for the...@>= +yy=-(mp_take_fraction(mp, x,hy)+mp_take_fraction(mp, y,-hx)); +xx=mp_take_fraction(mp, x,-wy)+mp_take_fraction(mp, y,wx); +d=mp_pyth_add(mp, xx,yy); +if ( d>0 ) { + xx=half(mp_make_fraction(mp, xx,d)); + yy=half(mp_make_fraction(mp, yy,d)); +} + +@ Finding the bounding box of a pen is easy except if the pen is elliptical. +But we can handle that case by just calling |find_offset| twice. The answer +is stored in the global variables |minx|, |maxx|, |miny|, and |maxy|. + +@c +static void mp_pen_bbox (MP mp,pointer h) { + pointer p; /* for scanning the knot list */ + if ( pen_is_elliptical(h) ) { + @<Find the bounding box of an elliptical pen@>; + } else { + mp_minx=mp_x_coord(h); mp_maxx=mp_minx; + mp_miny=mp_y_coord(h); mp_maxy=mp_miny; + p=mp_link(h); + while ( p!=h ) { + if ( mp_x_coord(p)<mp_minx ) mp_minx=mp_x_coord(p); + if ( mp_y_coord(p)<mp_miny ) mp_miny=mp_y_coord(p); + if ( mp_x_coord(p)>mp_maxx ) mp_maxx=mp_x_coord(p); + if ( mp_y_coord(p)>mp_maxy ) mp_maxy=mp_y_coord(p); + p=mp_link(p); + } + } +} + +@ @<Find the bounding box of an elliptical pen@>= +{ +mp_find_offset(mp, 0,fraction_one,h); +mp_maxx=mp->cur_x; +mp_minx=2*mp_x_coord(h)-mp->cur_x; +mp_find_offset(mp, -fraction_one,0,h); +mp_maxy=mp->cur_y; +mp_miny=2*mp_y_coord(h)-mp->cur_y; +} + +@* \[21] Edge structures. +Now we come to \MP's internal scheme for representing pictures. +The representation is very different from \MF's edge structures +because \MP\ pictures contain \ps\ graphics objects instead of pixel +images. However, the basic idea is somewhat similar in that shapes +are represented via their boundaries. + +The main purpose of edge structures is to keep track of graphical objects +until it is time to translate them into \ps. Since \MP\ does not need to +know anything about an edge structure other than how to translate it into +\ps\ and how to find its bounding box, edge structures can be just linked +lists of graphical objects. \MP\ has no easy way to determine whether +two such objects overlap, but it suffices to draw the first one first and +let the second one overwrite it if necessary. + +@(mplib.h@>= +enum mp_graphical_object_code { + @<Graphical object codes@> + mp_final_graphic +}; + +@ Let's consider the types of graphical objects one at a time. +First of all, a filled contour is represented by a eight-word node. The first +word contains |type| and |link| fields, and the next six words contain a +pointer to a cyclic path and the value to use for \ps' \&{currentrgbcolor} +parameter. If a pen is used for filling |pen_p|, |ljoin_val| and |miterlim_val| +give the relevant information. + +@d mp_path_p(A) mp_link((A)+1) + /* a pointer to the path that needs filling */ +@d mp_pen_p(A) mp_info((A)+1) + /* a pointer to the pen to fill or stroke with */ +@d mp_color_model(A) mp_type((A)+2) /* the color model */ +@d obj_red_loc(A) ((A)+3) /* the first of three locations for the color */ +@d obj_cyan_loc obj_red_loc /* the first of four locations for the color */ +@d obj_grey_loc obj_red_loc /* the location for the color */ +@d red_val(A) mp->mem[(A)+3].sc + /* the red component of the color in the range $0\ldots1$ */ +@d cyan_val red_val +@d grey_val red_val +@d green_val(A) mp->mem[(A)+4].sc + /* the green component of the color in the range $0\ldots1$ */ +@d magenta_val green_val +@d blue_val(A) mp->mem[(A)+5].sc + /* the blue component of the color in the range $0\ldots1$ */ +@d yellow_val blue_val +@d black_val(A) mp->mem[(A)+6].sc + /* the blue component of the color in the range $0\ldots1$ */ +@d ljoin_val(A) mp_name_type((A)) /* the value of \&{linejoin} */ +@:mp_linejoin_}{\&{linejoin} primitive@> +@d miterlim_val(A) mp->mem[(A)+7].sc /* the value of \&{miterlimit} */ +@:mp_miterlimit_}{\&{miterlimit} primitive@> +@d obj_color_part(A) mp->mem[(A)+3-red_part].sc + /* interpret an object pointer that has been offset by |red_part..blue_part| */ +@d mp_pre_script(A) mp->mem[(A)+8].hh.lh +@d mp_post_script(A) mp->mem[(A)+8].hh.rh +@d fill_node_size 9 + +@ @<Graphical object codes@>= +mp_fill_code=1, + +@ @c +static pointer mp_new_fill_node (MP mp,pointer p) { + /* make a fill node for cyclic path |p| and color black */ + pointer t; /* the new node */ + t=mp_get_node(mp, fill_node_size); + mp_type(t)=mp_fill_code; + mp_path_p(t)=p; + mp_pen_p(t)=null; /* |null| means don't use a pen */ + red_val(t)=0; + green_val(t)=0; + blue_val(t)=0; + black_val(t)=0; + mp_color_model(t)=mp_uninitialized_model; + mp_pre_script(t)=null; + mp_post_script(t)=null; + @<Set the |ljoin_val| and |miterlim_val| fields in object |t|@>; + return t; +} + +@ @<Set the |ljoin_val| and |miterlim_val| fields in object |t|@>= +if ( mp->internal[mp_linejoin]>unity ) ljoin_val(t)=2; +else if ( mp->internal[mp_linejoin]>0 ) ljoin_val(t)=1; +else ljoin_val(t)=0; +if ( mp->internal[mp_miterlimit]<unity ) + miterlim_val(t)=unity; +else + miterlim_val(t)=mp->internal[mp_miterlimit] + +@ A stroked path is represented by an eight-word node that is like a filled +contour node except that it contains the current \&{linecap} value, a scale +factor for the dash pattern, and a pointer that is non-null if the stroke +is to be dashed. The purpose of the scale factor is to allow a picture to +be transformed without touching the picture that |dash_p| points to. + +@d mp_dash_p(A) mp_link((A)+9) + /* a pointer to the edge structure that gives the dash pattern */ +@d lcap_val(A) mp_type((A)+9) + /* the value of \&{linecap} */ +@:mp_linecap_}{\&{linecap} primitive@> +@d dash_scale(A) mp->mem[(A)+10].sc /* dash lengths are scaled by this factor */ +@d stroked_node_size 11 + +@ @<Graphical object codes@>= +mp_stroked_code=2, + +@ @c +static pointer mp_new_stroked_node (MP mp,pointer p) { + /* make a stroked node for path |p| with |mp_pen_p(p)| temporarily |null| */ + pointer t; /* the new node */ + t=mp_get_node(mp, stroked_node_size); + mp_type(t)=mp_stroked_code; + mp_path_p(t)=p; mp_pen_p(t)=null; + mp_dash_p(t)=null; + dash_scale(t)=unity; + red_val(t)=0; + green_val(t)=0; + blue_val(t)=0; + black_val(t)=0; + mp_color_model(t)=mp_uninitialized_model; + mp_pre_script(t)=null; + mp_post_script(t)=null; + @<Set the |ljoin_val| and |miterlim_val| fields in object |t|@>; + if ( mp->internal[mp_linecap]>unity ) lcap_val(t)=2; + else if ( mp->internal[mp_linecap]>0 ) lcap_val(t)=1; + else lcap_val(t)=0; + return t; +} + +@ When a dashed line is computed in a transformed coordinate system, the dash +lengths get scaled like the pen shape and we need to compensate for this. Since +there is no unique scale factor for an arbitrary transformation, we use the +the square root of the determinant. The properties of the determinant make it +easier to maintain the |dash_scale|. The computation is fairly straight-forward +except for the initialization of the scale factor |s|. The factor of 64 is +needed because |square_rt| scales its result by $2^8$ while we need $2^{14}$ +to counteract the effect of |take_fraction|. + +@ @c +scaled mp_sqrt_det (MP mp,scaled a, scaled b, scaled c, scaled d) { + scaled maxabs; /* $max(|a|,|b|,|c|,|d|)$ */ + unsigned s; /* amount by which the result of |square_rt| needs to be scaled */ + @<Initialize |maxabs|@>; + s=64; + while ( (maxabs<fraction_one) && (s>1) ){ + a+=a; b+=b; c+=c; d+=d; + maxabs+=maxabs; s=(unsigned)(halfp(s)); + } + return (scaled)(s*mp_square_rt(mp, abs(mp_take_fraction(mp, a,d)-mp_take_fraction(mp, b,c)))); +} +@# +static scaled mp_get_pen_scale (MP mp,pointer p) { + return mp_sqrt_det(mp, + mp_left_x(p)-mp_x_coord(p), mp_right_x(p)-mp_x_coord(p), + mp_left_y(p)-mp_y_coord(p), mp_right_y(p)-mp_y_coord(p)); +} + +@ @<Declarations@>= +static scaled mp_sqrt_det (MP mp,scaled a, scaled b, scaled c, scaled d) ; + + +@ @<Initialize |maxabs|@>= +maxabs=abs(a); +if ( abs(b)>maxabs ) maxabs=abs(b); +if ( abs(c)>maxabs ) maxabs=abs(c); +if ( abs(d)>maxabs ) maxabs=abs(d) + +@ When a picture contains text, this is represented by a fourteen-word node +where the color information and |type| and |link| fields are augmented by +additional fields that describe the text and how it is transformed. +The |path_p| and |mp_pen_p| pointers are replaced by a number that identifies +the font and a string number that gives the text to be displayed. +The |width|, |height|, and |depth| fields +give the dimensions of the text at its design size, and the remaining six +words give a transformation to be applied to the text. The |new_text_node| +function initializes everything to default values so that the text comes out +black with its reference point at the origin. + +@d mp_text_p(A) mp_link((A)+1) /* a string pointer for the text to display */ +@d mp_font_n(A) mp_info((A)+1) /* the font number */ +@d width_val(A) mp->mem[(A)+7].sc /* unscaled width of the text */ +@d height_val(A) mp->mem[(A)+9].sc /* unscaled height of the text */ +@d depth_val(A) mp->mem[(A)+10].sc /* unscaled depth of the text */ +@d text_tx_loc(A) ((A)+11) + /* the first of six locations for transformation parameters */ +@d tx_val(A) mp->mem[(A)+11].sc /* $x$ shift amount */ +@d ty_val(A) mp->mem[(A)+12].sc /* $y$ shift amount */ +@d txx_val(A) mp->mem[(A)+13].sc /* |txx| transformation parameter */ +@d txy_val(A) mp->mem[(A)+14].sc /* |txy| transformation parameter */ +@d tyx_val(A) mp->mem[(A)+15].sc /* |tyx| transformation parameter */ +@d tyy_val(A) mp->mem[(A)+16].sc /* |tyy| transformation parameter */ +@d text_trans_part(A) mp->mem[(A)+11-x_part].sc + /* interpret a text node pointer that has been offset by |x_part..yy_part| */ +@d text_node_size 17 + +@ @<Graphical object codes@>= +mp_text_code=3, + +@ @c +static pointer mp_new_text_node (MP mp,char *f,str_number s) { + /* make a text node for font |f| and text string |s| */ + pointer t; /* the new node */ + t=mp_get_node(mp, text_node_size); + mp_type(t)=mp_text_code; + mp_text_p(t)=s; + mp_font_n(t)=(halfword)mp_find_font(mp, f); /* this identifies the font */ + red_val(t)=0; + green_val(t)=0; + blue_val(t)=0; + black_val(t)=0; + mp_color_model(t)=mp_uninitialized_model; + mp_pre_script(t)=null; + mp_post_script(t)=null; + tx_val(t)=0; ty_val(t)=0; + txx_val(t)=unity; txy_val(t)=0; + tyx_val(t)=0; tyy_val(t)=unity; + mp_set_text_box(mp, t); /* this finds the bounding box */ + return t; +} + +@ The last two types of graphical objects that can occur in an edge structure +are clipping paths and \&{setbounds} paths. These are slightly more difficult +@:set_bounds_}{\&{setbounds} primitive@> +to implement because we must keep track of exactly what is being clipped or +bounded when pictures get merged together. For this reason, each clipping or +\&{setbounds} operation is represented by a pair of nodes: first comes a +two-word node whose |path_p| gives the relevant path, then there is the list +of objects to clip or bound followed by a two-word node whose second word is +unused. + +Using at least two words for each graphical object node allows them all to be +allocated and deallocated similarly with a global array |gr_object_size| to +give the size in words for each object type. + +@d start_clip_size 2 +@d start_bounds_size 2 +@d stop_clip_size 2 /* the second word is not used here */ +@d stop_bounds_size 2 /* the second word is not used here */ +@# +@d stop_type(A) ((A)+2) + /* matching |type| for |start_clip_code| or |start_bounds_code| */ +@d has_color(A) (mp_type((A))<mp_start_clip_code) + /* does a graphical object have color fields? */ +@d has_pen(A) (mp_type((A))<mp_text_code) + /* does a graphical object have a |mp_pen_p| field? */ +@d is_start_or_stop(A) (mp_type((A))>=mp_start_clip_code) +@d is_stop(A) (mp_type((A))>=mp_stop_clip_code) + +@ @<Graphical object codes@>= +mp_start_clip_code=4, /* |type| of a node that starts clipping */ +mp_start_bounds_code=5, /* |type| of a node that gives a \&{setbounds} path */ +mp_stop_clip_code=6, /* |type| of a node that stops clipping */ +mp_stop_bounds_code=7, /* |type| of a node that stops \&{setbounds} */ + +@ @c +static pointer mp_new_bounds_node (MP mp,pointer p, quarterword c) { + /* make a node of type |c| where |p| is the clipping or \&{setbounds} path */ + pointer t; /* the new node */ + t=mp_get_node(mp, mp->gr_object_size[c]); + mp_type(t)=c; + mp_path_p(t)=p; + return t; +} + +@ We need an array to keep track of the sizes of graphical objects. + +@<Glob...@>= +quarterword gr_object_size[mp_stop_bounds_code+1]; + +@ @<Set init...@>= +mp->gr_object_size[mp_fill_code]=fill_node_size; +mp->gr_object_size[mp_stroked_code]=stroked_node_size; +mp->gr_object_size[mp_text_code]=text_node_size; +mp->gr_object_size[mp_start_clip_code]=start_clip_size; +mp->gr_object_size[mp_stop_clip_code]=stop_clip_size; +mp->gr_object_size[mp_start_bounds_code]=start_bounds_size; +mp->gr_object_size[mp_stop_bounds_code]=stop_bounds_size; + +@ All the essential information in an edge structure is encoded as a linked list +of graphical objects as we have just seen, but it is helpful to add some +redundant information. A single edge structure might be used as a dash pattern +many times, and it would be nice to avoid scanning the same structure +repeatedly. Thus, an edge structure known to be a suitable dash pattern +has a header that gives a list of dashes in a sorted order designed for rapid +translation into \ps. + +Each dash is represented by a three-word node containing the initial and final +$x$~coordinates as well as the usual |link| field. The |link| fields points to +the dash node with the next higher $x$-coordinates and the final link points +to a special location called |null_dash|. (There should be no overlap between +dashes). Since the $y$~coordinate of the dash pattern is needed to determine +the period of repetition, this needs to be stored in the edge header along +with a pointer to the list of dash nodes. + +@d start_x(A) mp->mem[(A)+1].sc /* the starting $x$~coordinate in a dash node */ +@d stop_x(A) mp->mem[(A)+2].sc /* the ending $x$~coordinate in a dash node */ +@d dash_node_size 3 +@d dash_list mp_link + /* in an edge header this points to the first dash node */ +@d dash_y(A) mp->mem[(A)+1].sc /* $y$ value for the dash list in an edge header */ + +@ It is also convenient for an edge header to contain the bounding +box information needed by the \&{llcorner} and \&{urcorner} operators +so that this does not have to be recomputed unnecessarily. This is done by +adding fields for the $x$~and $y$ extremes as well as a pointer that indicates +how far the bounding box computation has gotten. Thus if the user asks for +the bounding box and then adds some more text to the picture before asking +for more bounding box information, the second computation need only look at +the additional text. + +When the bounding box has not been computed, the |bblast| pointer points +to a dummy link at the head of the graphical object list while the |minx_val| +and |miny_val| fields contain |el_gordo| and the |maxx_val| and |maxy_val| +fields contain |-el_gordo|. + +Since the bounding box of pictures containing objects of type +|mp_start_bounds_code| depends on the value of \&{truecorners}, the bounding box +@:mp_true_corners_}{\&{truecorners} primitive@> +data might not be valid for all values of this parameter. Hence, the |bbtype| +field is needed to keep track of this. + +@d minx_val(A) mp->mem[(A)+2].sc +@d miny_val(A) mp->mem[(A)+3].sc +@d maxx_val(A) mp->mem[(A)+4].sc +@d maxy_val(A) mp->mem[(A)+5].sc +@d bblast(A) mp_link((A)+6) /* last item considered in bounding box computation */ +@d bbtype(A) mp_info((A)+6) /* tells how bounding box data depends on \&{truecorners} */ +@d dummy_loc(A) ((A)+7) /* where the object list begins in an edge header */ +@d no_bounds 0 + /* |bbtype| value when bounding box data is valid for all \&{truecorners} values */ +@d bounds_set 1 + /* |bbtype| value when bounding box data is for \&{truecorners}${}\le 0$ */ +@d bounds_unset 2 + /* |bbtype| value when bounding box data is for \&{truecorners}${}>0$ */ + +@c +static void mp_init_bbox (MP mp,pointer h) { + /* Initialize the bounding box information in edge structure |h| */ + bblast(h)=dummy_loc(h); + bbtype(h)=no_bounds; + minx_val(h)=el_gordo; + miny_val(h)=el_gordo; + maxx_val(h)=-el_gordo; + maxy_val(h)=-el_gordo; +} + +@ The only other entries in an edge header are a reference count in the first +word and a pointer to the tail of the object list in the last word. + +@d obj_tail(A) mp_info((A)+7) /* points to the last entry in the object list */ +@d edge_header_size 8 + +@c +static void mp_init_edges (MP mp,pointer h) { + /* initialize an edge header to null values */ + dash_list(h)=null_dash; + obj_tail(h)=dummy_loc(h); + mp_link(dummy_loc(h))=null; + ref_count(h)=null; + mp_init_bbox(mp, h); +} + +@ Here is how edge structures are deleted. The process can be recursive because +of the need to dereference edge structures that are used as dash patterns. +@^recursion@> + +@d add_edge_ref(A) incr(ref_count(A)) +@d delete_edge_ref(A) { + if ( ref_count((A))==null ) + mp_toss_edges(mp, A); + else + decr(ref_count(A)); + } + +@<Declarations@>= +static void mp_flush_dash_list (MP mp,pointer h); +static pointer mp_toss_gr_object (MP mp,pointer p) ; +static void mp_toss_edges (MP mp,pointer h) ; + +@ @c void mp_toss_edges (MP mp,pointer h) { + pointer p,q; /* pointers that scan the list being recycled */ + pointer r; /* an edge structure that object |p| refers to */ + mp_flush_dash_list(mp, h); + q=mp_link(dummy_loc(h)); + while ( (q!=null) ) { + p=q; q=mp_link(q); + r=mp_toss_gr_object(mp, p); + if ( r!=null ) delete_edge_ref(r); + } + mp_free_node(mp, h,edge_header_size); +} +void mp_flush_dash_list (MP mp,pointer h) { + pointer p,q; /* pointers that scan the list being recycled */ + q=dash_list(h); + while ( q!=null_dash ) { + p=q; q=mp_link(q); + mp_free_node(mp, p,dash_node_size); + } + dash_list(h)=null_dash; +} +pointer mp_toss_gr_object (MP mp,pointer p) { + /* returns an edge structure that needs to be dereferenced */ + pointer e; /* the edge structure to return */ + e=null; + @<Prepare to recycle graphical object |p|@>; + mp_free_node(mp, p,mp->gr_object_size[mp_type(p)]); + return e; +} + +@ @<Prepare to recycle graphical object |p|@>= +switch (mp_type(p)) { +case mp_fill_code: + mp_toss_knot_list(mp, mp_path_p(p)); + if ( mp_pen_p(p)!=null ) mp_toss_knot_list(mp, mp_pen_p(p)); + if ( mp_pre_script(p)!=null ) delete_str_ref(mp_pre_script(p)); + if ( mp_post_script(p)!=null ) delete_str_ref(mp_post_script(p)); + break; +case mp_stroked_code: + mp_toss_knot_list(mp, mp_path_p(p)); + if ( mp_pen_p(p)!=null ) mp_toss_knot_list(mp, mp_pen_p(p)); + if ( mp_pre_script(p)!=null ) delete_str_ref(mp_pre_script(p)); + if ( mp_post_script(p)!=null ) delete_str_ref(mp_post_script(p)); + e=mp_dash_p(p); + break; +case mp_text_code: + delete_str_ref(mp_text_p(p)); + if ( mp_pre_script(p)!=null ) delete_str_ref(mp_pre_script(p)); + if ( mp_post_script(p)!=null ) delete_str_ref(mp_post_script(p)); + break; +case mp_start_clip_code: +case mp_start_bounds_code: + mp_toss_knot_list(mp, mp_path_p(p)); + break; +case mp_stop_clip_code: +case mp_stop_bounds_code: + break; +} /* there are no other cases */ + +@ If we use |add_edge_ref| to ``copy'' edge structures, the real copying needs +to be done before making a significant change to an edge structure. Much of +the work is done in a separate routine |copy_objects| that copies a list of +graphical objects into a new edge header. + +@c +static pointer mp_private_edges (MP mp,pointer h) { + /* make a private copy of the edge structure headed by |h| */ + pointer hh; /* the edge header for the new copy */ + pointer p,pp; /* pointers for copying the dash list */ + if ( ref_count(h)==null ) { + return h; + } else { + decr(ref_count(h)); + hh=mp_copy_objects(mp, mp_link(dummy_loc(h)),null); + @<Copy the dash list from |h| to |hh|@>; + @<Copy the bounding box information from |h| to |hh| and make |bblast(hh)| + point into the new object list@>; + return hh; + } +} + +@ Here we use the fact that |dash_list(hh)=mp_link(hh)|. +@^data structure assumptions@> + +@<Copy the dash list from |h| to |hh|@>= +pp=hh; p=dash_list(h); +while ( (p!=null_dash) ) { + mp_link(pp)=mp_get_node(mp, dash_node_size); + pp=mp_link(pp); + start_x(pp)=start_x(p); + stop_x(pp)=stop_x(p); + p=mp_link(p); +} +mp_link(pp)=null_dash; +dash_y(hh)=dash_y(h) + + +@ |h| is an edge structure + +@c +static mp_dash_object *mp_export_dashes (MP mp, pointer q, scaled *w) { + mp_dash_object *d; + pointer p, h; + scaled scf; /* scale factor */ + int *dashes = NULL; + int num_dashes = 1; + h = mp_dash_p(q); + if (h==null || dash_list(h)==null_dash) + return NULL; + p = dash_list(h); + scf=mp_get_pen_scale(mp, mp_pen_p(q)); + if (scf==0) { + if (*w==0) scf = dash_scale(q); else return NULL; + } else { + scf=mp_make_scaled(mp, *w,scf); + scf=mp_take_scaled(mp, scf,dash_scale(q)); + } + *w = scf; + d = xmalloc(1,sizeof(mp_dash_object)); + start_x(null_dash)=start_x(p)+dash_y(h); + while (p != null_dash) { + dashes = xrealloc(dashes, (num_dashes+2), sizeof(scaled)); + dashes[(num_dashes-1)] = + mp_take_scaled(mp,(stop_x(p)-start_x(p)),scf); + dashes[(num_dashes)] = + mp_take_scaled(mp,(start_x(mp_link(p))-stop_x(p)),scf); + dashes[(num_dashes+1)] = -1; /* terminus */ + num_dashes+=2; + p=mp_link(p); + } + d->array = dashes; + d->offset = mp_take_scaled(mp,mp_dash_offset(mp, h),scf); + return d; +} + + + +@ @<Copy the bounding box information from |h| to |hh|...@>= +minx_val(hh)=minx_val(h); +miny_val(hh)=miny_val(h); +maxx_val(hh)=maxx_val(h); +maxy_val(hh)=maxy_val(h); +bbtype(hh)=bbtype(h); +p=dummy_loc(h); pp=dummy_loc(hh); +while ((p!=bblast(h)) ) { + if ( p==null ) mp_confusion(mp, "bblast"); +@:this can't happen bblast}{\quad bblast@> + p=mp_link(p); pp=mp_link(pp); +} +bblast(hh)=pp + +@ Here is the promised routine for copying graphical objects into a new edge +structure. It starts copying at object~|p| and stops just before object~|q|. +If |q| is null, it copies the entire sublist headed at |p|. The resulting edge +structure requires further initialization by |init_bbox|. + +@<Declarations@>= +static pointer mp_copy_objects (MP mp, pointer p, pointer q); + +@ @c +pointer mp_copy_objects (MP mp, pointer p, pointer q) { + pointer hh; /* the new edge header */ + pointer pp; /* the last newly copied object */ + quarterword k; /* temporary register */ + hh=mp_get_node(mp, edge_header_size); + dash_list(hh)=null_dash; + ref_count(hh)=null; + pp=dummy_loc(hh); + while ( (p!=q) ) { + @<Make |mp_link(pp)| point to a copy of object |p|, and update |p| and |pp|@>; + } + obj_tail(hh)=pp; + mp_link(pp)=null; + return hh; +} + +@ @<Make |mp_link(pp)| point to a copy of object |p|, and update |p| and |pp|@>= +{ k=mp->gr_object_size[mp_type(p)]; + mp_link(pp)=mp_get_node(mp, k); + pp=mp_link(pp); + while ( (k>0) ) { decr(k); mp->mem[pp+k]=mp->mem[p+k]; }; + @<Fix anything in graphical object |pp| that should differ from the + corresponding field in |p|@>; + p=mp_link(p); +} + +@ @<Fix anything in graphical object |pp| that should differ from the...@>= +switch (mp_type(p)) { +case mp_start_clip_code: +case mp_start_bounds_code: + mp_path_p(pp)=mp_copy_path(mp, mp_path_p(p)); + break; +case mp_fill_code: + mp_path_p(pp)=mp_copy_path(mp, mp_path_p(p)); + if ( mp_pre_script(p)!=null ) add_str_ref(mp_pre_script(p)); + if ( mp_post_script(p)!=null ) add_str_ref(mp_post_script(p)); + if ( mp_pen_p(p)!=null ) mp_pen_p(pp)=copy_pen(mp_pen_p(p)); + break; +case mp_stroked_code: + if ( mp_pre_script(p)!=null ) add_str_ref(mp_pre_script(p)); + if ( mp_post_script(p)!=null ) add_str_ref(mp_post_script(p)); + mp_path_p(pp)=mp_copy_path(mp, mp_path_p(p)); + mp_pen_p(pp)=copy_pen(mp_pen_p(p)); + if ( mp_dash_p(p)!=null ) add_edge_ref(mp_dash_p(pp)); + break; +case mp_text_code: + if ( mp_pre_script(p)!=null ) add_str_ref(mp_pre_script(p)); + if ( mp_post_script(p)!=null ) add_str_ref(mp_post_script(p)); + add_str_ref(mp_text_p(pp)); + break; +case mp_stop_clip_code: +case mp_stop_bounds_code: + break; +} /* there are no other cases */ + +@ Here is one way to find an acceptable value for the second argument to +|copy_objects|. Given a non-null graphical object list, |skip_1component| +skips past one picture component, where a ``picture component'' is a single +graphical object, or a start bounds or start clip object and everything up +through the matching stop bounds or stop clip object. The macro version avoids +procedure call overhead and error handling: |skip_component(p)(e)| advances |p| +unless |p| points to a stop bounds or stop clip node, in which case it executes +|e| instead. + +@d skip_component(A) + if ( ! is_start_or_stop((A)) ) (A)=mp_link((A)); + else if ( ! is_stop((A)) ) (A)=mp_skip_1component(mp, (A)); + else + +@c +static pointer mp_skip_1component (MP mp,pointer p) { + integer lev; /* current nesting level */ + lev=0; + do { + if ( is_start_or_stop(p) ) { + if ( is_stop(p) ) decr(lev); else incr(lev); + } + p=mp_link(p); + } while (lev!=0); + return p; +} + +@ Here is a diagnostic routine for printing an edge structure in symbolic form. + +@<Declarations@>= +static void mp_print_edges (MP mp,pointer h, const char *s, boolean nuline) ; + +@ @c +void mp_print_edges (MP mp,pointer h, const char *s, boolean nuline) { + pointer p; /* a graphical object to be printed */ + pointer hh,pp; /* temporary pointers */ + scaled scf; /* a scale factor for the dash pattern */ + boolean ok_to_dash; /* |false| for polygonal pen strokes */ + mp_print_diagnostic(mp, "Edge structure",s,nuline); + p=dummy_loc(h); + while ( mp_link(p)!=null ) { + p=mp_link(p); + mp_print_ln(mp); + switch (mp_type(p)) { + @<Cases for printing graphical object node |p|@>; + default: + mp_print(mp, "[unknown object type!]"); + break; + } + } + mp_print_nl(mp, "End edges"); + if ( p!=obj_tail(h) ) mp_print(mp, "?"); +@.End edges?@> + mp_end_diagnostic(mp, true); +} + +@ @<Cases for printing graphical object node |p|@>= +case mp_fill_code: + mp_print(mp, "Filled contour "); + mp_print_obj_color(mp, p); + mp_print_char(mp, xord(':')); mp_print_ln(mp); + mp_pr_path(mp, mp_path_p(p)); mp_print_ln(mp); + if ( (mp_pen_p(p)!=null) ) { + @<Print join type for graphical object |p|@>; + mp_print(mp, " with pen"); mp_print_ln(mp); + mp_pr_pen(mp, mp_pen_p(p)); + } + break; + +@ @<Print join type for graphical object |p|@>= +switch (ljoin_val(p)) { +case 0: + mp_print(mp, "mitered joins limited "); + mp_print_scaled(mp, miterlim_val(p)); + break; +case 1: + mp_print(mp, "round joins"); + break; +case 2: + mp_print(mp, "beveled joins"); + break; +default: + mp_print(mp, "?? joins"); +@.??@> + break; +} + +@ For stroked nodes, we need to print |lcap_val(p)| as well. + +@<Print join and cap types for stroked node |p|@>= +switch (lcap_val(p)) { +case 0:mp_print(mp, "butt"); break; +case 1:mp_print(mp, "round"); break; +case 2:mp_print(mp, "square"); break; +default: mp_print(mp, "??"); break; +@.??@> +} +mp_print(mp, " ends, "); +@<Print join type for graphical object |p|@> + +@ Here is a routine that prints the color of a graphical object if it isn't +black (the default color). + +@<Declarations@>= +static void mp_print_obj_color (MP mp,pointer p) ; + +@ @c +void mp_print_obj_color (MP mp,pointer p) { + if ( mp_color_model(p)==mp_grey_model ) { + if ( grey_val(p)>0 ) { + mp_print(mp, "greyed "); + mp_print_compact_node(mp, obj_grey_loc(p),1); + }; + } else if ( mp_color_model(p)==mp_cmyk_model ) { + if ( (cyan_val(p)>0) || (magenta_val(p)>0) || + (yellow_val(p)>0) || (black_val(p)>0) ) { + mp_print(mp, "processcolored "); + mp_print_compact_node(mp, obj_cyan_loc(p),4); + }; + } else if ( mp_color_model(p)==mp_rgb_model ) { + if ( (red_val(p)>0) || (green_val(p)>0) || (blue_val(p)>0) ) { + mp_print(mp, "colored "); + mp_print_compact_node(mp, obj_red_loc(p),3); + }; + } +} + +@ We also need a procedure for printing consecutive scaled values as if they +were a known big node. + +@<Declarations@>= +static void mp_print_compact_node (MP mp,pointer p, quarterword k) ; + +@ @c +void mp_print_compact_node (MP mp,pointer p, quarterword k) { + pointer q; /* last location to print */ + q=p+k-1; + mp_print_char(mp, xord('(')); + while ( p<=q ){ + mp_print_scaled(mp, mp->mem[p].sc); + if ( p<q ) mp_print_char(mp, xord(',')); + incr(p); + } + mp_print_char(mp, xord(')')); +} + +@ @<Cases for printing graphical object node |p|@>= +case mp_stroked_code: + mp_print(mp, "Filled pen stroke "); + mp_print_obj_color(mp, p); + mp_print_char(mp, xord(':')); mp_print_ln(mp); + mp_pr_path(mp, mp_path_p(p)); + if ( mp_dash_p(p)!=null ) { + mp_print_nl(mp, "dashed ("); + @<Finish printing the dash pattern that |p| refers to@>; + } + mp_print_ln(mp); + @<Print join and cap types for stroked node |p|@>; + mp_print(mp, " with pen"); mp_print_ln(mp); + if ( mp_pen_p(p)==null ) mp_print(mp, "???"); /* shouldn't happen */ +@.???@> + else mp_pr_pen(mp, mp_pen_p(p)); + break; + +@ Normally, the |dash_list| field in an edge header is set to |null_dash| +when it is not known to define a suitable dash pattern. This is disallowed +here because the |mp_dash_p| field should never point to such an edge header. +Note that memory is allocated for |start_x(null_dash)| and we are free to +give it any convenient value. + +@<Finish printing the dash pattern that |p| refers to@>= +ok_to_dash=pen_is_elliptical(mp_pen_p(p)); +if ( ! ok_to_dash ) scf=unity; else scf=dash_scale(p); +hh=mp_dash_p(p); +pp=dash_list(hh); +if ( (pp==null_dash) || (dash_y(hh)<0) ) { + mp_print(mp, " ??"); +} else { start_x(null_dash)=start_x(pp)+dash_y(hh); + while ( pp!=null_dash ) { + mp_print(mp, "on "); + mp_print_scaled(mp, mp_take_scaled(mp, stop_x(pp)-start_x(pp),scf)); + mp_print(mp, " off "); + mp_print_scaled(mp, mp_take_scaled(mp, start_x(mp_link(pp))-stop_x(pp),scf)); + pp = mp_link(pp); + if ( pp!=null_dash ) mp_print_char(mp, xord(' ')); + } + mp_print(mp, ") shifted "); + mp_print_scaled(mp, -mp_take_scaled(mp, mp_dash_offset(mp, hh),scf)); + if ( ! ok_to_dash || (dash_y(hh)==0) ) mp_print(mp, " (this will be ignored)"); +} + +@ @<Declarations@>= +static scaled mp_dash_offset (MP mp,pointer h) ; + +@ @c +scaled mp_dash_offset (MP mp,pointer h) { + scaled x; /* the answer */ + if (dash_list(h)==null_dash || dash_y(h)<0) mp_confusion(mp, "dash0"); +@:this can't happen dash0}{\quad dash0@> + if ( dash_y(h)==0 ) { + x=0; + } else { + x=-(start_x(dash_list(h)) % dash_y(h)); + if ( x<0 ) x=x+dash_y(h); + } + return x; +} + +@ @<Cases for printing graphical object node |p|@>= +case mp_text_code: + mp_print_char(mp, xord('"')); mp_print_str(mp,mp_text_p(p)); + mp_print(mp, "\" infont \""); mp_print(mp, mp->font_name[mp_font_n(p)]); + mp_print_char(mp, xord('"')); mp_print_ln(mp); + mp_print_obj_color(mp, p); + mp_print(mp, "transformed "); + mp_print_compact_node(mp, text_tx_loc(p),6); + break; + +@ @<Cases for printing graphical object node |p|@>= +case mp_start_clip_code: + mp_print(mp, "clipping path:"); + mp_print_ln(mp); + mp_pr_path(mp, mp_path_p(p)); + break; +case mp_stop_clip_code: + mp_print(mp, "stop clipping"); + break; + +@ @<Cases for printing graphical object node |p|@>= +case mp_start_bounds_code: + mp_print(mp, "setbounds path:"); + mp_print_ln(mp); + mp_pr_path(mp, mp_path_p(p)); + break; +case mp_stop_bounds_code: + mp_print(mp, "end of setbounds"); + break; + +@ To initialize the |dash_list| field in an edge header~|h|, we need a +subroutine that scans an edge structure and tries to interpret it as a dash +pattern. This can only be done when there are no filled regions or clipping +paths and all the pen strokes have the same color. The first step is to let +$y_0$ be the initial $y$~coordinate of the first pen stroke. Then we implicitly +project all the pen stroke paths onto the line $y=y_0$ and require that there +be no retracing. If the resulting paths cover a range of $x$~coordinates of +length $\Delta x$, we set |dash_y(h)| to the length of the dash pattern by +finding the maximum of $\Delta x$ and the absolute value of~$y_0$. + +@c +static pointer mp_make_dashes (MP mp,pointer h) { /* returns |h| or |null| */ + pointer p; /* this scans the stroked nodes in the object list */ + pointer p0; /* if not |null| this points to the first stroked node */ + pointer pp,qq,rr; /* pointers into |mp_path_p(p)| */ + pointer d,dd; /* pointers used to create the dash list */ + scaled y0; + @<Other local variables in |make_dashes|@>; + y0=0; /* the initial $y$ coordinate */ + if ( dash_list(h)!=null_dash ) + return h; + p0=null; + p=mp_link(dummy_loc(h)); + while ( p!=null ) { + if ( mp_type(p)!=mp_stroked_code ) { + @<Compain that the edge structure contains a node of the wrong type + and |goto not_found|@>; + } + pp=mp_path_p(p); + if ( p0==null ){ p0=p; y0=mp_y_coord(pp); }; + @<Make |d| point to a new dash node created from stroke |p| and path |pp| + or |goto not_found| if there is an error@>; + @<Insert |d| into the dash list and |goto not_found| if there is an error@>; + p=mp_link(p); + } + if ( dash_list(h)==null_dash ) + goto NOT_FOUND; /* No error message */ + @<Scan |dash_list(h)| and deal with any dashes that are themselves dashed@>; + @<Set |dash_y(h)| and merge the first and last dashes if necessary@>; + return h; +NOT_FOUND: + @<Flush the dash list, recycle |h| and return |null|@>; +} + +@ @<Compain that the edge structure contains a node of the wrong type...@>= +{ +print_err("Picture is too complicated to use as a dash pattern"); +help3("When you say `dashed p', picture p should not contain any", + "text, filled regions, or clipping paths. This time it did", + "so I'll just make it a solid line instead."); +mp_put_get_error(mp); +goto NOT_FOUND; +} + +@ A similar error occurs when monotonicity fails. + +@<Declarations@>= +static void mp_x_retrace_error (MP mp) ; + +@ @c +void mp_x_retrace_error (MP mp) { +print_err("Picture is too complicated to use as a dash pattern"); +help3("When you say `dashed p', every path in p should be monotone", + "in x and there must be no overlapping. This failed", + "so I'll just make it a solid line instead."); +mp_put_get_error(mp); +} + +@ We stash |p| in |mp_info(d)| if |mp_dash_p(p)<>0| so that subsequent processing can +handle the case where the pen stroke |p| is itself dashed. + +@<Make |d| point to a new dash node created from stroke |p| and path...@>= +@<Make sure |p| and |p0| are the same color and |goto not_found| if there is + an error@>; +rr=pp; +if ( mp_link(pp)!=pp ) { + do { + qq=rr; rr=mp_link(rr); + @<Check for retracing between knots |qq| and |rr| and |goto not_found| + if there is a problem@>; + } while (mp_right_type(rr)!=mp_endpoint); +} +d=mp_get_node(mp, dash_node_size); +if ( mp_dash_p(p)==0 ) mp_info(d)=0; else mp_info(d)=p; +if ( mp_x_coord(pp)<mp_x_coord(rr) ) { + start_x(d)=mp_x_coord(pp); + stop_x(d)=mp_x_coord(rr); +} else { + start_x(d)=mp_x_coord(rr); + stop_x(d)=mp_x_coord(pp); +} + +@ We also need to check for the case where the segment from |qq| to |rr| is +monotone in $x$ but is reversed relative to the path from |pp| to |qq|. + +@<Check for retracing between knots |qq| and |rr| and |goto not_found|...@>= +x0=mp_x_coord(qq); +x1=mp_right_x(qq); +x2=mp_left_x(rr); +x3=mp_x_coord(rr); +if ( (x0>x1) || (x1>x2) || (x2>x3) ) { + if ( (x0<x1) || (x1<x2) || (x2<x3) ) { + if ( mp_ab_vs_cd(mp, x2-x1,x2-x1,x1-x0,x3-x2)>0 ) { + mp_x_retrace_error(mp); goto NOT_FOUND; + } + } +} +if ( (mp_x_coord(pp)>x0) || (x0>x3) ) { + if ( (mp_x_coord(pp)<x0) || (x0<x3) ) { + mp_x_retrace_error(mp); goto NOT_FOUND; + } +} + +@ @<Other local variables in |make_dashes|@>= + scaled x0,x1,x2,x3; /* $x$ coordinates of the segment from |qq| to |rr| */ + +@ @<Make sure |p| and |p0| are the same color and |goto not_found|...@>= +if ( (red_val(p)!=red_val(p0)) || (black_val(p)!=black_val(p0)) || + (green_val(p)!=green_val(p0)) || (blue_val(p)!=blue_val(p0)) ) { + print_err("Picture is too complicated to use as a dash pattern"); + help3("When you say `dashed p', everything in picture p should", + "be the same color. I can\'t handle your color changes", + "so I'll just make it a solid line instead."); + mp_put_get_error(mp); + goto NOT_FOUND; +} + +@ @<Insert |d| into the dash list and |goto not_found| if there is an error@>= +start_x(null_dash)=stop_x(d); +dd=h; /* this makes |mp_link(dd)=dash_list(h)| */ +while ( start_x(mp_link(dd))<stop_x(d) ) + dd=mp_link(dd); +if ( dd!=h ) { + if ( (stop_x(dd)>start_x(d)) ) + { mp_x_retrace_error(mp); goto NOT_FOUND; }; +} +mp_link(d)=mp_link(dd); +mp_link(dd)=d + +@ @<Set |dash_y(h)| and merge the first and last dashes if necessary@>= +d=dash_list(h); +while ( (mp_link(d)!=null_dash) ) + d=mp_link(d); +dd=dash_list(h); +dash_y(h)=stop_x(d)-start_x(dd); +if ( abs(y0)>dash_y(h) ) { + dash_y(h)=abs(y0); +} else if ( d!=dd ) { + dash_list(h)=mp_link(dd); + stop_x(d)=stop_x(dd)+dash_y(h); + mp_free_node(mp, dd,dash_node_size); +} + +@ We get here when the argument is a null picture or when there is an error. +Recovering from an error involves making |dash_list(h)| empty to indicate +that |h| is not known to be a valid dash pattern. We also dereference |h| +since it is not being used for the return value. + +@<Flush the dash list, recycle |h| and return |null|@>= +mp_flush_dash_list(mp, h); +delete_edge_ref(h); +return null + +@ Having carefully saved the dashed stroked nodes in the +corresponding dash nodes, we must be prepared to break up these dashes into +smaller dashes. + +@<Scan |dash_list(h)| and deal with any dashes that are themselves dashed@>= +d=h; /* now |mp_link(d)=dash_list(h)| */ +while ( mp_link(d)!=null_dash ) { + ds=mp_info(mp_link(d)); + if ( ds==null ) { + d=mp_link(d); + } else { + hh=mp_dash_p(ds); + hsf=dash_scale(ds); + if ( (hh==null) ) mp_confusion(mp, "dash1"); +@:this can't happen dash0}{\quad dash1@> + if ( dash_y(hh)==0 ) { + d=mp_link(d); + } else { + if ( dash_list(hh)==null ) mp_confusion(mp, "dash1"); +@:this can't happen dash0}{\quad dash1@> + @<Replace |mp_link(d)| by a dashed version as determined by edge header + |hh| and scale factor |ds|@>; + } + } +} + +@ @<Other local variables in |make_dashes|@>= +pointer dln; /* |mp_link(d)| */ +pointer hh; /* an edge header that tells how to break up |dln| */ +scaled hsf; /* the dash pattern from |hh| gets scaled by this */ +pointer ds; /* the stroked node from which |hh| and |hsf| are derived */ +scaled xoff; /* added to $x$ values in |dash_list(hh)| to match |dln| */ + +@ @<Replace |mp_link(d)| by a dashed version as determined by edge header...@>= +dln=mp_link(d); +dd=dash_list(hh); +xoff=start_x(dln)-mp_take_scaled(mp, hsf,start_x(dd))- + mp_take_scaled(mp, hsf,mp_dash_offset(mp, hh)); +start_x(null_dash)=mp_take_scaled(mp, hsf,start_x(dd)) + +mp_take_scaled(mp, hsf,dash_y(hh)); +stop_x(null_dash)=start_x(null_dash); +@<Advance |dd| until finding the first dash that overlaps |dln| when + offset by |xoff|@>; +while ( start_x(dln)<=stop_x(dln) ) { + @<If |dd| has `fallen off the end', back up to the beginning and fix |xoff|@>; + @<Insert a dash between |d| and |dln| for the overlap with the offset version + of |dd|@>; + dd=mp_link(dd); + start_x(dln)=xoff+mp_take_scaled(mp, hsf,start_x(dd)); +} +mp_link(d)=mp_link(dln); +mp_free_node(mp, dln,dash_node_size) + +@ The name of this module is a bit of a lie because we just find the +first |dd| where |take_scaled (hsf, stop_x(dd))| is large enough to make an +overlap possible. It could be that the unoffset version of dash |dln| falls +in the gap between |dd| and its predecessor. + +@<Advance |dd| until finding the first dash that overlaps |dln| when...@>= +while ( xoff+mp_take_scaled(mp, hsf,stop_x(dd))<start_x(dln) ) { + dd=mp_link(dd); +} + +@ @<If |dd| has `fallen off the end', back up to the beginning and fix...@>= +if ( dd==null_dash ) { + dd=dash_list(hh); + xoff=xoff+mp_take_scaled(mp, hsf,dash_y(hh)); +} + +@ At this point we already know that +|start_x(dln)<=xoff+take_scaled(hsf,stop_x(dd))|. + +@<Insert a dash between |d| and |dln| for the overlap with the offset...@>= +if ( (xoff+mp_take_scaled(mp, hsf,start_x(dd)))<=stop_x(dln) ) { + mp_link(d)=mp_get_node(mp, dash_node_size); + d=mp_link(d); + mp_link(d)=dln; + if ( start_x(dln)>(xoff+mp_take_scaled(mp, hsf,start_x(dd)))) + start_x(d)=start_x(dln); + else + start_x(d)=xoff+mp_take_scaled(mp, hsf,start_x(dd)); + if ( stop_x(dln)<(xoff+mp_take_scaled(mp, hsf,stop_x(dd)))) + stop_x(d)=stop_x(dln); + else + stop_x(d)=xoff+mp_take_scaled(mp, hsf,stop_x(dd)); +} + +@ The next major task is to update the bounding box information in an edge +header~|h|. This is done via a procedure |adjust_bbox| that enlarges an edge +header's bounding box to accommodate the box computed by |path_bbox| or +|pen_bbox|. (This is stored in global variables |minx|, |miny|, |maxx|, and +|maxy|.) + +@c static void mp_adjust_bbox (MP mp,pointer h) { + if ( mp_minx<minx_val(h) ) minx_val(h)=mp_minx; + if ( mp_miny<miny_val(h) ) miny_val(h)=mp_miny; + if ( mp_maxx>maxx_val(h) ) maxx_val(h)=mp_maxx; + if ( mp_maxy>maxy_val(h) ) maxy_val(h)=mp_maxy; +} + +@ Here is a special routine for updating the bounding box information in +edge header~|h| to account for the squared-off ends of a non-cyclic path~|p| +that is to be stroked with the pen~|pp|. + +@c static void mp_box_ends (MP mp, pointer p, pointer pp, pointer h) { + pointer q; /* a knot node adjacent to knot |p| */ + fraction dx,dy; /* a unit vector in the direction out of the path at~|p| */ + scaled d; /* a factor for adjusting the length of |(dx,dy)| */ + scaled z; /* a coordinate being tested against the bounding box */ + scaled xx,yy; /* the extreme pen vertex in the |(dx,dy)| direction */ + integer i; /* a loop counter */ + if ( mp_right_type(p)!=mp_endpoint ) { + q=mp_link(p); + while (1) { + @<Make |(dx,dy)| the final direction for the path segment from + |q| to~|p|; set~|d|@>; + d=mp_pyth_add(mp, dx,dy); + if ( d>0 ) { + @<Normalize the direction |(dx,dy)| and find the pen offset |(xx,yy)|@>; + for (i=1;i<= 2;i++) { + @<Use |(dx,dy)| to generate a vertex of the square end cap and + update the bounding box to accommodate it@>; + dx=-dx; dy=-dy; + } + } + if ( mp_right_type(p)==mp_endpoint ) { + return; + } else { + @<Advance |p| to the end of the path and make |q| the previous knot@>; + } + } + } +} + +@ @<Make |(dx,dy)| the final direction for the path segment from...@>= +if ( q==mp_link(p) ) { + dx=mp_x_coord(p)-mp_right_x(p); + dy=mp_y_coord(p)-mp_right_y(p); + if ( (dx==0)&&(dy==0) ) { + dx=mp_x_coord(p)-mp_left_x(q); + dy=mp_y_coord(p)-mp_left_y(q); + } +} else { + dx=mp_x_coord(p)-mp_left_x(p); + dy=mp_y_coord(p)-mp_left_y(p); + if ( (dx==0)&&(dy==0) ) { + dx=mp_x_coord(p)-mp_right_x(q); + dy=mp_y_coord(p)-mp_right_y(q); + } +} +dx=mp_x_coord(p)-mp_x_coord(q); +dy=mp_y_coord(p)-mp_y_coord(q) + +@ @<Normalize the direction |(dx,dy)| and find the pen offset |(xx,yy)|@>= +dx=mp_make_fraction(mp, dx,d); +dy=mp_make_fraction(mp, dy,d); +mp_find_offset(mp, -dy,dx,pp); +xx=mp->cur_x; yy=mp->cur_y + +@ @<Use |(dx,dy)| to generate a vertex of the square end cap and...@>= +mp_find_offset(mp, dx,dy,pp); +d=mp_take_fraction(mp, xx-mp->cur_x,dx)+mp_take_fraction(mp, yy-mp->cur_y,dy); +if ( ((d<0)&&(i==1)) || ((d>0)&&(i==2))) + mp_confusion(mp, "box_ends"); +@:this can't happen box ends}{\quad\\{box\_ends}@> +z=mp_x_coord(p)+mp->cur_x+mp_take_fraction(mp, d,dx); +if ( z<minx_val(h) ) minx_val(h)=z; +if ( z>maxx_val(h) ) maxx_val(h)=z; +z=mp_y_coord(p)+mp->cur_y+mp_take_fraction(mp, d,dy); +if ( z<miny_val(h) ) miny_val(h)=z; +if ( z>maxy_val(h) ) maxy_val(h)=z + +@ @<Advance |p| to the end of the path and make |q| the previous knot@>= +do { + q=p; + p=mp_link(p); +} while (mp_right_type(p)!=mp_endpoint) + +@ The major difficulty in finding the bounding box of an edge structure is the +effect of clipping paths. We treat them conservatively by only clipping to the +clipping path's bounding box, but this still +requires recursive calls to |set_bbox| in order to find the bounding box of +@^recursion@> +the objects to be clipped. Such calls are distinguished by the fact that the +boolean parameter |top_level| is false. + +@c +void mp_set_bbox (MP mp,pointer h, boolean top_level) { + pointer p; /* a graphical object being considered */ + scaled sminx,sminy,smaxx,smaxy; + /* for saving the bounding box during recursive calls */ + scaled x0,x1,y0,y1; /* temporary registers */ + integer lev; /* nesting level for |mp_start_bounds_code| nodes */ + @<Wipe out any existing bounding box information if |bbtype(h)| is + incompatible with |internal[mp_true_corners]|@>; + while ( mp_link(bblast(h))!=null ) { + p=mp_link(bblast(h)); + bblast(h)=p; + switch (mp_type(p)) { + case mp_stop_clip_code: + if ( top_level ) mp_confusion(mp, "bbox"); else return; +@:this can't happen bbox}{\quad bbox@> + break; + @<Other cases for updating the bounding box based on the type of object |p|@>; + } /* all cases are enumerated above */ + } + if ( ! top_level ) mp_confusion(mp, "bbox"); +} + +@ @<Declarations@>= +static void mp_set_bbox (MP mp,pointer h, boolean top_level); + +@ @<Wipe out any existing bounding box information if |bbtype(h)| is...@>= +switch (bbtype(h)) { +case no_bounds: + break; +case bounds_set: + if ( mp->internal[mp_true_corners]>0 ) mp_init_bbox(mp, h); + break; +case bounds_unset: + if ( mp->internal[mp_true_corners]<=0 ) mp_init_bbox(mp, h); + break; +} /* there are no other cases */ + +@ @<Other cases for updating the bounding box...@>= +case mp_fill_code: + mp_path_bbox(mp, mp_path_p(p)); + if ( mp_pen_p(p)!=null ) { + x0=mp_minx; y0=mp_miny; + x1=mp_maxx; y1=mp_maxy; + mp_pen_bbox(mp, mp_pen_p(p)); + mp_minx=mp_minx+x0; + mp_miny=mp_miny+y0; + mp_maxx=mp_maxx+x1; + mp_maxy=mp_maxy+y1; + } + mp_adjust_bbox(mp, h); + break; + +@ @<Other cases for updating the bounding box...@>= +case mp_start_bounds_code: + if ( mp->internal[mp_true_corners]>0 ) { + bbtype(h)=bounds_unset; + } else { + bbtype(h)=bounds_set; + mp_path_bbox(mp, mp_path_p(p)); + mp_adjust_bbox(mp, h); + @<Scan to the matching |mp_stop_bounds_code| node and update |p| and + |bblast(h)|@>; + } + break; +case mp_stop_bounds_code: + if ( mp->internal[mp_true_corners]<=0 ) mp_confusion(mp, "bbox2"); +@:this can't happen bbox2}{\quad bbox2@> + break; + +@ @<Scan to the matching |mp_stop_bounds_code| node and update |p| and...@>= +lev=1; +while ( lev!=0 ) { + if ( mp_link(p)==null ) mp_confusion(mp, "bbox2"); +@:this can't happen bbox2}{\quad bbox2@> + p=mp_link(p); + if ( mp_type(p)==mp_start_bounds_code ) incr(lev); + else if ( mp_type(p)==mp_stop_bounds_code ) decr(lev); +} +bblast(h)=p + +@ It saves a lot of grief here to be slightly conservative and not account for +omitted parts of dashed lines. We also don't worry about the material omitted +when using butt end caps. The basic computation is for round end caps and +|box_ends| augments it for square end caps. + +@<Other cases for updating the bounding box...@>= +case mp_stroked_code: + mp_path_bbox(mp, mp_path_p(p)); + x0=mp_minx; y0=mp_miny; + x1=mp_maxx; y1=mp_maxy; + mp_pen_bbox(mp, mp_pen_p(p)); + mp_minx=mp_minx+x0; + mp_miny=mp_miny+y0; + mp_maxx=mp_maxx+x1; + mp_maxy=mp_maxy+y1; + mp_adjust_bbox(mp, h); + if ( (mp_left_type(mp_path_p(p))==mp_endpoint)&&(lcap_val(p)==2) ) + mp_box_ends(mp, mp_path_p(p), mp_pen_p(p), h); + break; + +@ The height width and depth information stored in a text node determines a +rectangle that needs to be transformed according to the transformation +parameters stored in the text node. + +@<Other cases for updating the bounding box...@>= +case mp_text_code: + x1=mp_take_scaled(mp, txx_val(p),width_val(p)); + y0=mp_take_scaled(mp, txy_val(p),-depth_val(p)); + y1=mp_take_scaled(mp, txy_val(p),height_val(p)); + mp_minx=tx_val(p); + mp_maxx=mp_minx; + if ( y0<y1 ) { mp_minx=mp_minx+y0; mp_maxx=mp_maxx+y1; } + else { mp_minx=mp_minx+y1; mp_maxx=mp_maxx+y0; } + if ( x1<0 ) mp_minx=mp_minx+x1; else mp_maxx=mp_maxx+x1; + x1=mp_take_scaled(mp, tyx_val(p),width_val(p)); + y0=mp_take_scaled(mp, tyy_val(p),-depth_val(p)); + y1=mp_take_scaled(mp, tyy_val(p),height_val(p)); + mp_miny=ty_val(p); + mp_maxy=mp_miny; + if ( y0<y1 ) { mp_miny=mp_miny+y0; mp_maxy=mp_maxy+y1; } + else { mp_miny=mp_miny+y1; mp_maxy=mp_maxy+y0; } + if ( x1<0 ) mp_miny=mp_miny+x1; else mp_maxy=mp_maxy+x1; + mp_adjust_bbox(mp, h); + break; + +@ This case involves a recursive call that advances |bblast(h)| to the node of +type |mp_stop_clip_code| that matches |p|. + +@<Other cases for updating the bounding box...@>= +case mp_start_clip_code: + mp_path_bbox(mp, mp_path_p(p)); + x0=mp_minx; y0=mp_miny; + x1=mp_maxx; y1=mp_maxy; + sminx=minx_val(h); sminy=miny_val(h); + smaxx=maxx_val(h); smaxy=maxy_val(h); + @<Reinitialize the bounding box in header |h| and call |set_bbox| recursively + starting at |mp_link(p)|@>; + @<Clip the bounding box in |h| to the rectangle given by |x0|, |x1|, + |y0|, |y1|@>; + mp_minx=sminx; mp_miny=sminy; + mp_maxx=smaxx; mp_maxy=smaxy; + mp_adjust_bbox(mp, h); + break; + +@ @<Reinitialize the bounding box in header |h| and call |set_bbox|...@>= +minx_val(h)=el_gordo; +miny_val(h)=el_gordo; +maxx_val(h)=-el_gordo; +maxy_val(h)=-el_gordo; +mp_set_bbox(mp, h,false) + +@ @<Clip the bounding box in |h| to the rectangle given by |x0|, |x1|,...@>= +if ( minx_val(h)<x0 ) minx_val(h)=x0; +if ( miny_val(h)<y0 ) miny_val(h)=y0; +if ( maxx_val(h)>x1 ) maxx_val(h)=x1; +if ( maxy_val(h)>y1 ) maxy_val(h)=y1 + +@* \[22] Finding an envelope. +When \MP\ has a path and a polygonal pen, it needs to express the desired +shape in terms of things \ps\ can understand. The present task is to compute +a new path that describes the region to be filled. It is convenient to +define this as a two step process where the first step is determining what +offset to use for each segment of the path. + +@ Given a pointer |c| to a cyclic path, +and a pointer~|h| to the first knot of a pen polygon, +the |offset_prep| routine changes the path into cubics that are +associated with particular pen offsets. Thus if the cubic between |p| +and~|q| is associated with the |k|th offset and the cubic between |q| and~|r| +has offset |l| then |mp_info(q)=zero_off+l-k|. (The constant |zero_off| is added +to because |l-k| could be negative.) + +After overwriting the type information with offset differences, we no longer +have a true path so we refer to the knot list returned by |offset_prep| as an +``envelope spec.'' +@^envelope spec@> +Since an envelope spec only determines relative changes in pen offsets, +|offset_prep| sets a global variable |spec_offset| to the relative change from +|h| to the first offset. + +@d zero_off 16384 /* added to offset changes to make them positive */ + +@<Glob...@>= +integer spec_offset; /* number of pen edges between |h| and the initial offset */ + +@ @c +static pointer mp_offset_prep (MP mp,pointer c, pointer h) { + halfword n; /* the number of vertices in the pen polygon */ + pointer c0,p,q,q0,r,w, ww; /* for list manipulation */ + integer k_needed; /* amount to be added to |mp_info(p)| when it is computed */ + pointer w0; /* a pointer to pen offset to use just before |p| */ + scaled dxin,dyin; /* the direction into knot |p| */ + integer turn_amt; /* change in pen offsets for the current cubic */ + @<Other local variables for |offset_prep|@>; + dx0=0; dy0=0; + @<Initialize the pen size~|n|@>; + @<Initialize the incoming direction and pen offset at |c|@>; + p=c; c0=c; k_needed=0; + do { + q=mp_link(p); + @<Split the cubic between |p| and |q|, if necessary, into cubics + associated with single offsets, after which |q| should + point to the end of the final such cubic@>; + NOT_FOUND: + @<Advance |p| to node |q|, removing any ``dead'' cubics that + might have been introduced by the splitting process@>; + } while (q!=c); + @<Fix the offset change in |mp_info(c)| and set |c| to the return value of + |offset_prep|@>; + return c; +} + +@ We shall want to keep track of where certain knots on the cyclic path +wind up in the envelope spec. It doesn't suffice just to keep pointers to +knot nodes because some nodes are deleted while removing dead cubics. Thus +|offset_prep| updates the following pointers + +@<Glob...@>= +pointer spec_p1; +pointer spec_p2; /* pointers to distinguished knots */ + +@ @<Set init...@>= +mp->spec_p1=null; mp->spec_p2=null; + +@ @<Initialize the pen size~|n|@>= +n=0; p=h; +do { + incr(n); + p=mp_link(p); +} while (p!=h) + +@ Since the true incoming direction isn't known yet, we just pick a direction +consistent with the pen offset~|h|. If this is wrong, it can be corrected +later. + +@<Initialize the incoming direction and pen offset at |c|@>= +dxin=mp_x_coord(mp_link(h))-mp_x_coord(knil(h)); +dyin=mp_y_coord(mp_link(h))-mp_y_coord(knil(h)); +if ( (dxin==0)&&(dyin==0) ) { + dxin=mp_y_coord(knil(h))-mp_y_coord(h); + dyin=mp_x_coord(h)-mp_x_coord(knil(h)); +} +w0=h + +@ We must be careful not to remove the only cubic in a cycle. + +But we must also be careful for another reason. If the user-supplied +path starts with a set of degenerate cubics, the target node |q| can +be collapsed to the initial node |p| which might be the same as the +initial node |c| of the curve. This would cause the |offset_prep| routine +to bail out too early, causing distress later on. (See for example +the testcase reported by Bogus\l{}aw Jackowski in tracker id 267, case 52c +on Sarovar.) + +@<Advance |p| to node |q|, removing any ``dead'' cubics...@>= +q0=q; +do { + r=mp_link(p); + if ( mp_x_coord(p)==mp_right_x(p) && mp_y_coord(p)==mp_right_y(p) && + mp_x_coord(p)==mp_left_x(r) && mp_y_coord(p)==mp_left_y(r) && + mp_x_coord(p)==mp_x_coord(r) && mp_y_coord(p)==mp_y_coord(r) && + r!=p ) { + @<Remove the cubic following |p| and update the data structures + to merge |r| into |p|@>; + } + p=r; +} while (p!=q); +/* Check if we removed too much */ +if ((q!=q0)&&(q!=c||c==c0)) + q = mp_link(q) + +@ @<Remove the cubic following |p| and update the data structures...@>= +{ k_needed=mp_info(p)-zero_off; + if ( r==q ) { + q=p; + } else { + mp_info(p)=k_needed+mp_info(r); + k_needed=0; + }; + if ( r==c ) { mp_info(p)=mp_info(c); c=p; }; + if ( r==mp->spec_p1 ) mp->spec_p1=p; + if ( r==mp->spec_p2 ) mp->spec_p2=p; + r=p; mp_remove_cubic(mp, p); +} + +@ Not setting the |info| field of the newly created knot allows the splitting +routine to work for paths. + +@<Declarations@>= +static void mp_split_cubic (MP mp,pointer p, fraction t) ; + +@ @c +void mp_split_cubic (MP mp,pointer p, fraction t) { /* splits the cubic after |p| */ + scaled v; /* an intermediate value */ + pointer q,r; /* for list manipulation */ + q=mp_link(p); r=mp_get_node(mp, knot_node_size); mp_link(p)=r; mp_link(r)=q; + mp_originator(r)=mp_program_code; + mp_left_type(r)=mp_explicit; mp_right_type(r)=mp_explicit; + v=t_of_the_way(mp_right_x(p),mp_left_x(q)); + mp_right_x(p)=t_of_the_way(mp_x_coord(p),mp_right_x(p)); + mp_left_x(q)=t_of_the_way(mp_left_x(q),mp_x_coord(q)); + mp_left_x(r)=t_of_the_way(mp_right_x(p),v); + mp_right_x(r)=t_of_the_way(v,mp_left_x(q)); + mp_x_coord(r)=t_of_the_way(mp_left_x(r),mp_right_x(r)); + v=t_of_the_way(mp_right_y(p),mp_left_y(q)); + mp_right_y(p)=t_of_the_way(mp_y_coord(p),mp_right_y(p)); + mp_left_y(q)=t_of_the_way(mp_left_y(q),mp_y_coord(q)); + mp_left_y(r)=t_of_the_way(mp_right_y(p),v); + mp_right_y(r)=t_of_the_way(v,mp_left_y(q)); + mp_y_coord(r)=t_of_the_way(mp_left_y(r),mp_right_y(r)); +} + +@ This does not set |mp_info(p)| or |mp_right_type(p)|. + +@<Declarations@>= +static void mp_remove_cubic (MP mp,pointer p) ; + +@ @c +void mp_remove_cubic (MP mp,pointer p) { /* removes the dead cubic following~|p| */ + pointer q; /* the node that disappears */ + q=mp_link(p); mp_link(p)=mp_link(q); + mp_right_x(p)=mp_right_x(q); mp_right_y(p)=mp_right_y(q); + mp_free_node(mp, q,knot_node_size); +} + +@ Let $d\prec d'$ mean that the counter-clockwise angle from $d$ to~$d'$ is +strictly between zero and $180^\circ$. Then we can define $d\preceq d'$ to +mean that the angle could be zero or $180^\circ$. If $w_k=(u_k,v_k)$ is the +$k$th pen offset, the $k$th pen edge direction is defined by the formula +$$d_k=(u\k-u_k,\,v\k-v_k).$$ +When listed by increasing $k$, these directions occur in counter-clockwise +order so that $d_k\preceq d\k$ for all~$k$. +The goal of |offset_prep| is to find an offset index~|k| to associate with +each cubic, such that the direction $d(t)$ of the cubic satisfies +$$d_{k-1}\preceq d(t)\preceq d_k\qquad\hbox{for $0\le t\le 1$.}\eqno(*)$$ +We may have to split a cubic into many pieces before each +piece corresponds to a unique offset. + +@<Split the cubic between |p| and |q|, if necessary, into cubics...@>= +mp_info(p)=zero_off+k_needed; +k_needed=0; +@<Prepare for derivative computations; + |goto not_found| if the current cubic is dead@>; +@<Find the initial direction |(dx,dy)|@>; +@<Update |mp_info(p)| and find the offset $w_k$ such that + $d_{k-1}\preceq(\\{dx},\\{dy})\prec d_k$; also advance |w0| for + the direction change at |p|@>; +@<Find the final direction |(dxin,dyin)|@>; +@<Decide on the net change in pen offsets and set |turn_amt|@>; +@<Complete the offset splitting process@>; +w0=mp_pen_walk(mp, w0,turn_amt) + +@ @<Declarations@>= +static pointer mp_pen_walk (MP mp,pointer w, integer k) ; + +@ @c +pointer mp_pen_walk (MP mp,pointer w, integer k) { + /* walk |k| steps around a pen from |w| */ + while ( k>0 ) { w=mp_link(w); decr(k); }; + while ( k<0 ) { w=knil(w); incr(k); }; + return w; +} + +@ The direction of a cubic $B(z_0,z_1,z_2,z_3;t)=\bigl(x(t),y(t)\bigr)$ can be +calculated from the quadratic polynomials +${1\over3}x'(t)=B(x_1-x_0,x_2-x_1,x_3-x_2;t)$ and +${1\over3}y'(t)=B(y_1-y_0,y_2-y_1,y_3-y_2;t)$. +Since we may be calculating directions from several cubics +split from the current one, it is desirable to do these calculations +without losing too much precision. ``Scaled up'' values of the +derivatives, which will be less tainted by accumulated errors than +derivatives found from the cubics themselves, are maintained in +local variables |x0|, |x1|, and |x2|, representing $X_0=2^l(x_1-x_0)$, +$X_1=2^l(x_2-x_1)$, and $X_2=2^l(x_3-x_2)$; similarly |y0|, |y1|, and~|y2| +represent $Y_0=2^l(y_1-y_0)$, $Y_1=2^l(y_2-y_1)$, and $Y_2=2^l(y_3-y_2)$. + +@<Other local variables for |offset_prep|@>= +integer x0,x1,x2,y0,y1,y2; /* representatives of derivatives */ +integer t0,t1,t2; /* coefficients of polynomial for slope testing */ +integer du,dv,dx,dy; /* for directions of the pen and the curve */ +integer dx0,dy0; /* initial direction for the first cubic in the curve */ +integer max_coef; /* used while scaling */ +integer x0a,x1a,x2a,y0a,y1a,y2a; /* intermediate values */ +fraction t; /* where the derivative passes through zero */ +fraction s; /* a temporary value */ + +@ @<Prepare for derivative computations...@>= +x0=mp_right_x(p)-mp_x_coord(p); +x2=mp_x_coord(q)-mp_left_x(q); +x1=mp_left_x(q)-mp_right_x(p); +y0=mp_right_y(p)-mp_y_coord(p); y2=mp_y_coord(q)-mp_left_y(q); +y1=mp_left_y(q)-mp_right_y(p); +max_coef=abs(x0); +if ( abs(x1)>max_coef ) max_coef=abs(x1); +if ( abs(x2)>max_coef ) max_coef=abs(x2); +if ( abs(y0)>max_coef ) max_coef=abs(y0); +if ( abs(y1)>max_coef ) max_coef=abs(y1); +if ( abs(y2)>max_coef ) max_coef=abs(y2); +if ( max_coef==0 ) goto NOT_FOUND; +while ( max_coef<fraction_half ) { + double(max_coef); + double(x0); double(x1); double(x2); + double(y0); double(y1); double(y2); +} + +@ Let us first solve a special case of the problem: Suppose we +know an index~$k$ such that either (i)~$d(t)\succeq d_{k-1}$ for all~$t$ +and $d(0)\prec d_k$, or (ii)~$d(t)\preceq d_k$ for all~$t$ and +$d(0)\succ d_{k-1}$. +Then, in a sense, we're halfway done, since one of the two relations +in $(*)$ is satisfied, and the other couldn't be satisfied for +any other value of~|k|. + +Actually, the conditions can be relaxed somewhat since a relation such as +$d(t)\succeq d_{k-1}$ restricts $d(t)$ to a half plane when all that really +matters is whether $d(t)$ crosses the ray in the $d_{k-1}$ direction from +the origin. The condition for case~(i) becomes $d_{k-1}\preceq d(0)\prec d_k$ +and $d(t)$ never crosses the $d_{k-1}$ ray in the clockwise direction. +Case~(ii) is similar except $d(t)$ cannot cross the $d_k$ ray in the +counterclockwise direction. + +The |fin_offset_prep| subroutine solves the stated subproblem. +It has a parameter called |rise| that is |1| in +case~(i), |-1| in case~(ii). Parameters |x0| through |y2| represent +the derivative of the cubic following |p|. +The |w| parameter should point to offset~$w_k$ and |mp_info(p)| should already +be set properly. The |turn_amt| parameter gives the absolute value of the +overall net change in pen offsets. + +@<Declarations@>= +static void mp_fin_offset_prep (MP mp,pointer p, pointer w, integer + x0,integer x1, integer x2, integer y0, integer y1, integer y2, + integer rise, integer turn_amt) ; + +@ @c +void mp_fin_offset_prep (MP mp,pointer p, pointer w, integer + x0,integer x1, integer x2, integer y0, integer y1, integer y2, + integer rise, integer turn_amt) { + pointer ww; /* for list manipulation */ + scaled du,dv; /* for slope calculation */ + integer t0,t1,t2; /* test coefficients */ + fraction t; /* place where the derivative passes a critical slope */ + fraction s; /* slope or reciprocal slope */ + integer v; /* intermediate value for updating |x0..y2| */ + pointer q; /* original |mp_link(p)| */ + q=mp_link(p); + while (1) { + if ( rise>0 ) ww=mp_link(w); /* a pointer to $w\k$ */ + else ww=knil(w); /* a pointer to $w_{k-1}$ */ + @<Compute test coefficients |(t0,t1,t2)| + for $d(t)$ versus $d_k$ or $d_{k-1}$@>; + t=mp_crossing_point(mp, t0,t1,t2); + if ( t>=fraction_one ) { + if ( turn_amt>0 ) t=fraction_one; else return; + } + @<Split the cubic at $t$, + and split off another cubic if the derivative crosses back@>; + w=ww; + } +} + +@ We want $B(\\{t0},\\{t1},\\{t2};t)$ to be the dot product of $d(t)$ with a +$-90^\circ$ rotation of the vector from |w| to |ww|. This makes the resulting +function cross from positive to negative when $d_{k-1}\preceq d(t)\preceq d_k$ +begins to fail. + +@<Compute test coefficients |(t0,t1,t2)| for $d(t)$ versus...@>= +du=mp_x_coord(ww)-mp_x_coord(w); dv=mp_y_coord(ww)-mp_y_coord(w); +if ( abs(du)>=abs(dv) ) { + s=mp_make_fraction(mp, dv,du); + t0=mp_take_fraction(mp, x0,s)-y0; + t1=mp_take_fraction(mp, x1,s)-y1; + t2=mp_take_fraction(mp, x2,s)-y2; + if ( du<0 ) { negate(t0); negate(t1); negate(t2); } +} else { + s=mp_make_fraction(mp, du,dv); + t0=x0-mp_take_fraction(mp, y0,s); + t1=x1-mp_take_fraction(mp, y1,s); + t2=x2-mp_take_fraction(mp, y2,s); + if ( dv<0 ) { negate(t0); negate(t1); negate(t2); } +} +if ( t0<0 ) t0=0 /* should be positive without rounding error */ + +@ The curve has crossed $d_k$ or $d_{k-1}$; its initial segment satisfies +$(*)$, and it might cross again and return towards $s_{k-1}$ or $s_k$, +respectively, yielding another solution of $(*)$. + +@<Split the cubic at $t$, and split off another...@>= +{ +mp_split_cubic(mp, p,t); p=mp_link(p); mp_info(p)=zero_off+rise; +decr(turn_amt); +v=t_of_the_way(x0,x1); x1=t_of_the_way(x1,x2); +x0=t_of_the_way(v,x1); +v=t_of_the_way(y0,y1); y1=t_of_the_way(y1,y2); +y0=t_of_the_way(v,y1); +if ( turn_amt<0 ) { + t1=t_of_the_way(t1,t2); + if ( t1>0 ) t1=0; /* without rounding error, |t1| would be |<=0| */ + t=mp_crossing_point(mp, 0,-t1,-t2); + if ( t>fraction_one ) t=fraction_one; + incr(turn_amt); + if ( (t==fraction_one)&&(mp_link(p)!=q) ) { + mp_info(mp_link(p))=mp_info(mp_link(p))-rise; + } else { + mp_split_cubic(mp, p,t); mp_info(mp_link(p))=zero_off-rise; + v=t_of_the_way(x1,x2); x1=t_of_the_way(x0,x1); + x2=t_of_the_way(x1,v); + v=t_of_the_way(y1,y2); y1=t_of_the_way(y0,y1); + y2=t_of_the_way(y1,v); + } +} +} + +@ Now we must consider the general problem of |offset_prep|, when +nothing is known about a given cubic. We start by finding its +direction in the vicinity of |t=0|. + +If $z'(t)=0$, the given cubic is numerically unstable but |offset_prep| +has not yet introduced any more numerical errors. Thus we can compute +the true initial direction for the given cubic, even if it is almost +degenerate. + +@<Find the initial direction |(dx,dy)|@>= +dx=x0; dy=y0; +if ( dx==0 && dy==0 ) { + dx=x1; dy=y1; + if ( dx==0 && dy==0 ) { + dx=x2; dy=y2; + } +} +if ( p==c ) { dx0=dx; dy0=dy; } + +@ @<Find the final direction |(dxin,dyin)|@>= +dxin=x2; dyin=y2; +if ( dxin==0 && dyin==0 ) { + dxin=x1; dyin=y1; + if ( dxin==0 && dyin==0 ) { + dxin=x0; dyin=y0; + } +} + +@ The next step is to bracket the initial direction between consecutive +edges of the pen polygon. We must be careful to turn clockwise only if +this makes the turn less than $180^\circ$. (A $180^\circ$ turn must be +counter-clockwise in order to make \&{doublepath} envelopes come out +@:double_path_}{\&{doublepath} primitive@> +right.) This code depends on |w0| being the offset for |(dxin,dyin)|. + +@<Update |mp_info(p)| and find the offset $w_k$ such that...@>= +turn_amt=mp_get_turn_amt(mp,w0,dx,dy,(mp_ab_vs_cd(mp, dy,dxin,dx,dyin)>=0)); +w=mp_pen_walk(mp, w0, turn_amt); +w0=w; +mp_info(p)=mp_info(p)+turn_amt + +@ Decide how many pen offsets to go away from |w| in order to find the offset +for |(dx,dy)|, going counterclockwise if |ccw| is |true|. This assumes that +|w| is the offset for some direction $(x',y')$ from which the angle to |(dx,dy)| +in the sense determined by |ccw| is less than or equal to $180^\circ$. + +If the pen polygon has only two edges, they could both be parallel +to |(dx,dy)|. In this case, we must be careful to stop after crossing the first +such edge in order to avoid an infinite loop. + +@<Declarations@>= +static integer mp_get_turn_amt (MP mp,pointer w, scaled dx, + scaled dy, boolean ccw); + +@ @c +integer mp_get_turn_amt (MP mp,pointer w, scaled dx, + scaled dy, boolean ccw) { + pointer ww; /* a neighbor of knot~|w| */ + integer s; /* turn amount so far */ + integer t; /* |ab_vs_cd| result */ + s=0; + if ( ccw ) { + ww=mp_link(w); + do { + t=mp_ab_vs_cd(mp, dy,(mp_x_coord(ww)-mp_x_coord(w)), + dx,(mp_y_coord(ww)-mp_y_coord(w))); + if ( t<0 ) break; + incr(s); + w=ww; ww=mp_link(ww); + } while (t>0); + } else { + ww=knil(w); + while ( mp_ab_vs_cd(mp, dy,(mp_x_coord(w)-mp_x_coord(ww)), + dx,(mp_y_coord(w)-mp_y_coord(ww))) < 0) { + decr(s); + w=ww; ww=knil(ww); + } + } + return s; +} + +@ When we're all done, the final offset is |w0| and the final curve direction +is |(dxin,dyin)|. With this knowledge of the incoming direction at |c|, we +can correct |mp_info(c)| which was erroneously based on an incoming offset +of~|h|. + +@d fix_by(A) mp_info(c)=mp_info(c)+(A) + +@<Fix the offset change in |mp_info(c)| and set |c| to the return value of...@>= +mp->spec_offset=mp_info(c)-zero_off; +if ( mp_link(c)==c ) { + mp_info(c)=zero_off+n; +} else { + fix_by(k_needed); + while ( w0!=h ) { fix_by(1); w0=mp_link(w0); }; + while ( mp_info(c)<=zero_off-n ) fix_by(n); + while ( mp_info(c)>zero_off ) fix_by(-n); + if ( (mp_info(c)!=zero_off)&&(mp_ab_vs_cd(mp, dy0,dxin,dx0,dyin)>=0) ) fix_by(n); +} + +@ Finally we want to reduce the general problem to situations that +|fin_offset_prep| can handle. We split the cubic into at most three parts +with respect to $d_{k-1}$, and apply |fin_offset_prep| to each part. + +@<Complete the offset splitting process@>= +ww=knil(w); +@<Compute test coeff...@>; +@<Find the first |t| where $d(t)$ crosses $d_{k-1}$ or set + |t:=fraction_one+1|@>; +if ( t>fraction_one ) { + mp_fin_offset_prep(mp, p,w,x0,x1,x2,y0,y1,y2,1,turn_amt); +} else { + mp_split_cubic(mp, p,t); r=mp_link(p); + x1a=t_of_the_way(x0,x1); x1=t_of_the_way(x1,x2); + x2a=t_of_the_way(x1a,x1); + y1a=t_of_the_way(y0,y1); y1=t_of_the_way(y1,y2); + y2a=t_of_the_way(y1a,y1); + mp_fin_offset_prep(mp, p,w,x0,x1a,x2a,y0,y1a,y2a,1,0); x0=x2a; y0=y2a; + mp_info(r)=zero_off-1; + if ( turn_amt>=0 ) { + t1=t_of_the_way(t1,t2); + if ( t1>0 ) t1=0; + t=mp_crossing_point(mp, 0,-t1,-t2); + if ( t>fraction_one ) t=fraction_one; + @<Split off another rising cubic for |fin_offset_prep|@>; + mp_fin_offset_prep(mp, r,ww,x0,x1,x2,y0,y1,y2,-1,0); + } else { + mp_fin_offset_prep(mp, r,ww,x0,x1,x2,y0,y1,y2,-1,(-1-turn_amt)); + } +} + +@ @<Split off another rising cubic for |fin_offset_prep|@>= +mp_split_cubic(mp, r,t); mp_info(mp_link(r))=zero_off+1; +x1a=t_of_the_way(x1,x2); x1=t_of_the_way(x0,x1); +x0a=t_of_the_way(x1,x1a); +y1a=t_of_the_way(y1,y2); y1=t_of_the_way(y0,y1); +y0a=t_of_the_way(y1,y1a); +mp_fin_offset_prep(mp, mp_link(r),w,x0a,x1a,x2,y0a,y1a,y2,1,turn_amt); +x2=x0a; y2=y0a + +@ At this point, the direction of the incoming pen edge is |(-du,-dv)|. +When the component of $d(t)$ perpendicular to |(-du,-dv)| crosses zero, we +need to decide whether the directions are parallel or antiparallel. We +can test this by finding the dot product of $d(t)$ and |(-du,-dv)|, but this +should be avoided when the value of |turn_amt| already determines the +answer. If |t2<0|, there is one crossing and it is antiparallel only if +|turn_amt>=0|. If |turn_amt<0|, there should always be at least one +crossing and the first crossing cannot be antiparallel. + +@<Find the first |t| where $d(t)$ crosses $d_{k-1}$ or set...@>= +t=mp_crossing_point(mp, t0,t1,t2); +if ( turn_amt>=0 ) { + if ( t2<0 ) { + t=fraction_one+1; + } else { + u0=t_of_the_way(x0,x1); + u1=t_of_the_way(x1,x2); + ss=mp_take_fraction(mp, -du,t_of_the_way(u0,u1)); + v0=t_of_the_way(y0,y1); + v1=t_of_the_way(y1,y2); + ss=ss+mp_take_fraction(mp, -dv,t_of_the_way(v0,v1)); + if ( ss<0 ) t=fraction_one+1; + } +} else if ( t>fraction_one ) { + t=fraction_one; +} + +@ @<Other local variables for |offset_prep|@>= +integer u0,u1,v0,v1; /* intermediate values for $d(t)$ calculation */ +integer ss = 0; /* the part of the dot product computed so far */ +int d_sign; /* sign of overall change in direction for this cubic */ + +@ If the cubic almost has a cusp, it is a numerically ill-conditioned +problem to decide which way it loops around but that's OK as long we're +consistent. To make \&{doublepath} envelopes work properly, reversing +the path should always change the sign of |turn_amt|. + +@<Decide on the net change in pen offsets and set |turn_amt|@>= +d_sign=mp_ab_vs_cd(mp, dx,dyin, dxin,dy); +if ( d_sign==0 ) { + @<Check rotation direction based on node position@> +} +if ( d_sign==0 ) { + if ( dx==0 ) { + if ( dy>0 ) d_sign=1; else d_sign=-1; + } else { + if ( dx>0 ) d_sign=1; else d_sign=-1; + } +} +@<Make |ss| negative if and only if the total change in direction is + more than $180^\circ$@>; +turn_amt=mp_get_turn_amt(mp, w, dxin, dyin, (d_sign>0)); +if ( ss<0 ) turn_amt=turn_amt-d_sign*n + +@ We check rotation direction by looking at the vector connecting the current +node with the next. If its angle with incoming and outgoing tangents has the +same sign, we pick this as |d_sign|, since it means we have a flex, not a cusp. +Otherwise we proceed to the cusp code. + +@<Check rotation direction based on node position@>= +u0=mp_x_coord(q)-mp_x_coord(p); +u1=mp_y_coord(q)-mp_y_coord(p); +d_sign = half(mp_ab_vs_cd(mp, dx, u1, u0, dy)+ + mp_ab_vs_cd(mp, u0, dyin, dxin, u1)); + +@ In order to be invariant under path reversal, the result of this computation +should not change when |x0|, |y0|, $\ldots$ are all negated and |(x0,y0)| is +then swapped with |(x2,y2)|. We make use of the identities +|take_fraction(-a,-b)=take_fraction(a,b)| and +|t_of_the_way(-a,-b)=-(t_of_the_way(a,b))|. + +@<Make |ss| negative if and only if the total change in direction is...@>= +t0=half(mp_take_fraction(mp, x0,y2))-half(mp_take_fraction(mp, x2,y0)); +t1=half(mp_take_fraction(mp, x1,(y0+y2)))-half(mp_take_fraction(mp, y1,(x0+x2))); +if ( t0==0 ) t0=d_sign; /* path reversal always negates |d_sign| */ +if ( t0>0 ) { + t=mp_crossing_point(mp, t0,t1,-t0); + u0=t_of_the_way(x0,x1); + u1=t_of_the_way(x1,x2); + v0=t_of_the_way(y0,y1); + v1=t_of_the_way(y1,y2); +} else { + t=mp_crossing_point(mp, -t0,t1,t0); + u0=t_of_the_way(x2,x1); + u1=t_of_the_way(x1,x0); + v0=t_of_the_way(y2,y1); + v1=t_of_the_way(y1,y0); +} +ss=mp_take_fraction(mp, (x0+x2),t_of_the_way(u0,u1))+ + mp_take_fraction(mp, (y0+y2),t_of_the_way(v0,v1)) + +@ Here's a routine that prints an envelope spec in symbolic form. It assumes +that the |cur_pen| has not been walked around to the first offset. + +@c +static void mp_print_spec (MP mp,pointer cur_spec, pointer cur_pen, const char *s) { + pointer p,q; /* list traversal */ + pointer w; /* the current pen offset */ + mp_print_diagnostic(mp, "Envelope spec",s,true); + p=cur_spec; w=mp_pen_walk(mp, cur_pen,mp->spec_offset); + mp_print_ln(mp); + mp_print_two(mp, mp_x_coord(cur_spec),mp_y_coord(cur_spec)); + mp_print(mp, " % beginning with offset "); + mp_print_two(mp, mp_x_coord(w),mp_y_coord(w)); + do { + while (1) { + q=mp_link(p); + @<Print the cubic between |p| and |q|@>; + p=q; + if ((p==cur_spec) || (mp_info(p)!=zero_off)) + break; + } + if ( mp_info(p)!=zero_off ) { + @<Update |w| as indicated by |mp_info(p)| and print an explanation@>; + } + } while (p!=cur_spec); + mp_print_nl(mp, " & cycle"); + mp_end_diagnostic(mp, true); +} + +@ @<Update |w| as indicated by |mp_info(p)| and print an explanation@>= +{ + w=mp_pen_walk(mp, w, (mp_info(p)-zero_off)); + mp_print(mp, " % "); + if ( mp_info(p)>zero_off ) mp_print(mp, "counter"); + mp_print(mp, "clockwise to offset "); + mp_print_two(mp, mp_x_coord(w),mp_y_coord(w)); +} + +@ @<Print the cubic between |p| and |q|@>= +{ + mp_print_nl(mp, " ..controls "); + mp_print_two(mp, mp_right_x(p),mp_right_y(p)); + mp_print(mp, " and "); + mp_print_two(mp, mp_left_x(q),mp_left_y(q)); + mp_print_nl(mp, " .."); + mp_print_two(mp, mp_x_coord(q),mp_y_coord(q)); +} + +@ Once we have an envelope spec, the remaining task to construct the actual +envelope by offsetting each cubic as determined by the |info| fields in +the knots. First we use |offset_prep| to convert the |c| into an envelope +spec. Then we add the offsets so that |c| becomes a cyclic path that represents +the envelope. + +The |ljoin| and |miterlim| parameters control the treatment of points where the +pen offset changes, and |lcap| controls the endpoints of a \&{doublepath}. +The endpoints are easily located because |c| is given in undoubled form +and then doubled in this procedure. We use |spec_p1| and |spec_p2| to keep +track of the endpoints and treat them like very sharp corners. +Butt end caps are treated like beveled joins; round end caps are treated like +round joins; and square end caps are achieved by setting |join_type:=3|. + +None of these parameters apply to inside joins where the convolution tracing +has retrograde lines. In such cases we use a simple connect-the-endpoints +approach that is achieved by setting |join_type:=2|. + +@c +static pointer mp_make_envelope (MP mp,pointer c, pointer h, quarterword ljoin, + quarterword lcap, scaled miterlim) { + pointer p,q,r,q0; /* for manipulating the path */ + int join_type=0; /* codes |0..3| for mitered, round, beveled, or square */ + pointer w,w0; /* the pen knot for the current offset */ + scaled qx,qy; /* unshifted coordinates of |q| */ + halfword k,k0; /* controls pen edge insertion */ + @<Other local variables for |make_envelope|@>; + dxin=0; dyin=0; dxout=0; dyout=0; + mp->spec_p1=null; mp->spec_p2=null; + @<If endpoint, double the path |c|, and set |spec_p1| and |spec_p2|@>; + @<Use |offset_prep| to compute the envelope spec then walk |h| around to + the initial offset@>; + w=h; + p=c; + do { + q=mp_link(p); q0=q; + qx=mp_x_coord(q); qy=mp_y_coord(q); + k=mp_info(q); + k0=k; w0=w; + if ( k!=zero_off ) { + @<Set |join_type| to indicate how to handle offset changes at~|q|@>; + } + @<Add offset |w| to the cubic from |p| to |q|@>; + while ( k!=zero_off ) { + @<Step |w| and move |k| one step closer to |zero_off|@>; + if ( (join_type==1)||(k==zero_off) ) + q=mp_insert_knot(mp, q,qx+mp_x_coord(w),qy+mp_y_coord(w)); + }; + if ( q!=mp_link(p) ) { + @<Set |p=mp_link(p)| and add knots between |p| and |q| as + required by |join_type|@>; + } + p=q; + } while (q0!=c); + return c; +} + +@ @<Use |offset_prep| to compute the envelope spec then walk |h| around to...@>= +c=mp_offset_prep(mp, c,h); +if ( mp->internal[mp_tracing_specs]>0 ) + mp_print_spec(mp, c,h,""); +h=mp_pen_walk(mp, h,mp->spec_offset) + +@ Mitered and squared-off joins depend on path directions that are difficult to +compute for degenerate cubics. The envelope spec computed by |offset_prep| can +have degenerate cubics only if the entire cycle collapses to a single +degenerate cubic. Setting |join_type:=2| in this case makes the computed +envelope degenerate as well. + +@<Set |join_type| to indicate how to handle offset changes at~|q|@>= +if ( k<zero_off ) { + join_type=2; +} else { + if ( (q!=mp->spec_p1)&&(q!=mp->spec_p2) ) join_type=ljoin; + else if ( lcap==2 ) join_type=3; + else join_type=2-lcap; + if ( (join_type==0)||(join_type==3) ) { + @<Set the incoming and outgoing directions at |q|; in case of + degeneracy set |join_type:=2|@>; + if ( join_type==0 ) { + @<If |miterlim| is less than the secant of half the angle at |q| + then set |join_type:=2|@>; + } + } +} + +@ @<If |miterlim| is less than the secant of half the angle at |q|...@>= +{ + tmp=mp_take_fraction(mp, miterlim,fraction_half+ + half(mp_take_fraction(mp, dxin,dxout)+mp_take_fraction(mp, dyin,dyout))); + if ( tmp<unity ) + if ( mp_take_scaled(mp, miterlim,tmp)<unity ) join_type=2; +} + +@ @<Other local variables for |make_envelope|@>= +fraction dxin,dyin,dxout,dyout; /* directions at |q| when square or mitered */ +scaled tmp; /* a temporary value */ + +@ The coordinates of |p| have already been shifted unless |p| is the first +knot in which case they get shifted at the very end. + +@<Add offset |w| to the cubic from |p| to |q|@>= +mp_right_x(p)=mp_right_x(p)+mp_x_coord(w); +mp_right_y(p)=mp_right_y(p)+mp_y_coord(w); +mp_left_x(q)=mp_left_x(q)+mp_x_coord(w); +mp_left_y(q)=mp_left_y(q)+mp_y_coord(w); +mp_x_coord(q)=mp_x_coord(q)+mp_x_coord(w); +mp_y_coord(q)=mp_y_coord(q)+mp_y_coord(w); +mp_left_type(q)=mp_explicit; +mp_right_type(q)=mp_explicit + +@ @<Step |w| and move |k| one step closer to |zero_off|@>= +if ( k>zero_off ){ w=mp_link(w); decr(k); } +else { w=knil(w); incr(k); } + +@ The cubic from |q| to the new knot at |(x,y)| becomes a line segment and +the |mp_right_x| and |mp_right_y| fields of |r| are set from |q|. This is done in +case the cubic containing these control points is ``yet to be examined.'' + +@<Declarations@>= +static pointer mp_insert_knot (MP mp,pointer q, scaled x, scaled y); + +@ @c +pointer mp_insert_knot (MP mp,pointer q, scaled x, scaled y) { + /* returns the inserted knot */ + pointer r; /* the new knot */ + r=mp_get_node(mp, knot_node_size); + mp_link(r)=mp_link(q); mp_link(q)=r; + mp_right_x(r)=mp_right_x(q); + mp_right_y(r)=mp_right_y(q); + mp_x_coord(r)=x; + mp_y_coord(r)=y; + mp_right_x(q)=mp_x_coord(q); + mp_right_y(q)=mp_y_coord(q); + mp_left_x(r)=mp_x_coord(r); + mp_left_y(r)=mp_y_coord(r); + mp_left_type(r)=mp_explicit; + mp_right_type(r)=mp_explicit; + mp_originator(r)=mp_program_code; + return r; +} + +@ After setting |p:=mp_link(p)|, either |join_type=1| or |q=mp_link(p)|. + +@<Set |p=mp_link(p)| and add knots between |p| and |q| as...@>= +{ + p=mp_link(p); + if ( (join_type==0)||(join_type==3) ) { + if ( join_type==0 ) { + @<Insert a new knot |r| between |p| and |q| as required for a mitered join@> + } else { + @<Make |r| the last of two knots inserted between |p| and |q| to form a + squared join@>; + } + if ( r!=null ) { + mp_right_x(r)=mp_x_coord(r); + mp_right_y(r)=mp_y_coord(r); + } + } +} + +@ For very small angles, adding a knot is unnecessary and would cause numerical +problems, so we just set |r:=null| in that case. + +@<Insert a new knot |r| between |p| and |q| as required for a mitered join@>= +{ + det=mp_take_fraction(mp, dyout,dxin)-mp_take_fraction(mp, dxout,dyin); + if ( abs(det)<26844 ) { + r=null; /* sine $<10^{-4}$ */ + } else { + tmp=mp_take_fraction(mp, mp_x_coord(q)-mp_x_coord(p),dyout)- + mp_take_fraction(mp, mp_y_coord(q)-mp_y_coord(p),dxout); + tmp=mp_make_fraction(mp, tmp,det); + r=mp_insert_knot(mp, p,mp_x_coord(p)+mp_take_fraction(mp, tmp,dxin), + mp_y_coord(p)+mp_take_fraction(mp, tmp,dyin)); + } +} + +@ @<Other local variables for |make_envelope|@>= +fraction det; /* a determinant used for mitered join calculations */ + +@ @<Make |r| the last of two knots inserted between |p| and |q| to form a...@>= +{ + ht_x=mp_y_coord(w)-mp_y_coord(w0); + ht_y=mp_x_coord(w0)-mp_x_coord(w); + while ( (abs(ht_x)<fraction_half)&&(abs(ht_y)<fraction_half) ) { + ht_x+=ht_x; ht_y+=ht_y; + } + @<Scan the pen polygon between |w0| and |w| and make |max_ht| the range dot + product with |(ht_x,ht_y)|@>; + tmp=mp_make_fraction(mp, max_ht,mp_take_fraction(mp, dxin,ht_x)+ + mp_take_fraction(mp, dyin,ht_y)); + r=mp_insert_knot(mp, p,mp_x_coord(p)+mp_take_fraction(mp, tmp,dxin), + mp_y_coord(p)+mp_take_fraction(mp, tmp,dyin)); + tmp=mp_make_fraction(mp, max_ht,mp_take_fraction(mp, dxout,ht_x)+ + mp_take_fraction(mp, dyout,ht_y)); + r=mp_insert_knot(mp, r,mp_x_coord(q)+mp_take_fraction(mp, tmp,dxout), + mp_y_coord(q)+mp_take_fraction(mp, tmp,dyout)); +} + +@ @<Other local variables for |make_envelope|@>= +fraction ht_x,ht_y; /* perpendicular to the segment from |p| to |q| */ +scaled max_ht; /* maximum height of the pen polygon above the |w0|-|w| line */ +halfword kk; /* keeps track of the pen vertices being scanned */ +pointer ww; /* the pen vertex being tested */ + +@ The dot product of the vector from |w0| to |ww| with |(ht_x,ht_y)| ranges +from zero to |max_ht|. + +@<Scan the pen polygon between |w0| and |w| and make |max_ht| the range...@>= +max_ht=0; +kk=zero_off; +ww=w; +while (1) { + @<Step |ww| and move |kk| one step closer to |k0|@>; + if ( kk==k0 ) break; + tmp=mp_take_fraction(mp, (mp_x_coord(ww)-mp_x_coord(w0)),ht_x)+ + mp_take_fraction(mp, (mp_y_coord(ww)-mp_y_coord(w0)),ht_y); + if ( tmp>max_ht ) max_ht=tmp; +} + + +@ @<Step |ww| and move |kk| one step closer to |k0|@>= +if ( kk>k0 ) { ww=mp_link(ww); decr(kk); } +else { ww=knil(ww); incr(kk); } + +@ @<If endpoint, double the path |c|, and set |spec_p1| and |spec_p2|@>= +if ( mp_left_type(c)==mp_endpoint ) { + mp->spec_p1=mp_htap_ypoc(mp, c); + mp->spec_p2=mp->path_tail; + mp_originator(mp->spec_p1)=mp_program_code; + mp_link(mp->spec_p2)=mp_link(mp->spec_p1); + mp_link(mp->spec_p1)=c; + mp_remove_cubic(mp, mp->spec_p1); + c=mp->spec_p1; + if ( c!=mp_link(c) ) { + mp_originator(mp->spec_p2)=mp_program_code; + mp_remove_cubic(mp, mp->spec_p2); + } else { + @<Make |c| look like a cycle of length one@>; + } +} + +@ @<Make |c| look like a cycle of length one@>= +{ + mp_left_type(c)=mp_explicit; mp_right_type(c)=mp_explicit; + mp_left_x(c)=mp_x_coord(c); mp_left_y(c)=mp_y_coord(c); + mp_right_x(c)=mp_x_coord(c); mp_right_y(c)=mp_y_coord(c); +} + +@ In degenerate situations we might have to look at the knot preceding~|q|. +That knot is |p| but if |p<>c|, its coordinates have already been offset by |w|. + +@<Set the incoming and outgoing directions at |q|; in case of...@>= +dxin=mp_x_coord(q)-mp_left_x(q); +dyin=mp_y_coord(q)-mp_left_y(q); +if ( (dxin==0)&&(dyin==0) ) { + dxin=mp_x_coord(q)-mp_right_x(p); + dyin=mp_y_coord(q)-mp_right_y(p); + if ( (dxin==0)&&(dyin==0) ) { + dxin=mp_x_coord(q)-mp_x_coord(p); + dyin=mp_y_coord(q)-mp_y_coord(p); + if ( p!=c ) { /* the coordinates of |p| have been offset by |w| */ + dxin=dxin+mp_x_coord(w); + dyin=dyin+mp_y_coord(w); + } + } +} +tmp=mp_pyth_add(mp, dxin,dyin); +if ( tmp==0 ) { + join_type=2; +} else { + dxin=mp_make_fraction(mp, dxin,tmp); + dyin=mp_make_fraction(mp, dyin,tmp); + @<Set the outgoing direction at |q|@>; +} + +@ If |q=c| then the coordinates of |r| and the control points between |q| +and~|r| have already been offset by |h|. + +@<Set the outgoing direction at |q|@>= +dxout=mp_right_x(q)-mp_x_coord(q); +dyout=mp_right_y(q)-mp_y_coord(q); +if ( (dxout==0)&&(dyout==0) ) { + r=mp_link(q); + dxout=mp_left_x(r)-mp_x_coord(q); + dyout=mp_left_y(r)-mp_y_coord(q); + if ( (dxout==0)&&(dyout==0) ) { + dxout=mp_x_coord(r)-mp_x_coord(q); + dyout=mp_y_coord(r)-mp_y_coord(q); + } +} +if ( q==c ) { + dxout=dxout-mp_x_coord(h); + dyout=dyout-mp_y_coord(h); +} +tmp=mp_pyth_add(mp, dxout,dyout); +if ( tmp==0 ) mp_confusion(mp, "degenerate spec"); +@:this can't happen degerate spec}{\quad degenerate spec@> +dxout=mp_make_fraction(mp, dxout,tmp); +dyout=mp_make_fraction(mp, dyout,tmp) + +@* \[23] Direction and intersection times. +A path of length $n$ is defined parametrically by functions $x(t)$ and +$y(t)$, for |0<=t<=n|; we can regard $t$ as the ``time'' at which the path +reaches the point $\bigl(x(t),y(t)\bigr)$. In this section of the program +we shall consider operations that determine special times associated with +given paths: the first time that a path travels in a given direction, and +a pair of times at which two paths cross each other. + +@ Let's start with the easier task. The function |find_direction_time| is +given a direction |(x,y)| and a path starting at~|h|. If the path never +travels in direction |(x,y)|, the direction time will be~|-1|; otherwise +it will be nonnegative. + +Certain anomalous cases can arise: If |(x,y)=(0,0)|, so that the given +direction is undefined, the direction time will be~0. If $\bigl(x'(t), +y'(t)\bigr)=(0,0)$, so that the path direction is undefined, it will be +assumed to match any given direction at time~|t|. + +The routine solves this problem in nondegenerate cases by rotating the path +and the given direction so that |(x,y)=(1,0)|; i.e., the main task will be +to find when a given path first travels ``due east.'' + +@c +static scaled mp_find_direction_time (MP mp,scaled x, scaled y, pointer h) { + scaled max; /* $\max\bigl(\vert x\vert,\vert y\vert\bigr)$ */ + pointer p,q; /* for list traversal */ + scaled n; /* the direction time at knot |p| */ + scaled tt; /* the direction time within a cubic */ + @<Other local variables for |find_direction_time|@>; + @<Normalize the given direction for better accuracy; + but |return| with zero result if it's zero@>; + n=0; p=h; phi=0; + while (1) { + if ( mp_right_type(p)==mp_endpoint ) break; + q=mp_link(p); + @<Rotate the cubic between |p| and |q|; then + |goto found| if the rotated cubic travels due east at some time |tt|; + but |break| if an entire cyclic path has been traversed@>; + p=q; n=n+unity; + } + return (-unity); +FOUND: + return (n+tt); +} + +@ @<Normalize the given direction for better accuracy...@>= +if ( abs(x)<abs(y) ) { + x=mp_make_fraction(mp, x,abs(y)); + if ( y>0 ) y=fraction_one; else y=-fraction_one; +} else if ( x==0 ) { + return 0; +} else { + y=mp_make_fraction(mp, y,abs(x)); + if ( x>0 ) x=fraction_one; else x=-fraction_one; +} + +@ Since we're interested in the tangent directions, we work with the +derivative $${1\over3}B'(x_0,x_1,x_2,x_3;t)= +B(x_1-x_0,x_2-x_1,x_3-x_2;t)$$ instead of +$B(x_0,x_1,x_2,x_3;t)$ itself. The derived coefficients are also scaled up +in order to achieve better accuracy. + +The given path may turn abruptly at a knot, and it might pass the critical +tangent direction at such a time. Therefore we remember the direction |phi| +in which the previous rotated cubic was traveling. (The value of |phi| will be +undefined on the first cubic, i.e., when |n=0|.) + +@<Rotate the cubic between |p| and |q|; then...@>= +tt=0; +@<Set local variables |x1,x2,x3| and |y1,y2,y3| to multiples of the control + points of the rotated derivatives@>; +if ( y1==0 ) if ( x1>=0 ) goto FOUND; +if ( n>0 ) { + @<Exit to |found| if an eastward direction occurs at knot |p|@>; + if ( p==h ) break; + }; +if ( (x3!=0)||(y3!=0) ) phi=mp_n_arg(mp, x3,y3); +@<Exit to |found| if the curve whose derivatives are specified by + |x1,x2,x3,y1,y2,y3| travels eastward at some time~|tt|@> + +@ @<Other local variables for |find_direction_time|@>= +scaled x1,x2,x3,y1,y2,y3; /* multiples of rotated derivatives */ +angle theta,phi; /* angles of exit and entry at a knot */ +fraction t; /* temp storage */ + +@ @<Set local variables |x1,x2,x3| and |y1,y2,y3| to multiples...@>= +x1=mp_right_x(p)-mp_x_coord(p); x2=mp_left_x(q)-mp_right_x(p); +x3=mp_x_coord(q)-mp_left_x(q); +y1=mp_right_y(p)-mp_y_coord(p); y2=mp_left_y(q)-mp_right_y(p); +y3=mp_y_coord(q)-mp_left_y(q); +max=abs(x1); +if ( abs(x2)>max ) max=abs(x2); +if ( abs(x3)>max ) max=abs(x3); +if ( abs(y1)>max ) max=abs(y1); +if ( abs(y2)>max ) max=abs(y2); +if ( abs(y3)>max ) max=abs(y3); +if ( max==0 ) goto FOUND; +while ( max<fraction_half ){ + max+=max; x1+=x1; x2+=x2; x3+=x3; + y1+=y1; y2+=y2; y3+=y3; +} +t=x1; x1=mp_take_fraction(mp, x1,x)+mp_take_fraction(mp, y1,y); +y1=mp_take_fraction(mp, y1,x)-mp_take_fraction(mp, t,y); +t=x2; x2=mp_take_fraction(mp, x2,x)+mp_take_fraction(mp, y2,y); +y2=mp_take_fraction(mp, y2,x)-mp_take_fraction(mp, t,y); +t=x3; x3=mp_take_fraction(mp, x3,x)+mp_take_fraction(mp, y3,y); +y3=mp_take_fraction(mp, y3,x)-mp_take_fraction(mp, t,y) + +@ @<Exit to |found| if an eastward direction occurs at knot |p|@>= +theta=mp_n_arg(mp, x1,y1); +if ( theta>=0 ) if ( phi<=0 ) if ( phi>=theta-one_eighty_deg ) goto FOUND; +if ( theta<=0 ) if ( phi>=0 ) if ( phi<=theta+one_eighty_deg ) goto FOUND + +@ In this step we want to use the |crossing_point| routine to find the +roots of the quadratic equation $B(y_1,y_2,y_3;t)=0$. +Several complications arise: If the quadratic equation has a double root, +the curve never crosses zero, and |crossing_point| will find nothing; +this case occurs iff $y_1y_3=y_2^2$ and $y_1y_2<0$. If the quadratic +equation has simple roots, or only one root, we may have to negate it +so that $B(y_1,y_2,y_3;t)$ crosses from positive to negative at its first root. +And finally, we need to do special things if $B(y_1,y_2,y_3;t)$ is +identically zero. + +@ @<Exit to |found| if the curve whose derivatives are specified by...@>= +if ( x1<0 ) if ( x2<0 ) if ( x3<0 ) goto DONE; +if ( mp_ab_vs_cd(mp, y1,y3,y2,y2)==0 ) { + @<Handle the test for eastward directions when $y_1y_3=y_2^2$; + either |goto found| or |goto done|@>; +} +if ( y1<=0 ) { + if ( y1<0 ) { y1=-y1; y2=-y2; y3=-y3; } + else if ( y2>0 ){ y2=-y2; y3=-y3; }; +} +@<Check the places where $B(y_1,y_2,y_3;t)=0$ to see if + $B(x_1,x_2,x_3;t)\ge0$@>; +DONE: + +@ The quadratic polynomial $B(y_1,y_2,y_3;t)$ begins |>=0| and has at most +two roots, because we know that it isn't identically zero. + +It must be admitted that the |crossing_point| routine is not perfectly accurate; +rounding errors might cause it to find a root when $y_1y_3>y_2^2$, or to +miss the roots when $y_1y_3<y_2^2$. The rotation process is itself +subject to rounding errors. Yet this code optimistically tries to +do the right thing. + +@d we_found_it { tt=(t+04000) / 010000; goto FOUND; } + +@<Check the places where $B(y_1,y_2,y_3;t)=0$...@>= +t=mp_crossing_point(mp, y1,y2,y3); +if ( t>fraction_one ) goto DONE; +y2=t_of_the_way(y2,y3); +x1=t_of_the_way(x1,x2); +x2=t_of_the_way(x2,x3); +x1=t_of_the_way(x1,x2); +if ( x1>=0 ) we_found_it; +if ( y2>0 ) y2=0; +tt=t; t=mp_crossing_point(mp, 0,-y2,-y3); +if ( t>fraction_one ) goto DONE; +x1=t_of_the_way(x1,x2); +x2=t_of_the_way(x2,x3); +if ( t_of_the_way(x1,x2)>=0 ) { + t=t_of_the_way(tt,fraction_one); we_found_it; +} + +@ @<Handle the test for eastward directions when $y_1y_3=y_2^2$; + either |goto found| or |goto done|@>= +{ + if ( mp_ab_vs_cd(mp, y1,y2,0,0)<0 ) { + t=mp_make_fraction(mp, y1,y1-y2); + x1=t_of_the_way(x1,x2); + x2=t_of_the_way(x2,x3); + if ( t_of_the_way(x1,x2)>=0 ) we_found_it; + } else if ( y3==0 ) { + if ( y1==0 ) { + @<Exit to |found| if the derivative $B(x_1,x_2,x_3;t)$ becomes |>=0|@>; + } else if ( x3>=0 ) { + tt=unity; goto FOUND; + } + } + goto DONE; +} + +@ At this point we know that the derivative of |y(t)| is identically zero, +and that |x1<0|; but either |x2>=0| or |x3>=0|, so there's some hope of +traveling east. + +@<Exit to |found| if the derivative $B(x_1,x_2,x_3;t)$ becomes |>=0|...@>= +{ + t=mp_crossing_point(mp, -x1,-x2,-x3); + if ( t<=fraction_one ) we_found_it; + if ( mp_ab_vs_cd(mp, x1,x3,x2,x2)<=0 ) { + t=mp_make_fraction(mp, x1,x1-x2); we_found_it; + } +} + +@ The intersection of two cubics can be found by an interesting variant +of the general bisection scheme described in the introduction to +|crossing_point|.\ +Given $w(t)=B(w_0,w_1,w_2,w_3;t)$ and $z(t)=B(z_0,z_1,z_2,z_3;t)$, +we wish to find a pair of times $(t_1,t_2)$ such that $w(t_1)=z(t_2)$, +if an intersection exists. First we find the smallest rectangle that +encloses the points $\{w_0,w_1,w_2,w_3\}$ and check that it overlaps +the smallest rectangle that encloses +$\{z_0,z_1,z_2,z_3\}$; if not, the cubics certainly don't intersect. +But if the rectangles do overlap, we bisect the intervals, getting +new cubics $w'$ and~$w''$, $z'$~and~$z''$; the intersection routine first +tries for an intersection between $w'$ and~$z'$, then (if unsuccessful) +between $w'$ and~$z''$, then (if still unsuccessful) between $w''$ and~$z'$, +finally (if thrice unsuccessful) between $w''$ and~$z''$. After $l$~successful +levels of bisection we will have determined the intersection times $t_1$ +and~$t_2$ to $l$~bits of accuracy. + +\def\submin{_{\rm min}} \def\submax{_{\rm max}} +As before, it is better to work with the numbers $W_k=2^l(w_k-w_{k-1})$ +and $Z_k=2^l(z_k-z_{k-1})$ rather than the coefficients $w_k$ and $z_k$ +themselves. We also need one other quantity, $\Delta=2^l(w_0-z_0)$, +to determine when the enclosing rectangles overlap. Here's why: +The $x$~coordinates of~$w(t)$ are between $u\submin$ and $u\submax$, +and the $x$~coordinates of~$z(t)$ are between $x\submin$ and $x\submax$, +if we write $w_k=(u_k,v_k)$ and $z_k=(x_k,y_k)$ and $u\submin= +\min(u_0,u_1,u_2,u_3)$, etc. These intervals of $x$~coordinates +overlap if and only if $u\submin\L x\submax$ and +$x\submin\L u\submax$. Letting +$$U\submin=\min(0,U_1,U_1+U_2,U_1+U_2+U_3),\; + U\submax=\max(0,U_1,U_1+U_2,U_1+U_2+U_3),$$ +we have $2^lu\submin=2^lu_0+U\submin$, etc.; the condition for overlap +reduces to +$$X\submin-U\submax\L 2^l(u_0-x_0)\L X\submax-U\submin.$$ +Thus we want to maintain the quantity $2^l(u_0-x_0)$; similarly, +the quantity $2^l(v_0-y_0)$ accounts for the $y$~coordinates. The +coordinates of $\Delta=2^l(w_0-z_0)$ must stay bounded as $l$ increases, +because of the overlap condition; i.e., we know that $X\submin$, +$X\submax$, and their relatives are bounded, hence $X\submax- +U\submin$ and $X\submin-U\submax$ are bounded. + +@ Incidentally, if the given cubics intersect more than once, the process +just sketched will not necessarily find the lexicographically smallest pair +$(t_1,t_2)$. The solution actually obtained will be smallest in ``shuffled +order''; i.e., if $t_1=(.a_1a_2\ldots a_{16})_2$ and +$t_2=(.b_1b_2\ldots b_{16})_2$, then we will minimize +$a_1b_1a_2b_2\ldots a_{16}b_{16}$, not +$a_1a_2\ldots a_{16}b_1b_2\ldots b_{16}$. +Shuffled order agrees with lexicographic order if all pairs of solutions +$(t_1,t_2)$ and $(t_1',t_2')$ have the property that $t_1<t_1'$ iff +$t_2<t_2'$; but in general, lexicographic order can be quite different, +and the bisection algorithm would be substantially less efficient if it were +constrained by lexicographic order. + +For example, suppose that an overlap has been found for $l=3$ and +$(t_1,t_2)= (.101,.011)$ in binary, but that no overlap is produced by +either of the alternatives $(.1010,.0110)$, $(.1010,.0111)$ at level~4. +Then there is probably an intersection in one of the subintervals +$(.1011,.011x)$; but lexicographic order would require us to explore +$(.1010,.1xxx)$ and $(.1011,.00xx)$ and $(.1011,.010x)$ first. We wouldn't +want to store all of the subdivision data for the second path, so the +subdivisions would have to be regenerated many times. Such inefficiencies +would be associated with every `1' in the binary representation of~$t_1$. + +@ The subdivision process introduces rounding errors, hence we need to +make a more liberal test for overlap. It is not hard to show that the +computed values of $U_i$ differ from the truth by at most~$l$, on +level~$l$, hence $U\submin$ and $U\submax$ will be at most $3l$ in error. +If $\beta$ is an upper bound on the absolute error in the computed +components of $\Delta=(|delx|,|dely|)$ on level~$l$, we will replace +the test `$X\submin-U\submax\L|delx|$' by the more liberal test +`$X\submin-U\submax\L|delx|+|tol|$', where $|tol|=6l+\beta$. + +More accuracy is obtained if we try the algorithm first with |tol=0|; +the more liberal tolerance is used only if an exact approach fails. +It is convenient to do this double-take by letting `3' in the preceding +paragraph be a parameter, which is first 0, then 3. + +@<Glob...@>= +unsigned int tol_step; /* either 0 or 3, usually */ + +@ We shall use an explicit stack to implement the recursive bisection +method described above. The |bisect_stack| array will contain numerous 5-word +packets like $(U_1,U_2,U_3,U\submin,U\submax)$, as well as 20-word packets +comprising the 5-word packets for $U$, $V$, $X$, and~$Y$. + +The following macros define the allocation of stack positions to +the quantities needed for bisection-intersection. + +@d stack_1(A) mp->bisect_stack[(A)] /* $U_1$, $V_1$, $X_1$, or $Y_1$ */ +@d stack_2(A) mp->bisect_stack[(A)+1] /* $U_2$, $V_2$, $X_2$, or $Y_2$ */ +@d stack_3(A) mp->bisect_stack[(A)+2] /* $U_3$, $V_3$, $X_3$, or $Y_3$ */ +@d stack_min(A) mp->bisect_stack[(A)+3] + /* $U\submin$, $V\submin$, $X\submin$, or $Y\submin$ */ +@d stack_max(A) mp->bisect_stack[(A)+4] + /* $U\submax$, $V\submax$, $X\submax$, or $Y\submax$ */ +@d int_packets 20 /* number of words to represent $U_k$, $V_k$, $X_k$, and $Y_k$ */ +@# +@d u_packet(A) ((A)-5) +@d v_packet(A) ((A)-10) +@d x_packet(A) ((A)-15) +@d y_packet(A) ((A)-20) +@d l_packets (mp->bisect_ptr-int_packets) +@d r_packets mp->bisect_ptr +@d ul_packet u_packet(l_packets) /* base of $U'_k$ variables */ +@d vl_packet v_packet(l_packets) /* base of $V'_k$ variables */ +@d xl_packet x_packet(l_packets) /* base of $X'_k$ variables */ +@d yl_packet y_packet(l_packets) /* base of $Y'_k$ variables */ +@d ur_packet u_packet(r_packets) /* base of $U''_k$ variables */ +@d vr_packet v_packet(r_packets) /* base of $V''_k$ variables */ +@d xr_packet x_packet(r_packets) /* base of $X''_k$ variables */ +@d yr_packet y_packet(r_packets) /* base of $Y''_k$ variables */ +@# +@d u1l stack_1(ul_packet) /* $U'_1$ */ +@d u2l stack_2(ul_packet) /* $U'_2$ */ +@d u3l stack_3(ul_packet) /* $U'_3$ */ +@d v1l stack_1(vl_packet) /* $V'_1$ */ +@d v2l stack_2(vl_packet) /* $V'_2$ */ +@d v3l stack_3(vl_packet) /* $V'_3$ */ +@d x1l stack_1(xl_packet) /* $X'_1$ */ +@d x2l stack_2(xl_packet) /* $X'_2$ */ +@d x3l stack_3(xl_packet) /* $X'_3$ */ +@d y1l stack_1(yl_packet) /* $Y'_1$ */ +@d y2l stack_2(yl_packet) /* $Y'_2$ */ +@d y3l stack_3(yl_packet) /* $Y'_3$ */ +@d u1r stack_1(ur_packet) /* $U''_1$ */ +@d u2r stack_2(ur_packet) /* $U''_2$ */ +@d u3r stack_3(ur_packet) /* $U''_3$ */ +@d v1r stack_1(vr_packet) /* $V''_1$ */ +@d v2r stack_2(vr_packet) /* $V''_2$ */ +@d v3r stack_3(vr_packet) /* $V''_3$ */ +@d x1r stack_1(xr_packet) /* $X''_1$ */ +@d x2r stack_2(xr_packet) /* $X''_2$ */ +@d x3r stack_3(xr_packet) /* $X''_3$ */ +@d y1r stack_1(yr_packet) /* $Y''_1$ */ +@d y2r stack_2(yr_packet) /* $Y''_2$ */ +@d y3r stack_3(yr_packet) /* $Y''_3$ */ +@# +@d stack_dx mp->bisect_stack[mp->bisect_ptr] /* stacked value of |delx| */ +@d stack_dy mp->bisect_stack[mp->bisect_ptr+1] /* stacked value of |dely| */ +@d stack_tol mp->bisect_stack[mp->bisect_ptr+2] /* stacked value of |tol| */ +@d stack_uv mp->bisect_stack[mp->bisect_ptr+3] /* stacked value of |uv| */ +@d stack_xy mp->bisect_stack[mp->bisect_ptr+4] /* stacked value of |xy| */ +@d int_increment (int_packets+int_packets+5) /* number of stack words per level */ + +@<Glob...@>= +integer *bisect_stack; +integer bisect_ptr; + +@ @<Allocate or initialize ...@>= +mp->bisect_stack = xmalloc((bistack_size+1),sizeof(integer)); + +@ @<Dealloc variables@>= +xfree(mp->bisect_stack); + +@ @<Check the ``constant''...@>= +if ( int_packets+17*int_increment>bistack_size ) mp->bad=19; + +@ Computation of the min and max is a tedious but fairly fast sequence of +instructions; exactly four comparisons are made in each branch. + +@d set_min_max(A) + if ( stack_1((A))<0 ) { + if ( stack_3((A))>=0 ) { + if ( stack_2((A))<0 ) stack_min((A))=stack_1((A))+stack_2((A)); + else stack_min((A))=stack_1((A)); + stack_max((A))=stack_1((A))+stack_2((A))+stack_3((A)); + if ( stack_max((A))<0 ) stack_max((A))=0; + } else { + stack_min((A))=stack_1((A))+stack_2((A))+stack_3((A)); + if ( stack_min((A))>stack_1((A)) ) stack_min((A))=stack_1((A)); + stack_max((A))=stack_1((A))+stack_2((A)); + if ( stack_max((A))<0 ) stack_max((A))=0; + } + } else if ( stack_3((A))<=0 ) { + if ( stack_2((A))>0 ) stack_max((A))=stack_1((A))+stack_2((A)); + else stack_max((A))=stack_1((A)); + stack_min((A))=stack_1((A))+stack_2((A))+stack_3((A)); + if ( stack_min((A))>0 ) stack_min((A))=0; + } else { + stack_max((A))=stack_1((A))+stack_2((A))+stack_3((A)); + if ( stack_max((A))<stack_1((A)) ) stack_max((A))=stack_1((A)); + stack_min((A))=stack_1((A))+stack_2((A)); + if ( stack_min((A))>0 ) stack_min((A))=0; + } + +@ It's convenient to keep the current values of $l$, $t_1$, and $t_2$ in +the integer form $2^l+2^lt_1$ and $2^l+2^lt_2$. The |cubic_intersection| +routine uses global variables |cur_t| and |cur_tt| for this purpose; +after successful completion, |cur_t| and |cur_tt| will contain |unity| +plus the |scaled| values of $t_1$ and~$t_2$. + +The values of |cur_t| and |cur_tt| will be set to zero if |cubic_intersection| +finds no intersection. The routine gives up and gives an approximate answer +if it has backtracked +more than 5000 times (otherwise there are cases where several minutes +of fruitless computation would be possible). + +@d max_patience 5000 + +@<Glob...@>= +integer cur_t;integer cur_tt; /* controls and results of |cubic_intersection| */ +integer time_to_go; /* this many backtracks before giving up */ +integer max_t; /* maximum of $2^{l+1}$ so far achieved */ + +@ The given cubics $B(w_0,w_1,w_2,w_3;t)$ and +$B(z_0,z_1,z_2,z_3;t)$ are specified in adjacent knot nodes |(p,mp_link(p))| +and |(pp,mp_link(pp))|, respectively. + +@c +static void mp_cubic_intersection (MP mp,pointer p, pointer pp) { + pointer q,qq; /* |mp_link(p)|, |mp_link(pp)| */ + mp->time_to_go=max_patience; mp->max_t=2; + @<Initialize for intersections at level zero@>; +CONTINUE: + while (1) { + if ( mp->delx-mp->tol<=stack_max(x_packet(mp->xy))-stack_min(u_packet(mp->uv))) + if ( mp->delx+mp->tol>=stack_min(x_packet(mp->xy))-stack_max(u_packet(mp->uv))) + if ( mp->dely-mp->tol<=stack_max(y_packet(mp->xy))-stack_min(v_packet(mp->uv))) + if ( mp->dely+mp->tol>=stack_min(y_packet(mp->xy))-stack_max(v_packet(mp->uv))) + { + if ( mp->cur_t>=mp->max_t ){ + if ( mp->max_t==two ) { /* we've done 17 bisections */ + mp->cur_t=halfp(mp->cur_t+1); + mp->cur_tt=halfp(mp->cur_tt+1); + return; + } + mp->max_t+=mp->max_t; mp->appr_t=mp->cur_t; mp->appr_tt=mp->cur_tt; + } + @<Subdivide for a new level of intersection@>; + goto CONTINUE; + } + if ( mp->time_to_go>0 ) { + decr(mp->time_to_go); + } else { + while ( mp->appr_t<unity ) { + mp->appr_t+=mp->appr_t; mp->appr_tt+=mp->appr_tt; + } + mp->cur_t=mp->appr_t; mp->cur_tt=mp->appr_tt; return; + } + @<Advance to the next pair |(cur_t,cur_tt)|@>; + } +} + +@ The following variables are global, although they are used only by +|cubic_intersection|, because it is necessary on some machines to +split |cubic_intersection| up into two procedures. + +@<Glob...@>= +integer delx;integer dely; /* the components of $\Delta=2^l(w_0-z_0)$ */ +integer tol; /* bound on the uncertainty in the overlap test */ +integer uv; +integer xy; /* pointers to the current packets of interest */ +integer three_l; /* |tol_step| times the bisection level */ +integer appr_t;integer appr_tt; /* best approximations known to the answers */ + +@ We shall assume that the coordinates are sufficiently non-extreme that +integer overflow will not occur. +@^overflow in arithmetic@> + +@<Initialize for intersections at level zero@>= +q=mp_link(p); qq=mp_link(pp); mp->bisect_ptr=int_packets; +u1r=mp_right_x(p)-mp_x_coord(p); u2r=mp_left_x(q)-mp_right_x(p); +u3r=mp_x_coord(q)-mp_left_x(q); set_min_max(ur_packet); +v1r=mp_right_y(p)-mp_y_coord(p); v2r=mp_left_y(q)-mp_right_y(p); +v3r=mp_y_coord(q)-mp_left_y(q); set_min_max(vr_packet); +x1r=mp_right_x(pp)-mp_x_coord(pp); x2r=mp_left_x(qq)-mp_right_x(pp); +x3r=mp_x_coord(qq)-mp_left_x(qq); set_min_max(xr_packet); +y1r=mp_right_y(pp)-mp_y_coord(pp); y2r=mp_left_y(qq)-mp_right_y(pp); +y3r=mp_y_coord(qq)-mp_left_y(qq); set_min_max(yr_packet); +mp->delx=mp_x_coord(p)-mp_x_coord(pp); mp->dely=mp_y_coord(p)-mp_y_coord(pp); +mp->tol=0; mp->uv=r_packets; mp->xy=r_packets; +mp->three_l=0; mp->cur_t=1; mp->cur_tt=1 + +@ @<Subdivide for a new level of intersection@>= +stack_dx=mp->delx; stack_dy=mp->dely; stack_tol=mp->tol; +stack_uv=mp->uv; stack_xy=mp->xy; +mp->bisect_ptr=mp->bisect_ptr+int_increment; +mp->cur_t+=mp->cur_t; mp->cur_tt+=mp->cur_tt; +u1l=stack_1(u_packet(mp->uv)); u3r=stack_3(u_packet(mp->uv)); +u2l=half(u1l+stack_2(u_packet(mp->uv))); +u2r=half(u3r+stack_2(u_packet(mp->uv))); +u3l=half(u2l+u2r); u1r=u3l; +set_min_max(ul_packet); set_min_max(ur_packet); +v1l=stack_1(v_packet(mp->uv)); v3r=stack_3(v_packet(mp->uv)); +v2l=half(v1l+stack_2(v_packet(mp->uv))); +v2r=half(v3r+stack_2(v_packet(mp->uv))); +v3l=half(v2l+v2r); v1r=v3l; +set_min_max(vl_packet); set_min_max(vr_packet); +x1l=stack_1(x_packet(mp->xy)); x3r=stack_3(x_packet(mp->xy)); +x2l=half(x1l+stack_2(x_packet(mp->xy))); +x2r=half(x3r+stack_2(x_packet(mp->xy))); +x3l=half(x2l+x2r); x1r=x3l; +set_min_max(xl_packet); set_min_max(xr_packet); +y1l=stack_1(y_packet(mp->xy)); y3r=stack_3(y_packet(mp->xy)); +y2l=half(y1l+stack_2(y_packet(mp->xy))); +y2r=half(y3r+stack_2(y_packet(mp->xy))); +y3l=half(y2l+y2r); y1r=y3l; +set_min_max(yl_packet); set_min_max(yr_packet); +mp->uv=l_packets; mp->xy=l_packets; +mp->delx+=mp->delx; mp->dely+=mp->dely; +mp->tol=mp->tol-mp->three_l+mp->tol_step; +mp->tol+=mp->tol; mp->three_l=mp->three_l+mp->tol_step + +@ @<Advance to the next pair |(cur_t,cur_tt)|@>= +NOT_FOUND: +if ( odd(mp->cur_tt) ) { + if ( odd(mp->cur_t) ) { + @<Descend to the previous level and |goto not_found|@>; + } else { + incr(mp->cur_t); + mp->delx=mp->delx+stack_1(u_packet(mp->uv))+stack_2(u_packet(mp->uv)) + +stack_3(u_packet(mp->uv)); + mp->dely=mp->dely+stack_1(v_packet(mp->uv))+stack_2(v_packet(mp->uv)) + +stack_3(v_packet(mp->uv)); + mp->uv=mp->uv+int_packets; /* switch from |l_packets| to |r_packets| */ + decr(mp->cur_tt); mp->xy=mp->xy-int_packets; + /* switch from |r_packets| to |l_packets| */ + mp->delx=mp->delx+stack_1(x_packet(mp->xy))+stack_2(x_packet(mp->xy)) + +stack_3(x_packet(mp->xy)); + mp->dely=mp->dely+stack_1(y_packet(mp->xy))+stack_2(y_packet(mp->xy)) + +stack_3(y_packet(mp->xy)); + } +} else { + incr(mp->cur_tt); mp->tol=mp->tol+mp->three_l; + mp->delx=mp->delx-stack_1(x_packet(mp->xy))-stack_2(x_packet(mp->xy)) + -stack_3(x_packet(mp->xy)); + mp->dely=mp->dely-stack_1(y_packet(mp->xy))-stack_2(y_packet(mp->xy)) + -stack_3(y_packet(mp->xy)); + mp->xy=mp->xy+int_packets; /* switch from |l_packets| to |r_packets| */ +} + +@ @<Descend to the previous level...@>= +{ + mp->cur_t=halfp(mp->cur_t); mp->cur_tt=halfp(mp->cur_tt); + if ( mp->cur_t==0 ) return; + mp->bisect_ptr=mp->bisect_ptr-int_increment; + mp->three_l=mp->three_l-mp->tol_step; + mp->delx=stack_dx; mp->dely=stack_dy; mp->tol=stack_tol; + mp->uv=stack_uv; mp->xy=stack_xy; + goto NOT_FOUND; +} + +@ The |path_intersection| procedure is much simpler. +It invokes |cubic_intersection| in lexicographic order until finding a +pair of cubics that intersect. The final intersection times are placed in +|cur_t| and~|cur_tt|. + +@c +static void mp_path_intersection (MP mp,pointer h, pointer hh) { + pointer p,pp; /* link registers that traverse the given paths */ + integer n,nn; /* integer parts of intersection times, minus |unity| */ + @<Change one-point paths into dead cycles@>; + mp->tol_step=0; + do { + n=-unity; p=h; + do { + if ( mp_right_type(p)!=mp_endpoint ) { + nn=-unity; pp=hh; + do { + if ( mp_right_type(pp)!=mp_endpoint ) { + mp_cubic_intersection(mp, p,pp); + if ( mp->cur_t>0 ) { + mp->cur_t=mp->cur_t+n; mp->cur_tt=mp->cur_tt+nn; + return; + } + } + nn=nn+unity; pp=mp_link(pp); + } while (pp!=hh); + } + n=n+unity; p=mp_link(p); + } while (p!=h); + mp->tol_step=mp->tol_step+3; + } while (mp->tol_step<=3); + mp->cur_t=-unity; mp->cur_tt=-unity; +} + +@ @<Change one-point paths...@>= +if ( mp_right_type(h)==mp_endpoint ) { + mp_right_x(h)=mp_x_coord(h); mp_left_x(h)=mp_x_coord(h); + mp_right_y(h)=mp_y_coord(h); mp_left_y(h)=mp_y_coord(h); mp_right_type(h)=mp_explicit; +} +if ( mp_right_type(hh)==mp_endpoint ) { + mp_right_x(hh)=mp_x_coord(hh); mp_left_x(hh)=mp_x_coord(hh); + mp_right_y(hh)=mp_y_coord(hh); mp_left_y(hh)=mp_y_coord(hh); mp_right_type(hh)=mp_explicit; +} + +@* \[24] Dynamic linear equations. +\MP\ users define variables implicitly by stating equations that should be +satisfied; the computer is supposed to be smart enough to solve those equations. +And indeed, the computer tries valiantly to do so, by distinguishing five +different types of numeric values: + +\smallskip\hang +|type(p)=mp_known| is the nice case, when |value(p)| is the |scaled| value +of the variable whose address is~|p|. + +\smallskip\hang +|type(p)=mp_dependent| means that |value(p)| is not present, but |dep_list(p)| +points to a {\sl dependency list\/} that expresses the value of variable~|p| +as a |scaled| number plus a sum of independent variables with |fraction| +coefficients. + +\smallskip\hang +|type(p)=mp_independent| means that |value(p)=64s+m|, where |s>0| is a ``serial +number'' reflecting the time this variable was first used in an equation; +also |0<=m<64|, and each dependent variable +that refers to this one is actually referring to the future value of +this variable times~$2^m$. (Usually |m=0|, but higher degrees of +scaling are sometimes needed to keep the coefficients in dependency lists +from getting too large. The value of~|m| will always be even.) + +\smallskip\hang +|type(p)=mp_numeric_type| means that variable |p| hasn't appeared in an +equation before, but it has been explicitly declared to be numeric. + +\smallskip\hang +|type(p)=undefined| means that variable |p| hasn't appeared before. + +\smallskip\noindent +We have actually discussed these five types in the reverse order of their +history during a computation: Once |known|, a variable never again +becomes |dependent|; once |dependent|, it almost never again becomes +|mp_independent|; once |mp_independent|, it never again becomes |mp_numeric_type|; +and once |mp_numeric_type|, it never again becomes |undefined| (except +of course when the user specifically decides to scrap the old value +and start again). A backward step may, however, take place: Sometimes +a |dependent| variable becomes |mp_independent| again, when one of the +independent variables it depends on is reverting to |undefined|. + + +The next patch detects overflow of independent-variable serial +numbers. Diagnosed and patched by Thorsten Dahlheimer. + +@d s_scale 64 /* the serial numbers are multiplied by this factor */ +@d new_indep(A) /* create a new independent variable */ + { if ( mp->serial_no>el_gordo-s_scale ) + mp_fatal_error(mp, "variable instance identifiers exhausted"); + mp_type((A))=mp_independent; mp->serial_no=mp->serial_no+s_scale; + value((A))=mp->serial_no; + } + +@<Glob...@>= +integer serial_no; /* the most recent serial number, times |s_scale| */ + +@ @<Make variable |q+s| newly independent@>=new_indep(q+s) + +@ But how are dependency lists represented? It's simple: The linear combination +$\alpha_1v_1+\cdots+\alpha_kv_k+\beta$ appears in |k+1| value nodes. If +|q=dep_list(p)| points to this list, and if |k>0|, then |value(q)= +@t$\alpha_1$@>| (which is a |fraction|); |mp_info(q)| points to the location +of $\alpha_1$; and |mp_link(p)| points to the dependency list +$\alpha_2v_2+\cdots+\alpha_kv_k+\beta$. On the other hand if |k=0|, +then |value(q)=@t$\beta$@>| (which is |scaled|) and |mp_info(q)=null|. +The independent variables $v_1$, \dots,~$v_k$ have been sorted so that +they appear in decreasing order of their |value| fields (i.e., of +their serial numbers). \ (It is convenient to use decreasing order, +since |value(null)=0|. If the independent variables were not sorted by +serial number but by some other criterion, such as their location in |mem|, +the equation-solving mechanism would be too system-dependent, because +the ordering can affect the computed results.) + +The |link| field in the node that contains the constant term $\beta$ is +called the {\sl final link\/} of the dependency list. \MP\ maintains +a doubly-linked master list of all dependency lists, in terms of a permanently +allocated node +in |mem| called |dep_head|. If there are no dependencies, we have +|mp_link(dep_head)=dep_head| and |prev_dep(dep_head)=dep_head|; +otherwise |mp_link(dep_head)| points to the first dependent variable, say~|p|, +and |prev_dep(p)=dep_head|. We have |type(p)=mp_dependent|, and |dep_list(p)| +points to its dependency list. If the final link of that dependency list +occurs in location~|q|, then |mp_link(q)| points to the next dependent +variable (say~|r|); and we have |prev_dep(r)=q|, etc. + +@d dep_list(A) mp_link(value_loc((A))) + /* half of the |value| field in a |dependent| variable */ +@d prev_dep(A) mp_info(value_loc((A))) + /* the other half; makes a doubly linked list */ +@d dep_node_size 2 /* the number of words per dependency node */ + +@<Initialize table entries...@>= mp->serial_no=0; +mp_link(dep_head)=dep_head; prev_dep(dep_head)=dep_head; +mp_info(dep_head)=null; dep_list(dep_head)=null; + +@ Actually the description above contains a little white lie. There's +another kind of variable called |mp_proto_dependent|, which is +just like a |dependent| one except that the $\alpha$ coefficients +in its dependency list are |scaled| instead of being fractions. +Proto-dependency lists are mixed with dependency lists in the +nodes reachable from |dep_head|. + +@ Here is a procedure that prints a dependency list in symbolic form. +The second parameter should be either |dependent| or |mp_proto_dependent|, +to indicate the scaling of the coefficients. + +@<Declarations@>= +static void mp_print_dependency (MP mp,pointer p, quarterword t); + +@ @c +void mp_print_dependency (MP mp,pointer p, quarterword t) { + integer v; /* a coefficient */ + pointer pp,q; /* for list manipulation */ + pp=p; + while (true) { + v=abs(value(p)); q=mp_info(p); + if ( q==null ) { /* the constant term */ + if ( (v!=0)||(p==pp) ) { + if ( value(p)>0 ) if ( p!=pp ) mp_print_char(mp, xord('+')); + mp_print_scaled(mp, value(p)); + } + return; + } + @<Print the coefficient, unless it's $\pm1.0$@>; + if ( mp_type(q)!=mp_independent ) mp_confusion(mp, "dep"); +@:this can't happen dep}{\quad dep@> + mp_print_variable_name(mp, q); v=value(q) % s_scale; + while ( v>0 ) { mp_print(mp, "*4"); v=v-2; } + p=mp_link(p); + } +} + +@ @<Print the coefficient, unless it's $\pm1.0$@>= +if ( value(p)<0 ) mp_print_char(mp, xord('-')); +else if ( p!=pp ) mp_print_char(mp, xord('+')); +if ( t==mp_dependent ) v=mp_round_fraction(mp, v); +if ( v!=unity ) mp_print_scaled(mp, v) + +@ The maximum absolute value of a coefficient in a given dependency list +is returned by the following simple function. + +@c +static fraction mp_max_coef (MP mp,pointer p) { + fraction x; /* the maximum so far */ + x=0; + while ( mp_info(p)!=null ) { + if ( abs(value(p))>x ) x=abs(value(p)); + p=mp_link(p); + } + return x; +} + +@ One of the main operations needed on dependency lists is to add a multiple +of one list to the other; we call this |p_plus_fq|, where |p| and~|q| point +to dependency lists and |f| is a fraction. + +If the coefficient of any independent variable becomes |coef_bound| or +more, in absolute value, this procedure changes the type of that variable +to `|independent_needing_fix|', and sets the global variable |fix_needed| +to~|true|. The value of $|coef_bound|=\mu$ is chosen so that +$\mu^2+\mu<8$; this means that the numbers we deal with won't +get too large. (Instead of the ``optimum'' $\mu=(\sqrt{33}-1)/2\approx +2.3723$, the safer value 7/3 is taken as the threshold.) + +The changes mentioned in the preceding paragraph are actually done only if +the global variable |watch_coefs| is |true|. But it usually is; in fact, +it is |false| only when \MP\ is making a dependency list that will soon +be equated to zero. + +Several procedures that act on dependency lists, including |p_plus_fq|, +set the global variable |dep_final| to the final (constant term) node of +the dependency list that they produce. + +@d coef_bound 04525252525 /* |fraction| approximation to 7/3 */ +@d independent_needing_fix 0 + +@<Glob...@>= +boolean fix_needed; /* does at least one |independent| variable need scaling? */ +boolean watch_coefs; /* should we scale coefficients that exceed |coef_bound|? */ +pointer dep_final; /* location of the constant term and final link */ + +@ @<Set init...@>= +mp->fix_needed=false; mp->watch_coefs=true; + +@ The |p_plus_fq| procedure has a fourth parameter, |t|, that should be +set to |mp_proto_dependent| if |p| is a proto-dependency list. In this +case |f| will be |scaled|, not a |fraction|. Similarly, the fifth parameter~|tt| +should be |mp_proto_dependent| if |q| is a proto-dependency list. + +List |q| is unchanged by the operation; but list |p| is totally destroyed. + +The final link of the dependency list or proto-dependency list returned +by |p_plus_fq| is the same as the original final link of~|p|. Indeed, the +constant term of the result will be located in the same |mem| location +as the original constant term of~|p|. + +Coefficients of the result are assumed to be zero if they are less than +a certain threshold. This compensates for inevitable rounding errors, +and tends to make more variables `|known|'. The threshold is approximately +$10^{-5}$ in the case of normal dependency lists, $10^{-4}$ for +proto-dependencies. + +@d fraction_threshold 2685 /* a |fraction| coefficient less than this is zeroed */ +@d half_fraction_threshold 1342 /* half of |fraction_threshold| */ +@d scaled_threshold 8 /* a |scaled| coefficient less than this is zeroed */ +@d half_scaled_threshold 4 /* half of |scaled_threshold| */ + +@<Declarations@>= +static pointer mp_p_plus_fq ( MP mp, pointer p, integer f, + pointer q, quarterword t, quarterword tt) ; + +@ @c +pointer mp_p_plus_fq ( MP mp, pointer p, integer f, + pointer q, quarterword t, quarterword tt) { + pointer pp,qq; /* |mp_info(p)| and |mp_info(q)|, respectively */ + pointer r,s; /* for list manipulation */ + integer threshold; /* defines a neighborhood of zero */ + integer v; /* temporary register */ + if ( t==mp_dependent ) threshold=fraction_threshold; + else threshold=scaled_threshold; + r=temp_head; pp=mp_info(p); qq=mp_info(q); + while (1) { + if ( pp==qq ) { + if ( pp==null ) { + break; + } else { + @<Contribute a term from |p|, plus |f| times the + corresponding term from |q|@> + } + } else if ( value(pp)<value(qq) ) { + @<Contribute a term from |q|, multiplied by~|f|@> + } else { + mp_link(r)=p; r=p; p=mp_link(p); pp=mp_info(p); + } + } + if ( t==mp_dependent ) + value(p)=mp_slow_add(mp, value(p),mp_take_fraction(mp, value(q),f)); + else + value(p)=mp_slow_add(mp, value(p),mp_take_scaled(mp, value(q),f)); + mp_link(r)=p; mp->dep_final=p; + return mp_link(temp_head); +} + +@ @<Contribute a term from |p|, plus |f|...@>= +{ + if ( tt==mp_dependent ) v=value(p)+mp_take_fraction(mp, f,value(q)); + else v=value(p)+mp_take_scaled(mp, f,value(q)); + value(p)=v; s=p; p=mp_link(p); + if ( abs(v)<threshold ) { + mp_free_node(mp, s,dep_node_size); + } else { + if ( (abs(v)>=coef_bound) && mp->watch_coefs ) { + mp_type(qq)=independent_needing_fix; mp->fix_needed=true; + } + mp_link(r)=s; r=s; + }; + pp=mp_info(p); q=mp_link(q); qq=mp_info(q); +} + +@ @<Contribute a term from |q|, multiplied by~|f|@>= +{ + if ( tt==mp_dependent ) v=mp_take_fraction(mp, f,value(q)); + else v=mp_take_scaled(mp, f,value(q)); + if ( abs(v)>halfp(threshold) ) { + s=mp_get_node(mp, dep_node_size); mp_info(s)=qq; value(s)=v; + if ( (abs(v)>=coef_bound) && mp->watch_coefs ) { + mp_type(qq)=independent_needing_fix; mp->fix_needed=true; + } + mp_link(r)=s; r=s; + } + q=mp_link(q); qq=mp_info(q); +} + +@ It is convenient to have another subroutine for the special case +of |p_plus_fq| when |f=1.0|. In this routine lists |p| and |q| are +both of the same type~|t| (either |dependent| or |mp_proto_dependent|). + +@c +static pointer mp_p_plus_q (MP mp,pointer p, pointer q, quarterword t) { + pointer pp,qq; /* |mp_info(p)| and |mp_info(q)|, respectively */ + pointer r,s; /* for list manipulation */ + integer threshold; /* defines a neighborhood of zero */ + integer v; /* temporary register */ + if ( t==mp_dependent ) threshold=fraction_threshold; + else threshold=scaled_threshold; + r=temp_head; pp=mp_info(p); qq=mp_info(q); + while (1) { + if ( pp==qq ) { + if ( pp==null ) { + break; + } else { + @<Contribute a term from |p|, plus the + corresponding term from |q|@> + } + } else { + if ( value(pp)<value(qq) ) { + s=mp_get_node(mp, dep_node_size); mp_info(s)=qq; value(s)=value(q); + q=mp_link(q); qq=mp_info(q); mp_link(r)=s; r=s; + } else { + mp_link(r)=p; r=p; p=mp_link(p); pp=mp_info(p); + } + } + } + value(p)=mp_slow_add(mp, value(p),value(q)); + mp_link(r)=p; mp->dep_final=p; + return mp_link(temp_head); +} + +@ @<Contribute a term from |p|, plus the...@>= +{ + v=value(p)+value(q); + value(p)=v; s=p; p=mp_link(p); pp=mp_info(p); + if ( abs(v)<threshold ) { + mp_free_node(mp, s,dep_node_size); + } else { + if ( (abs(v)>=coef_bound ) && mp->watch_coefs ) { + mp_type(qq)=independent_needing_fix; mp->fix_needed=true; + } + mp_link(r)=s; r=s; + } + q=mp_link(q); qq=mp_info(q); +} + +@ A somewhat simpler routine will multiply a dependency list +by a given constant~|v|. The constant is either a |fraction| less than +|fraction_one|, or it is |scaled|. In the latter case we might be forced to +convert a dependency list to a proto-dependency list. +Parameters |t0| and |t1| are the list types before and after; +they should agree unless |t0=mp_dependent| and |t1=mp_proto_dependent| +and |v_is_scaled=true|. + +@c +static pointer mp_p_times_v (MP mp,pointer p, integer v, quarterword t0, + quarterword t1, boolean v_is_scaled) { + pointer r,s; /* for list manipulation */ + integer w; /* tentative coefficient */ + integer threshold; + boolean scaling_down; + if ( t0!=t1 ) scaling_down=true; else scaling_down=(!v_is_scaled); + if ( t1==mp_dependent ) threshold=half_fraction_threshold; + else threshold=half_scaled_threshold; + r=temp_head; + while ( mp_info(p)!=null ) { + if ( scaling_down ) w=mp_take_fraction(mp, v,value(p)); + else w=mp_take_scaled(mp, v,value(p)); + if ( abs(w)<=threshold ) { + s=mp_link(p); mp_free_node(mp, p,dep_node_size); p=s; + } else { + if ( abs(w)>=coef_bound ) { + mp->fix_needed=true; mp_type(mp_info(p))=independent_needing_fix; + } + mp_link(r)=p; r=p; value(p)=w; p=mp_link(p); + } + } + mp_link(r)=p; + if ( v_is_scaled ) value(p)=mp_take_scaled(mp, value(p),v); + else value(p)=mp_take_fraction(mp, value(p),v); + return mp_link(temp_head); +} + +@ Similarly, we sometimes need to divide a dependency list +by a given |scaled| constant. + +@<Declarations@>= +static pointer mp_p_over_v (MP mp,pointer p, scaled v, quarterword + t0, quarterword t1) ; + +@ @c +pointer mp_p_over_v (MP mp,pointer p, scaled v, quarterword + t0, quarterword t1) { + pointer r,s; /* for list manipulation */ + integer w; /* tentative coefficient */ + integer threshold; + boolean scaling_down; + if ( t0!=t1 ) scaling_down=true; else scaling_down=false; + if ( t1==mp_dependent ) threshold=half_fraction_threshold; + else threshold=half_scaled_threshold; + r=temp_head; + while ( mp_info( p)!=null ) { + if ( scaling_down ) { + if ( abs(v)<02000000 ) w=mp_make_scaled(mp, value(p),v*010000); + else w=mp_make_scaled(mp, mp_round_fraction(mp, value(p)),v); + } else { + w=mp_make_scaled(mp, value(p),v); + } + if ( abs(w)<=threshold ) { + s=mp_link(p); mp_free_node(mp, p,dep_node_size); p=s; + } else { + if ( abs(w)>=coef_bound ) { + mp->fix_needed=true; mp_type(mp_info(p))=independent_needing_fix; + } + mp_link(r)=p; r=p; value(p)=w; p=mp_link(p); + } + } + mp_link(r)=p; value(p)=mp_make_scaled(mp, value(p),v); + return mp_link(temp_head); +} + +@ Here's another utility routine for dependency lists. When an independent +variable becomes dependent, we want to remove it from all existing +dependencies. The |p_with_x_becoming_q| function computes the +dependency list of~|p| after variable~|x| has been replaced by~|q|. + +This procedure has basically the same calling conventions as |p_plus_fq|: +List~|q| is unchanged; list~|p| is destroyed; the constant node and the +final link are inherited from~|p|; and the fourth parameter tells whether +or not |p| is |mp_proto_dependent|. However, the global variable |dep_final| +is not altered if |x| does not occur in list~|p|. + +@c +static pointer mp_p_with_x_becoming_q (MP mp,pointer p, + pointer x, pointer q, quarterword t) { + pointer r,s; /* for list manipulation */ + integer v; /* coefficient of |x| */ + integer sx; /* serial number of |x| */ + s=p; r=temp_head; sx=value(x); + while ( value(mp_info(s))>sx ) { r=s; s=mp_link(s); }; + if ( mp_info(s)!=x ) { + return p; + } else { + mp_link(temp_head)=p; mp_link(r)=mp_link(s); v=value(s); + mp_free_node(mp, s,dep_node_size); + return mp_p_plus_fq(mp, mp_link(temp_head),v,q,t,mp_dependent); + } +} + +@ Here's a simple procedure that reports an error when a variable +has just received a known value that's out of the required range. + +@<Declarations@>= +static void mp_val_too_big (MP mp,scaled x) ; + +@ @c void mp_val_too_big (MP mp,scaled x) { + if ( mp->internal[mp_warning_check]>0 ) { + print_err("Value is too large ("); mp_print_scaled(mp, x); mp_print_char(mp, xord(')')); +@.Value is too large@> + help4("The equation I just processed has given some variable", + "a value of 4096 or more. Continue and I'll try to cope", + "with that big value; but it might be dangerous.", + "(Set warningcheck:=0 to suppress this message.)"); + mp_error(mp); + } +} + +@ When a dependent variable becomes known, the following routine +removes its dependency list. Here |p| points to the variable, and +|q| points to the dependency list (which is one node long). + +@<Declarations@>= +static void mp_make_known (MP mp,pointer p, pointer q) ; + +@ @c void mp_make_known (MP mp,pointer p, pointer q) { + int t; /* the previous type */ + prev_dep(mp_link(q))=prev_dep(p); + mp_link(prev_dep(p))=mp_link(q); t=mp_type(p); + mp_type(p)=mp_known; value(p)=value(q); mp_free_node(mp, q,dep_node_size); + if ( abs(value(p))>=fraction_one ) mp_val_too_big(mp, value(p)); + if (( mp->internal[mp_tracing_equations]>0) && mp_interesting(mp, p) ) { + mp_begin_diagnostic(mp); mp_print_nl(mp, "#### "); +@:]]]\#\#\#\#_}{\.{\#\#\#\#}@> + mp_print_variable_name(mp, p); + mp_print_char(mp, xord('=')); mp_print_scaled(mp, value(p)); + mp_end_diagnostic(mp, false); + } + if (( mp->cur_exp==p ) && mp->cur_type==t ) { + mp->cur_type=mp_known; mp->cur_exp=value(p); + mp_free_node(mp, p,value_node_size); + } +} + +@ The |fix_dependencies| routine is called into action when |fix_needed| +has been triggered. The program keeps a list~|s| of independent variables +whose coefficients must be divided by~4. + +In unusual cases, this fixup process might reduce one or more coefficients +to zero, so that a variable will become known more or less by default. + +@<Declarations@>= +static void mp_fix_dependencies (MP mp); + +@ @c +static void mp_fix_dependencies (MP mp) { + pointer p,q,r,s,t; /* list manipulation registers */ + pointer x; /* an independent variable */ + r=mp_link(dep_head); s=null; + while ( r!=dep_head ){ + t=r; + @<Run through the dependency list for variable |t|, fixing + all nodes, and ending with final link~|q|@>; + r=mp_link(q); + if ( q==dep_list(t) ) mp_make_known(mp, t,q); + } + while ( s!=null ) { + p=mp_link(s); x=mp_info(s); free_avail(s); s=p; + mp_type(x)=mp_independent; value(x)=value(x)+2; + } + mp->fix_needed=false; +} + +@ @d independent_being_fixed 1 /* this variable already appears in |s| */ + +@<Run through the dependency list for variable |t|...@>= +r=value_loc(t); /* |mp_link(r)=dep_list(t)| */ +while (1) { + q=mp_link(r); x=mp_info(q); + if ( x==null ) break; + if ( mp_type(x)<=independent_being_fixed ) { + if ( mp_type(x)<independent_being_fixed ) { + p=mp_get_avail(mp); mp_link(p)=s; s=p; + mp_info(s)=x; mp_type(x)=independent_being_fixed; + } + value(q)=value(q) / 4; + if ( value(q)==0 ) { + mp_link(r)=mp_link(q); mp_free_node(mp, q,dep_node_size); q=r; + } + } + r=q; +} + + +@ The |new_dep| routine installs a dependency list~|p| into the value node~|q|, +linking it into the list of all known dependencies. We assume that +|dep_final| points to the final node of list~|p|. + +@c +static void mp_new_dep (MP mp,pointer q, pointer p) { + pointer r; /* what used to be the first dependency */ + dep_list(q)=p; prev_dep(q)=dep_head; + r=mp_link(dep_head); mp_link(mp->dep_final)=r; prev_dep(r)=mp->dep_final; + mp_link(dep_head)=q; +} + +@ Here is one of the ways a dependency list gets started. +The |const_dependency| routine produces a list that has nothing but +a constant term. + +@c static pointer mp_const_dependency (MP mp, scaled v) { + mp->dep_final=mp_get_node(mp, dep_node_size); + value(mp->dep_final)=v; mp_info(mp->dep_final)=null; + return mp->dep_final; +} + +@ And here's a more interesting way to start a dependency list from scratch: +The parameter to |single_dependency| is the location of an +independent variable~|x|, and the result is the simple dependency list +`|x+0|'. + +In the unlikely event that the given independent variable has been doubled so +often that we can't refer to it with a nonzero coefficient, +|single_dependency| returns the simple list `0'. This case can be +recognized by testing that the returned list pointer is equal to +|dep_final|. + +@c +static pointer mp_single_dependency (MP mp,pointer p) { + pointer q; /* the new dependency list */ + integer m; /* the number of doublings */ + m=value(p) % s_scale; + if ( m>28 ) { + return mp_const_dependency(mp, 0); + } else { + q=mp_get_node(mp, dep_node_size); + value(q)=(integer)two_to_the(28-m); mp_info(q)=p; + mp_link(q)=mp_const_dependency(mp, 0); + return q; + } +} + +@ We sometimes need to make an exact copy of a dependency list. + +@c +static pointer mp_copy_dep_list (MP mp,pointer p) { + pointer q; /* the new dependency list */ + q=mp_get_node(mp, dep_node_size); mp->dep_final=q; + while (1) { + mp_info(mp->dep_final)=mp_info(p); value(mp->dep_final)=value(p); + if ( mp_info(mp->dep_final)==null ) break; + mp_link(mp->dep_final)=mp_get_node(mp, dep_node_size); + mp->dep_final=mp_link(mp->dep_final); p=mp_link(p); + } + return q; +} + +@ But how do variables normally become known? Ah, now we get to the heart of the +equation-solving mechanism. The |linear_eq| procedure is given a |dependent| +or |mp_proto_dependent| list,~|p|, in which at least one independent variable +appears. It equates this list to zero, by choosing an independent variable +with the largest coefficient and making it dependent on the others. The +newly dependent variable is eliminated from all current dependencies, +thereby possibly making other dependent variables known. + +The given list |p| is, of course, totally destroyed by all this processing. + +@c +static void mp_linear_eq (MP mp, pointer p, quarterword t) { + pointer q,r,s; /* for link manipulation */ + pointer x; /* the variable that loses its independence */ + integer n; /* the number of times |x| had been halved */ + integer v; /* the coefficient of |x| in list |p| */ + pointer prev_r; /* lags one step behind |r| */ + pointer final_node; /* the constant term of the new dependency list */ + integer w; /* a tentative coefficient */ + @<Find a node |q| in list |p| whose coefficient |v| is largest@>; + x=mp_info(q); n=value(x) % s_scale; + @<Divide list |p| by |-v|, removing node |q|@>; + if ( mp->internal[mp_tracing_equations]>0 ) { + @<Display the new dependency@>; + } + @<Simplify all existing dependencies by substituting for |x|@>; + @<Change variable |x| from |independent| to |dependent| or |known|@>; + if ( mp->fix_needed ) mp_fix_dependencies(mp); +} + +@ @<Find a node |q| in list |p| whose coefficient |v| is largest@>= +q=p; r=mp_link(p); v=value(q); +while ( mp_info(r)!=null ) { + if ( abs(value(r))>abs(v) ) { q=r; v=value(r); }; + r=mp_link(r); +} + +@ Here we want to change the coefficients from |scaled| to |fraction|, +except in the constant term. In the common case of a trivial equation +like `\.{x=3.14}', we will have |v=-fraction_one|, |q=p|, and |t=mp_dependent|. + +@<Divide list |p| by |-v|, removing node |q|@>= +s=temp_head; mp_link(s)=p; r=p; +do { + if ( r==q ) { + mp_link(s)=mp_link(r); mp_free_node(mp, r,dep_node_size); + } else { + w=mp_make_fraction(mp, value(r),v); + if ( abs(w)<=half_fraction_threshold ) { + mp_link(s)=mp_link(r); mp_free_node(mp, r,dep_node_size); + } else { + value(r)=-w; s=r; + } + } + r=mp_link(s); +} while (mp_info(r)!=null); +if ( t==mp_proto_dependent ) { + value(r)=-mp_make_scaled(mp, value(r),v); +} else if ( v!=-fraction_one ) { + value(r)=-mp_make_fraction(mp, value(r),v); +} +final_node=r; p=mp_link(temp_head) + +@ @<Display the new dependency@>= +if ( mp_interesting(mp, x) ) { + mp_begin_diagnostic(mp); mp_print_nl(mp, "## "); + mp_print_variable_name(mp, x); +@:]]]\#\#_}{\.{\#\#}@> + w=n; + while ( w>0 ) { mp_print(mp, "*4"); w=w-2; }; + mp_print_char(mp, xord('=')); mp_print_dependency(mp, p,mp_dependent); + mp_end_diagnostic(mp, false); +} + +@ @<Simplify all existing dependencies by substituting for |x|@>= +prev_r=dep_head; r=mp_link(dep_head); +while ( r!=dep_head ) { + s=dep_list(r); q=mp_p_with_x_becoming_q(mp, s,x,p,mp_type(r)); + if ( mp_info(q)==null ) { + mp_make_known(mp, r,q); + } else { + dep_list(r)=q; + do { q=mp_link(q); } while (mp_info(q)!=null); + prev_r=q; + } + r=mp_link(prev_r); +} + +@ @<Change variable |x| from |independent| to |dependent| or |known|@>= +if ( n>0 ) @<Divide list |p| by $2^n$@>; +if ( mp_info(p)==null ) { + mp_type(x)=mp_known; + value(x)=value(p); + if ( abs(value(x))>=fraction_one ) mp_val_too_big(mp, value(x)); + mp_free_node(mp, p,dep_node_size); + if ( mp->cur_exp==x ) if ( mp->cur_type==mp_independent ) { + mp->cur_exp=value(x); mp->cur_type=mp_known; + mp_free_node(mp, x,value_node_size); + } +} else { + mp_type(x)=mp_dependent; mp->dep_final=final_node; mp_new_dep(mp, x,p); + if ( mp->cur_exp==x ) if ( mp->cur_type==mp_independent ) mp->cur_type=mp_dependent; +} + +@ @<Divide list |p| by $2^n$@>= +{ + s=temp_head; mp_link(temp_head)=p; r=p; + do { + if ( n>30 ) w=0; + else w=value(r) / two_to_the(n); + if ( (abs(w)<=half_fraction_threshold)&&(mp_info(r)!=null) ) { + mp_link(s)=mp_link(r); + mp_free_node(mp, r,dep_node_size); + } else { + value(r)=w; s=r; + } + r=mp_link(s); + } while (mp_info(s)!=null); + p=mp_link(temp_head); +} + +@ The |check_mem| procedure, which is used only when \MP\ is being +debugged, makes sure that the current dependency lists are well formed. + +@<Check the list of linear dependencies@>= +q=dep_head; p=mp_link(q); +while ( p!=dep_head ) { + if ( prev_dep(p)!=q ) { + mp_print_nl(mp, "Bad PREVDEP at "); mp_print_int(mp, p); +@.Bad PREVDEP...@> + } + p=dep_list(p); + while (1) { + r=mp_info(p); q=p; p=mp_link(q); + if ( r==null ) break; + if ( value(mp_info(p))>=value(r) ) { + mp_print_nl(mp, "Out of order at "); mp_print_int(mp, p); +@.Out of order...@> + } + } +} + +@* \[25] Dynamic nonlinear equations. +Variables of numeric type are maintained by the general scheme of +independent, dependent, and known values that we have just studied; +and the components of pair and transform variables are handled in the +same way. But \MP\ also has five other types of values: \&{boolean}, +\&{string}, \&{pen}, \&{path}, and \&{picture}; what about them? + +Equations are allowed between nonlinear quantities, but only in a +simple form. Two variables that haven't yet been assigned values are +either equal to each other, or they're not. + +Before a boolean variable has received a value, its type is |mp_unknown_boolean|; +similarly, there are variables whose type is |mp_unknown_string|, |mp_unknown_pen|, +|mp_unknown_path|, and |mp_unknown_picture|. In such cases the value is either +|null| (which means that no other variables are equivalent to this one), or +it points to another variable of the same undefined type. The pointers in the +latter case form a cycle of nodes, which we shall call a ``ring.'' +Rings of undefined variables may include capsules, which arise as +intermediate results within expressions or as \&{expr} parameters to macros. + +When one member of a ring receives a value, the same value is given to +all the other members. In the case of paths and pictures, this implies +making separate copies of a potentially large data structure; users should +restrain their enthusiasm for such generality, unless they have lots and +lots of memory space. + +@ The following procedure is called when a capsule node is being +added to a ring (e.g., when an unknown variable is mentioned in an expression). + +@c +static pointer mp_new_ring_entry (MP mp,pointer p) { + pointer q; /* the new capsule node */ + q=mp_get_node(mp, value_node_size); mp_name_type(q)=mp_capsule; + mp_type(q)=mp_type(p); + if ( value(p)==null ) value(q)=p; else value(q)=value(p); + value(p)=q; + return q; +} + +@ Conversely, we might delete a capsule or a variable before it becomes known. +The following procedure simply detaches a quantity from its ring, +without recycling the storage. + +@<Declarations@>= +static void mp_ring_delete (MP mp,pointer p); + +@ @c +void mp_ring_delete (MP mp,pointer p) { + pointer q; + q=value(p); + if ( q!=null ) if ( q!=p ){ + while ( value(q)!=p ) q=value(q); + value(q)=value(p); + } +} + +@ Eventually there might be an equation that assigns values to all of the +variables in a ring. The |nonlinear_eq| subroutine does the necessary +propagation of values. + +If the parameter |flush_p| is |true|, node |p| itself needn't receive a +value, it will soon be recycled. + +@c +static void mp_nonlinear_eq (MP mp,integer v, pointer p, boolean flush_p) { + quarterword t; /* the type of ring |p| */ + pointer q,r; /* link manipulation registers */ + t=mp_type(p)-unknown_tag; q=value(p); + if ( flush_p ) mp_type(p)=mp_vacuous; else p=q; + do { + r=value(q); mp_type(q)=t; + switch (t) { + case mp_boolean_type: value(q)=v; break; + case mp_string_type: value(q)=v; add_str_ref(v); break; + case mp_pen_type: value(q)=copy_pen(v); break; + case mp_path_type: value(q)=mp_copy_path(mp, v); break; + case mp_picture_type: value(q)=v; add_edge_ref(v); break; + } /* there ain't no more cases */ + q=r; + } while (q!=p); +} + +@ If two members of rings are equated, and if they have the same type, +the |ring_merge| procedure is called on to make them equivalent. + +@c +static void mp_ring_merge (MP mp,pointer p, pointer q) { + pointer r; /* traverses one list */ + r=value(p); + while ( r!=p ) { + if ( r==q ) { + @<Exclaim about a redundant equation@>; + return; + }; + r=value(r); + } + r=value(p); value(p)=value(q); value(q)=r; +} + +@ @<Exclaim about a redundant equation@>= +{ + print_err("Redundant equation"); +@.Redundant equation@> + help2("I already knew that this equation was true.", + "But perhaps no harm has been done; let's continue."); + mp_put_get_error(mp); +} + +@* \[26] Introduction to the syntactic routines. +Let's pause a moment now and try to look at the Big Picture. +The \MP\ program consists of three main parts: syntactic routines, +semantic routines, and output routines. The chief purpose of the +syntactic routines is to deliver the user's input to the semantic routines, +while parsing expressions and locating operators and operands. The +semantic routines act as an interpreter responding to these operators, +which may be regarded as commands. And the output routines are +periodically called on to produce compact font descriptions that can be +used for typesetting or for making interim proof drawings. We have +discussed the basic data structures and many of the details of semantic +operations, so we are good and ready to plunge into the part of \MP\ that +actually controls the activities. + +Our current goal is to come to grips with the |get_next| procedure, +which is the keystone of \MP's input mechanism. Each call of |get_next| +sets the value of three variables |cur_cmd|, |cur_mod|, and |cur_sym|, +representing the next input token. +$$\vbox{\halign{#\hfil\cr + \hbox{|cur_cmd| denotes a command code from the long list of codes + given earlier;}\cr + \hbox{|cur_mod| denotes a modifier of the command code;}\cr + \hbox{|cur_sym| is the hash address of the symbolic token that was + just scanned,}\cr + \hbox{\qquad or zero in the case of a numeric or string + or capsule token.}\cr}}$$ +Underlying this external behavior of |get_next| is all the machinery +necessary to convert from character files to tokens. At a given time we +may be only partially finished with the reading of several files (for +which \&{input} was specified), and partially finished with the expansion +of some user-defined macros and/or some macro parameters, and partially +finished reading some text that the user has inserted online, +and so on. When reading a character file, the characters must be +converted to tokens; comments and blank spaces must +be removed, numeric and string tokens must be evaluated. + +To handle these situations, which might all be present simultaneously, +\MP\ uses various stacks that hold information about the incomplete +activities, and there is a finite state control for each level of the +input mechanism. These stacks record the current state of an implicitly +recursive process, but the |get_next| procedure is not recursive. + +@<Glob...@>= +integer cur_cmd; /* current command set by |get_next| */ +integer cur_mod; /* operand of current command */ +halfword cur_sym; /* hash address of current symbol */ + +@ The |print_cmd_mod| routine prints a symbolic interpretation of a +command code and its modifier. +It consists of a rather tedious sequence of print +commands, and most of it is essentially an inverse to the |primitive| +routine that enters a \MP\ primitive into |hash| and |eqtb|. Therefore almost +all of this procedure appears elsewhere in the program, together with the +corresponding |primitive| calls. + +@<Declarations@>= +static void mp_print_cmd_mod (MP mp,integer c, integer m) ; + +@ @c +void mp_print_cmd_mod (MP mp,integer c, integer m) { + switch (c) { + @<Cases of |print_cmd_mod| for symbolic printing of primitives@> + default: mp_print(mp, "[unknown command code!]"); break; + } +} + +@ Here is a procedure that displays a given command in braces, in the +user's transcript file. + +@d show_cur_cmd_mod mp_show_cmd_mod(mp, mp->cur_cmd,mp->cur_mod) + +@c +static void mp_show_cmd_mod (MP mp,integer c, integer m) { + mp_begin_diagnostic(mp); mp_print_nl(mp, "{"); + mp_print_cmd_mod(mp, c,m); mp_print_char(mp, xord('}')); + mp_end_diagnostic(mp, false); +} + +@* \[27] Input stacks and states. +The state of \MP's input mechanism appears in the input stack, whose +entries are records with five fields, called |index|, |start|, |loc|, +|limit|, and |name|. The top element of this stack is maintained in a +global variable for which no subscripting needs to be done; the other +elements of the stack appear in an array. Hence the stack is declared thus: + +@<Types...@>= +typedef struct { + quarterword index_field; + halfword start_field, loc_field, limit_field, name_field; +} in_state_record; + +@ @<Glob...@>= +in_state_record *input_stack; +integer input_ptr; /* first unused location of |input_stack| */ +integer max_in_stack; /* largest value of |input_ptr| when pushing */ +in_state_record cur_input; /* the ``top'' input state */ +int stack_size; /* maximum number of simultaneous input sources */ + +@ @<Allocate or initialize ...@>= +mp->stack_size = 300; +mp->input_stack = xmalloc((mp->stack_size+1),sizeof(in_state_record)); + +@ @<Dealloc variables@>= +xfree(mp->input_stack); + +@ We've already defined the special variable |loc==cur_input.loc_field| +in our discussion of basic input-output routines. The other components of +|cur_input| are defined in the same way: + +@d iindex mp->cur_input.index_field /* reference for buffer information */ +@d start mp->cur_input.start_field /* starting position in |buffer| */ +@d limit mp->cur_input.limit_field /* end of current line in |buffer| */ +@d name mp->cur_input.name_field /* name of the current file */ + +@ Let's look more closely now at the five control variables +(|index|,~|start|,~|loc|,~|limit|,~|name|), +assuming that \MP\ is reading a line of characters that have been input +from some file or from the user's terminal. There is an array called +|buffer| that acts as a stack of all lines of characters that are +currently being read from files, including all lines on subsidiary +levels of the input stack that are not yet completed. \MP\ will return to +the other lines when it is finished with the present input file. + +(Incidentally, on a machine with byte-oriented addressing, it would be +appropriate to combine |buffer| with the |str_pool| array, +letting the buffer entries grow downward from the top of the string pool +and checking that these two tables don't bump into each other.) + +The line we are currently working on begins in position |start| of the +buffer; the next character we are about to read is |buffer[loc]|; and +|limit| is the location of the last character present. We always have +|loc<=limit|. For convenience, |buffer[limit]| has been set to |"%"|, so +that the end of a line is easily sensed. + +The |name| variable is a string number that designates the name of +the current file, if we are reading an ordinary text file. Special codes +|is_term..max_spec_src| indicate other sources of input text. + +@d is_term 0 /* |name| value when reading from the terminal for normal input */ +@d is_read 1 /* |name| value when executing a \&{readstring} or \&{readfrom} */ +@d is_scantok 2 /* |name| value when reading text generated by \&{scantokens} */ +@d max_spec_src is_scantok + +@ Additional information about the current line is available via the +|index| variable, which counts how many lines of characters are present +in the buffer below the current level. We have |index=0| when reading +from the terminal and prompting the user for each line; then if the user types, +e.g., `\.{input figs}', we will have |index=1| while reading +the file \.{figs.mp}. However, it does not follow that |index| is the +same as the input stack pointer, since many of the levels on the input +stack may come from token lists and some |index| values may correspond +to \.{MPX} files that are not currently on the stack. + +The global variable |in_open| is equal to the highest |index| value counting +\.{MPX} files but excluding token-list input levels. Thus, the number of +partially read lines in the buffer is |in_open+1| and we have |in_open>=index| +when we are not reading a token list. + +If we are not currently reading from the terminal, +we are reading from the file variable |input_file[index]|. We use +the notation |terminal_input| as a convenient abbreviation for |name=is_term|, +and |cur_file| as an abbreviation for |input_file[index]|. + +When \MP\ is not reading from the terminal, the global variable |line| contains +the line number in the current file, for use in error messages. More precisely, +|line| is a macro for |line_stack[index]| and the |line_stack| array gives +the line number for each file in the |input_file| array. + +When an \.{MPX} file is opened the file name is stored in the |mpx_name| +array so that the name doesn't get lost when the file is temporarily removed +from the input stack. +Thus when |input_file[k]| is an \.{MPX} file, its name is |mpx_name[k]| +and it contains translated \TeX\ pictures for |input_file[k-1]|. +Since this is not an \.{MPX} file, we have +$$ \hbox{|mpx_name[k-1]<=absent|}. $$ +This |name| field is set to |finished| when |input_file[k]| is completely +read. + +If more information about the input state is needed, it can be +included in small arrays like those shown here. For example, +the current page or segment number in the input file might be put +into a variable |page|, that is really a macro for the current entry +in `\ignorespaces|page_stack:array[0..max_in_open] of integer|\unskip' +by analogy with |line_stack|. +@^system dependencies@> + +@d terminal_input (name==is_term) /* are we reading from the terminal? */ +@d cur_file mp->input_file[iindex] /* the current |void *| variable */ +@d line mp->line_stack[iindex] /* current line number in the current source file */ +@d in_name mp->iname_stack[iindex] /* a string used to construct \.{MPX} file names */ +@d in_area mp->iarea_stack[iindex] /* another string for naming \.{MPX} files */ +@d absent 1 /* |name_field| value for unused |mpx_in_stack| entries */ +@d mpx_reading (mp->mpx_name[iindex]>absent) + /* when reading a file, is it an \.{MPX} file? */ +@d mpx_finished 0 + /* |name_field| value when the corresponding \.{MPX} file is finished */ + +@<Glob...@>= +integer in_open; /* the number of lines in the buffer, less one */ +integer in_open_max; /* highest value of |in_open| ever seen */ +unsigned int open_parens; /* the number of open text files */ +void * *input_file ; +integer *line_stack ; /* the line number for each file */ +char * *iname_stack; /* used for naming \.{MPX} files */ +char * *iarea_stack; /* used for naming \.{MPX} files */ +halfword*mpx_name ; + +@ @<Allocate or ...@>= +mp->input_file = xmalloc((mp->max_in_open+1),sizeof(void *)); +mp->line_stack = xmalloc((mp->max_in_open+1),sizeof(integer)); +mp->iname_stack = xmalloc((mp->max_in_open+1),sizeof(char *)); +mp->iarea_stack = xmalloc((mp->max_in_open+1),sizeof(char *)); +mp->mpx_name = xmalloc((mp->max_in_open+1),sizeof(halfword)); +{ + int k; + for (k=0;k<=mp->max_in_open;k++) { + mp->iname_stack[k] =NULL; + mp->iarea_stack[k] =NULL; + } +} + +@ @<Dealloc variables@>= +{ + int l; + for (l=0;l<=mp->max_in_open;l++) { + xfree(mp->iname_stack[l]); + xfree(mp->iarea_stack[l]); + } +} +xfree(mp->input_file); +xfree(mp->line_stack); +xfree(mp->iname_stack); +xfree(mp->iarea_stack); +xfree(mp->mpx_name); + + +@ However, all this discussion about input state really applies only to the +case that we are inputting from a file. There is another important case, +namely when we are currently getting input from a token list. In this case +|iindex>max_in_open|, and the conventions about the other state variables +are different: + +\yskip\hang|loc| is a pointer to the current node in the token list, i.e., +the node that will be read next. If |loc=null|, the token list has been +fully read. + +\yskip\hang|start| points to the first node of the token list; this node +may or may not contain a reference count, depending on the type of token +list involved. + +\yskip\hang|token_type|, which takes the place of |iindex| in the +discussion above, is a code number that explains what kind of token list +is being scanned. + +\yskip\hang|name| points to the |eqtb| address of the control sequence +being expanded, if the current token list is a macro not defined by +\&{vardef}. Macros defined by \&{vardef} have |name=null|; their name +can be deduced by looking at their first two parameters. + +\yskip\hang|param_start|, which takes the place of |limit|, tells where +the parameters of the current macro or loop text begin in the |param_stack|. + +\yskip\noindent The |token_type| can take several values, depending on +where the current token list came from: + +\yskip +\indent|forever_text|, if the token list being scanned is the body of +a \&{forever} loop; + +\indent|loop_text|, if the token list being scanned is the body of +a \&{for} or \&{forsuffixes} loop; + +\indent|parameter|, if a \&{text} or \&{suffix} parameter is being scanned; + +\indent|backed_up|, if the token list being scanned has been inserted as +`to be read again'. + +\indent|inserted|, if the token list being scanned has been inserted as +part of error recovery; + +\indent|macro|, if the expansion of a user-defined symbolic token is being +scanned. + +\yskip\noindent +The token list begins with a reference count if and only if |token_type= +macro|. +@^reference counts@> + +@d token_type iindex /* type of current token list */ +@d token_state (iindex>(int)mp->max_in_open) /* are we scanning a token list? */ +@d file_state (iindex<=(int)mp->max_in_open) /* are we scanning a file line? */ +@d param_start limit /* base of macro parameters in |param_stack| */ +@d forever_text (mp->max_in_open+1) /* |token_type| code for loop texts */ +@d loop_text (mp->max_in_open+2) /* |token_type| code for loop texts */ +@d parameter (mp->max_in_open+3) /* |token_type| code for parameter texts */ +@d backed_up (mp->max_in_open+4) /* |token_type| code for texts to be reread */ +@d inserted (mp->max_in_open+5) /* |token_type| code for inserted texts */ +@d macro (mp->max_in_open+6) /* |token_type| code for macro replacement texts */ + +@ The |param_stack| is an auxiliary array used to hold pointers to the token +lists for parameters at the current level and subsidiary levels of input. +This stack grows at a different rate from the others. + +@<Glob...@>= +pointer *param_stack; /* token list pointers for parameters */ +integer param_ptr; /* first unused entry in |param_stack| */ +integer max_param_stack; /* largest value of |param_ptr| */ + +@ @<Allocate or initialize ...@>= +mp->param_stack = xmalloc((mp->param_size+1),sizeof(pointer)); + +@ @<Dealloc variables@>= +xfree(mp->param_stack); + +@ Notice that the |line| isn't valid when |token_state| is true because it +depends on |iindex|. If we really need to know the line number for the +topmost file in the iindex stack we use the following function. If a page +number or other information is needed, this routine should be modified to +compute it as well. +@^system dependencies@> + +@<Declarations@>= +static integer mp_true_line (MP mp) ; + +@ @c +integer mp_true_line (MP mp) { + int k; /* an index into the input stack */ + if ( file_state && (name>max_spec_src) ) { + return line; + } else { + k=mp->input_ptr; + while ((k>0) && + ((mp->input_stack[(k-1)].index_field>mp->max_in_open)|| + (mp->input_stack[(k-1)].name_field<=max_spec_src))) { + decr(k); + } + return (k>0 ? mp->line_stack[(k-1)] : 0 ); + } +} + +@ Thus, the ``current input state'' can be very complicated indeed; there +can be many levels and each level can arise in a variety of ways. The +|show_context| procedure, which is used by \MP's error-reporting routine to +print out the current input state on all levels down to the most recent +line of characters from an input file, illustrates most of these conventions. +The global variable |file_ptr| contains the lowest level that was +displayed by this procedure. + +@<Glob...@>= +integer file_ptr; /* shallowest level shown by |show_context| */ + +@ The status at each level is indicated by printing two lines, where the first +line indicates what was read so far and the second line shows what remains +to be read. The context is cropped, if necessary, so that the first line +contains at most |half_error_line| characters, and the second contains +at most |error_line|. Non-current input levels whose |token_type| is +`|backed_up|' are shown only if they have not been fully read. + +@c void mp_show_context (MP mp) { /* prints where the scanner is */ + unsigned old_setting; /* saved |selector| setting */ + @<Local variables for formatting calculations@> + mp->file_ptr=mp->input_ptr; mp->input_stack[mp->file_ptr]=mp->cur_input; + /* store current state */ + while (1) { + mp->cur_input=mp->input_stack[mp->file_ptr]; /* enter into the context */ + @<Display the current context@>; + if ( file_state ) + if ( (name>max_spec_src) || (mp->file_ptr==0) ) break; + decr(mp->file_ptr); + } + mp->cur_input=mp->input_stack[mp->input_ptr]; /* restore original state */ +} + +@ @<Display the current context@>= +if ( (mp->file_ptr==mp->input_ptr) || file_state || + (token_type!=backed_up) || (loc!=null) ) { + /* we omit backed-up token lists that have already been read */ + mp->tally=0; /* get ready to count characters */ + old_setting=mp->selector; + if ( file_state ) { + @<Print location of current line@>; + @<Pseudoprint the line@>; + } else { + @<Print type of token list@>; + @<Pseudoprint the token list@>; + } + mp->selector=old_setting; /* stop pseudoprinting */ + @<Print two lines using the tricky pseudoprinted information@>; +} + +@ This routine should be changed, if necessary, to give the best possible +indication of where the current line resides in the input file. +For example, on some systems it is best to print both a page and line number. +@^system dependencies@> + +@<Print location of current line@>= +if ( name>max_spec_src ) { + mp_print_nl(mp, "l."); mp_print_int(mp, mp_true_line(mp)); +} else if ( terminal_input ) { + if ( mp->file_ptr==0 ) mp_print_nl(mp, "<*>"); + else mp_print_nl(mp, "<insert>"); +} else if ( name==is_scantok ) { + mp_print_nl(mp, "<scantokens>"); +} else { + mp_print_nl(mp, "<read>"); +} +mp_print_char(mp, xord(' ')) + +@ Can't use case statement here because the |token_type| is not +a constant expression. + +@<Print type of token list@>= +{ + if(token_type==forever_text) { + mp_print_nl(mp, "<forever> "); + } else if (token_type==loop_text) { + @<Print the current loop value@>; + } else if (token_type==parameter) { + mp_print_nl(mp, "<argument> "); + } else if (token_type==backed_up) { + if ( loc==null ) mp_print_nl(mp, "<recently read> "); + else mp_print_nl(mp, "<to be read again> "); + } else if (token_type==inserted) { + mp_print_nl(mp, "<inserted text> "); + } else if (token_type==macro) { + mp_print_ln(mp); + if ( name!=null ) mp_print_text(name); + else @<Print the name of a \&{vardef}'d macro@>; + mp_print(mp, "->"); + } else { + mp_print_nl(mp, "?");/* this should never happen */ +@.?\relax@> + } +} + +@ The parameter that corresponds to a loop text is either a token list +(in the case of \&{forsuffixes}) or a ``capsule'' (in the case of \&{for}). +We'll discuss capsules later; for now, all we need to know is that +the |link| field in a capsule parameter is |void| and that +|print_exp(p,0)| displays the value of capsule~|p| in abbreviated form. + +@<Print the current loop value@>= +{ mp_print_nl(mp, "<for("); p=mp->param_stack[param_start]; + if ( p!=null ) { + if ( mp_link(p)==mp_void ) mp_print_exp(mp, p,0); /* we're in a \&{for} loop */ + else mp_show_token_list(mp, p,null,20,mp->tally); + } + mp_print(mp, ")> "); +} + +@ The first two parameters of a macro defined by \&{vardef} will be token +lists representing the macro's prefix and ``at point.'' By putting these +together, we get the macro's full name. + +@<Print the name of a \&{vardef}'d macro@>= +{ p=mp->param_stack[param_start]; + if ( p==null ) { + mp_show_token_list(mp, mp->param_stack[param_start+1],null,20,mp->tally); + } else { + q=p; + while ( mp_link(q)!=null ) q=mp_link(q); + mp_link(q)=mp->param_stack[param_start+1]; + mp_show_token_list(mp, p,null,20,mp->tally); + mp_link(q)=null; + } +} + +@ Now it is necessary to explain a little trick. We don't want to store a long +string that corresponds to a token list, because that string might take up +lots of memory; and we are printing during a time when an error message is +being given, so we dare not do anything that might overflow one of \MP's +tables. So `pseudoprinting' is the answer: We enter a mode of printing +that stores characters into a buffer of length |error_line|, where character +$k+1$ is placed into \hbox{|trick_buf[k mod error_line]|} if +|k<trick_count|, otherwise character |k| is dropped. Initially we set +|tally:=0| and |trick_count:=1000000|; then when we reach the +point where transition from line 1 to line 2 should occur, we +set |first_count:=tally| and |trick_count:=@tmax@>(error_line, +tally+1+error_line-half_error_line)|. At the end of the +pseudoprinting, the values of |first_count|, |tally|, and +|trick_count| give us all the information we need to print the two lines, +and all of the necessary text is in |trick_buf|. + +Namely, let |l| be the length of the descriptive information that appears +on the first line. The length of the context information gathered for that +line is |k=first_count|, and the length of the context information +gathered for line~2 is $m=\min(|tally|, |trick_count|)-k$. If |l+k<=h|, +where |h=half_error_line|, we print |trick_buf[0..k-1]| after the +descriptive information on line~1, and set |n:=l+k|; here |n| is the +length of line~1. If $l+k>h$, some cropping is necessary, so we set |n:=h| +and print `\.{...}' followed by +$$\hbox{|trick_buf[(l+k-h+3)..k-1]|,}$$ +where subscripts of |trick_buf| are circular modulo |error_line|. The +second line consists of |n|~spaces followed by |trick_buf[k..(k+m-1)]|, +unless |n+m>error_line|; in the latter case, further cropping is done. +This is easier to program than to explain. + +@<Local variables for formatting...@>= +int i; /* index into |buffer| */ +integer l; /* length of descriptive information on line 1 */ +integer m; /* context information gathered for line 2 */ +int n; /* length of line 1 */ +integer p; /* starting or ending place in |trick_buf| */ +integer q; /* temporary index */ + +@ The following code tells the print routines to gather +the desired information. + +@d begin_pseudoprint { + l=mp->tally; mp->tally=0; mp->selector=pseudo; + mp->trick_count=1000000; +} +@d set_trick_count { + mp->first_count=mp->tally; + mp->trick_count=mp->tally+1+mp->error_line-mp->half_error_line; + if ( mp->trick_count<mp->error_line ) mp->trick_count=mp->error_line; +} + +@ And the following code uses the information after it has been gathered. + +@<Print two lines using the tricky pseudoprinted information@>= +if ( mp->trick_count==1000000 ) set_trick_count; + /* |set_trick_count| must be performed */ +if ( mp->tally<mp->trick_count ) m=mp->tally-mp->first_count; +else m=mp->trick_count-mp->first_count; /* context on line 2 */ +if ( l+mp->first_count<=mp->half_error_line ) { + p=0; n=l+mp->first_count; +} else { + mp_print(mp, "..."); p=l+mp->first_count-mp->half_error_line+3; + n=mp->half_error_line; +} +for (q=p;q<=mp->first_count-1;q++) { + mp_print_char(mp, mp->trick_buf[q % mp->error_line]); +} +mp_print_ln(mp); +for (q=1;q<=n;q++) { + mp_print_char(mp, xord(' ')); /* print |n| spaces to begin line~2 */ +} +if ( m+n<=mp->error_line ) p=mp->first_count+m; +else p=mp->first_count+(mp->error_line-n-3); +for (q=mp->first_count;q<=p-1;q++) { + mp_print_char(mp, mp->trick_buf[q % mp->error_line]); +} +if ( m+n>mp->error_line ) mp_print(mp, "...") + +@ But the trick is distracting us from our current goal, which is to +understand the input state. So let's concentrate on the data structures that +are being pseudoprinted as we finish up the |show_context| procedure. + +@<Pseudoprint the line@>= +begin_pseudoprint; +if ( limit>0 ) { + for (i=start;i<=limit-1;i++) { + if ( i==loc ) set_trick_count; + mp_print_str(mp, mp->buffer[i]); + } +} + +@ @<Pseudoprint the token list@>= +begin_pseudoprint; +if ( token_type!=macro ) mp_show_token_list(mp, start,loc,100000,0); +else mp_show_macro(mp, start,loc,100000) + +@ Here is the missing piece of |show_token_list| that is activated when the +token beginning line~2 is about to be shown: + +@<Do magic computation@>=set_trick_count + +@* \[28] Maintaining the input stacks. +The following subroutines change the input status in commonly needed ways. + +First comes |push_input|, which stores the current state and creates a +new level (having, initially, the same properties as the old). + +@d push_input { /* enter a new input level, save the old */ + if ( mp->input_ptr>mp->max_in_stack ) { + mp->max_in_stack=mp->input_ptr; + if ( mp->input_ptr==mp->stack_size ) { + int l = (mp->stack_size+(mp->stack_size/4)); + XREALLOC(mp->input_stack, l, in_state_record); + mp->stack_size = l; + } + } + mp->input_stack[mp->input_ptr]=mp->cur_input; /* stack the record */ + incr(mp->input_ptr); +} + +@ And of course what goes up must come down. + +@d pop_input { /* leave an input level, re-enter the old */ + decr(mp->input_ptr); mp->cur_input=mp->input_stack[mp->input_ptr]; + } + +@ Here is a procedure that starts a new level of token-list input, given +a token list |p| and its type |t|. If |t=macro|, the calling routine should +set |name|, reset~|loc|, and increase the macro's reference count. + +@d back_list(A) mp_begin_token_list(mp, (A),backed_up) /* backs up a simple token list */ + +@c +static void mp_begin_token_list (MP mp,pointer p, quarterword t) { + push_input; start=p; token_type=t; + param_start=mp->param_ptr; loc=p; +} + +@ When a token list has been fully scanned, the following computations +should be done as we leave that level of input. +@^inner loop@> + +@c +static void mp_end_token_list (MP mp) { /* leave a token-list input level */ + pointer p; /* temporary register */ + if ( token_type>=backed_up ) { /* token list to be deleted */ + if ( token_type<=inserted ) { + mp_flush_token_list(mp, start); goto DONE; + } else { + mp_delete_mac_ref(mp, start); /* update reference count */ + } + } + while ( mp->param_ptr>param_start ) { /* parameters must be flushed */ + decr(mp->param_ptr); + p=mp->param_stack[mp->param_ptr]; + if ( p!=null ) { + if ( mp_link(p)==mp_void ) { /* it's an \&{expr} parameter */ + mp_recycle_value(mp, p); mp_free_node(mp, p,value_node_size); + } else { + mp_flush_token_list(mp, p); /* it's a \&{suffix} or \&{text} parameter */ + } + } + } +DONE: + pop_input; check_interrupt; +} + +@ The contents of |cur_cmd,cur_mod,cur_sym| are placed into an equivalent +token by the |cur_tok| routine. +@^inner loop@> + +@c @<Declare the procedure called |make_exp_copy|@> +static pointer mp_cur_tok (MP mp) { + pointer p; /* a new token node */ + quarterword save_type; /* |cur_type| to be restored */ + integer save_exp; /* |cur_exp| to be restored */ + if ( mp->cur_sym==0 ) { + if ( mp->cur_cmd==capsule_token ) { + save_type=mp->cur_type; save_exp=mp->cur_exp; + mp_make_exp_copy(mp, mp->cur_mod); p=mp_stash_cur_exp(mp); mp_link(p)=null; + mp->cur_type=save_type; mp->cur_exp=save_exp; + } else { + p=mp_get_node(mp, token_node_size); + value(p)=mp->cur_mod; mp_name_type(p)=mp_token; + if ( mp->cur_cmd==numeric_token ) mp_type(p)=mp_known; + else mp_type(p)=mp_string_type; + } + } else { + fast_get_avail(p); mp_info(p)=mp->cur_sym; + } + return p; +} + +@ Sometimes \MP\ has read too far and wants to ``unscan'' what it has +seen. The |back_input| procedure takes care of this by putting the token +just scanned back into the input stream, ready to be read again. +If |cur_sym<>0|, the values of |cur_cmd| and |cur_mod| are irrelevant. + +@<Declarations@>= +static void mp_back_input (MP mp); + +@ @c void mp_back_input (MP mp) {/* undoes one token of input */ + pointer p; /* a token list of length one */ + p=mp_cur_tok(mp); + while ( token_state &&(loc==null) ) + mp_end_token_list(mp); /* conserve stack space */ + back_list(p); +} + +@ The |back_error| routine is used when we want to restore or replace an +offending token just before issuing an error message. We disable interrupts +during the call of |back_input| so that the help message won't be lost. + +@ @c static void mp_back_error (MP mp) { /* back up one token and call |error| */ + mp->OK_to_interrupt=false; + mp_back_input(mp); + mp->OK_to_interrupt=true; mp_error(mp); +} +static void mp_ins_error (MP mp) { /* back up one inserted token and call |error| */ + mp->OK_to_interrupt=false; + mp_back_input(mp); token_type=inserted; + mp->OK_to_interrupt=true; mp_error(mp); +} + +@ The |begin_file_reading| procedure starts a new level of input for lines +of characters to be read from a file, or as an insertion from the +terminal. It does not take care of opening the file, nor does it set |loc| +or |limit| or |line|. +@^system dependencies@> + +@c void mp_begin_file_reading (MP mp) { + if ( mp->in_open==mp->max_in_open ) + mp_overflow(mp, "text input levels",mp->max_in_open); +@:MetaPost capacity exceeded text input levels}{\quad text input levels@> + if ( mp->first==mp->buf_size ) + mp_reallocate_buffer(mp,(mp->buf_size+(mp->buf_size/4))); + incr(mp->in_open); push_input; iindex=mp->in_open; + if (mp->in_open_max<mp->in_open) + mp->in_open_max=mp->in_open; + mp->mpx_name[iindex]=absent; + start=(halfword)mp->first; + name=is_term; /* |terminal_input| is now |true| */ +} + +@ Conversely, the variables must be downdated when such a level of input +is finished. Any associated \.{MPX} file must also be closed and popped +off the file stack. + +@c static void mp_end_file_reading (MP mp) { + if ( mp->in_open>iindex ) { + if ( (mp->mpx_name[mp->in_open]==absent)||(name<=max_spec_src) ) { + mp_confusion(mp, "endinput"); +@:this can't happen endinput}{\quad endinput@> + } else { + (mp->close_file)(mp,mp->input_file[mp->in_open]); /* close an \.{MPX} file */ + delete_str_ref(mp->mpx_name[mp->in_open]); + decr(mp->in_open); + } + } + mp->first=(size_t)start; + if ( iindex!=mp->in_open ) mp_confusion(mp, "endinput"); + if ( name>max_spec_src ) { + (mp->close_file)(mp,cur_file); + delete_str_ref(name); + xfree(in_name); + xfree(in_area); + } + pop_input; decr(mp->in_open); +} + +@ Here is a function that tries to resume input from an \.{MPX} file already +associated with the current input file. It returns |false| if this doesn't +work. + +@c static boolean mp_begin_mpx_reading (MP mp) { + if ( mp->in_open!=iindex+1 ) { + return false; + } else { + if ( mp->mpx_name[mp->in_open]<=absent ) mp_confusion(mp, "mpx"); +@:this can't happen mpx}{\quad mpx@> + if ( mp->first==mp->buf_size ) + mp_reallocate_buffer(mp,(mp->buf_size+(mp->buf_size/4))); + push_input; iindex=mp->in_open; + start=(halfword)mp->first; + name=mp->mpx_name[mp->in_open]; add_str_ref(name); + @<Put an empty line in the input buffer@>; + return true; + } +} + +@ This procedure temporarily stops reading an \.{MPX} file. + +@c static void mp_end_mpx_reading (MP mp) { + if ( mp->in_open!=iindex ) mp_confusion(mp, "mpx"); +@:this can't happen mpx}{\quad mpx@> + if ( loc<limit ) { + @<Complain that we are not at the end of a line in the \.{MPX} file@>; + } + mp->first=(size_t)start; + pop_input; +} + +@ Here we enforce a restriction that simplifies the input stacks considerably. +This should not inconvenience the user because \.{MPX} files are generated +by an auxiliary program called \.{DVItoMP}. + +@ @<Complain that we are not at the end of a line in the \.{MPX} file@>= +{ +print_err("`mpxbreak' must be at the end of a line"); +help4("This file contains picture expressions for btex...etex", + "blocks. Such files are normally generated automatically", + "but this one seems to be messed up. I'm going to ignore", + "the rest of this line."); +mp_error(mp); +} + +@ In order to keep the stack from overflowing during a long sequence of +inserted `\.{show}' commands, the following routine removes completed +error-inserted lines from memory. + +@c void mp_clear_for_error_prompt (MP mp) { + while ( file_state && terminal_input && + (mp->input_ptr>0)&&(loc==limit) ) mp_end_file_reading(mp); + mp_print_ln(mp); clear_terminal; +} + +@ To get \MP's whole input mechanism going, we perform the following +actions. + +@<Initialize the input routines@>= +{ mp->input_ptr=0; mp->max_in_stack=0; + mp->in_open=0; mp->open_parens=0; mp->max_buf_stack=0; + mp->param_ptr=0; mp->max_param_stack=0; + mp->first=1; + start=1; iindex=0; line=0; name=is_term; + mp->mpx_name[0]=absent; + mp->force_eof=false; + if ( ! mp_init_terminal(mp) ) mp_jump_out(mp); + limit=(halfword)mp->last; mp->first=mp->last+1; + /* |init_terminal| has set |loc| and |last| */ +} + +@* \[29] Getting the next token. +The heart of \MP's input mechanism is the |get_next| procedure, which +we shall develop in the next few sections of the program. Perhaps we +shouldn't actually call it the ``heart,'' however; it really acts as \MP's +eyes and mouth, reading the source files and gobbling them up. And it also +helps \MP\ to regurgitate stored token lists that are to be processed again. + +The main duty of |get_next| is to input one token and to set |cur_cmd| +and |cur_mod| to that token's command code and modifier. Furthermore, if +the input token is a symbolic token, that token's |hash| address +is stored in |cur_sym|; otherwise |cur_sym| is set to zero. + +Underlying this simple description is a certain amount of complexity +because of all the cases that need to be handled. +However, the inner loop of |get_next| is reasonably short and fast. + +@ Before getting into |get_next|, we need to consider a mechanism by which +\MP\ helps keep errors from propagating too far. Whenever the program goes +into a mode where it keeps calling |get_next| repeatedly until a certain +condition is met, it sets |scanner_status| to some value other than |normal|. +Then if an input file ends, or if an `\&{outer}' symbol appears, +an appropriate error recovery will be possible. + +The global variable |warning_info| helps in this error recovery by providing +additional information. For example, |warning_info| might indicate the +name of a macro whose replacement text is being scanned. + +@d normal 0 /* |scanner_status| at ``quiet times'' */ +@d skipping 1 /* |scanner_status| when false conditional text is being skipped */ +@d flushing 2 /* |scanner_status| when junk after a statement is being ignored */ +@d absorbing 3 /* |scanner_status| when a \&{text} parameter is being scanned */ +@d var_defining 4 /* |scanner_status| when a \&{vardef} is being scanned */ +@d op_defining 5 /* |scanner_status| when a macro \&{def} is being scanned */ +@d loop_defining 6 /* |scanner_status| when a \&{for} loop is being scanned */ +@d tex_flushing 7 /* |scanner_status| when skipping \TeX\ material */ + +@<Glob...@>= +integer scanner_status; /* are we scanning at high speed? */ +integer warning_info; /* if so, what else do we need to know, + in case an error occurs? */ + +@ @<Initialize the input routines@>= +mp->scanner_status=normal; + +@ The following subroutine +is called when an `\&{outer}' symbolic token has been scanned or +when the end of a file has been reached. These two cases are distinguished +by |cur_sym|, which is zero at the end of a file. + +@c +static boolean mp_check_outer_validity (MP mp) { + pointer p; /* points to inserted token list */ + if ( mp->scanner_status==normal ) { + return true; + } else if ( mp->scanner_status==tex_flushing ) { + @<Check if the file has ended while flushing \TeX\ material and set the + result value for |check_outer_validity|@>; + } else { + mp->deletions_allowed=false; + @<Back up an outer symbolic token so that it can be reread@>; + if ( mp->scanner_status>skipping ) { + @<Tell the user what has run away and try to recover@>; + } else { + print_err("Incomplete if; all text was ignored after line "); +@.Incomplete if...@> + mp_print_int(mp, mp->warning_info); + help3("A forbidden `outer' token occurred in skipped text.", + "This kind of error happens when you say `if...' and forget", + "the matching `fi'. I've inserted a `fi'; this might work."); + if ( mp->cur_sym==0 ) + mp->help_line[2]="The file ended while I was skipping conditional text."; + mp->cur_sym=frozen_fi; mp_ins_error(mp); + } + mp->deletions_allowed=true; + return false; + } +} + +@ @<Check if the file has ended while flushing \TeX\ material and set...@>= +if ( mp->cur_sym!=0 ) { + return true; +} else { + mp->deletions_allowed=false; + print_err("TeX mode didn't end; all text was ignored after line "); + mp_print_int(mp, mp->warning_info); + help2("The file ended while I was looking for the `etex' to", + "finish this TeX material. I've inserted `etex' now."); + mp->cur_sym = frozen_etex; + mp_ins_error(mp); + mp->deletions_allowed=true; + return false; +} + +@ @<Back up an outer symbolic token so that it can be reread@>= +if ( mp->cur_sym!=0 ) { + p=mp_get_avail(mp); mp_info(p)=mp->cur_sym; + back_list(p); /* prepare to read the symbolic token again */ +} + +@ @<Tell the user what has run away...@>= +{ + mp_runaway(mp); /* print the definition-so-far */ + if ( mp->cur_sym==0 ) { + print_err("File ended"); +@.File ended while scanning...@> + } else { + print_err("Forbidden token found"); +@.Forbidden token found...@> + } + mp_print(mp, " while scanning "); + help4("I suspect you have forgotten an `enddef',", + "causing me to read past where you wanted me to stop.", + "I'll try to recover; but if the error is serious,", + "you'd better type `E' or `X' now and fix your file."); + switch (mp->scanner_status) { + @<Complete the error message, + and set |cur_sym| to a token that might help recover from the error@> + } /* there are no other cases */ + mp_ins_error(mp); +} + +@ As we consider various kinds of errors, it is also appropriate to +change the first line of the help message just given; |help_line[3]| +points to the string that might be changed. + +@<Complete the error message,...@>= +case flushing: + mp_print(mp, "to the end of the statement"); + mp->help_line[3]="A previous error seems to have propagated,"; + mp->cur_sym=frozen_semicolon; + break; +case absorbing: + mp_print(mp, "a text argument"); + mp->help_line[3]="It seems that a right delimiter was left out,"; + if ( mp->warning_info==0 ) { + mp->cur_sym=frozen_end_group; + } else { + mp->cur_sym=frozen_right_delimiter; + equiv(frozen_right_delimiter)=mp->warning_info; + } + break; +case var_defining: +case op_defining: + mp_print(mp, "the definition of "); + if ( mp->scanner_status==op_defining ) + mp_print_text(mp->warning_info); + else + mp_print_variable_name(mp, mp->warning_info); + mp->cur_sym=frozen_end_def; + break; +case loop_defining: + mp_print(mp, "the text of a "); + mp_print_text(mp->warning_info); + mp_print(mp, " loop"); + mp->help_line[3]="I suspect you have forgotten an `endfor',"; + mp->cur_sym=frozen_end_for; + break; + +@ The |runaway| procedure displays the first part of the text that occurred +when \MP\ began its special |scanner_status|, if that text has been saved. + +@<Declarations@>= +static void mp_runaway (MP mp) ; + +@ @c +void mp_runaway (MP mp) { + if ( mp->scanner_status>flushing ) { + mp_print_nl(mp, "Runaway "); + switch (mp->scanner_status) { + case absorbing: mp_print(mp, "text?"); break; + case var_defining: + case op_defining: mp_print(mp,"definition?"); break; + case loop_defining: mp_print(mp, "loop?"); break; + } /* there are no other cases */ + mp_print_ln(mp); + mp_show_token_list(mp, mp_link(hold_head),null,mp->error_line-10,0); + } +} + +@ We need to mention a procedure that may be called by |get_next|. + +@<Declarations@>= +static void mp_firm_up_the_line (MP mp); + +@ And now we're ready to take the plunge into |get_next| itself. +Note that the behavior depends on the |scanner_status| because percent signs +and double quotes need to be passed over when skipping TeX material. + +@c +void mp_get_next (MP mp) { + /* sets |cur_cmd|, |cur_mod|, |cur_sym| to next token */ +@^inner loop@> + /*restart*/ /* go here to get the next input token */ + /*exit*/ /* go here when the next input token has been got */ + /*|common_ending|*/ /* go here to finish getting a symbolic token */ + /*found*/ /* go here when the end of a symbolic token has been found */ + /*switch*/ /* go here to branch on the class of an input character */ + /*|start_numeric_token|,|start_decimal_token|,|fin_numeric_token|,|done|*/ + /* go here at crucial stages when scanning a number */ + int k; /* an index into |buffer| */ + ASCII_code c; /* the current character in the buffer */ + int class; /* its class number */ + integer n,f; /* registers for decimal-to-binary conversion */ +RESTART: + mp->cur_sym=0; + if ( file_state ) { + @<Input from external file; |goto restart| if no input found, + or |return| if a non-symbolic token is found@>; + } else { + @<Input from token list; |goto restart| if end of list or + if a parameter needs to be expanded, + or |return| if a non-symbolic token is found@>; + } +COMMON_ENDING: + @<Finish getting the symbolic token in |cur_sym|; + |goto restart| if it is illegal@>; +} + +@ When a symbolic token is declared to be `\&{outer}', its command code +is increased by |outer_tag|. +@^inner loop@> + +@<Finish getting the symbolic token in |cur_sym|...@>= +mp->cur_cmd=eq_type(mp->cur_sym); mp->cur_mod=equiv(mp->cur_sym); +if ( mp->cur_cmd>=outer_tag ) { + if ( mp_check_outer_validity(mp) ) + mp->cur_cmd=mp->cur_cmd-outer_tag; + else + goto RESTART; +} + +@ A percent sign appears in |buffer[limit]|; this makes it unnecessary +to have a special test for end-of-line. +@^inner loop@> + +@<Input from external file;...@>= +{ +SWITCH: + c=mp->buffer[loc]; incr(loc); class=mp->char_class[c]; + switch (class) { + case digit_class: goto START_NUMERIC_TOKEN; break; + case period_class: + class=mp->char_class[mp->buffer[loc]]; + if ( class>period_class ) { + goto SWITCH; + } else if ( class<period_class ) { /* |class=digit_class| */ + n=0; goto START_DECIMAL_TOKEN; + } +@:. }{\..\ token@> + break; + case space_class: goto SWITCH; break; + case percent_class: + if ( mp->scanner_status==tex_flushing ) { + if ( loc<limit ) goto SWITCH; + } + @<Move to next line of file, or |goto restart| if there is no next line@>; + check_interrupt; + goto SWITCH; + break; + case string_class: + if ( mp->scanner_status==tex_flushing ) goto SWITCH; + else @<Get a string token and |return|@>; + break; + case isolated_classes: + k=loc-1; goto FOUND; break; + case invalid_class: + if ( mp->scanner_status==tex_flushing ) goto SWITCH; + else @<Decry the invalid character and |goto restart|@>; + break; + default: break; /* letters, etc. */ + } + k=loc-1; + while ( mp->char_class[mp->buffer[loc]]==class ) incr(loc); + goto FOUND; +START_NUMERIC_TOKEN: + @<Get the integer part |n| of a numeric token; + set |f:=0| and |goto fin_numeric_token| if there is no decimal point@>; +START_DECIMAL_TOKEN: + @<Get the fraction part |f| of a numeric token@>; +FIN_NUMERIC_TOKEN: + @<Pack the numeric and fraction parts of a numeric token + and |return|@>; +FOUND: + mp->cur_sym=mp_id_lookup(mp, k,loc-k); +} + +@ We go to |restart| instead of to |SWITCH|, because we might enter +|token_state| after the error has been dealt with +(cf.\ |clear_for_error_prompt|). + +@<Decry the invalid...@>= +{ + print_err("Text line contains an invalid character"); +@.Text line contains...@> + help2("A funny symbol that I can\'t read has just been input.", + "Continue, and I'll forget that it ever happened."); + mp->deletions_allowed=false; mp_error(mp); mp->deletions_allowed=true; + goto RESTART; +} + +@ @<Get a string token and |return|@>= +{ + if ( mp->buffer[loc]=='"' ) { + mp->cur_mod=null_str; + } else { + k=loc; mp->buffer[limit+1]=xord('"'); + do { + incr(loc); + } while (mp->buffer[loc]!='"'); + if ( loc>limit ) { + @<Decry the missing string delimiter and |goto restart|@>; + } + if ( loc==k+1 ) { + mp->cur_mod=mp->buffer[k]; + } else { + str_room(loc-k); + do { + append_char(mp->buffer[k]); incr(k); + } while (k!=loc); + mp->cur_mod=mp_make_string(mp); + } + } + incr(loc); mp->cur_cmd=string_token; + return; +} + +@ We go to |restart| after this error message, not to |SWITCH|, +because the |clear_for_error_prompt| routine might have reinstated +|token_state| after |error| has finished. + +@<Decry the missing string delimiter and |goto restart|@>= +{ + loc=limit; /* the next character to be read on this line will be |"%"| */ + print_err("Incomplete string token has been flushed"); +@.Incomplete string token...@> + help3("Strings should finish on the same line as they began.", + "I've deleted the partial string; you might want to", + "insert another by typing, e.g., `I\"new string\"'."); + mp->deletions_allowed=false; mp_error(mp); + mp->deletions_allowed=true; + goto RESTART; +} + +@ @<Get the integer part |n| of a numeric token...@>= +n=c-'0'; +while ( mp->char_class[mp->buffer[loc]]==digit_class ) { + if ( n<32768 ) n=10*n+mp->buffer[loc]-'0'; + incr(loc); +} +if ( mp->buffer[loc]=='.' ) + if ( mp->char_class[mp->buffer[loc+1]]==digit_class ) + goto DONE; +f=0; +goto FIN_NUMERIC_TOKEN; +DONE: incr(loc) + +@ @<Get the fraction part |f| of a numeric token@>= +k=0; +do { + if ( k<17 ) { /* digits for |k>=17| cannot affect the result */ + mp->dig[k]=mp->buffer[loc]-'0'; incr(k); + } + incr(loc); +} while (mp->char_class[mp->buffer[loc]]==digit_class); +f=mp_round_decimals(mp, k); +if ( f==unity ) { + incr(n); f=0; +} + +@ @<Pack the numeric and fraction parts of a numeric token and |return|@>= +if ( n<32768 ) { + @<Set |cur_mod:=n*unity+f| and check if it is uncomfortably large@>; +} else if ( mp->scanner_status!=tex_flushing ) { + print_err("Enormous number has been reduced"); +@.Enormous number...@> + help2("I can\'t handle numbers bigger than 32767.99998;", + "so I've changed your constant to that maximum amount."); + mp->deletions_allowed=false; mp_error(mp); mp->deletions_allowed=true; + mp->cur_mod=el_gordo; +} +mp->cur_cmd=numeric_token; return + +@ @<Set |cur_mod:=n*unity+f| and check if it is uncomfortably large@>= +{ + mp->cur_mod=n*unity+f; + if ( mp->cur_mod>=fraction_one ) { + if ( (mp->internal[mp_warning_check]>0) && + (mp->scanner_status!=tex_flushing) ) { + print_err("Number is too large ("); + mp_print_scaled(mp, mp->cur_mod); + mp_print_char(mp, xord(')')); + help3("It is at least 4096. Continue and I'll try to cope", + "with that big value; but it might be dangerous.", + "(Set warningcheck:=0 to suppress this message.)"); + mp_error(mp); + } + } +} + +@ Let's consider now what happens when |get_next| is looking at a token list. +@^inner loop@> + +@<Input from token list;...@>= +if ( loc>=mp->hi_mem_min ) { /* one-word token */ + mp->cur_sym=mp_info(loc); loc=mp_link(loc); /* move to next */ + if ( mp->cur_sym>=expr_base ) { + if ( mp->cur_sym>=suffix_base ) { + @<Insert a suffix or text parameter and |goto restart|@>; + } else { + mp->cur_cmd=capsule_token; + mp->cur_mod=mp->param_stack[param_start+mp->cur_sym-(expr_base)]; + mp->cur_sym=0; return; + } + } +} else if ( loc>null ) { + @<Get a stored numeric or string or capsule token and |return|@> +} else { /* we are done with this token list */ + mp_end_token_list(mp); goto RESTART; /* resume previous level */ +} + +@ @<Insert a suffix or text parameter...@>= +{ + if ( mp->cur_sym>=text_base ) mp->cur_sym=mp->cur_sym-mp->param_size; + /* |param_size=text_base-suffix_base| */ + mp_begin_token_list(mp, + mp->param_stack[param_start+mp->cur_sym-(suffix_base)], + parameter); + goto RESTART; +} + +@ @<Get a stored numeric or string or capsule token...@>= +{ + if ( mp_name_type(loc)==mp_token ) { + mp->cur_mod=value(loc); + if ( mp_type(loc)==mp_known ) { + mp->cur_cmd=numeric_token; + } else { + mp->cur_cmd=string_token; add_str_ref(mp->cur_mod); + } + } else { + mp->cur_mod=loc; mp->cur_cmd=capsule_token; + }; + loc=mp_link(loc); return; +} + +@ All of the easy branches of |get_next| have now been taken care of. +There is one more branch. + +@<Move to next line of file, or |goto restart|...@>= +if ( name>max_spec_src) { + @<Read next line of file into |buffer|, or + |goto restart| if the file has ended@>; +} else { + if ( mp->input_ptr>0 ) { + /* text was inserted during error recovery or by \&{scantokens} */ + mp_end_file_reading(mp); goto RESTART; /* resume previous level */ + } + if (mp->job_name == NULL && ( mp->selector<log_only || mp->selector>=write_file)) + mp_open_log_file(mp); + if ( mp->interaction>mp_nonstop_mode ) { + if ( limit==start ) /* previous line was empty */ + mp_print_nl(mp, "(Please type a command or say `end')"); +@.Please type...@> + mp_print_ln(mp); mp->first=(size_t)start; + prompt_input("*"); /* input on-line into |buffer| */ +@.*\relax@> + limit=(halfword)mp->last; mp->buffer[limit]=xord('%'); + mp->first=(size_t)(limit+1); loc=start; + } else { + mp_fatal_error(mp, "*** (job aborted, no legal end found)"); +@.job aborted@> + /* nonstop mode, which is intended for overnight batch processing, + never waits for on-line input */ + } +} + +@ The global variable |force_eof| is normally |false|; it is set |true| +by an \&{endinput} command. + +@<Glob...@>= +boolean force_eof; /* should the next \&{input} be aborted early? */ + +@ We must decrement |loc| in order to leave the buffer in a valid state +when an error condition causes us to |goto restart| without calling +|end_file_reading|. + +@<Read next line of file into |buffer|, or + |goto restart| if the file has ended@>= +{ + incr(line); mp->first=(size_t)start; + if ( ! mp->force_eof ) { + if ( mp_input_ln(mp, cur_file ) ) /* not end of file */ + mp_firm_up_the_line(mp); /* this sets |limit| */ + else + mp->force_eof=true; + }; + if ( mp->force_eof ) { + mp->force_eof=false; + decr(loc); + if ( mpx_reading ) { + @<Complain that the \.{MPX} file ended unexpectly; then set + |cur_sym:=frozen_mpx_break| and |goto comon_ending|@>; + } else { + mp_print_char(mp, xord(')')); decr(mp->open_parens); + update_terminal; /* show user that file has been read */ + mp_end_file_reading(mp); /* resume previous level */ + if ( mp_check_outer_validity(mp) ) goto RESTART; + else goto RESTART; + } + } + mp->buffer[limit]=xord('%'); mp->first=(size_t)(limit+1); loc=start; /* ready to read */ +} + +@ We should never actually come to the end of an \.{MPX} file because such +files should have an \&{mpxbreak} after the translation of the last +\&{btex}$\,\ldots\,$\&{etex} block. + +@<Complain that the \.{MPX} file ended unexpectly; then set...@>= +{ + mp->mpx_name[iindex]=mpx_finished; + print_err("mpx file ended unexpectedly"); + help4("The file had too few picture expressions for btex...etex", + "blocks. Such files are normally generated automatically", + "but this one got messed up. You might want to insert a", + "picture expression now."); + mp->deletions_allowed=false; mp_error(mp); mp->deletions_allowed=true; + mp->cur_sym=frozen_mpx_break; goto COMMON_ENDING; +} + +@ Sometimes we want to make it look as though we have just read a blank line +without really doing so. + +@<Put an empty line in the input buffer@>= +mp->last=mp->first; limit=(halfword)mp->last; + /* simulate |input_ln| and |firm_up_the_line| */ +mp->buffer[limit]=xord('%'); mp->first=(size_t)(limit+1); loc=start + +@ If the user has set the |mp_pausing| parameter to some positive value, +and if nonstop mode has not been selected, each line of input is displayed +on the terminal and the transcript file, followed by `\.{=>}'. +\MP\ waits for a response. If the response is null (i.e., if nothing is +typed except perhaps a few blank spaces), the original +line is accepted as it stands; otherwise the line typed is +used instead of the line in the file. + +@c void mp_firm_up_the_line (MP mp) { + size_t k; /* an index into |buffer| */ + limit=(halfword)mp->last; + if ((!mp->noninteractive) + && (mp->internal[mp_pausing]>0 ) + && (mp->interaction>mp_nonstop_mode )) { + wake_up_terminal; mp_print_ln(mp); + if ( start<limit ) { + for (k=(size_t)start;k<(size_t)limit;k++) { + mp_print_str(mp, mp->buffer[k]); + } + } + mp->first=(size_t)limit; prompt_input("=>"); /* wait for user response */ +@.=>@> + if ( mp->last>mp->first ) { + for (k=mp->first;k<mp->last;k++) { /* move line down in buffer */ + mp->buffer[k+start-mp->first]=mp->buffer[k]; + } + limit=(halfword)(start+mp->last-mp->first); + } + } +} + +@* \[30] Dealing with \TeX\ material. +The \&{btex}$\,\ldots\,$\&{etex} and \&{verbatimtex}$\,\ldots\,$\&{etex} +features need to be implemented at a low level in the scanning process +so that \MP\ can stay in synch with the a preprocessor that treats +blocks of \TeX\ material as they occur in the input file without trying +to expand \MP\ macros. Thus we need a special version of |get_next| +that does not expand macros and such but does handle \&{btex}, +\&{verbatimtex}, etc. + +The special version of |get_next| is called |get_t_next|. It works by flushing +\&{btex}$\,\ldots\,$\&{etex} and \&{verbatimtex}\allowbreak +$\,\ldots\,$\&{etex} blocks, switching to the \.{MPX} file when it sees +\&{btex}, and switching back when it sees \&{mpxbreak}. + +@d btex_code 0 +@d verbatim_code 1 + +@ @<Put each...@>= +mp_primitive(mp, "btex",start_tex,btex_code); +@:btex_}{\&{btex} primitive@> +mp_primitive(mp, "verbatimtex",start_tex,verbatim_code); +@:verbatimtex_}{\&{verbatimtex} primitive@> +mp_primitive(mp, "etex",etex_marker,0); mp->eqtb[frozen_etex]=mp->eqtb[mp->cur_sym]; +@:etex_}{\&{etex} primitive@> +mp_primitive(mp, "mpxbreak",mpx_break,0); mp->eqtb[frozen_mpx_break]=mp->eqtb[mp->cur_sym]; +@:mpx_break_}{\&{mpxbreak} primitive@> + +@ @<Cases of |print_cmd...@>= +case start_tex: if ( m==btex_code ) mp_print(mp, "btex"); + else mp_print(mp, "verbatimtex"); break; +case etex_marker: mp_print(mp, "etex"); break; +case mpx_break: mp_print(mp, "mpxbreak"); break; + +@ Actually, |get_t_next| is a macro that avoids procedure overhead except +in the unusual case where \&{btex}, \&{verbatimtex}, \&{etex}, or \&{mpxbreak} +is encountered. + +@d get_t_next {mp_get_next(mp); if ( mp->cur_cmd<=max_pre_command ) mp_t_next(mp); } + +@<Declarations@>= +static void mp_start_mpx_input (MP mp); + +@ @c +static void mp_t_next (MP mp) { + int old_status; /* saves the |scanner_status| */ + integer old_info; /* saves the |warning_info| */ + while ( mp->cur_cmd<=max_pre_command ) { + if ( mp->cur_cmd==mpx_break ) { + if ( ! file_state || (mp->mpx_name[iindex]==absent) ) { + @<Complain about a misplaced \&{mpxbreak}@>; + } else { + mp_end_mpx_reading(mp); + goto TEX_FLUSH; + } + } else if ( mp->cur_cmd==start_tex ) { + if ( token_state || (name<=max_spec_src) ) { + @<Complain that we are not reading a file@>; + } else if ( mpx_reading ) { + @<Complain that \.{MPX} files cannot contain \TeX\ material@>; + } else if ( (mp->cur_mod!=verbatim_code)&& + (mp->mpx_name[iindex]!=mpx_finished) ) { + if ( ! mp_begin_mpx_reading(mp) ) mp_start_mpx_input(mp); + } else { + goto TEX_FLUSH; + } + } else { + @<Complain about a misplaced \&{etex}@>; + } + goto COMMON_ENDING; + TEX_FLUSH: + @<Flush the \TeX\ material@>; + COMMON_ENDING: + mp_get_next(mp); + } +} + +@ We could be in the middle of an operation such as skipping false conditional +text when \TeX\ material is encountered, so we must be careful to save the +|scanner_status|. + +@<Flush the \TeX\ material@>= +old_status=mp->scanner_status; +old_info=mp->warning_info; +mp->scanner_status=tex_flushing; +mp->warning_info=line; +do { mp_get_next(mp); } while (mp->cur_cmd!=etex_marker); +mp->scanner_status=old_status; +mp->warning_info=old_info + +@ @<Complain that \.{MPX} files cannot contain \TeX\ material@>= +{ print_err("An mpx file cannot contain btex or verbatimtex blocks"); +help4("This file contains picture expressions for btex...etex", + "blocks. Such files are normally generated automatically", + "but this one seems to be messed up. I'll just keep going", + "and hope for the best."); +mp_error(mp); +} + +@ @<Complain that we are not reading a file@>= +{ print_err("You can only use `btex' or `verbatimtex' in a file"); +help3("I'll have to ignore this preprocessor command because it", + "only works when there is a file to preprocess. You might", + "want to delete everything up to the next `etex`."); +mp_error(mp); +} + +@ @<Complain about a misplaced \&{mpxbreak}@>= +{ print_err("Misplaced mpxbreak"); +help2("I'll ignore this preprocessor command because it", + "doesn't belong here"); +mp_error(mp); +} + +@ @<Complain about a misplaced \&{etex}@>= +{ print_err("Extra etex will be ignored"); +help1("There is no btex or verbatimtex for this to match"); +mp_error(mp); +} + +@* \[31] Scanning macro definitions. +\MP\ has a variety of ways to tuck tokens away into token lists for later +use: Macros can be defined with \&{def}, \&{vardef}, \&{primarydef}, etc.; +repeatable code can be defined with \&{for}, \&{forever}, \&{forsuffixes}. +All such operations are handled by the routines in this part of the program. + +The modifier part of each command code is zero for the ``ending delimiters'' +like \&{enddef} and \&{endfor}. + +@d start_def 1 /* command modifier for \&{def} */ +@d var_def 2 /* command modifier for \&{vardef} */ +@d end_def 0 /* command modifier for \&{enddef} */ +@d start_forever 1 /* command modifier for \&{forever} */ +@d end_for 0 /* command modifier for \&{endfor} */ + +@<Put each...@>= +mp_primitive(mp, "def",macro_def,start_def); +@:def_}{\&{def} primitive@> +mp_primitive(mp, "vardef",macro_def,var_def); +@:var_def_}{\&{vardef} primitive@> +mp_primitive(mp, "primarydef",macro_def,secondary_primary_macro); +@:primary_def_}{\&{primarydef} primitive@> +mp_primitive(mp, "secondarydef",macro_def,tertiary_secondary_macro); +@:secondary_def_}{\&{secondarydef} primitive@> +mp_primitive(mp, "tertiarydef",macro_def,expression_tertiary_macro); +@:tertiary_def_}{\&{tertiarydef} primitive@> +mp_primitive(mp, "enddef",macro_def,end_def); mp->eqtb[frozen_end_def]=mp->eqtb[mp->cur_sym]; +@:end_def_}{\&{enddef} primitive@> +@# +mp_primitive(mp, "for",iteration,expr_base); +@:for_}{\&{for} primitive@> +mp_primitive(mp, "forsuffixes",iteration,suffix_base); +@:for_suffixes_}{\&{forsuffixes} primitive@> +mp_primitive(mp, "forever",iteration,start_forever); +@:forever_}{\&{forever} primitive@> +mp_primitive(mp, "endfor",iteration,end_for); mp->eqtb[frozen_end_for]=mp->eqtb[mp->cur_sym]; +@:end_for_}{\&{endfor} primitive@> + +@ @<Cases of |print_cmd...@>= +case macro_def: + if ( m<=var_def ) { + if ( m==start_def ) mp_print(mp, "def"); + else if ( m<start_def ) mp_print(mp, "enddef"); + else mp_print(mp, "vardef"); + } else if ( m==secondary_primary_macro ) { + mp_print(mp, "primarydef"); + } else if ( m==tertiary_secondary_macro ) { + mp_print(mp, "secondarydef"); + } else { + mp_print(mp, "tertiarydef"); + } + break; +case iteration: + if ( m<=start_forever ) { + if ( m==start_forever ) mp_print(mp, "forever"); + else mp_print(mp, "endfor"); + } else if ( m==expr_base ) { + mp_print(mp, "for"); + } else { + mp_print(mp, "forsuffixes"); + } + break; + +@ Different macro-absorbing operations have different syntaxes, but they +also have a lot in common. There is a list of special symbols that are to +be replaced by parameter tokens; there is a special command code that +ends the definition; the quotation conventions are identical. Therefore +it makes sense to have most of the work done by a single subroutine. That +subroutine is called |scan_toks|. + +The first parameter to |scan_toks| is the command code that will +terminate scanning (either |macro_def| or |iteration|). + +The second parameter, |subst_list|, points to a (possibly empty) list +of two-word nodes whose |info| and |value| fields specify symbol tokens +before and after replacement. The list will be returned to free storage +by |scan_toks|. + +The third parameter is simply appended to the token list that is built. +And the final parameter tells how many of the special operations +\.{\#\AT!}, \.{\AT!}, and \.{\AT!\#} are to be replaced by suffix parameters. +When such parameters are present, they are called \.{(SUFFIX0)}, +\.{(SUFFIX1)}, and \.{(SUFFIX2)}. + +@c static pointer mp_scan_toks (MP mp,command_code terminator, pointer + subst_list, pointer tail_end, quarterword suffix_count) { + pointer p; /* tail of the token list being built */ + pointer q; /* temporary for link management */ + integer balance; /* left delimiters minus right delimiters */ + p=hold_head; balance=1; mp_link(hold_head)=null; + while (1) { + get_t_next; + if ( mp->cur_sym>0 ) { + @<Substitute for |cur_sym|, if it's on the |subst_list|@>; + if ( mp->cur_cmd==terminator ) { + @<Adjust the balance; |break| if it's zero@>; + } else if ( mp->cur_cmd==macro_special ) { + @<Handle quoted symbols, \.{\#\AT!}, \.{\AT!}, or \.{\AT!\#}@>; + } + } + mp_link(p)=mp_cur_tok(mp); p=mp_link(p); + } + mp_link(p)=tail_end; mp_flush_node_list(mp, subst_list); + return mp_link(hold_head); +} + +@ @<Substitute for |cur_sym|...@>= +{ + q=subst_list; + while ( q!=null ) { + if ( mp_info(q)==mp->cur_sym ) { + mp->cur_sym=value(q); mp->cur_cmd=relax; break; + } + q=mp_link(q); + } +} + +@ @<Adjust the balance; |break| if it's zero@>= +if ( mp->cur_mod>0 ) { + incr(balance); +} else { + decr(balance); + if ( balance==0 ) + break; +} + +@ Four commands are intended to be used only within macro texts: \&{quote}, +\.{\#\AT!}, \.{\AT!}, and \.{\AT!\#}. They are variants of a single command +code called |macro_special|. + +@d quote 0 /* |macro_special| modifier for \&{quote} */ +@d macro_prefix 1 /* |macro_special| modifier for \.{\#\AT!} */ +@d macro_at 2 /* |macro_special| modifier for \.{\AT!} */ +@d macro_suffix 3 /* |macro_special| modifier for \.{\AT!\#} */ + +@<Put each...@>= +mp_primitive(mp, "quote",macro_special,quote); +@:quote_}{\&{quote} primitive@> +mp_primitive(mp, "#@@",macro_special,macro_prefix); +@:]]]\#\AT!_}{\.{\#\AT!} primitive@> +mp_primitive(mp, "@@",macro_special,macro_at); +@:]]]\AT!_}{\.{\AT!} primitive@> +mp_primitive(mp, "@@#",macro_special,macro_suffix); +@:]]]\AT!\#_}{\.{\AT!\#} primitive@> + +@ @<Cases of |print_cmd...@>= +case macro_special: + switch (m) { + case macro_prefix: mp_print(mp, "#@@"); break; + case macro_at: mp_print_char(mp, xord('@@')); break; + case macro_suffix: mp_print(mp, "@@#"); break; + default: mp_print(mp, "quote"); break; + } + break; + +@ @<Handle quoted...@>= +{ + if ( mp->cur_mod==quote ) { get_t_next; } + else if ( mp->cur_mod<=suffix_count ) + mp->cur_sym=suffix_base-1+mp->cur_mod; +} + +@ Here is a routine that's used whenever a token will be redefined. If +the user's token is unredefinable, the `|frozen_inaccessible|' token is +substituted; the latter is redefinable but essentially impossible to use, +hence \MP's tables won't get fouled up. + +@c static void mp_get_symbol (MP mp) { /* sets |cur_sym| to a safe symbol */ +RESTART: + get_t_next; + if ( (mp->cur_sym==0)||(mp->cur_sym>(integer)frozen_inaccessible) ) { + print_err("Missing symbolic token inserted"); +@.Missing symbolic token...@> + help3("Sorry: You can\'t redefine a number, string, or expr.", + "I've inserted an inaccessible symbol so that your", + "definition will be completed without mixing me up too badly."); + if ( mp->cur_sym>0 ) + mp->help_line[2]="Sorry: You can\'t redefine my error-recovery tokens."; + else if ( mp->cur_cmd==string_token ) + delete_str_ref(mp->cur_mod); + mp->cur_sym=frozen_inaccessible; mp_ins_error(mp); goto RESTART; + } +} + +@ Before we actually redefine a symbolic token, we need to clear away its +former value, if it was a variable. The following stronger version of +|get_symbol| does that. + +@c static void mp_get_clear_symbol (MP mp) { + mp_get_symbol(mp); mp_clear_symbol(mp, mp->cur_sym,false); +} + +@ Here's another little subroutine; it checks that an equals sign +or assignment sign comes along at the proper place in a macro definition. + +@c static void mp_check_equals (MP mp) { + if ( mp->cur_cmd!=equals ) if ( mp->cur_cmd!=assignment ) { + mp_missing_err(mp, "="); +@.Missing `='@> + help5("The next thing in this `def' should have been `=',", + "because I've already looked at the definition heading.", + "But don't worry; I'll pretend that an equals sign", + "was present. Everything from here to `enddef'", + "will be the replacement text of this macro."); + mp_back_error(mp); + } +} + +@ A \&{primarydef}, \&{secondarydef}, or \&{tertiarydef} is rather easily +handled now that we have |scan_toks|. In this case there are +two parameters, which will be \.{EXPR0} and \.{EXPR1} (i.e., +|expr_base| and |expr_base+1|). + +@c static void mp_make_op_def (MP mp) { + command_code m; /* the type of definition */ + pointer p,q,r; /* for list manipulation */ + m=mp->cur_mod; + mp_get_symbol(mp); q=mp_get_node(mp, token_node_size); + mp_info(q)=mp->cur_sym; value(q)=expr_base; + mp_get_clear_symbol(mp); mp->warning_info=mp->cur_sym; + mp_get_symbol(mp); p=mp_get_node(mp, token_node_size); + mp_info(p)=mp->cur_sym; value(p)=expr_base+1; mp_link(p)=q; + get_t_next; mp_check_equals(mp); + mp->scanner_status=op_defining; q=mp_get_avail(mp); ref_count(q)=null; + r=mp_get_avail(mp); mp_link(q)=r; mp_info(r)=general_macro; + mp_link(r)=mp_scan_toks(mp, macro_def,p,null,0); + mp->scanner_status=normal; eq_type(mp->warning_info)=m; + equiv(mp->warning_info)=q; mp_get_x_next(mp); +} + +@ Parameters to macros are introduced by the keywords \&{expr}, +\&{suffix}, \&{text}, \&{primary}, \&{secondary}, and \&{tertiary}. + +@<Put each...@>= +mp_primitive(mp, "expr",param_type,expr_base); +@:expr_}{\&{expr} primitive@> +mp_primitive(mp, "suffix",param_type,suffix_base); +@:suffix_}{\&{suffix} primitive@> +mp_primitive(mp, "text",param_type,text_base); +@:text_}{\&{text} primitive@> +mp_primitive(mp, "primary",param_type,primary_macro); +@:primary_}{\&{primary} primitive@> +mp_primitive(mp, "secondary",param_type,secondary_macro); +@:secondary_}{\&{secondary} primitive@> +mp_primitive(mp, "tertiary",param_type,tertiary_macro); +@:tertiary_}{\&{tertiary} primitive@> + +@ @<Cases of |print_cmd...@>= +case param_type: + if ( m>=expr_base ) { + if ( m==expr_base ) mp_print(mp, "expr"); + else if ( m==suffix_base ) mp_print(mp, "suffix"); + else mp_print(mp, "text"); + } else if ( m<secondary_macro ) { + mp_print(mp, "primary"); + } else if ( m==secondary_macro ) { + mp_print(mp, "secondary"); + } else { + mp_print(mp, "tertiary"); + } + break; + +@ Let's turn next to the more complex processing associated with \&{def} +and \&{vardef}. When the following procedure is called, |cur_mod| +should be either |start_def| or |var_def|. + +@c +static void mp_scan_def (MP mp) { + int m; /* the type of definition */ + int n; /* the number of special suffix parameters */ + int k; /* the total number of parameters */ + int c; /* the kind of macro we're defining */ + pointer r; /* parameter-substitution list */ + pointer q; /* tail of the macro token list */ + pointer p; /* temporary storage */ + halfword base; /* |expr_base|, |suffix_base|, or |text_base| */ + pointer l_delim,r_delim; /* matching delimiters */ + m=mp->cur_mod; c=general_macro; mp_link(hold_head)=null; + q=mp_get_avail(mp); ref_count(q)=null; r=null; + @<Scan the token or variable to be defined; + set |n|, |scanner_status|, and |warning_info|@>; + k=n; + if ( mp->cur_cmd==left_delimiter ) { + @<Absorb delimited parameters, putting them into lists |q| and |r|@>; + } + if ( mp->cur_cmd==param_type ) { + @<Absorb undelimited parameters, putting them into list |r|@>; + } + mp_check_equals(mp); + p=mp_get_avail(mp); mp_info(p)=c; mp_link(q)=p; + @<Attach the replacement text to the tail of node |p|@>; + mp->scanner_status=normal; mp_get_x_next(mp); +} + +@ We don't put `|frozen_end_group|' into the replacement text of +a \&{vardef}, because the user may want to redefine `\.{endgroup}'. + +@<Attach the replacement text to the tail of node |p|@>= +if ( m==start_def ) { + mp_link(p)=mp_scan_toks(mp, macro_def,r,null,n); +} else { + q=mp_get_avail(mp); mp_info(q)=mp->bg_loc; mp_link(p)=q; + p=mp_get_avail(mp); mp_info(p)=mp->eg_loc; + mp_link(q)=mp_scan_toks(mp, macro_def,r,p,n); +} +if ( mp->warning_info==bad_vardef ) + mp_flush_token_list(mp, value(bad_vardef)) + +@ @<Glob...@>= +int bg_loc; +int eg_loc; /* hash addresses of `\.{begingroup}' and `\.{endgroup}' */ + +@ @<Scan the token or variable to be defined;...@>= +if ( m==start_def ) { + mp_get_clear_symbol(mp); mp->warning_info=mp->cur_sym; get_t_next; + mp->scanner_status=op_defining; n=0; + eq_type(mp->warning_info)=defined_macro; equiv(mp->warning_info)=q; +} else { + p=mp_scan_declared_variable(mp); + mp_flush_variable(mp, equiv(mp_info(p)),mp_link(p),true); + mp->warning_info=mp_find_variable(mp, p); mp_flush_list(mp, p); + if ( mp->warning_info==null ) @<Change to `\.{a bad variable}'@>; + mp->scanner_status=var_defining; n=2; + if ( mp->cur_cmd==macro_special ) if ( mp->cur_mod==macro_suffix ) {/* \.{\AT!\#} */ + n=3; get_t_next; + } + mp_type(mp->warning_info)=mp_unsuffixed_macro-2+n; value(mp->warning_info)=q; +} /* |mp_suffixed_macro=mp_unsuffixed_macro+1| */ + +@ @<Change to `\.{a bad variable}'@>= +{ + print_err("This variable already starts with a macro"); +@.This variable already...@> + help2("After `vardef a' you can\'t say `vardef a.b'.", + "So I'll have to discard this definition."); + mp_error(mp); mp->warning_info=bad_vardef; +} + +@ @<Initialize table entries...@>= +mp_name_type(bad_vardef)=mp_root; mp_link(bad_vardef)=frozen_bad_vardef; +equiv(frozen_bad_vardef)=bad_vardef; eq_type(frozen_bad_vardef)=tag_token; + +@ @<Absorb delimited parameters, putting them into lists |q| and |r|@>= +do { + l_delim=mp->cur_sym; r_delim=mp->cur_mod; get_t_next; + if ( (mp->cur_cmd==param_type)&&(mp->cur_mod>=expr_base) ) { + base=mp->cur_mod; + } else { + print_err("Missing parameter type; `expr' will be assumed"); +@.Missing parameter type@> + help1("You should've had `expr' or `suffix' or `text' here."); + mp_back_error(mp); base=expr_base; + } + @<Absorb parameter tokens for type |base|@>; + mp_check_delimiter(mp, l_delim,r_delim); + get_t_next; +} while (mp->cur_cmd==left_delimiter) + +@ @<Absorb parameter tokens for type |base|@>= +do { + mp_link(q)=mp_get_avail(mp); q=mp_link(q); mp_info(q)=base+k; + mp_get_symbol(mp); p=mp_get_node(mp, token_node_size); + value(p)=base+k; mp_info(p)=mp->cur_sym; + if ( k==mp->param_size ) mp_overflow(mp, "parameter stack size",mp->param_size); +@:MetaPost capacity exceeded parameter stack size}{\quad parameter stack size@> + incr(k); mp_link(p)=r; r=p; get_t_next; +} while (mp->cur_cmd==comma) + +@ @<Absorb undelimited parameters, putting them into list |r|@>= +{ + p=mp_get_node(mp, token_node_size); + if ( mp->cur_mod<expr_base ) { + c=mp->cur_mod; value(p)=expr_base+k; + } else { + value(p)=mp->cur_mod+k; + if ( mp->cur_mod==expr_base ) c=expr_macro; + else if ( mp->cur_mod==suffix_base ) c=suffix_macro; + else c=text_macro; + } + if ( k==mp->param_size ) mp_overflow(mp, "parameter stack size",mp->param_size); + incr(k); mp_get_symbol(mp); mp_info(p)=mp->cur_sym; mp_link(p)=r; r=p; get_t_next; + if ( c==expr_macro ) if ( mp->cur_cmd==of_token ) { + c=of_macro; p=mp_get_node(mp, token_node_size); + if ( k==mp->param_size ) mp_overflow(mp, "parameter stack size",mp->param_size); + value(p)=expr_base+k; mp_get_symbol(mp); mp_info(p)=mp->cur_sym; + mp_link(p)=r; r=p; get_t_next; + } +} + +@* \[32] Expanding the next token. +Only a few command codes |<min_command| can possibly be returned by +|get_t_next|; in increasing order, they are +|if_test|, |fi_or_else|, |input|, |iteration|, |repeat_loop|, +|exit_test|, |relax|, |scan_tokens|, |expand_after|, and |defined_macro|. + +\MP\ usually gets the next token of input by saying |get_x_next|. This is +like |get_t_next| except that it keeps getting more tokens until +finding |cur_cmd>=min_command|. In other words, |get_x_next| expands +macros and removes conditionals or iterations or input instructions that +might be present. + +It follows that |get_x_next| might invoke itself recursively. In fact, +there is massive recursion, since macro expansion can involve the +scanning of arbitrarily complex expressions, which in turn involve +macro expansion and conditionals, etc. +@^recursion@> + +Therefore it's necessary to declare a whole bunch of |forward| +procedures at this point, and to insert some other procedures +that will be invoked by |get_x_next|. + +@<Declarations@>= +static void mp_scan_primary (MP mp); +static void mp_scan_secondary (MP mp); +static void mp_scan_tertiary (MP mp); +static void mp_scan_expression (MP mp); +static void mp_scan_suffix (MP mp); +static void mp_get_boolean (MP mp); +static void mp_pass_text (MP mp); +static void mp_conditional (MP mp); +static void mp_start_input (MP mp); +static void mp_begin_iteration (MP mp); +static void mp_resume_iteration (MP mp); +static void mp_stop_iteration (MP mp); + +@ An auxiliary subroutine called |expand| is used by |get_x_next| +when it has to do exotic expansion commands. + +@c +static void mp_expand (MP mp) { + pointer p; /* for list manipulation */ + size_t k; /* something that we hope is |<=buf_size| */ + pool_pointer j; /* index into |str_pool| */ + if ( mp->internal[mp_tracing_commands]>unity ) + if ( mp->cur_cmd!=defined_macro ) + show_cur_cmd_mod; + switch (mp->cur_cmd) { + case if_test: + mp_conditional(mp); /* this procedure is discussed in Part 36 below */ + break; + case fi_or_else: + @<Terminate the current conditional and skip to \&{fi}@>; + break; + case input: + @<Initiate or terminate input from a file@>; + break; + case iteration: + if ( mp->cur_mod==end_for ) { + @<Scold the user for having an extra \&{endfor}@>; + } else { + mp_begin_iteration(mp); /* this procedure is discussed in Part 37 below */ + } + break; + case repeat_loop: + @<Repeat a loop@>; + break; + case exit_test: + @<Exit a loop if the proper time has come@>; + break; + case relax: + break; + case expand_after: + @<Expand the token after the next token@>; + break; + case scan_tokens: + @<Put a string into the input buffer@>; + break; + case defined_macro: + mp_macro_call(mp, mp->cur_mod,null,mp->cur_sym); + break; + }; /* there are no other cases */ +} + +@ @<Scold the user...@>= +{ + print_err("Extra `endfor'"); +@.Extra `endfor'@> + help2("I'm not currently working on a for loop,", + "so I had better not try to end anything."); + mp_error(mp); +} + +@ The processing of \&{input} involves the |start_input| subroutine, +which will be declared later; the processing of \&{endinput} is trivial. + +@<Put each...@>= +mp_primitive(mp, "input",input,0); +@:input_}{\&{input} primitive@> +mp_primitive(mp, "endinput",input,1); +@:end_input_}{\&{endinput} primitive@> + +@ @<Cases of |print_cmd_mod|...@>= +case input: + if ( m==0 ) mp_print(mp, "input"); + else mp_print(mp, "endinput"); + break; + +@ @<Initiate or terminate input...@>= +if ( mp->cur_mod>0 ) mp->force_eof=true; +else mp_start_input(mp) + +@ We'll discuss the complicated parts of loop operations later. For now +it suffices to know that there's a global variable called |loop_ptr| +that will be |null| if no loop is in progress. + +@<Repeat a loop@>= +{ while ( token_state &&(loc==null) ) + mp_end_token_list(mp); /* conserve stack space */ + if ( mp->loop_ptr==null ) { + print_err("Lost loop"); +@.Lost loop@> + help2("I'm confused; after exiting from a loop, I still seem", + "to want to repeat it. I'll try to forget the problem."); + mp_error(mp); + } else { + mp_resume_iteration(mp); /* this procedure is in Part 37 below */ + } +} + +@ @<Exit a loop if the proper time has come@>= +{ mp_get_boolean(mp); + if ( mp->internal[mp_tracing_commands]>unity ) + mp_show_cmd_mod(mp, nullary,mp->cur_exp); + if ( mp->cur_exp==true_code ) { + if ( mp->loop_ptr==null ) { + print_err("No loop is in progress"); +@.No loop is in progress@> + help1("Why say `exitif' when there's nothing to exit from?"); + if ( mp->cur_cmd==semicolon ) mp_error(mp); else mp_back_error(mp); + } else { + @<Exit prematurely from an iteration@>; + } + } else if ( mp->cur_cmd!=semicolon ) { + mp_missing_err(mp, ";"); +@.Missing `;'@> + help2("After `exitif <boolean exp>' I expect to see a semicolon.", + "I shall pretend that one was there."); mp_back_error(mp); + } +} + +@ Here we use the fact that |forever_text| is the only |token_type| that +is less than |loop_text|. + +@<Exit prematurely...@>= +{ p=null; + do { + if ( file_state ) { + mp_end_file_reading(mp); + } else { + if ( token_type<=loop_text ) p=start; + mp_end_token_list(mp); + } + } while (p==null); + if ( p!=mp_info(mp->loop_ptr) ) mp_fatal_error(mp, "*** (loop confusion)"); +@.loop confusion@> + mp_stop_iteration(mp); /* this procedure is in Part 34 below */ +} + +@ @<Expand the token after the next token@>= +{ get_t_next; + p=mp_cur_tok(mp); get_t_next; + if ( mp->cur_cmd<min_command ) mp_expand(mp); + else mp_back_input(mp); + back_list(p); +} + +@ @<Put a string into the input buffer@>= +{ mp_get_x_next(mp); mp_scan_primary(mp); + if ( mp->cur_type!=mp_string_type ) { + mp_disp_err(mp, null,"Not a string"); +@.Not a string@> + help2("I'm going to flush this expression, since", + "scantokens should be followed by a known string."); + mp_put_get_flush_error(mp, 0); + } else { + mp_back_input(mp); + if ( length(mp->cur_exp)>0 ) + @<Pretend we're reading a new one-line file@>; + } +} + +@ @<Pretend we're reading a new one-line file@>= +{ mp_begin_file_reading(mp); name=is_scantok; + k=mp->first+length(mp->cur_exp); + if ( k>=mp->max_buf_stack ) { + while ( k>=mp->buf_size ) { + mp_reallocate_buffer(mp,(mp->buf_size+(mp->buf_size/4))); + } + mp->max_buf_stack=k+1; + } + j=mp->str_start[mp->cur_exp]; limit=(halfword)k; + while ( mp->first<(size_t)limit ) { + mp->buffer[mp->first]=mp->str_pool[j]; incr(j); incr(mp->first); + } + mp->buffer[limit]=xord('%'); mp->first=(size_t)(limit+1); loc=start; + mp_flush_cur_exp(mp, 0); +} + +@ Here finally is |get_x_next|. + +The expression scanning routines to be considered later +communicate via the global quantities |cur_type| and |cur_exp|; +we must be very careful to save and restore these quantities while +macros are being expanded. +@^inner loop@> + +@<Declarations@>= +static void mp_get_x_next (MP mp); + +@ @c void mp_get_x_next (MP mp) { + pointer save_exp; /* a capsule to save |cur_type| and |cur_exp| */ + get_t_next; + if ( mp->cur_cmd<min_command ) { + save_exp=mp_stash_cur_exp(mp); + do { + if ( mp->cur_cmd==defined_macro ) + mp_macro_call(mp, mp->cur_mod,null,mp->cur_sym); + else + mp_expand(mp); + get_t_next; + } while (mp->cur_cmd<min_command); + mp_unstash_cur_exp(mp, save_exp); /* that restores |cur_type| and |cur_exp| */ + } +} + +@ Now let's consider the |macro_call| procedure, which is used to start up +all user-defined macros. Since the arguments to a macro might be expressions, +|macro_call| is recursive. +@^recursion@> + +The first parameter to |macro_call| points to the reference count of the +token list that defines the macro. The second parameter contains any +arguments that have already been parsed (see below). The third parameter +points to the symbolic token that names the macro. If the third parameter +is |null|, the macro was defined by \&{vardef}, so its name can be +reconstructed from the prefix and ``at'' arguments found within the +second parameter. + +What is this second parameter? It's simply a linked list of one-word items, +whose |info| fields point to the arguments. In other words, if |arg_list=null|, +no arguments have been scanned yet; otherwise |mp_info(arg_list)| points to +the first scanned argument, and |mp_link(arg_list)| points to the list of +further arguments (if any). + +Arguments of type \&{expr} are so-called capsules, which we will +discuss later when we concentrate on expressions; they can be +recognized easily because their |link| field is |void|. Arguments of type +\&{suffix} and \&{text} are token lists without reference counts. + +@ After argument scanning is complete, the arguments are moved to the +|param_stack|. (They can't be put on that stack any sooner, because +the stack is growing and shrinking in unpredictable ways as more arguments +are being acquired.) Then the macro body is fed to the scanner; i.e., +the replacement text of the macro is placed at the top of the \MP's +input stack, so that |get_t_next| will proceed to read it next. + +@<Declarations@>= +static void mp_macro_call (MP mp,pointer def_ref, pointer arg_list, + pointer macro_name) ; + +@ @c +void mp_macro_call (MP mp,pointer def_ref, pointer arg_list, + pointer macro_name) { + /* invokes a user-defined control sequence */ + pointer r; /* current node in the macro's token list */ + pointer p,q; /* for list manipulation */ + integer n; /* the number of arguments */ + pointer tail = 0; /* tail of the argument list */ + pointer l_delim=0,r_delim=0; /* a delimiter pair */ + r=mp_link(def_ref); add_mac_ref(def_ref); + if ( arg_list==null ) { + n=0; + } else { + @<Determine the number |n| of arguments already supplied, + and set |tail| to the tail of |arg_list|@>; + } + if ( mp->internal[mp_tracing_macros]>0 ) { + @<Show the text of the macro being expanded, and the existing arguments@>; + } + @<Scan the remaining arguments, if any; set |r| to the first token + of the replacement text@>; + @<Feed the arguments and replacement text to the scanner@>; +} + +@ @<Show the text of the macro...@>= +mp_begin_diagnostic(mp); mp_print_ln(mp); +mp_print_macro_name(mp, arg_list,macro_name); +if ( n==3 ) mp_print(mp, "@@#"); /* indicate a suffixed macro */ +mp_show_macro(mp, def_ref,null,100000); +if ( arg_list!=null ) { + n=0; p=arg_list; + do { + q=mp_info(p); + mp_print_arg(mp, q,n,0); + incr(n); p=mp_link(p); + } while (p!=null); +} +mp_end_diagnostic(mp, false) + + +@ @<Declarations@>= +static void mp_print_macro_name (MP mp,pointer a, pointer n); + +@ @c +void mp_print_macro_name (MP mp,pointer a, pointer n) { + pointer p,q; /* they traverse the first part of |a| */ + if ( n!=null ) { + mp_print_text(n); + } else { + p=mp_info(a); + if ( p==null ) { + mp_print_text(mp_info(mp_info(mp_link(a)))); + } else { + q=p; + while ( mp_link(q)!=null ) q=mp_link(q); + mp_link(q)=mp_info(mp_link(a)); + mp_show_token_list(mp, p,null,1000,0); + mp_link(q)=null; + } + } +} + +@ @<Declarations@>= +static void mp_print_arg (MP mp,pointer q, integer n, pointer b) ; + +@ @c +void mp_print_arg (MP mp,pointer q, integer n, pointer b) { + if ( mp_link(q)==mp_void ) mp_print_nl(mp, "(EXPR"); + else if ( (b<text_base)&&(b!=text_macro) ) mp_print_nl(mp, "(SUFFIX"); + else mp_print_nl(mp, "(TEXT"); + mp_print_int(mp, n); mp_print(mp, ")<-"); + if ( mp_link(q)==mp_void ) mp_print_exp(mp, q,1); + else mp_show_token_list(mp, q,null,1000,0); +} + +@ @<Determine the number |n| of arguments already supplied...@>= +{ + n=1; tail=arg_list; + while ( mp_link(tail)!=null ) { + incr(n); tail=mp_link(tail); + } +} + +@ @<Scan the remaining arguments, if any; set |r|...@>= +mp->cur_cmd=comma+1; /* anything |<>comma| will do */ +while ( mp_info(r)>=expr_base ) { + @<Scan the delimited argument represented by |mp_info(r)|@>; + r=mp_link(r); +} +if ( mp->cur_cmd==comma ) { + print_err("Too many arguments to "); +@.Too many arguments...@> + mp_print_macro_name(mp, arg_list,macro_name); mp_print_char(mp, xord(';')); + mp_print_nl(mp, " Missing `"); mp_print_text(r_delim); +@.Missing `)'...@> + mp_print(mp, "' has been inserted"); + help3("I'm going to assume that the comma I just read was a", + "right delimiter, and then I'll begin expanding the macro.", + "You might want to delete some tokens before continuing."); + mp_error(mp); +} +if ( mp_info(r)!=general_macro ) { + @<Scan undelimited argument(s)@>; +} +r=mp_link(r) + +@ At this point, the reader will find it advisable to review the explanation +of token list format that was presented earlier, paying special attention to +the conventions that apply only at the beginning of a macro's token list. + +On the other hand, the reader will have to take the expression-parsing +aspects of the following program on faith; we will explain |cur_type| +and |cur_exp| later. (Several things in this program depend on each other, +and it's necessary to jump into the circle somewhere.) + +@<Scan the delimited argument represented by |mp_info(r)|@>= +if ( mp->cur_cmd!=comma ) { + mp_get_x_next(mp); + if ( mp->cur_cmd!=left_delimiter ) { + print_err("Missing argument to "); +@.Missing argument...@> + mp_print_macro_name(mp, arg_list,macro_name); + help3("That macro has more parameters than you thought.", + "I'll continue by pretending that each missing argument", + "is either zero or null."); + if ( mp_info(r)>=suffix_base ) { + mp->cur_exp=null; mp->cur_type=mp_token_list; + } else { + mp->cur_exp=0; mp->cur_type=mp_known; + } + mp_back_error(mp); mp->cur_cmd=right_delimiter; + goto FOUND; + } + l_delim=mp->cur_sym; r_delim=mp->cur_mod; +} +@<Scan the argument represented by |mp_info(r)|@>; +if ( mp->cur_cmd!=comma ) + @<Check that the proper right delimiter was present@>; +FOUND: +@<Append the current expression to |arg_list|@> + +@ @<Check that the proper right delim...@>= +if ( (mp->cur_cmd!=right_delimiter)||(mp->cur_mod!=l_delim) ) { + if ( mp_info(mp_link(r))>=expr_base ) { + mp_missing_err(mp, ","); +@.Missing `,'@> + help3("I've finished reading a macro argument and am about to", + "read another; the arguments weren't delimited correctly.", + "You might want to delete some tokens before continuing."); + mp_back_error(mp); mp->cur_cmd=comma; + } else { + mp_missing_err(mp, str(text(r_delim))); +@.Missing `)'@> + help2("I've gotten to the end of the macro parameter list.", + "You might want to delete some tokens before continuing."); + mp_back_error(mp); + } +} + +@ A \&{suffix} or \&{text} parameter will have been scanned as +a token list pointed to by |cur_exp|, in which case we will have +|cur_type=token_list|. + +@<Append the current expression to |arg_list|@>= +{ + p=mp_get_avail(mp); + if ( mp->cur_type==mp_token_list ) mp_info(p)=mp->cur_exp; + else mp_info(p)=mp_stash_cur_exp(mp); + if ( mp->internal[mp_tracing_macros]>0 ) { + mp_begin_diagnostic(mp); mp_print_arg(mp, mp_info(p),n,mp_info(r)); + mp_end_diagnostic(mp, false); + } + if ( arg_list==null ) arg_list=p; + else mp_link(tail)=p; + tail=p; incr(n); +} + +@ @<Scan the argument represented by |mp_info(r)|@>= +if ( mp_info(r)>=text_base ) { + mp_scan_text_arg(mp, l_delim,r_delim); +} else { + mp_get_x_next(mp); + if ( mp_info(r)>=suffix_base ) mp_scan_suffix(mp); + else mp_scan_expression(mp); +} + +@ The parameters to |scan_text_arg| are either a pair of delimiters +or zero; the latter case is for undelimited text arguments, which +end with the first semicolon or \&{endgroup} or \&{end} that is not +contained in a group. + +@<Declarations@>= +static void mp_scan_text_arg (MP mp,pointer l_delim, pointer r_delim) ; + +@ @c +void mp_scan_text_arg (MP mp,pointer l_delim, pointer r_delim) { + integer balance; /* excess of |l_delim| over |r_delim| */ + pointer p; /* list tail */ + mp->warning_info=l_delim; mp->scanner_status=absorbing; + p=hold_head; balance=1; mp_link(hold_head)=null; + while (1) { + get_t_next; + if ( l_delim==0 ) { + @<Adjust the balance for an undelimited argument; |break| if done@>; + } else { + @<Adjust the balance for a delimited argument; |break| if done@>; + } + mp_link(p)=mp_cur_tok(mp); p=mp_link(p); + } + mp->cur_exp=mp_link(hold_head); mp->cur_type=mp_token_list; + mp->scanner_status=normal; +} + +@ @<Adjust the balance for a delimited argument...@>= +if ( mp->cur_cmd==right_delimiter ) { + if ( mp->cur_mod==l_delim ) { + decr(balance); + if ( balance==0 ) break; + } +} else if ( mp->cur_cmd==left_delimiter ) { + if ( mp->cur_mod==r_delim ) incr(balance); +} + +@ @<Adjust the balance for an undelimited...@>= +if ( end_of_statement ) { /* |cur_cmd=semicolon|, |end_group|, or |stop| */ + if ( balance==1 ) { break; } + else { if ( mp->cur_cmd==end_group ) decr(balance); } +} else if ( mp->cur_cmd==begin_group ) { + incr(balance); +} + +@ @<Scan undelimited argument(s)@>= +{ + if ( mp_info(r)<text_macro ) { + mp_get_x_next(mp); + if ( mp_info(r)!=suffix_macro ) { + if ( (mp->cur_cmd==equals)||(mp->cur_cmd==assignment) ) mp_get_x_next(mp); + } + } + switch (mp_info(r)) { + case primary_macro:mp_scan_primary(mp); break; + case secondary_macro:mp_scan_secondary(mp); break; + case tertiary_macro:mp_scan_tertiary(mp); break; + case expr_macro:mp_scan_expression(mp); break; + case of_macro: + @<Scan an expression followed by `\&{of} $\langle$primary$\rangle$'@>; + break; + case suffix_macro: + @<Scan a suffix with optional delimiters@>; + break; + case text_macro:mp_scan_text_arg(mp, 0,0); break; + } /* there are no other cases */ + mp_back_input(mp); + @<Append the current expression to |arg_list|@>; +} + +@ @<Scan an expression followed by `\&{of} $\langle$primary$\rangle$'@>= +{ + mp_scan_expression(mp); p=mp_get_avail(mp); mp_info(p)=mp_stash_cur_exp(mp); + if ( mp->internal[mp_tracing_macros]>0 ) { + mp_begin_diagnostic(mp); mp_print_arg(mp, mp_info(p),n,0); + mp_end_diagnostic(mp, false); + } + if ( arg_list==null ) arg_list=p; else mp_link(tail)=p; + tail=p;incr(n); + if ( mp->cur_cmd!=of_token ) { + mp_missing_err(mp, "of"); mp_print(mp, " for "); +@.Missing `of'@> + mp_print_macro_name(mp, arg_list,macro_name); + help1("I've got the first argument; will look now for the other."); + mp_back_error(mp); + } + mp_get_x_next(mp); mp_scan_primary(mp); +} + +@ @<Scan a suffix with optional delimiters@>= +{ + if ( mp->cur_cmd!=left_delimiter ) { + l_delim=null; + } else { + l_delim=mp->cur_sym; r_delim=mp->cur_mod; mp_get_x_next(mp); + }; + mp_scan_suffix(mp); + if ( l_delim!=null ) { + if ((mp->cur_cmd!=right_delimiter)||(mp->cur_mod!=l_delim) ) { + mp_missing_err(mp, str(text(r_delim))); +@.Missing `)'@> + help2("I've gotten to the end of the macro parameter list.", + "You might want to delete some tokens before continuing."); + mp_back_error(mp); + } + mp_get_x_next(mp); + } +} + +@ Before we put a new token list on the input stack, it is wise to clean off +all token lists that have recently been depleted. Then a user macro that ends +with a call to itself will not require unbounded stack space. + +@<Feed the arguments and replacement text to the scanner@>= +while ( token_state &&(loc==null) ) mp_end_token_list(mp); /* conserve stack space */ +if ( mp->param_ptr+n>mp->max_param_stack ) { + mp->max_param_stack=mp->param_ptr+n; + if ( mp->max_param_stack>mp->param_size ) + mp_overflow(mp, "parameter stack size",mp->param_size); +@:MetaPost capacity exceeded parameter stack size}{\quad parameter stack size@> +} +mp_begin_token_list(mp, def_ref,macro); name=macro_name; loc=r; +if ( n>0 ) { + p=arg_list; + do { + mp->param_stack[mp->param_ptr]=mp_info(p); incr(mp->param_ptr); p=mp_link(p); + } while (p!=null); + mp_flush_list(mp, arg_list); +} + +@ It's sometimes necessary to put a single argument onto |param_stack|. +The |stack_argument| subroutine does this. + +@c +static void mp_stack_argument (MP mp,pointer p) { + if ( mp->param_ptr==mp->max_param_stack ) { + incr(mp->max_param_stack); + if ( mp->max_param_stack>mp->param_size ) + mp_overflow(mp, "parameter stack size",mp->param_size); +@:MetaPost capacity exceeded parameter stack size}{\quad parameter stack size@> + } + mp->param_stack[mp->param_ptr]=p; incr(mp->param_ptr); +} + +@* \[33] Conditional processing. +Let's consider now the way \&{if} commands are handled. + +Conditions can be inside conditions, and this nesting has a stack +that is independent of other stacks. +Four global variables represent the top of the condition stack: +|cond_ptr| points to pushed-down entries, if~any; |cur_if| tells whether +we are processing \&{if} or \&{elseif}; |if_limit| specifies +the largest code of a |fi_or_else| command that is syntactically legal; +and |if_line| is the line number at which the current conditional began. + +If no conditions are currently in progress, the condition stack has the +special state |cond_ptr=null|, |if_limit=normal|, |cur_if=0|, |if_line=0|. +Otherwise |cond_ptr| points to a two-word node; the |type|, |name_type|, and +|link| fields of the first word contain |if_limit|, |cur_if|, and +|cond_ptr| at the next level, and the second word contains the +corresponding |if_line|. + +@d if_node_size 2 /* number of words in stack entry for conditionals */ +@d if_line_field(A) mp->mem[(A)+1].cint +@d if_code 1 /* code for \&{if} being evaluated */ +@d fi_code 2 /* code for \&{fi} */ +@d else_code 3 /* code for \&{else} */ +@d else_if_code 4 /* code for \&{elseif} */ + +@<Glob...@>= +pointer cond_ptr; /* top of the condition stack */ +integer if_limit; /* upper bound on |fi_or_else| codes */ +quarterword cur_if; /* type of conditional being worked on */ +integer if_line; /* line where that conditional began */ + +@ @<Set init...@>= +mp->cond_ptr=null; mp->if_limit=normal; mp->cur_if=0; mp->if_line=0; + +@ @<Put each...@>= +mp_primitive(mp, "if",if_test,if_code); +@:if_}{\&{if} primitive@> +mp_primitive(mp, "fi",fi_or_else,fi_code); mp->eqtb[frozen_fi]=mp->eqtb[mp->cur_sym]; +@:fi_}{\&{fi} primitive@> +mp_primitive(mp, "else",fi_or_else,else_code); +@:else_}{\&{else} primitive@> +mp_primitive(mp, "elseif",fi_or_else,else_if_code); +@:else_if_}{\&{elseif} primitive@> + +@ @<Cases of |print_cmd_mod|...@>= +case if_test: +case fi_or_else: + switch (m) { + case if_code:mp_print(mp, "if"); break; + case fi_code:mp_print(mp, "fi"); break; + case else_code:mp_print(mp, "else"); break; + default: mp_print(mp, "elseif"); break; + } + break; + +@ Here is a procedure that ignores text until coming to an \&{elseif}, +\&{else}, or \&{fi} at level zero of $\&{if}\ldots\&{fi}$ +nesting. After it has acted, |cur_mod| will indicate the token that +was found. + +\MP's smallest two command codes are |if_test| and |fi_or_else|; this +makes the skipping process a bit simpler. + +@c +void mp_pass_text (MP mp) { + integer l = 0; + mp->scanner_status=skipping; + mp->warning_info=mp_true_line(mp); + while (1) { + get_t_next; + if ( mp->cur_cmd<=fi_or_else ) { + if ( mp->cur_cmd<fi_or_else ) { + incr(l); + } else { + if ( l==0 ) break; + if ( mp->cur_mod==fi_code ) decr(l); + } + } else { + @<Decrease the string reference count, + if the current token is a string@>; + } + } + mp->scanner_status=normal; +} + +@ @<Decrease the string reference count...@>= +if ( mp->cur_cmd==string_token ) { delete_str_ref(mp->cur_mod); } + +@ When we begin to process a new \&{if}, we set |if_limit:=if_code|; then +if \&{elseif} or \&{else} or \&{fi} occurs before the current \&{if} +condition has been evaluated, a colon will be inserted. +A construction like `\.{if fi}' would otherwise get \MP\ confused. + +@<Push the condition stack@>= +{ p=mp_get_node(mp, if_node_size); mp_link(p)=mp->cond_ptr; mp_type(p)=mp->if_limit; + mp_name_type(p)=mp->cur_if; if_line_field(p)=mp->if_line; + mp->cond_ptr=p; mp->if_limit=if_code; mp->if_line=mp_true_line(mp); + mp->cur_if=if_code; +} + +@ @<Pop the condition stack@>= +{ p=mp->cond_ptr; mp->if_line=if_line_field(p); + mp->cur_if=mp_name_type(p); mp->if_limit=mp_type(p); mp->cond_ptr=mp_link(p); + mp_free_node(mp, p,if_node_size); +} + +@ Here's a procedure that changes the |if_limit| code corresponding to +a given value of |cond_ptr|. + +@c +static void mp_change_if_limit (MP mp,quarterword l, pointer p) { + pointer q; + if ( p==mp->cond_ptr ) { + mp->if_limit=l; /* that's the easy case */ + } else { + q=mp->cond_ptr; + while (1) { + if ( q==null ) mp_confusion(mp, "if"); +@:this can't happen if}{\quad if@> + if ( mp_link(q)==p ) { + mp_type(q)=l; return; + } + q=mp_link(q); + } + } +} + +@ The user is supposed to put colons into the proper parts of conditional +statements. Therefore, \MP\ has to check for their presence. + +@c +static void mp_check_colon (MP mp) { + if ( mp->cur_cmd!=colon ) { + mp_missing_err(mp, ":"); +@.Missing `:'@> + help2("There should've been a colon after the condition.", + "I shall pretend that one was there."); + mp_back_error(mp); + } +} + +@ A condition is started when the |get_x_next| procedure encounters +an |if_test| command; in that case |get_x_next| calls |conditional|, +which is a recursive procedure. +@^recursion@> + +@c +void mp_conditional (MP mp) { + pointer save_cond_ptr; /* |cond_ptr| corresponding to this conditional */ + int new_if_limit; /* future value of |if_limit| */ + pointer p; /* temporary register */ + @<Push the condition stack@>; + save_cond_ptr=mp->cond_ptr; +RESWITCH: + mp_get_boolean(mp); new_if_limit=else_if_code; + if ( mp->internal[mp_tracing_commands]>unity ) { + @<Display the boolean value of |cur_exp|@>; + } +FOUND: + mp_check_colon(mp); + if ( mp->cur_exp==true_code ) { + mp_change_if_limit(mp, new_if_limit,save_cond_ptr); + return; /* wait for \&{elseif}, \&{else}, or \&{fi} */ + }; + @<Skip to \&{elseif} or \&{else} or \&{fi}, then |goto done|@>; +DONE: + mp->cur_if=mp->cur_mod; mp->if_line=mp_true_line(mp); + if ( mp->cur_mod==fi_code ) { + @<Pop the condition stack@> + } else if ( mp->cur_mod==else_if_code ) { + goto RESWITCH; + } else { + mp->cur_exp=true_code; new_if_limit=fi_code; mp_get_x_next(mp); + goto FOUND; + } +} + +@ In a construction like `\&{if} \&{if} \&{true}: $0=1$: \\{foo} +\&{else}: \\{bar} \&{fi}', the first \&{else} +that we come to after learning that the \&{if} is false is not the +\&{else} we're looking for. Hence the following curious logic is needed. + +@<Skip to \&{elseif}...@>= +while (1) { + mp_pass_text(mp); + if ( mp->cond_ptr==save_cond_ptr ) goto DONE; + else if ( mp->cur_mod==fi_code ) @<Pop the condition stack@>; +} + + +@ @<Display the boolean value...@>= +{ mp_begin_diagnostic(mp); + if ( mp->cur_exp==true_code ) mp_print(mp, "{true}"); + else mp_print(mp, "{false}"); + mp_end_diagnostic(mp, false); +} + +@ The processing of conditionals is complete except for the following +code, which is actually part of |get_x_next|. It comes into play when +\&{elseif}, \&{else}, or \&{fi} is scanned. + +@<Terminate the current conditional and skip to \&{fi}@>= +if ( mp->cur_mod>mp->if_limit ) { + if ( mp->if_limit==if_code ) { /* condition not yet evaluated */ + mp_missing_err(mp, ":"); +@.Missing `:'@> + mp_back_input(mp); mp->cur_sym=frozen_colon; mp_ins_error(mp); + } else { + print_err("Extra "); mp_print_cmd_mod(mp, fi_or_else,mp->cur_mod); +@.Extra else@> +@.Extra elseif@> +@.Extra fi@> + help1("I'm ignoring this; it doesn't match any if."); + mp_error(mp); + } +} else { + while ( mp->cur_mod!=fi_code ) mp_pass_text(mp); /* skip to \&{fi} */ + @<Pop the condition stack@>; +} + +@* \[34] Iterations. +To bring our treatment of |get_x_next| to a close, we need to consider what +\MP\ does when it sees \&{for}, \&{forsuffixes}, and \&{forever}. + +There's a global variable |loop_ptr| that keeps track of the \&{for} loops +that are currently active. If |loop_ptr=null|, no loops are in progress; +otherwise |mp_info(loop_ptr)| points to the iterative text of the current +(innermost) loop, and |mp_link(loop_ptr)| points to the data for any other +loops that enclose the current one. + +A loop-control node also has two other fields, called |loop_type| and +|loop_list|, whose contents depend on the type of loop: + +\yskip\indent|loop_type(loop_ptr)=null| means that |loop_list(loop_ptr)| +points to a list of one-word nodes whose |info| fields point to the +remaining argument values of a suffix list and expression list. + +\yskip\indent|loop_type(loop_ptr)=mp_void| means that the current loop is +`\&{forever}'. + +\yskip\indent|loop_type(loop_ptr)=progression_flag| means that +|p=loop_list(loop_ptr)| points to a ``progression node'' and |value(p)|, +|step_size(p)|, and |final_value(p)| contain the data for an arithmetic +progression. + +\yskip\indent|loop_type(loop_ptr)=p>mp_void| means that |p| points to an edge +header and |loop_list(loop_ptr)| points into the graphical object list for +that edge header. + +\yskip\noindent In the case of a progression node, the first word is not used +because the link field of words in the dynamic memory area cannot be arbitrary. + +@d loop_list_loc(A) ((A)+1) /* where the |loop_list| field resides */ +@d loop_type(A) mp_info(loop_list_loc((A))) /* the type of \&{for} loop */ +@d loop_list(A) mp_link(loop_list_loc((A))) /* the remaining list elements */ +@d loop_node_size 2 /* the number of words in a loop control node */ +@d progression_node_size 4 /* the number of words in a progression node */ +@d step_size(A) mp->mem[(A)+2].sc /* the step size in an arithmetic progression */ +@d final_value(A) mp->mem[(A)+3].sc /* the final value in an arithmetic progression */ +@d progression_flag (null+2) + /* |loop_type| value when |loop_list| points to a progression node */ + +@<Glob...@>= +pointer loop_ptr; /* top of the loop-control-node stack */ + +@ @<Set init...@>= +mp->loop_ptr=null; + +@ If the expressions that define an arithmetic progression in +a \&{for} loop don't have known numeric values, the |bad_for| +subroutine screams at the user. + +@c +static void mp_bad_for (MP mp, const char * s) { + mp_disp_err(mp, null,"Improper "); /* show the bad expression above the message */ +@.Improper...replaced by 0@> + mp_print(mp, s); mp_print(mp, " has been replaced by 0"); + help4("When you say `for x=a step b until c',", + "the initial value `a' and the step size `b'", + "and the final value `c' must have known numeric values.", + "I'm zeroing this one. Proceed, with fingers crossed."); + mp_put_get_flush_error(mp, 0); +} + +@ Here's what \MP\ does when \&{for}, \&{forsuffixes}, or \&{forever} +has just been scanned. (This code requires slight familiarity with +expression-parsing routines that we have not yet discussed; but it seems +to belong in the present part of the program, even though the original author +didn't write it until later. The reader may wish to come back to it.) + +@c void mp_begin_iteration (MP mp) { + halfword m; /* |expr_base| (\&{for}) or |suffix_base| (\&{forsuffixes}) */ + halfword n; /* hash address of the current symbol */ + pointer s; /* the new loop-control node */ + pointer p; /* substitution list for |scan_toks| */ + pointer q; /* link manipulation register */ + pointer pp; /* a new progression node */ + m=mp->cur_mod; n=mp->cur_sym; s=mp_get_node(mp, loop_node_size); + if ( m==start_forever ){ + loop_type(s)=mp_void; p=null; mp_get_x_next(mp); + } else { + mp_get_symbol(mp); p=mp_get_node(mp, token_node_size); + mp_info(p)=mp->cur_sym; value(p)=m; + mp_get_x_next(mp); + if ( mp->cur_cmd==within_token ) { + @<Set up a picture iteration@>; + } else { + @<Check for the |"="| or |":="| in a loop header@>; + @<Scan the values to be used in the loop@>; + } + } + @<Check for the presence of a colon@>; + @<Scan the loop text and put it on the loop control stack@>; + mp_resume_iteration(mp); +} + +@ @<Check for the |"="| or |":="| in a loop header@>= +if ( (mp->cur_cmd!=equals)&&(mp->cur_cmd!=assignment) ) { + mp_missing_err(mp, "="); +@.Missing `='@> + help3("The next thing in this loop should have been `=' or `:='.", + "But don't worry; I'll pretend that an equals sign", + "was present, and I'll look for the values next."); + mp_back_error(mp); +} + +@ @<Check for the presence of a colon@>= +if ( mp->cur_cmd!=colon ) { + mp_missing_err(mp, ":"); +@.Missing `:'@> + help3("The next thing in this loop should have been a `:'.", + "So I'll pretend that a colon was present;", + "everything from here to `endfor' will be iterated."); + mp_back_error(mp); +} + +@ We append a special |frozen_repeat_loop| token in place of the +`\&{endfor}' at the end of the loop. This will come through \MP's scanner +at the proper time to cause the loop to be repeated. + +(If the user tries some shenanigan like `\&{for} $\ldots$ \&{let} \&{endfor}', +he will be foiled by the |get_symbol| routine, which keeps frozen +tokens unchanged. Furthermore the |frozen_repeat_loop| is an \&{outer} +token, so it won't be lost accidentally.) + +@ @<Scan the loop text...@>= +q=mp_get_avail(mp); mp_info(q)=frozen_repeat_loop; +mp->scanner_status=loop_defining; mp->warning_info=n; +mp_info(s)=mp_scan_toks(mp, iteration,p,q,0); mp->scanner_status=normal; +mp_link(s)=mp->loop_ptr; mp->loop_ptr=s + +@ @<Initialize table...@>= +eq_type(frozen_repeat_loop)=repeat_loop+outer_tag; +text(frozen_repeat_loop)=intern(" ENDFOR"); + +@ The loop text is inserted into \MP's scanning apparatus by the +|resume_iteration| routine. + +@c void mp_resume_iteration (MP mp) { + pointer p,q; /* link registers */ + p=loop_type(mp->loop_ptr); + if ( p==progression_flag ) { + p=loop_list(mp->loop_ptr); /* now |p| points to a progression node */ + mp->cur_exp=value(p); + if ( @<The arithmetic progression has ended@> ) { + mp_stop_iteration(mp); + return; + } + mp->cur_type=mp_known; q=mp_stash_cur_exp(mp); /* make |q| an \&{expr} argument */ + value(p)=mp->cur_exp+step_size(p); /* set |value(p)| for the next iteration */ + } else if ( p==null ) { + p=loop_list(mp->loop_ptr); + if ( p==null ) { + mp_stop_iteration(mp); + return; + } + loop_list(mp->loop_ptr)=mp_link(p); q=mp_info(p); free_avail(p); + } else if ( p==mp_void ) { + mp_begin_token_list(mp, mp_info(mp->loop_ptr),forever_text); return; + } else { + @<Make |q| a capsule containing the next picture component from + |loop_list(loop_ptr)| or |goto not_found|@>; + } + mp_begin_token_list(mp, mp_info(mp->loop_ptr),loop_text); + mp_stack_argument(mp, q); + if ( mp->internal[mp_tracing_commands]>unity ) { + @<Trace the start of a loop@>; + } + return; +NOT_FOUND: + mp_stop_iteration(mp); +} + +@ @<The arithmetic progression has ended@>= +((step_size(p)>0)&&(mp->cur_exp>final_value(p)))|| + ((step_size(p)<0)&&(mp->cur_exp<final_value(p))) + +@ @<Trace the start of a loop@>= +{ + mp_begin_diagnostic(mp); mp_print_nl(mp, "{loop value="); +@.loop value=n@> + if ( (q!=null)&&(mp_link(q)==mp_void) ) mp_print_exp(mp, q,1); + else mp_show_token_list(mp, q,null,50,0); + mp_print_char(mp, xord('}')); mp_end_diagnostic(mp, false); +} + +@ @<Make |q| a capsule containing the next picture component from...@>= +{ q=loop_list(mp->loop_ptr); + if ( q==null ) goto NOT_FOUND; + skip_component(q) goto NOT_FOUND; + mp->cur_exp=mp_copy_objects(mp, loop_list(mp->loop_ptr),q); + mp_init_bbox(mp, mp->cur_exp); + mp->cur_type=mp_picture_type; + loop_list(mp->loop_ptr)=q; + q=mp_stash_cur_exp(mp); +} + +@ A level of loop control disappears when |resume_iteration| has decided +not to resume, or when an \&{exitif} construction has removed the loop text +from the input stack. + +@c void mp_stop_iteration (MP mp) { + pointer p,q; /* the usual */ + p=loop_type(mp->loop_ptr); + if ( p==progression_flag ) { + mp_free_node(mp, loop_list(mp->loop_ptr),progression_node_size); + } else if ( p==null ){ + q=loop_list(mp->loop_ptr); + while ( q!=null ) { + p=mp_info(q); + if ( p!=null ) { + if ( mp_link(p)==mp_void ) { /* it's an \&{expr} parameter */ + mp_recycle_value(mp, p); mp_free_node(mp, p,value_node_size); + } else { + mp_flush_token_list(mp, p); /* it's a \&{suffix} or \&{text} parameter */ + } + } + p=q; q=mp_link(q); free_avail(p); + } + } else if ( p>progression_flag ) { + delete_edge_ref(p); + } + p=mp->loop_ptr; mp->loop_ptr=mp_link(p); mp_flush_token_list(mp, mp_info(p)); + mp_free_node(mp, p,loop_node_size); +} + +@ Now that we know all about loop control, we can finish up +the missing portion of |begin_iteration| and we'll be done. + +The following code is performed after the `\.=' has been scanned in +a \&{for} construction (if |m=expr_base|) or a \&{forsuffixes} construction +(if |m=suffix_base|). + +@<Scan the values to be used in the loop@>= +loop_type(s)=null; q=loop_list_loc(s); mp_link(q)=null; /* |mp_link(q)=loop_list(s)| */ +do { + mp_get_x_next(mp); + if ( m!=expr_base ) { + mp_scan_suffix(mp); + } else { + if ( mp->cur_cmd>=colon ) if ( mp->cur_cmd<=comma ) + goto CONTINUE; + mp_scan_expression(mp); + if ( mp->cur_cmd==step_token ) if ( q==loop_list_loc(s) ) { + @<Prepare for step-until construction and |break|@>; + } + mp->cur_exp=mp_stash_cur_exp(mp); + } + mp_link(q)=mp_get_avail(mp); q=mp_link(q); + mp_info(q)=mp->cur_exp; mp->cur_type=mp_vacuous; +CONTINUE: + ; +} while (mp->cur_cmd==comma) + +@ @<Prepare for step-until construction and |break|@>= +{ + if ( mp->cur_type!=mp_known ) mp_bad_for(mp, "initial value"); + pp=mp_get_node(mp, progression_node_size); value(pp)=mp->cur_exp; + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ) mp_bad_for(mp, "step size"); + step_size(pp)=mp->cur_exp; + if ( mp->cur_cmd!=until_token ) { + mp_missing_err(mp, "until"); +@.Missing `until'@> + help2("I assume you meant to say `until' after `step'.", + "So I'll look for the final value and colon next."); + mp_back_error(mp); + } + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ) mp_bad_for(mp, "final value"); + final_value(pp)=mp->cur_exp; loop_list(s)=pp; + loop_type(s)=progression_flag; + break; +} + +@ The last case is when we have just seen ``\&{within}'', and we need to +parse a picture expression and prepare to iterate over it. + +@<Set up a picture iteration@>= +{ mp_get_x_next(mp); + mp_scan_expression(mp); + @<Make sure the current expression is a known picture@>; + loop_type(s)=mp->cur_exp; mp->cur_type=mp_vacuous; + q=mp_link(dummy_loc(mp->cur_exp)); + if ( q!= null ) + if ( is_start_or_stop(q) ) + if ( mp_skip_1component(mp, q)==null ) q=mp_link(q); + loop_list(s)=q; +} + +@ @<Make sure the current expression is a known picture@>= +if ( mp->cur_type!=mp_picture_type ) { + mp_disp_err(mp, null,"Improper iteration spec has been replaced by nullpicture"); + help1("When you say `for x in p', p must be a known picture."); + mp_put_get_flush_error(mp, mp_get_node(mp, edge_header_size)); + mp_init_edges(mp, mp->cur_exp); mp->cur_type=mp_picture_type; +} + +@* \[35] File names. +It's time now to fret about file names. Besides the fact that different +operating systems treat files in different ways, we must cope with the +fact that completely different naming conventions are used by different +groups of people. The following programs show what is required for one +particular operating system; similar routines for other systems are not +difficult to devise. +@^system dependencies@> + +\MP\ assumes that a file name has three parts: the name proper; its +``extension''; and a ``file area'' where it is found in an external file +system. The extension of an input file is assumed to be +`\.{.mp}' unless otherwise specified; it is `\.{.log}' on the +transcript file that records each run of \MP; it is `\.{.tfm}' on the font +metric files that describe characters in any fonts created by \MP; it is +`\.{.ps}' or `.{\it nnn}' for some number {\it nnn} on the \ps\ output files; +and it is `\.{.mem}' on the mem files written by \.{INIMP} to initialize \MP. +The file area can be arbitrary on input files, but files are usually +output to the user's current area. If an input file cannot be +found on the specified area, \MP\ will look for it on a special system +area; this special area is intended for commonly used input files. + +Simple uses of \MP\ refer only to file names that have no explicit +extension or area. For example, a person usually says `\.{input} \.{cmr10}' +instead of `\.{input} \.{cmr10.new}'. Simple file +names are best, because they make the \MP\ source files portable; +whenever a file name consists entirely of letters and digits, it should be +treated in the same way by all implementations of \MP. However, users +need the ability to refer to other files in their environment, especially +when responding to error messages concerning unopenable files; therefore +we want to let them use the syntax that appears in their favorite +operating system. + +@ \MP\ uses the same conventions that have proved to be satisfactory for +\TeX\ and \MF. In order to isolate the system-dependent aspects of file names, +@^system dependencies@> +the system-independent parts of \MP\ are expressed in terms +of three system-dependent +procedures called |begin_name|, |more_name|, and |end_name|. In +essence, if the user-specified characters of the file name are $c_1\ldots c_n$, +the system-independent driver program does the operations +$$|begin_name|;\,|more_name|(c_1);\,\ldots\,;\,|more_name|(c_n); +\,|end_name|.$$ +These three procedures communicate with each other via global variables. +Afterwards the file name will appear in the string pool as three strings +called |cur_name|\penalty10000\hskip-.05em, +|cur_area|, and |cur_ext|; the latter two are null (i.e., +|""|), unless they were explicitly specified by the user. + +Actually the situation is slightly more complicated, because \MP\ needs +to know when the file name ends. The |more_name| routine is a function +(with side effects) that returns |true| on the calls |more_name|$(c_1)$, +\dots, |more_name|$(c_{n-1})$. The final call |more_name|$(c_n)$ +returns |false|; or, it returns |true| and $c_n$ is the last character +on the current input line. In other words, +|more_name| is supposed to return |true| unless it is sure that the +file name has been completely scanned; and |end_name| is supposed to be able +to finish the assembly of |cur_name|, |cur_area|, and |cur_ext| regardless of +whether $|more_name|(c_n)$ returned |true| or |false|. + +@<Glob...@>= +char * cur_name; /* name of file just scanned */ +char * cur_area; /* file area just scanned, or \.{""} */ +char * cur_ext; /* file extension just scanned, or \.{""} */ + +@ It is easier to maintain reference counts if we assign initial values. + +@<Set init...@>= +mp->cur_name=xstrdup(""); +mp->cur_area=xstrdup(""); +mp->cur_ext=xstrdup(""); + +@ @<Dealloc variables@>= +xfree(mp->cur_area); +xfree(mp->cur_name); +xfree(mp->cur_ext); + +@ The file names we shall deal with for illustrative purposes have the +following structure: If the name contains `\.>' or `\.:', the file area +consists of all characters up to and including the final such character; +otherwise the file area is null. If the remaining file name contains +`\..', the file extension consists of all such characters from the first +remaining `\..' to the end, otherwise the file extension is null. +@^system dependencies@> + +We can scan such file names easily by using two global variables that keep track +of the occurrences of area and extension delimiters. Note that these variables +cannot be of type |pool_pointer| because a string pool compaction could occur +while scanning a file name. + +@<Glob...@>= +integer area_delimiter; + /* most recent `\.>' or `\.:' relative to |str_start[str_ptr]| */ +integer ext_delimiter; /* the relevant `\..', if any */ +boolean quoted_filename; /* whether the filename is wrapped in " markers */ + +@ Here now is the first of the system-dependent routines for file name scanning. +@^system dependencies@> + +The file name length is limited to |file_name_size|. That is good, because +in the current configuration we cannot call |mp_do_compaction| while a name +is being scanned, |mp->area_delimiter| and |mp->ext_delimiter| are direct +offsets into |mp->str_pool|. I am not in a great hurry to fix this, because +calling |str_room()| just once is more efficient anyway. TODO. + +@<Declarations@>= +static void mp_begin_name (MP mp); +static boolean mp_more_name (MP mp, ASCII_code c); +static void mp_end_name (MP mp); + +@ @c +void mp_begin_name (MP mp) { + xfree(mp->cur_name); + xfree(mp->cur_area); + xfree(mp->cur_ext); + mp->area_delimiter=-1; + mp->ext_delimiter=-1; + mp->quoted_filename=false; + str_room(file_name_size); +} + +@ And here's the second. +@^system dependencies@> + +@d IS_DIR_SEP(c) (c=='/' || c=='\\') + +@c +boolean mp_more_name (MP mp, ASCII_code c) { + if (c=='"') { + mp->quoted_filename= ! mp->quoted_filename; + } else if ((c==' '|| c=='\t') && (mp->quoted_filename==false)) { + return false; + } else { + if (IS_DIR_SEP (c)) { + mp->area_delimiter=mp->pool_ptr; + mp->ext_delimiter=-1; + } else if ( c=='.' ) { + mp->ext_delimiter=mp->pool_ptr; + } + append_char(c); /* contribute |c| to the current string */ + } + return true; +} + +@ The third. +@^system dependencies@> + +@d copy_pool_segment(A,B,C) { + A = xmalloc(C+1,sizeof(char)); + strncpy(A,(char *)(mp->str_pool+B),C); + A[C] = 0;} + +@c +void mp_end_name (MP mp) { + pool_pointer s; /* length of area, name, and extension */ + unsigned int len; + /* "my/w.mp" */ + s = mp->str_start[mp->str_ptr]; + if ( mp->area_delimiter<0 ) { + mp->cur_area=xstrdup(""); + } else { + len = (unsigned)(mp->area_delimiter-s+1); + copy_pool_segment(mp->cur_area,s,len); + s += len; + } + if ( mp->ext_delimiter<0 ) { + mp->cur_ext=xstrdup(""); + len = (unsigned)(mp->pool_ptr-s); + } else { + copy_pool_segment(mp->cur_ext,mp->ext_delimiter,(size_t)(mp->pool_ptr-mp->ext_delimiter)); + len = (unsigned)(mp->ext_delimiter-s); + } + copy_pool_segment(mp->cur_name,s,len); + mp->pool_ptr=s; /* don't need this partial string */ +} + +@ Conversely, here is a routine that takes three strings and prints a file +name that might have produced them. (The routine is system dependent, because +some operating systems put the file area last instead of first.) +@^system dependencies@> + +@<Basic printing...@>= +static void mp_print_file_name (MP mp, char * n, char * a, char * e) { + boolean must_quote = false; + if (((a != NULL) && (strchr(a,' ') != NULL)) || + ((n != NULL) && (strchr(n,' ') != NULL)) || + ((e != NULL) && (strchr(e,' ') != NULL))) + must_quote = true; + if (must_quote) mp_print_char(mp, (ASCII_code)'"'); + mp_print(mp, a); mp_print(mp, n); mp_print(mp, e); + if (must_quote) mp_print_char(mp, (ASCII_code)'"'); +} + +@ Another system-dependent routine is needed to convert three internal +\MP\ strings +to the |name_of_file| value that is used to open files. The present code +allows both lowercase and uppercase letters in the file name. +@^system dependencies@> + +@d append_to_name(A) { c=xord((ASCII_code)(A)); + if ( k<file_name_size ) { + mp->name_of_file[k]=(char)xchr(c); + incr(k); + } +} + +@ @c +void mp_pack_file_name (MP mp, const char *n, const char *a, const char *e) { + integer k; /* number of positions filled in |name_of_file| */ + ASCII_code c; /* character being packed */ + const char *j; /* a character index */ + k=0; + assert(n!=NULL); + if (a!=NULL) { + for (j=a;*j!='\0';j++) { append_to_name(*j); } + } + for (j=n;*j!='\0';j++) { append_to_name(*j); } + if (e!=NULL) { + for (j=e;*j!='\0';j++) { append_to_name(*j); } + } + mp->name_of_file[k]=0; + mp->name_length=k; +} + +@ @<Internal library declarations@>= +void mp_pack_file_name (MP mp, const char *n, const char *a, const char *e) ; + +@ @<Option variables@>= +char *mem_name; /* for commandline */ + +@ @<Find constant sizes@>= +mp->mem_name = xstrdup(opt->mem_name); +if (mp->mem_name) { + size_t l = strlen(mp->mem_name); + if (l>4) { + char *test = strstr(mp->mem_name,".mem"); + if (test == mp->mem_name+l-4) { + *test = 0; + } + } +} + + +@ @<Dealloc variables@>= +xfree(mp->mem_name); + +@ This part of the program becomes active when a ``virgin'' \MP\ is +trying to get going, just after the preliminary initialization, or +when the user is substituting another mem file by typing `\.\&' after +the initial `\.{**}' prompt. The buffer contains the first line of +input in |buffer[loc..(last-1)]|, where |loc<last| and |buffer[loc]<>""|. + +@<Declarations@>= +static boolean mp_open_mem_name (MP mp) ; +static boolean mp_open_mem_file (MP mp) ; + +@ @c +boolean mp_open_mem_name (MP mp) { + if (mp->mem_name!=NULL) { + size_t l = strlen(mp->mem_name); + char *s = xstrdup (mp->mem_name); + if (l>4) { + char *test = strstr(s,".mem"); + if (test == NULL || test != s+l-4) { + s = xrealloc (s, l+5, 1); + strcat (s, ".mem"); + } + } else { + s = xrealloc (s, l+5, 1); + strcat (s, ".mem"); + } + mp->mem_file = (mp->open_file)(mp,s, "r", mp_filetype_memfile); + xfree(s); + if ( mp->mem_file ) return true; + } + return false; +} +boolean mp_open_mem_file (MP mp) { + if (mp->mem_file != NULL) + return true; + if (mp_open_mem_name(mp)) + return true; + if (mp_xstrcmp(mp->mem_name, "plain")) { + wake_up_terminal; + wterm_ln("Sorry, I can\'t find that mem file; will try PLAIN."); +@.Sorry, I can't find...@> + update_terminal; + /* now pull out all the stops: try for the system \.{plain} file */ + xfree(mp->mem_name); + mp->mem_name = xstrdup("plain"); + if (mp_open_mem_name(mp)) + return true; + } + wake_up_terminal; + wterm_ln("I can\'t find the PLAIN mem file!\n"); +@.I can't find PLAIN...@> +@.plain@> + return false; +} + +@ Operating systems often make it possible to determine the exact name (and +possible version number) of a file that has been opened. The following routine, +which simply makes a \MP\ string from the value of |name_of_file|, should +ideally be changed to deduce the full name of file~|f|, which is the file +most recently opened, if it is possible to do this. +@^system dependencies@> + +@<Declarations@>= +#define mp_a_make_name_string(A,B) mp_make_name_string(A) +#define mp_b_make_name_string(A,B) mp_make_name_string(A) +#define mp_w_make_name_string(A,B) mp_make_name_string(A) + +@ @c +static str_number mp_make_name_string (MP mp) { + int k; /* index into |name_of_file| */ + str_room(mp->name_length); + for (k=0;k<mp->name_length;k++) { + append_char(xord((ASCII_code)mp->name_of_file[k])); + } + return mp_make_string(mp); +} + +@ Now let's consider the ``driver'' +routines by which \MP\ deals with file names +in a system-independent manner. First comes a procedure that looks for a +file name in the input by taking the information from the input buffer. +(We can't use |get_next|, because the conversion to tokens would +destroy necessary information.) + +This procedure doesn't allow semicolons or percent signs to be part of +file names, because of other conventions of \MP. +{\sl The {\logos METAFONT\/}book} doesn't +use semicolons or percents immediately after file names, but some users +no doubt will find it natural to do so; therefore system-dependent +changes to allow such characters in file names should probably +be made with reluctance, and only when an entire file name that +includes special characters is ``quoted'' somehow. +@^system dependencies@> + +@c +static void mp_scan_file_name (MP mp) { + mp_begin_name(mp); + while ( mp->buffer[loc]==' ' ) incr(loc); + while (1) { + if ( (mp->buffer[loc]==';')||(mp->buffer[loc]=='%') ) break; + if ( ! mp_more_name(mp, mp->buffer[loc]) ) break; + incr(loc); + } + mp_end_name(mp); +} + +@ Here is another version that takes its input from a string. + +@<Declare subroutines for parsing file names@>= +void mp_str_scan_file (MP mp, str_number s) ; + +@ @c +void mp_str_scan_file (MP mp, str_number s) { + pool_pointer p,q; /* current position and stopping point */ + mp_begin_name(mp); + p=mp->str_start[s]; q=str_stop(s); + while ( p<q ){ + if ( ! mp_more_name(mp, mp->str_pool[p]) ) break; + incr(p); + } + mp_end_name(mp); +} + +@ And one that reads from a |char*|. + +@<Declare subroutines for parsing file names@>= +extern void mp_ptr_scan_file (MP mp, char *s); + +@ @c +void mp_ptr_scan_file (MP mp, char *s) { + char *p, *q; /* current position and stopping point */ + mp_begin_name(mp); + p=s; q=p+strlen(s); + while ( p<q ){ + if ( ! mp_more_name(mp, xord((ASCII_code)(*p)))) break; + p++; + } + mp_end_name(mp); +} + + +@ The global variable |job_name| contains the file name that was first +\&{input} by the user. This name is extended by `\.{.log}' and `\.{ps}' and +`\.{.mem}' and `\.{.tfm}' in order to make the names of \MP's output files. + +@<Glob...@>= +boolean log_opened; /* has the transcript file been opened? */ +char *log_name; /* full name of the log file */ + +@ @<Option variables@>= +char *job_name; /* principal file name */ + +@ Initially |job_name=NULL|; it becomes nonzero as soon as the true name is known. +We have |job_name=NULL| if and only if the `\.{log}' file has not been opened, +except of course for a short time just after |job_name| has become nonzero. + +@<Allocate or ...@>= +mp->job_name=mp_xstrdup(mp, opt->job_name); +if (opt->noninteractive && opt->ini_version) { + if (mp->job_name == NULL) + mp->job_name=mp_xstrdup(mp,mp->mem_name); + if (mp->job_name != NULL) { + size_t l = strlen(mp->job_name); + if (l>4) { + char *test = strstr(mp->job_name,".mem"); + if (test == mp->job_name+l-4) + *test = 0; + } + } +} +mp->log_opened=false; + +@ @<Dealloc variables@>= +xfree(mp->job_name); + +@ Here is a routine that manufactures the output file names, assuming that +|job_name<>0|. It ignores and changes the current settings of |cur_area| +and |cur_ext|. + +@d pack_cur_name mp_pack_file_name(mp, mp->cur_name,mp->cur_area,mp->cur_ext) + +@<Internal library ...@>= +void mp_pack_job_name (MP mp, const char *s) ; + +@ @c +void mp_pack_job_name (MP mp, const char *s) { /* |s = ".log"|, |".mem"|, |".ps"|, or .\\{nnn} */ + xfree(mp->cur_name); mp->cur_name=xstrdup(mp->job_name); + xfree(mp->cur_area); mp->cur_area=xstrdup(""); + xfree(mp->cur_ext); mp->cur_ext=xstrdup(s); + pack_cur_name; +} + +@ If some trouble arises when \MP\ tries to open a file, the following +routine calls upon the user to supply another file name. Parameter~|s| +is used in the error message to identify the type of file; parameter~|e| +is the default extension if none is given. Upon exit from the routine, +variables |cur_name|, |cur_area|, |cur_ext|, and |name_of_file| are +ready for another attempt at file opening. + +@<Internal library ...@>= +void mp_prompt_file_name (MP mp, const char * s, const char * e) ; + +@ @c void mp_prompt_file_name (MP mp, const char * s, const char * e) { + size_t k; /* index into |buffer| */ + char * saved_cur_name; + if ( mp->interaction==mp_scroll_mode ) + wake_up_terminal; + if (strcmp(s,"input file name")==0) { + print_err("I can\'t find file `"); +@.I can't find file x@> + } else { + print_err("I can\'t write on file `"); +@.I can't write on file x@> + } + mp_print_file_name(mp, mp->cur_name,mp->cur_area,mp->cur_ext); + mp_print(mp, "'."); + if (strcmp(e,"")==0) + mp_show_context(mp); + mp_print_nl(mp, "Please type another "); mp_print(mp, s); +@.Please type...@> + if (mp->noninteractive || mp->interaction<mp_scroll_mode ) + mp_fatal_error(mp, "*** (job aborted, file error in nonstop mode)"); +@.job aborted, file error...@> + saved_cur_name = xstrdup(mp->cur_name); + clear_terminal; prompt_input(": "); @<Scan file name in the buffer@>; + if (strcmp(mp->cur_ext,"")==0) + mp->cur_ext=xstrdup(e); + if (strlen(mp->cur_name)==0) { + mp->cur_name=saved_cur_name; + } else { + xfree(saved_cur_name); + } + pack_cur_name; +} + +@ @<Scan file name in the buffer@>= +{ + mp_begin_name(mp); k=mp->first; + while ( (mp->buffer[k]==' ')&&(k<mp->last) ) incr(k); + while (1) { + if ( k==mp->last ) break; + if ( ! mp_more_name(mp, mp->buffer[k]) ) break; + incr(k); + } + mp_end_name(mp); +} + +@ The |open_log_file| routine is used to open the transcript file and to help +it catch up to what has previously been printed on the terminal. + +@c void mp_open_log_file (MP mp) { + unsigned old_setting; /* previous |selector| setting */ + int k; /* index into |months| and |buffer| */ + int l; /* end of first input line */ + integer m; /* the current month */ + const char *months="JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC"; + /* abbreviations of month names */ + old_setting=mp->selector; + if ( mp->job_name==NULL ) { + mp->job_name=xstrdup("mpout"); + } + mp_pack_job_name(mp,".log"); + while ( ! mp_a_open_out(mp, &mp->log_file, mp_filetype_log) ) { + @<Try to get a different log file name@>; + } + mp->log_name=xstrdup(mp->name_of_file); + mp->selector=log_only; mp->log_opened=true; + @<Print the banner line, including the date and time@>; + mp->input_stack[mp->input_ptr]=mp->cur_input; + /* make sure bottom level is in memory */ + if (!mp->noninteractive) { + mp_print_nl(mp, "**"); +@.**@> + l=mp->input_stack[0].limit_field-1; /* last position of first line */ + for (k=0;k<=l;k++) mp_print_str(mp, mp->buffer[k]); + mp_print_ln(mp); /* now the transcript file contains the first line of input */ + } + mp->selector=old_setting+2; /* |log_only| or |term_and_log| */ +} + +@ @<Dealloc variables@>= +xfree(mp->log_name); + +@ Sometimes |open_log_file| is called at awkward moments when \MP\ is +unable to print error messages or even to |show_context|. +The |prompt_file_name| routine can result in a |fatal_error|, but the |error| +routine will not be invoked because |log_opened| will be false. + +The normal idea of |mp_batch_mode| is that nothing at all should be written +on the terminal. However, in the unusual case that +no log file could be opened, we make an exception and allow +an explanatory message to be seen. + +Incidentally, the program always refers to the log file as a `\.{transcript +file}', because some systems cannot use the extension `\.{.log}' for +this file. + +@<Try to get a different log file name@>= +{ + mp->selector=term_only; + mp_prompt_file_name(mp, "transcript file name",".log"); +} + +@ @<Print the banner...@>= +{ + wlog(mp->banner); + mp_print(mp, mp->mem_ident); mp_print(mp, " "); + mp_print_int(mp, mp_round_unscaled(mp, mp->internal[mp_day])); + mp_print_char(mp, xord(' ')); + m=mp_round_unscaled(mp, mp->internal[mp_month]); + for (k=3*m-3;k<3*m;k++) { wlog_chr((unsigned char)months[k]); } + mp_print_char(mp, xord(' ')); + mp_print_int(mp, mp_round_unscaled(mp, mp->internal[mp_year])); + mp_print_char(mp, xord(' ')); + m=mp_round_unscaled(mp, mp->internal[mp_time]); + mp_print_dd(mp, m / 60); mp_print_char(mp, xord(':')); mp_print_dd(mp, m % 60); +} + +@ The |try_extension| function tries to open an input file determined by +|cur_name|, |cur_area|, and the argument |ext|. It returns |false| if it +can't find the file in |cur_area| or the appropriate system area. + +@c +static boolean mp_try_extension (MP mp, const char *ext) { + mp_pack_file_name(mp, mp->cur_name,mp->cur_area, ext); + in_name=xstrdup(mp->cur_name); + in_area=xstrdup(mp->cur_area); + if ( mp_a_open_in(mp, &cur_file, mp_filetype_program) ) { + return true; + } else { + mp_pack_file_name(mp, mp->cur_name,NULL,ext); + return mp_a_open_in(mp, &cur_file, mp_filetype_program); + } +} + +@ Let's turn now to the procedure that is used to initiate file reading +when an `\.{input}' command is being processed. + +@c void mp_start_input (MP mp) { /* \MP\ will \.{input} something */ + char *fname = NULL; + @<Put the desired file name in |(cur_name,cur_ext,cur_area)|@>; + while (1) { + mp_begin_file_reading(mp); /* set up |cur_file| and new level of input */ + if ( strlen(mp->cur_ext)==0 ) { + if ( mp_try_extension(mp, ".mp") ) break; + else if ( mp_try_extension(mp, "") ) break; + else if ( mp_try_extension(mp, ".mf") ) break; + /* |else do_nothing; | */ + } else if ( mp_try_extension(mp, mp->cur_ext) ) { + break; + } + mp_end_file_reading(mp); /* remove the level that didn't work */ + mp_prompt_file_name(mp, "input file name",""); + } + name=mp_a_make_name_string(mp, cur_file); + fname = xstrdup(mp->name_of_file); + if ( mp->job_name==NULL ) { + mp->job_name=xstrdup(mp->cur_name); + mp_open_log_file(mp); + } /* |open_log_file| doesn't |show_context|, so |limit| + and |loc| needn't be set to meaningful values yet */ + if ( ((int)mp->term_offset+(int)strlen(fname)) > (mp->max_print_line-2)) mp_print_ln(mp); + else if ( (mp->term_offset>0)||(mp->file_offset>0) ) mp_print_char(mp, xord(' ')); + mp_print_char(mp, xord('(')); incr(mp->open_parens); mp_print(mp, fname); + xfree(fname); + update_terminal; + @<Flush |name| and replace it with |cur_name| if it won't be needed@>; + @<Read the first line of the new file@>; +} + +@ This code should be omitted if |a_make_name_string| returns something other +than just a copy of its argument and the full file name is needed for opening +\.{MPX} files or implementing the switch-to-editor option. +@^system dependencies@> + +@<Flush |name| and replace it with |cur_name| if it won't be needed@>= +mp_flush_string(mp, name); name=rts(mp->cur_name); xfree(mp->cur_name) + +@ If the file is empty, it is considered to contain a single blank line, +so there is no need to test the return value. + +@<Read the first line...@>= +{ + line=1; + (void)mp_input_ln(mp, cur_file ); + mp_firm_up_the_line(mp); + mp->buffer[limit]=xord('%'); mp->first=(size_t)(limit+1); loc=start; +} + +@ @<Put the desired file name in |(cur_name,cur_ext,cur_area)|@>= +while ( token_state &&(loc==null) ) mp_end_token_list(mp); +if ( token_state ) { + print_err("File names can't appear within macros"); +@.File names can't...@> + help3("Sorry...I've converted what follows to tokens,", + "possibly garbaging the name you gave.", + "Please delete the tokens and insert the name again."); + mp_error(mp); +} +if ( file_state ) { + mp_scan_file_name(mp); +} else { + xfree(mp->cur_name); mp->cur_name=xstrdup(""); + xfree(mp->cur_ext); mp->cur_ext =xstrdup(""); + xfree(mp->cur_area); mp->cur_area=xstrdup(""); +} + +@ The following simple routine starts reading the \.{MPX} file associated +with the current input file. + +@c void mp_start_mpx_input (MP mp) { + char *origname = NULL; /* a copy of nameoffile */ + mp_pack_file_name(mp, in_name, in_area, ".mpx"); + @<Try to make sure |name_of_file| refers to a valid \.{MPX} file and + |goto not_found| if there is a problem@>; + mp_begin_file_reading(mp); + if ( ! mp_a_open_in(mp, &cur_file, mp_filetype_program) ) { + mp_end_file_reading(mp); + goto NOT_FOUND; + } + name=mp_a_make_name_string(mp, cur_file); + mp->mpx_name[iindex]=name; add_str_ref(name); + @<Read the first line of the new file@>; + xfree(origname); + return; +NOT_FOUND: + @<Explain that the \.{MPX} file can't be read and |succumb|@>; + xfree(origname); +} + +@ This should ideally be changed to do whatever is necessary to create the +\.{MPX} file given by |name_of_file| if it does not exist or if it is out +of date. This requires invoking \.{MPtoTeX} on the |origname| and passing +the results through \TeX\ and \.{DVItoMP}. (It is possible to use a +completely different typesetting program if suitable postprocessor is +available to perform the function of \.{DVItoMP}.) +@^system dependencies@> + +@ @<Exported types@>= +typedef int (*mp_makempx_cmd)(MP mp, char *origname, char *mtxname); + +@ @<Option variables@>= +mp_makempx_cmd run_make_mpx; + +@ @<Allocate or initialize ...@>= +set_callback_option(run_make_mpx); + +@ @<Declarations@>= +static int mp_run_make_mpx (MP mp, char *origname, char *mtxname); + +@ The default does nothing. +@c +int mp_run_make_mpx (MP mp, char *origname, char *mtxname) { + (void)mp; + (void)origname; + (void)mtxname; + return false; +} + +@ @<Try to make sure |name_of_file| refers to a valid \.{MPX} file and + |goto not_found| if there is a problem@>= +origname = mp_xstrdup(mp,mp->name_of_file); +*(origname+strlen(origname)-1)=0; /* drop the x */ +if (!(mp->run_make_mpx)(mp, origname, mp->name_of_file)) + goto NOT_FOUND + +@ @<Explain that the \.{MPX} file can't be read and |succumb|@>= +if ( mp->interaction==mp_error_stop_mode ) wake_up_terminal; +mp_print_nl(mp, ">> "); +mp_print(mp, origname); +mp_print_nl(mp, ">> "); +mp_print(mp, mp->name_of_file); +mp_print_nl(mp, "! Unable to make mpx file"); +help4("The two files given above are one of your source files", + "and an auxiliary file I need to read to find out what your", + "btex..etex blocks mean. If you don't know why I had trouble,", + "try running it manually through MPtoTeX, TeX, and DVItoMP"); +succumb; + +@ The last file-opening commands are for files accessed via the \&{readfrom} +@:read_from_}{\&{readfrom} primitive@> +operator and the \&{write} command. Such files are stored in separate arrays. +@:write_}{\&{write} primitive@> + +@<Types in the outer block@>= +typedef unsigned int readf_index; /* |0..max_read_files| */ +typedef unsigned int write_index; /* |0..max_write_files| */ + +@ @<Glob...@>= +readf_index max_read_files; /* maximum number of simultaneously open \&{readfrom} files */ +void ** rd_file; /* \&{readfrom} files */ +char ** rd_fname; /* corresponding file name or 0 if file not open */ +readf_index read_files; /* number of valid entries in the above arrays */ +write_index max_write_files; /* maximum number of simultaneously open \&{write} */ +void ** wr_file; /* \&{write} files */ +char ** wr_fname; /* corresponding file name or 0 if file not open */ +write_index write_files; /* number of valid entries in the above arrays */ + +@ @<Allocate or initialize ...@>= +mp->max_read_files=8; +mp->rd_file = xmalloc((mp->max_read_files+1),sizeof(void *)); +mp->rd_fname = xmalloc((mp->max_read_files+1),sizeof(char *)); +memset(mp->rd_fname, 0, sizeof(char *)*(mp->max_read_files+1)); +mp->max_write_files=8; +mp->wr_file = xmalloc((mp->max_write_files+1),sizeof(void *)); +mp->wr_fname = xmalloc((mp->max_write_files+1),sizeof(char *)); +memset(mp->wr_fname, 0, sizeof(char *)*(mp->max_write_files+1)); + + +@ This routine starts reading the file named by string~|s| without setting +|loc|, |limit|, or |name|. It returns |false| if the file is empty or cannot +be opened. Otherwise it updates |rd_file[n]| and |rd_fname[n]|. + +@c +static boolean mp_start_read_input (MP mp,char *s, readf_index n) { + mp_ptr_scan_file(mp, s); + pack_cur_name; + mp_begin_file_reading(mp); + if ( ! mp_a_open_in(mp, &mp->rd_file[n], (int)(mp_filetype_text+n)) ) + goto NOT_FOUND; + if ( ! mp_input_ln(mp, mp->rd_file[n] ) ) { + (mp->close_file)(mp,mp->rd_file[n]); + goto NOT_FOUND; + } + mp->rd_fname[n]=xstrdup(s); + return true; +NOT_FOUND: + mp_end_file_reading(mp); + return false; +} + +@ Open |wr_file[n]| using file name~|s| and update |wr_fname[n]|. + +@<Declarations@>= +static void mp_open_write_file (MP mp, char *s, readf_index n) ; + +@ @c void mp_open_write_file (MP mp,char *s, readf_index n) { + mp_ptr_scan_file(mp, s); + pack_cur_name; + while ( ! mp_a_open_out(mp, &mp->wr_file[n], (int)(mp_filetype_text+n)) ) + mp_prompt_file_name(mp, "file name for write output",""); + mp->wr_fname[n]=xstrdup(s); +} + + +@* \[36] Introduction to the parsing routines. +We come now to the central nervous system that sparks many of \MP's activities. +By evaluating expressions, from their primary constituents to ever larger +subexpressions, \MP\ builds the structures that ultimately define complete +pictures or fonts of type. + +Four mutually recursive subroutines are involved in this process: We call them +$$\hbox{|scan_primary|, |scan_secondary|, |scan_tertiary|, +and |scan_expression|.}$$ +@^recursion@> +Each of them is parameterless and begins with the first token to be scanned +already represented in |cur_cmd|, |cur_mod|, and |cur_sym|. After execution, +the value of the primary or secondary or tertiary or expression that was +found will appear in the global variables |cur_type| and |cur_exp|. The +token following the expression will be represented in |cur_cmd|, |cur_mod|, +and |cur_sym|. + +Technically speaking, the parsing algorithms are ``LL(1),'' more or less; +backup mechanisms have been added in order to provide reasonable error +recovery. + +@<Glob...@>= +quarterword cur_type; /* the type of the expression just found */ +integer cur_exp; /* the value of the expression just found */ + +@ @<Set init...@>= +mp->cur_exp=0; + +@ Many different kinds of expressions are possible, so it is wise to have +precise descriptions of what |cur_type| and |cur_exp| mean in all cases: + +\smallskip\hang +|cur_type=mp_vacuous| means that this expression didn't turn out to have a +value at all, because it arose from a \&{begingroup}$\,\ldots\,$\&{endgroup} +construction in which there was no expression before the \&{endgroup}. +In this case |cur_exp| has some irrelevant value. + +\smallskip\hang +|cur_type=mp_boolean_type| means that |cur_exp| is either |true_code| +or |false_code|. + +\smallskip\hang +|cur_type=mp_unknown_boolean| means that |cur_exp| points to a capsule +node that is in +a ring of equivalent booleans whose value has not yet been defined. + +\smallskip\hang +|cur_type=mp_string_type| means that |cur_exp| is a string number (i.e., an +integer in the range |0<=cur_exp<str_ptr|). That string's reference count +includes this particular reference. + +\smallskip\hang +|cur_type=mp_unknown_string| means that |cur_exp| points to a capsule +node that is in +a ring of equivalent strings whose value has not yet been defined. + +\smallskip\hang +|cur_type=mp_pen_type| means that |cur_exp| points to a node in a pen. Nobody +else points to any of the nodes in this pen. The pen may be polygonal or +elliptical. + +\smallskip\hang +|cur_type=mp_unknown_pen| means that |cur_exp| points to a capsule +node that is in +a ring of equivalent pens whose value has not yet been defined. + +\smallskip\hang +|cur_type=mp_path_type| means that |cur_exp| points to a the first node of +a path; nobody else points to this particular path. The control points of +the path will have been chosen. + +\smallskip\hang +|cur_type=mp_unknown_path| means that |cur_exp| points to a capsule +node that is in +a ring of equivalent paths whose value has not yet been defined. + +\smallskip\hang +|cur_type=mp_picture_type| means that |cur_exp| points to an edge header node. +There may be other pointers to this particular set of edges. The header node +contains a reference count that includes this particular reference. + +\smallskip\hang +|cur_type=mp_unknown_picture| means that |cur_exp| points to a capsule +node that is in +a ring of equivalent pictures whose value has not yet been defined. + +\smallskip\hang +|cur_type=mp_transform_type| means that |cur_exp| points to a |mp_transform_type| +capsule node. The |value| part of this capsule +points to a transform node that contains six numeric values, +each of which is |independent|, |dependent|, |mp_proto_dependent|, or |known|. + +\smallskip\hang +|cur_type=mp_color_type| means that |cur_exp| points to a |color_type| +capsule node. The |value| part of this capsule +points to a color node that contains three numeric values, +each of which is |independent|, |dependent|, |mp_proto_dependent|, or |known|. + +\smallskip\hang +|cur_type=mp_cmykcolor_type| means that |cur_exp| points to a |mp_cmykcolor_type| +capsule node. The |value| part of this capsule +points to a color node that contains four numeric values, +each of which is |independent|, |dependent|, |mp_proto_dependent|, or |known|. + +\smallskip\hang +|cur_type=mp_pair_type| means that |cur_exp| points to a capsule +node whose type is |mp_pair_type|. The |value| part of this capsule +points to a pair node that contains two numeric values, +each of which is |independent|, |dependent|, |mp_proto_dependent|, or |known|. + +\smallskip\hang +|cur_type=mp_known| means that |cur_exp| is a |scaled| value. + +\smallskip\hang +|cur_type=mp_dependent| means that |cur_exp| points to a capsule node whose type +is |dependent|. The |dep_list| field in this capsule points to the associated +dependency list. + +\smallskip\hang +|cur_type=mp_proto_dependent| means that |cur_exp| points to a |mp_proto_dependent| +capsule node. The |dep_list| field in this capsule +points to the associated dependency list. + +\smallskip\hang +|cur_type=independent| means that |cur_exp| points to a capsule node +whose type is |independent|. This somewhat unusual case can arise, for +example, in the expression +`$x+\&{begingroup}\penalty0\,\&{string}\,x; 0\,\&{endgroup}$'. + +\smallskip\hang +|cur_type=mp_token_list| means that |cur_exp| points to a linked list of +tokens. + +\smallskip\noindent +The possible settings of |cur_type| have been listed here in increasing +numerical order. Notice that |cur_type| will never be |mp_numeric_type| or +|suffixed_macro| or |mp_unsuffixed_macro|, although variables of those types +are allowed. Conversely, \MP\ has no variables of type |mp_vacuous| or +|token_list|. + +@ Capsules are two-word nodes that have a similar meaning +to |cur_type| and |cur_exp|. Such nodes have |name_type=capsule|, +and their |type| field is one of the possibilities for |cur_type| listed above. +Also |link<=void| in capsules that aren't part of a token list. + +The |value| field of a capsule is, in most cases, the value that +corresponds to its |type|, as |cur_exp| corresponds to |cur_type|. +However, when |cur_exp| would point to a capsule, +no extra layer of indirection is present; the |value| +field is what would have been called |value(cur_exp)| if it had not been +encapsulated. Furthermore, if the type is |dependent| or +|mp_proto_dependent|, the |value| field of a capsule is replaced by +|dep_list| and |prev_dep| fields, since dependency lists in capsules are +always part of the general |dep_list| structure. + +The |get_x_next| routine is careful not to change the values of |cur_type| +and |cur_exp| when it gets an expanded token. However, |get_x_next| might +call a macro, which might parse an expression, which might execute lots of +commands in a group; hence it's possible that |cur_type| might change +from, say, |mp_unknown_boolean| to |mp_boolean_type|, or from |dependent| to +|known| or |independent|, during the time |get_x_next| is called. The +programs below are careful to stash sensitive intermediate results in +capsules, so that \MP's generality doesn't cause trouble. + +Here's a procedure that illustrates these conventions. It takes +the contents of $(|cur_type|\kern-.3pt,|cur_exp|\kern-.3pt)$ +and stashes them away in a +capsule. It is not used when |cur_type=mp_token_list|. +After the operation, |cur_type=mp_vacuous|; hence there is no need to +copy path lists or to update reference counts, etc. + +The special link |mp_void| is put on the capsule returned by +|stash_cur_exp|, because this procedure is used to store macro parameters +that must be easily distinguishable from token lists. + +@<Declare the stashing/unstashing routines@>= +static pointer mp_stash_cur_exp (MP mp) { + pointer p; /* the capsule that will be returned */ + switch (mp->cur_type) { + case unknown_types: + case mp_transform_type: + case mp_color_type: + case mp_pair_type: + case mp_dependent: + case mp_proto_dependent: + case mp_independent: + case mp_cmykcolor_type: + p=mp->cur_exp; + break; + default: + p=mp_get_node(mp, value_node_size); mp_name_type(p)=mp_capsule; + mp_type(p)=mp->cur_type; value(p)=mp->cur_exp; + break; + } + mp->cur_type=mp_vacuous; mp_link(p)=mp_void; + return p; +} + +@ The inverse of |stash_cur_exp| is the following procedure, which +deletes an unnecessary capsule and puts its contents into |cur_type| +and |cur_exp|. + +The program steps of \MP\ can be divided into two categories: those in +which |cur_type| and |cur_exp| are ``alive'' and those in which they are +``dead,'' in the sense that |cur_type| and |cur_exp| contain relevant +information or not. It's important not to ignore them when they're alive, +and it's important not to pay attention to them when they're dead. + +There's also an intermediate category: If |cur_type=mp_vacuous|, then +|cur_exp| is irrelevant, hence we can proceed without caring if |cur_type| +and |cur_exp| are alive or dead. In such cases we say that |cur_type| +and |cur_exp| are {\sl dormant}. It is permissible to call |get_x_next| +only when they are alive or dormant. + +The \\{stash} procedure above assumes that |cur_type| and |cur_exp| +are alive or dormant. The \\{unstash} procedure assumes that they are +dead or dormant; it resuscitates them. + +@<Declare the stashing/unstashing...@>= +static void mp_unstash_cur_exp (MP mp,pointer p) ; + +@ @c +void mp_unstash_cur_exp (MP mp,pointer p) { + mp->cur_type=mp_type(p); + switch (mp->cur_type) { + case unknown_types: + case mp_transform_type: + case mp_color_type: + case mp_pair_type: + case mp_dependent: + case mp_proto_dependent: + case mp_independent: + case mp_cmykcolor_type: + mp->cur_exp=p; + break; + default: + mp->cur_exp=value(p); + mp_free_node(mp, p,value_node_size); + break; + } +} + +@ The following procedure prints the values of expressions in an +abbreviated format. If its first parameter |p| is null, the value of +|(cur_type,cur_exp)| is displayed; otherwise |p| should be a capsule +containing the desired value. The second parameter controls the amount of +output. If it is~0, dependency lists will be abbreviated to +`\.{linearform}' unless they consist of a single term. If it is greater +than~1, complicated structures (pens, pictures, and paths) will be displayed +in full. +@.linearform@> + +@<Declarations@>= +@<Declare the procedure called |print_dp|@> +@<Declare the stashing/unstashing routines@> +static void mp_print_exp (MP mp,pointer p, quarterword verbosity) ; + +@ @c +void mp_print_exp (MP mp,pointer p, quarterword verbosity) { + boolean restore_cur_exp; /* should |cur_exp| be restored? */ + quarterword t; /* the type of the expression */ + pointer q; /* a big node being displayed */ + integer v=0; /* the value of the expression */ + if ( p!=null ) { + restore_cur_exp=false; + } else { + p=mp_stash_cur_exp(mp); restore_cur_exp=true; + } + t=mp_type(p); + if ( t<mp_dependent ) v=value(p); else if ( t<mp_independent ) v=dep_list(p); + @<Print an abbreviated value of |v| with format depending on |t|@>; + if ( restore_cur_exp ) mp_unstash_cur_exp(mp, p); +} + +@ @<Print an abbreviated value of |v| with format depending on |t|@>= +switch (t) { +case mp_vacuous:mp_print(mp, "mp_vacuous"); break; +case mp_boolean_type: + if ( v==true_code ) mp_print(mp, "true"); else mp_print(mp, "false"); + break; +case unknown_types: case mp_numeric_type: + @<Display a variable that's been declared but not defined@>; + break; +case mp_string_type: + mp_print_char(mp, xord('"')); mp_print_str(mp, v); mp_print_char(mp, xord('"')); + break; +case mp_pen_type: case mp_path_type: case mp_picture_type: + @<Display a complex type@>; + break; +case mp_transform_type: case mp_color_type: case mp_pair_type: case mp_cmykcolor_type: + if ( v==null ) mp_print_type(mp, t); + else @<Display a big node@>; + break; +case mp_known:mp_print_scaled(mp, v); break; +case mp_dependent: case mp_proto_dependent: + mp_print_dp(mp, t,v,verbosity); + break; +case mp_independent:mp_print_variable_name(mp, p); break; +default: mp_confusion(mp, "exp"); break; +@:this can't happen exp}{\quad exp@> +} + +@ @<Display a big node@>= +{ + mp_print_char(mp, xord('(')); q=v+mp->big_node_size[t]; + do { + if ( mp_type(v)==mp_known ) mp_print_scaled(mp, value(v)); + else if ( mp_type(v)==mp_independent ) mp_print_variable_name(mp, v); + else mp_print_dp(mp, mp_type(v),dep_list(v),verbosity); + v=v+2; + if ( v!=q ) mp_print_char(mp, xord(',')); + } while (v!=q); + mp_print_char(mp, xord(')')); +} + +@ Values of type \&{picture}, \&{path}, and \&{pen} are displayed verbosely +in the log file only, unless the user has given a positive value to +\\{tracingonline}. + +@<Display a complex type@>= +if ( verbosity<=1 ) { + mp_print_type(mp, t); +} else { + if ( mp->selector==term_and_log ) + if ( mp->internal[mp_tracing_online]<=0 ) { + mp->selector=term_only; + mp_print_type(mp, t); mp_print(mp, " (see the transcript file)"); + mp->selector=term_and_log; + }; + switch (t) { + case mp_pen_type:mp_print_pen(mp, v,"",false); break; + case mp_path_type:mp_print_path(mp, v,"",false); break; + case mp_picture_type:mp_print_edges(mp, v,"",false); break; + } /* there are no other cases */ +} + +@ @<Declare the procedure called |print_dp|@>= +static void mp_print_dp (MP mp, quarterword t, pointer p, + quarterword verbosity) { + pointer q; /* the node following |p| */ + q=mp_link(p); + if ( (mp_info(q)==null) || (verbosity>0) ) mp_print_dependency(mp, p,t); + else mp_print(mp, "linearform"); +} + +@ The displayed name of a variable in a ring will not be a capsule unless +the ring consists entirely of capsules. + +@<Display a variable that's been declared but not defined@>= +{ mp_print_type(mp, t); +if ( v!=null ) + { mp_print_char(mp, xord(' ')); + while ( (mp_name_type(v)==mp_capsule) && (v!=p) ) v=value(v); + mp_print_variable_name(mp, v); + }; +} + +@ When errors are detected during parsing, it is often helpful to +display an expression just above the error message, using |exp_err| +or |disp_err| instead of |print_err|. + +@d exp_err(A) mp_disp_err(mp, null,(A)) /* displays the current expression */ + +@<Declarations@>= +static void mp_disp_err (MP mp,pointer p, const char *s) ; + +@ @c +void mp_disp_err (MP mp,pointer p, const char *s) { + if ( mp->interaction==mp_error_stop_mode ) wake_up_terminal; + mp_print_nl(mp, ">> "); +@.>>@> + mp_print_exp(mp, p,1); /* ``medium verbose'' printing of the expression */ + if (strlen(s)>0) { + print_err(s); + } +} + +@ If |cur_type| and |cur_exp| contain relevant information that should +be recycled, we will use the following procedure, which changes |cur_type| +to |known| and stores a given value in |cur_exp|. We can think of |cur_type| +and |cur_exp| as either alive or dormant after this has been done, +because |cur_exp| will not contain a pointer value. + +@ @c +static void mp_flush_cur_exp (MP mp,scaled v) { + switch (mp->cur_type) { + case unknown_types: case mp_transform_type: case mp_color_type: case mp_pair_type: + case mp_dependent: case mp_proto_dependent: case mp_independent: case mp_cmykcolor_type: + mp_recycle_value(mp, mp->cur_exp); + mp_free_node(mp, mp->cur_exp,value_node_size); + break; + case mp_string_type: + delete_str_ref(mp->cur_exp); break; + case mp_pen_type: case mp_path_type: + mp_toss_knot_list(mp, mp->cur_exp); break; + case mp_picture_type: + delete_edge_ref(mp->cur_exp); break; + default: + break; + } + mp->cur_type=mp_known; mp->cur_exp=v; +} + +@ There's a much more general procedure that is capable of releasing +the storage associated with any two-word value packet. + +@<Declarations@>= +static void mp_recycle_value (MP mp,pointer p) ; + +@ @c +static void mp_recycle_value (MP mp,pointer p) { + quarterword t; /* a type code */ + integer vv; /* another value */ + pointer q,r,s,pp; /* link manipulation registers */ + integer v=0; /* a value */ + t=mp_type(p); + if ( t<mp_dependent ) v=value(p); + switch (t) { + case undefined: case mp_vacuous: case mp_boolean_type: case mp_known: + case mp_numeric_type: + break; + case unknown_types: + mp_ring_delete(mp, p); break; + case mp_string_type: + delete_str_ref(v); break; + case mp_path_type: case mp_pen_type: + mp_toss_knot_list(mp, v); break; + case mp_picture_type: + delete_edge_ref(v); break; + case mp_cmykcolor_type: case mp_pair_type: case mp_color_type: + case mp_transform_type: + @<Recycle a big node@>; break; + case mp_dependent: case mp_proto_dependent: + @<Recycle a dependency list@>; break; + case mp_independent: + @<Recycle an independent variable@>; break; + case mp_token_list: case mp_structured: + mp_confusion(mp, "recycle"); break; +@:this can't happen recycle}{\quad recycle@> + case mp_unsuffixed_macro: case mp_suffixed_macro: + mp_delete_mac_ref(mp, value(p)); break; + } /* there are no other cases */ + mp_type(p)=undefined; +} + +@ @<Recycle a big node@>= +if ( v!=null ){ + q=v+mp->big_node_size[t]; + do { + q=q-2; mp_recycle_value(mp, q); + } while (q!=v); + mp_free_node(mp, v,mp->big_node_size[t]); +} + +@ @<Recycle a dependency list@>= +{ + q=dep_list(p); + while ( mp_info(q)!=null ) q=mp_link(q); + mp_link(prev_dep(p))=mp_link(q); + prev_dep(mp_link(q))=prev_dep(p); + mp_link(q)=null; mp_flush_node_list(mp, dep_list(p)); +} + +@ When an independent variable disappears, it simply fades away, unless +something depends on it. In the latter case, a dependent variable whose +coefficient of dependence is maximal will take its place. +The relevant algorithm is due to Ignacio~A. Zabala, who implemented it +as part of his Ph.D. thesis (Stanford University, December 1982). +@^Zabala Salelles, Ignacio Andr\'es@> + +For example, suppose that variable $x$ is being recycled, and that the +only variables depending on~$x$ are $y=2x+a$ and $z=x+b$. In this case +we want to make $y$ independent and $z=.5y-.5a+b$; no other variables +will depend on~$y$. If $\\{tracingequations}>0$ in this situation, +we will print `\.{\#\#\# -2x=-y+a}'. + +There's a slight complication, however: An independent variable $x$ +can occur both in dependency lists and in proto-dependency lists. +This makes it necessary to be careful when deciding which coefficient +is maximal. + +Furthermore, this complication is not so slight when +a proto-dependent variable is chosen to become independent. For example, +suppose that $y=2x+100a$ is proto-dependent while $z=x+b$ is dependent; +then we must change $z=.5y-50a+b$ to a proto-dependency, because of the +large coefficient `50'. + +In order to deal with these complications without wasting too much time, +we shall link together the occurrences of~$x$ among all the linear +dependencies, maintaining separate lists for the dependent and +proto-dependent cases. + +@<Recycle an independent variable@>= +{ + mp->max_c[mp_dependent]=0; mp->max_c[mp_proto_dependent]=0; + mp->max_link[mp_dependent]=null; mp->max_link[mp_proto_dependent]=null; + q=mp_link(dep_head); + while ( q!=dep_head ) { + s=value_loc(q); /* now |mp_link(s)=dep_list(q)| */ + while (1) { + r=mp_link(s); + if ( mp_info(r)==null ) break; + if ( mp_info(r)!=p ) { + s=r; + } else { + t=mp_type(q); mp_link(s)=mp_link(r); mp_info(r)=q; + if ( abs(value(r))>mp->max_c[t] ) { + @<Record a new maximum coefficient of type |t|@>; + } else { + mp_link(r)=mp->max_link[t]; mp->max_link[t]=r; + } + } + } + q=mp_link(r); + } + if ( (mp->max_c[mp_dependent]>0)||(mp->max_c[mp_proto_dependent]>0) ) { + @<Choose a dependent variable to take the place of the disappearing + independent variable, and change all remaining dependencies + accordingly@>; + } +} + +@ The code for independency removal makes use of three two-word arrays. + +@<Glob...@>= +integer max_c[mp_proto_dependent+1]; /* max coefficient magnitude */ +pointer max_ptr[mp_proto_dependent+1]; /* where |p| occurs with |max_c| */ +pointer max_link[mp_proto_dependent+1]; /* other occurrences of |p| */ + +@ @<Record a new maximum coefficient...@>= +{ + if ( mp->max_c[t]>0 ) { + mp_link(mp->max_ptr[t])=mp->max_link[t]; mp->max_link[t]=mp->max_ptr[t]; + } + mp->max_c[t]=abs(value(r)); mp->max_ptr[t]=r; +} + +@ @<Choose a dependent...@>= +{ + if ( (mp->max_c[mp_dependent] / 010000) >= mp->max_c[mp_proto_dependent] ) + t=mp_dependent; + else + t=mp_proto_dependent; + @<Determine the dependency list |s| to substitute for the independent + variable~|p|@>; + t=mp_dependent+mp_proto_dependent-t; /* complement |t| */ + if ( mp->max_c[t]>0 ) { /* we need to pick up an unchosen dependency */ + mp_link(mp->max_ptr[t])=mp->max_link[t]; mp->max_link[t]=mp->max_ptr[t]; + } + if ( t!=mp_dependent ) { @<Substitute new dependencies in place of |p|@>; } + else { @<Substitute new proto-dependencies in place of |p|@>;} + mp_flush_node_list(mp, s); + if ( mp->fix_needed ) mp_fix_dependencies(mp); + check_arith; +} + +@ Let |s=max_ptr[t]|. At this point we have $|value|(s)=\pm|max_c|[t]$, +and |mp_info(s)| points to the dependent variable~|pp| of type~|t| from +whose dependency list we have removed node~|s|. We must reinsert +node~|s| into the dependency list, with coefficient $-1.0$, and with +|pp| as the new independent variable. Since |pp| will have a larger serial +number than any other variable, we can put node |s| at the head of the +list. + +@<Determine the dep...@>= +s=mp->max_ptr[t]; pp=mp_info(s); v=value(s); +if ( t==mp_dependent ) value(s)=-fraction_one; else value(s)=-unity; +r=dep_list(pp); mp_link(s)=r; +while ( mp_info(r)!=null ) r=mp_link(r); +q=mp_link(r); mp_link(r)=null; +prev_dep(q)=prev_dep(pp); mp_link(prev_dep(pp))=q; +new_indep(pp); +if ( mp->cur_exp==pp ) if ( mp->cur_type==t ) mp->cur_type=mp_independent; +if ( mp->internal[mp_tracing_equations]>0 ) { + @<Show the transformed dependency@>; +} + +@ Now $(-v)$ times the formerly independent variable~|p| is being replaced +by the dependency list~|s|. + +@<Show the transformed...@>= +if ( mp_interesting(mp, p) ) { + mp_begin_diagnostic(mp); mp_print_nl(mp, "### "); +@:]]]\#\#\#_}{\.{\#\#\#}@> + if ( v>0 ) mp_print_char(mp, xord('-')); + if ( t==mp_dependent ) vv=mp_round_fraction(mp, mp->max_c[mp_dependent]); + else vv=mp->max_c[mp_proto_dependent]; + if ( vv!=unity ) mp_print_scaled(mp, vv); + mp_print_variable_name(mp, p); + while ( value(p) % s_scale>0 ) { + mp_print(mp, "*4"); value(p)=value(p)-2; + } + if ( t==mp_dependent ) mp_print_char(mp, xord('=')); else mp_print(mp, " = "); + mp_print_dependency(mp, s,t); + mp_end_diagnostic(mp, false); +} + +@ Finally, there are dependent and proto-dependent variables whose +dependency lists must be brought up to date. + +@<Substitute new dependencies...@>= +for (t=mp_dependent;t<=mp_proto_dependent;t++){ + r=mp->max_link[t]; + while ( r!=null ) { + q=mp_info(r); + dep_list(q)=mp_p_plus_fq(mp, dep_list(q), + mp_make_fraction(mp, value(r),-v),s,t,mp_dependent); + if ( dep_list(q)==mp->dep_final ) mp_make_known(mp, q,mp->dep_final); + q=r; r=mp_link(r); mp_free_node(mp, q,dep_node_size); + } +} + +@ @<Substitute new proto...@>= +for (t=mp_dependent;t<=mp_proto_dependent;t++) { + r=mp->max_link[t]; + while ( r!=null ) { + q=mp_info(r); + if ( t==mp_dependent ) { /* for safety's sake, we change |q| to |mp_proto_dependent| */ + if ( mp->cur_exp==q ) if ( mp->cur_type==mp_dependent ) + mp->cur_type=mp_proto_dependent; + dep_list(q)=mp_p_over_v(mp, dep_list(q),unity, + mp_dependent,mp_proto_dependent); + mp_type(q)=mp_proto_dependent; + value(r)=mp_round_fraction(mp, value(r)); + } + dep_list(q)=mp_p_plus_fq(mp, dep_list(q), + mp_make_scaled(mp, value(r),-v),s, + mp_proto_dependent,mp_proto_dependent); + if ( dep_list(q)==mp->dep_final ) + mp_make_known(mp, q,mp->dep_final); + q=r; r=mp_link(r); mp_free_node(mp, q,dep_node_size); + } +} + +@ Here are some routines that provide handy combinations of actions +that are often needed during error recovery. For example, +`|flush_error|' flushes the current expression, replaces it by +a given value, and calls |error|. + +Errors often are detected after an extra token has already been scanned. +The `\\{put\_get}' routines put that token back before calling |error|; +then they get it back again. (Or perhaps they get another token, if +the user has changed things.) + +@<Declarations@>= +static void mp_flush_error (MP mp,scaled v); +static void mp_put_get_error (MP mp); +static void mp_put_get_flush_error (MP mp,scaled v) ; + +@ @c +void mp_flush_error (MP mp,scaled v) { + mp_error(mp); mp_flush_cur_exp(mp, v); +} +void mp_put_get_error (MP mp) { + mp_back_error(mp); mp_get_x_next(mp); +} +void mp_put_get_flush_error (MP mp,scaled v) { + mp_put_get_error(mp); + mp_flush_cur_exp(mp, v); +} + +@ A global variable |var_flag| is set to a special command code +just before \MP\ calls |scan_expression|, if the expression should be +treated as a variable when this command code immediately follows. For +example, |var_flag| is set to |assignment| at the beginning of a +statement, because we want to know the {\sl location\/} of a variable at +the left of `\.{:=}', not the {\sl value\/} of that variable. + +The |scan_expression| subroutine calls |scan_tertiary|, +which calls |scan_secondary|, which calls |scan_primary|, which sets +|var_flag:=0|. In this way each of the scanning routines ``knows'' +when it has been called with a special |var_flag|, but |var_flag| is +usually zero. + +A variable preceding a command that equals |var_flag| is converted to a +token list rather than a value. Furthermore, an `\.{=}' sign following an +expression with |var_flag=assignment| is not considered to be a relation +that produces boolean expressions. + + +@<Glob...@>= +int var_flag; /* command that wants a variable */ + +@ @<Set init...@>= +mp->var_flag=0; + +@* \[37] Parsing primary expressions. +The first parsing routine, |scan_primary|, is also the most complicated one, +since it involves so many different cases. But each case---with one +exception---is fairly simple by itself. + +When |scan_primary| begins, the first token of the primary to be scanned +should already appear in |cur_cmd|, |cur_mod|, and |cur_sym|. The values +of |cur_type| and |cur_exp| should be either dead or dormant, as explained +earlier. If |cur_cmd| is not between |min_primary_command| and +|max_primary_command|, inclusive, a syntax error will be signaled. + +@<Declare the basic parsing subroutines@>= +void mp_scan_primary (MP mp) { + pointer p,q,r; /* for list manipulation */ + quarterword c; /* a primitive operation code */ + int my_var_flag; /* initial value of |my_var_flag| */ + pointer l_delim,r_delim; /* hash addresses of a delimiter pair */ + @<Other local variables for |scan_primary|@>; + my_var_flag=mp->var_flag; mp->var_flag=0; +RESTART: + check_arith; + @<Supply diagnostic information, if requested@>; + switch (mp->cur_cmd) { + case left_delimiter: + @<Scan a delimited primary@>; break; + case begin_group: + @<Scan a grouped primary@>; break; + case string_token: + @<Scan a string constant@>; break; + case numeric_token: + @<Scan a primary that starts with a numeric token@>; break; + case nullary: + @<Scan a nullary operation@>; break; + case unary: case type_name: case cycle: case plus_or_minus: + @<Scan a unary operation@>; break; + case primary_binary: + @<Scan a binary operation with `\&{of}' between its operands@>; break; + case str_op: + @<Convert a suffix to a string@>; break; + case internal_quantity: + @<Scan an internal numeric quantity@>; break; + case capsule_token: + mp_make_exp_copy(mp, mp->cur_mod); break; + case tag_token: + @<Scan a variable primary; |goto restart| if it turns out to be a macro@>; break; + default: + mp_bad_exp(mp, "A primary"); goto RESTART; break; +@.A primary expression...@> + } + mp_get_x_next(mp); /* the routines |goto done| if they don't want this */ +DONE: + if ( mp->cur_cmd==left_bracket ) { + if ( mp->cur_type>=mp_known ) { + @<Scan a mediation construction@>; + } + } +} + + + +@ Errors at the beginning of expressions are flagged by |bad_exp|. + +@c +static void mp_bad_exp (MP mp, const char * s) { + int save_flag; + print_err(s); mp_print(mp, " expression can't begin with `"); + mp_print_cmd_mod(mp, mp->cur_cmd,mp->cur_mod); + mp_print_char(mp, xord('\'')); + help4("I'm afraid I need some sort of value in order to continue,", + "so I've tentatively inserted `0'. You may want to", + "delete this zero and insert something else;", + "see Chapter 27 of The METAFONTbook for an example."); +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> + mp_back_input(mp); mp->cur_sym=0; mp->cur_cmd=numeric_token; + mp->cur_mod=0; mp_ins_error(mp); + save_flag=mp->var_flag; mp->var_flag=0; mp_get_x_next(mp); + mp->var_flag=save_flag; +} + +@ @<Supply diagnostic information, if requested@>= +#ifdef DEBUG +if ( mp->panicking ) mp_check_mem(mp, false); +#endif +if ( mp->interrupt!=0 ) if ( mp->OK_to_interrupt ) { + mp_back_input(mp); check_interrupt; mp_get_x_next(mp); +} + +@ @<Scan a delimited primary@>= +{ + l_delim=mp->cur_sym; r_delim=mp->cur_mod; + mp_get_x_next(mp); mp_scan_expression(mp); + if ( (mp->cur_cmd==comma) && (mp->cur_type>=mp_known) ) { + @<Scan the rest of a delimited set of numerics@>; + } else { + mp_check_delimiter(mp, l_delim,r_delim); + } +} + +@ The |stash_in| subroutine puts the current (numeric) expression into a field +within a ``big node.'' + +@c +static void mp_stash_in (MP mp,pointer p) { + pointer q; /* temporary register */ + mp_type(p)=mp->cur_type; + if ( mp->cur_type==mp_known ) { + value(p)=mp->cur_exp; + } else { + if ( mp->cur_type==mp_independent ) { + @<Stash an independent |cur_exp| into a big node@>; + } else { + mp->mem[value_loc(p)]=mp->mem[value_loc(mp->cur_exp)]; + /* |dep_list(p):=dep_list(cur_exp)| and |prev_dep(p):=prev_dep(cur_exp)| */ + mp_link(prev_dep(p))=p; + } + mp_free_node(mp, mp->cur_exp,value_node_size); + } + mp->cur_type=mp_vacuous; +} + +@ In rare cases the current expression can become |independent|. There +may be many dependency lists pointing to such an independent capsule, +so we can't simply move it into place within a big node. Instead, +we copy it, then recycle it. + +@ @<Stash an independent |cur_exp|...@>= +{ + q=mp_single_dependency(mp, mp->cur_exp); + if ( q==mp->dep_final ){ + mp_type(p)=mp_known; value(p)=0; mp_free_node(mp, q,dep_node_size); + } else { + mp_type(p)=mp_dependent; mp_new_dep(mp, p,q); + } + mp_recycle_value(mp, mp->cur_exp); +} + +@ This code uses the fact that |red_part_loc| and |green_part_loc| +are synonymous with |x_part_loc| and |y_part_loc|. + +@<Scan the rest of a delimited set of numerics@>= +{ +p=mp_stash_cur_exp(mp); +mp_get_x_next(mp); mp_scan_expression(mp); +@<Make sure the second part of a pair or color has a numeric type@>; +q=mp_get_node(mp, value_node_size); mp_name_type(q)=mp_capsule; +if ( mp->cur_cmd==comma ) mp_type(q)=mp_color_type; +else mp_type(q)=mp_pair_type; +mp_init_big_node(mp, q); r=value(q); +mp_stash_in(mp, y_part_loc(r)); +mp_unstash_cur_exp(mp, p); +mp_stash_in(mp, x_part_loc(r)); +if ( mp->cur_cmd==comma ) { + @<Scan the last of a triplet of numerics@>; +} +if ( mp->cur_cmd==comma ) { + mp_type(q)=mp_cmykcolor_type; + mp_init_big_node(mp, q); t=value(q); + mp->mem[cyan_part_loc(t)]=mp->mem[red_part_loc(r)]; + value(cyan_part_loc(t))=value(red_part_loc(r)); + mp->mem[magenta_part_loc(t)]=mp->mem[green_part_loc(r)]; + value(magenta_part_loc(t))=value(green_part_loc(r)); + mp->mem[yellow_part_loc(t)]=mp->mem[blue_part_loc(r)]; + value(yellow_part_loc(t))=value(blue_part_loc(r)); + mp_recycle_value(mp, r); + r=t; + @<Scan the last of a quartet of numerics@>; +} +mp_check_delimiter(mp, l_delim,r_delim); +mp->cur_type=mp_type(q); +mp->cur_exp=q; +} + +@ @<Make sure the second part of a pair or color has a numeric type@>= +if ( mp->cur_type<mp_known ) { + exp_err("Nonnumeric ypart has been replaced by 0"); +@.Nonnumeric...replaced by 0@> + help4("I've started to scan a pair `(a,b)' or a color `(a,b,c)';", + "but after finding a nice `a' I found a `b' that isn't", + "of numeric type. So I've changed that part to zero.", + "(The b that I didn't like appears above the error message.)"); + mp_put_get_flush_error(mp, 0); +} + +@ @<Scan the last of a triplet of numerics@>= +{ + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type<mp_known ) { + exp_err("Nonnumeric third part has been replaced by 0"); +@.Nonnumeric...replaced by 0@> + help3("I've just scanned a color `(a,b,c)' or cmykcolor(a,b,c,d); but the `c'", + "isn't of numeric type. So I've changed that part to zero.", + "(The c that I didn't like appears above the error message.)"); + mp_put_get_flush_error(mp, 0); + } + mp_stash_in(mp, blue_part_loc(r)); +} + +@ @<Scan the last of a quartet of numerics@>= +{ + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type<mp_known ) { + exp_err("Nonnumeric blackpart has been replaced by 0"); +@.Nonnumeric...replaced by 0@> + help3("I've just scanned a cmykcolor `(c,m,y,k)'; but the `k' isn't", + "of numeric type. So I've changed that part to zero.", + "(The k that I didn't like appears above the error message.)"); + mp_put_get_flush_error(mp, 0); + } + mp_stash_in(mp, black_part_loc(r)); +} + +@ The local variable |group_line| keeps track of the line +where a \&{begingroup} command occurred; this will be useful +in an error message if the group doesn't actually end. + +@<Other local variables for |scan_primary|@>= +integer group_line; /* where a group began */ + +@ @<Scan a grouped primary@>= +{ + group_line=mp_true_line(mp); + if ( mp->internal[mp_tracing_commands]>0 ) show_cur_cmd_mod; + save_boundary_item(p); + do { + mp_do_statement(mp); /* ends with |cur_cmd>=semicolon| */ + } while (mp->cur_cmd==semicolon); + if ( mp->cur_cmd!=end_group ) { + print_err("A group begun on line "); +@.A group...never ended@> + mp_print_int(mp, group_line); + mp_print(mp, " never ended"); + help2("I saw a `begingroup' back there that hasn't been matched", + "by `endgroup'. So I've inserted `endgroup' now."); + mp_back_error(mp); mp->cur_cmd=end_group; + } + mp_unsave(mp); + /* this might change |cur_type|, if independent variables are recycled */ + if ( mp->internal[mp_tracing_commands]>0 ) show_cur_cmd_mod; +} + +@ @<Scan a string constant@>= +{ + mp->cur_type=mp_string_type; mp->cur_exp=mp->cur_mod; +} + +@ Later we'll come to procedures that perform actual operations like +addition, square root, and so on; our purpose now is to do the parsing. +But we might as well mention those future procedures now, so that the +suspense won't be too bad: + +\smallskip +|do_nullary(c)| does primitive operations that have no operands (e.g., +`\&{true}' or `\&{pencircle}'); + +\smallskip +|do_unary(c)| applies a primitive operation to the current expression; + +\smallskip +|do_binary(p,c)| applies a primitive operation to the capsule~|p| +and the current expression. + +@<Scan a nullary operation@>=mp_do_nullary(mp, mp->cur_mod) + +@ @<Scan a unary operation@>= +{ + c=mp->cur_mod; mp_get_x_next(mp); mp_scan_primary(mp); + mp_do_unary(mp, c); goto DONE; +} + +@ A numeric token might be a primary by itself, or it might be the +numerator of a fraction composed solely of numeric tokens, or it might +multiply the primary that follows (provided that the primary doesn't begin +with a plus sign or a minus sign). The code here uses the facts that +|max_primary_command=plus_or_minus| and +|max_primary_command-1=numeric_token|. If a fraction is found that is less +than unity, we try to retain higher precision when we use it in scalar +multiplication. + +@<Other local variables for |scan_primary|@>= +scaled num,denom; /* for primaries that are fractions, like `1/2' */ + +@ @<Scan a primary that starts with a numeric token@>= +{ + mp->cur_exp=mp->cur_mod; mp->cur_type=mp_known; mp_get_x_next(mp); + if ( mp->cur_cmd!=slash ) { + num=0; denom=0; + } else { + mp_get_x_next(mp); + if ( mp->cur_cmd!=numeric_token ) { + mp_back_input(mp); + mp->cur_cmd=slash; mp->cur_mod=over; mp->cur_sym=frozen_slash; + goto DONE; + } + num=mp->cur_exp; denom=mp->cur_mod; + if ( denom==0 ) { @<Protest division by zero@>; } + else { mp->cur_exp=mp_make_scaled(mp, num,denom); } + check_arith; mp_get_x_next(mp); + } + if ( mp->cur_cmd>=min_primary_command ) { + if ( mp->cur_cmd<numeric_token ) { /* in particular, |cur_cmd<>plus_or_minus| */ + p=mp_stash_cur_exp(mp); mp_scan_primary(mp); + if ( (abs(num)>=abs(denom))||(mp->cur_type<mp_color_type) ) { + mp_do_binary(mp, p,times); + } else { + mp_frac_mult(mp, num,denom); + mp_free_node(mp, p,value_node_size); + } + } + } + goto DONE; +} + +@ @<Protest division...@>= +{ + print_err("Division by zero"); +@.Division by zero@> + help1("I'll pretend that you meant to divide by 1."); mp_error(mp); +} + +@ @<Scan a binary operation with `\&{of}' between its operands@>= +{ + c=mp->cur_mod; mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_cmd!=of_token ) { + mp_missing_err(mp, "of"); mp_print(mp, " for "); + mp_print_cmd_mod(mp, primary_binary,c); +@.Missing `of'@> + help1("I've got the first argument; will look now for the other."); + mp_back_error(mp); + } + p=mp_stash_cur_exp(mp); mp_get_x_next(mp); mp_scan_primary(mp); + mp_do_binary(mp, p,c); goto DONE; +} + +@ @<Convert a suffix to a string@>= +{ + mp_get_x_next(mp); mp_scan_suffix(mp); + mp->old_setting=mp->selector; mp->selector=new_string; + mp_show_token_list(mp, mp->cur_exp,null,100000,0); + mp_flush_token_list(mp, mp->cur_exp); + mp->cur_exp=mp_make_string(mp); mp->selector=mp->old_setting; + mp->cur_type=mp_string_type; + goto DONE; +} + +@ If an internal quantity appears all by itself on the left of an +assignment, we return a token list of length one, containing the address +of the internal quantity plus |hash_end|. (This accords with the conventions +of the save stack, as described earlier.) + +@<Scan an internal...@>= +{ + q=mp->cur_mod; + if ( my_var_flag==assignment ) { + mp_get_x_next(mp); + if ( mp->cur_cmd==assignment ) { + mp->cur_exp=mp_get_avail(mp); + mp_info(mp->cur_exp)=q+hash_end; mp->cur_type=mp_token_list; + goto DONE; + } + mp_back_input(mp); + } + mp->cur_type=mp_known; mp->cur_exp=mp->internal[q]; + if (q == mp_output_format || q == mp_output_template) + mp->cur_type=mp_string_type; +} + +@ The most difficult part of |scan_primary| has been saved for last, since +it was necessary to build up some confidence first. We can now face the task +of scanning a variable. + +As we scan a variable, we build a token list containing the relevant +names and subscript values, simultaneously following along in the +``collective'' structure to see if we are actually dealing with a macro +instead of a value. + +The local variables |pre_head| and |post_head| will point to the beginning +of the prefix and suffix lists; |tail| will point to the end of the list +that is currently growing. + +Another local variable, |tt|, contains partial information about the +declared type of the variable-so-far. If |tt>=mp_unsuffixed_macro|, the +relation |tt=mp_type(q)| will always hold. If |tt=undefined|, the routine +doesn't bother to update its information about type. And if +|undefined<tt<mp_unsuffixed_macro|, the precise value of |tt| isn't critical. + +@ @<Other local variables for |scan_primary|@>= +pointer pre_head,post_head,tail; + /* prefix and suffix list variables */ +quarterword tt; /* approximation to the type of the variable-so-far */ +pointer t; /* a token */ +pointer macro_ref = 0; /* reference count for a suffixed macro */ + +@ @<Scan a variable primary...@>= +{ + fast_get_avail(pre_head); tail=pre_head; post_head=null; tt=mp_vacuous; + while (1) { + t=mp_cur_tok(mp); mp_link(tail)=t; + if ( tt!=undefined ) { + @<Find the approximate type |tt| and corresponding~|q|@>; + if ( tt>=mp_unsuffixed_macro ) { + @<Either begin an unsuffixed macro call or + prepare for a suffixed one@>; + } + } + mp_get_x_next(mp); tail=t; + if ( mp->cur_cmd==left_bracket ) { + @<Scan for a subscript; replace |cur_cmd| by |numeric_token| if found@>; + } + if ( mp->cur_cmd>max_suffix_token ) break; + if ( mp->cur_cmd<min_suffix_token ) break; + } /* now |cur_cmd| is |internal_quantity|, |tag_token|, or |numeric_token| */ + @<Handle unusual cases that masquerade as variables, and |goto restart| + or |goto done| if appropriate; + otherwise make a copy of the variable and |goto done|@>; +} + +@ @<Either begin an unsuffixed macro call or...@>= +{ + mp_link(tail)=null; + if ( tt>mp_unsuffixed_macro ) { /* |tt=mp_suffixed_macro| */ + post_head=mp_get_avail(mp); tail=post_head; mp_link(tail)=t; + tt=undefined; macro_ref=value(q); add_mac_ref(macro_ref); + } else { + @<Set up unsuffixed macro call and |goto restart|@>; + } +} + +@ @<Scan for a subscript; replace |cur_cmd| by |numeric_token| if found@>= +{ + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_cmd!=right_bracket ) { + @<Put the left bracket and the expression back to be rescanned@>; + } else { + if ( mp->cur_type!=mp_known ) mp_bad_subscript(mp); + mp->cur_cmd=numeric_token; mp->cur_mod=mp->cur_exp; mp->cur_sym=0; + } +} + +@ The left bracket that we thought was introducing a subscript might have +actually been the left bracket in a mediation construction like `\.{x[a,b]}'. +So we don't issue an error message at this point; but we do want to back up +so as to avoid any embarrassment about our incorrect assumption. + +@<Put the left bracket and the expression back to be rescanned@>= +{ + mp_back_input(mp); /* that was the token following the current expression */ + mp_back_expr(mp); mp->cur_cmd=left_bracket; + mp->cur_mod=0; mp->cur_sym=frozen_left_bracket; +} + +@ Here's a routine that puts the current expression back to be read again. + +@c +static void mp_back_expr (MP mp) { + pointer p; /* capsule token */ + p=mp_stash_cur_exp(mp); mp_link(p)=null; back_list(p); +} + +@ Unknown subscripts lead to the following error message. + +@c +static void mp_bad_subscript (MP mp) { + exp_err("Improper subscript has been replaced by zero"); +@.Improper subscript...@> + help3("A bracketed subscript must have a known numeric value;", + "unfortunately, what I found was the value that appears just", + "above this error message. So I'll try a zero subscript."); + mp_flush_error(mp, 0); +} + +@ Every time we call |get_x_next|, there's a chance that the variable we've +been looking at will disappear. Thus, we cannot safely keep |q| pointing +into the variable structure; we need to start searching from the root each time. + +@<Find the approximate type |tt| and corresponding~|q|@>= +@^inner loop@> +{ + p=mp_link(pre_head); q=mp_info(p); tt=undefined; + if ( eq_type(q) % outer_tag==tag_token ) { + q=equiv(q); + if ( q==null ) goto DONE2; + while (1) { + p=mp_link(p); + if ( p==null ) { + tt=mp_type(q); goto DONE2; + }; + if ( mp_type(q)!=mp_structured ) goto DONE2; + q=mp_link(attr_head(q)); /* the |collective_subscript| attribute */ + if ( p>=mp->hi_mem_min ) { /* it's not a subscript */ + do { q=mp_link(q); } while (! (attr_loc(q)>=mp_info(p))); + if ( attr_loc(q)>mp_info(p) ) goto DONE2; + } + } + } +DONE2: + ; +} + +@ How do things stand now? Well, we have scanned an entire variable name, +including possible subscripts and/or attributes; |cur_cmd|, |cur_mod|, and +|cur_sym| represent the token that follows. If |post_head=null|, a +token list for this variable name starts at |mp_link(pre_head)|, with all +subscripts evaluated. But if |post_head<>null|, the variable turned out +to be a suffixed macro; |pre_head| is the head of the prefix list, while +|post_head| is the head of a token list containing both `\.{\AT!}' and +the suffix. + +Our immediate problem is to see if this variable still exists. (Variable +structures can change drastically whenever we call |get_x_next|; users +aren't supposed to do this, but the fact that it is possible means that +we must be cautious.) + +The following procedure prints an error message when a variable +unexpectedly disappears. Its help message isn't quite right for +our present purposes, but we'll be able to fix that up. + +@c +static void mp_obliterated (MP mp,pointer q) { + print_err("Variable "); mp_show_token_list(mp, q,null,1000,0); + mp_print(mp, " has been obliterated"); +@.Variable...obliterated@> + help5("It seems you did a nasty thing---probably by accident,", + "but nevertheless you nearly hornswoggled me...", + "While I was evaluating the right-hand side of this", + "command, something happened, and the left-hand side", + "is no longer a variable! So I won't change anything."); +} + +@ If the variable does exist, we also need to check +for a few other special cases before deciding that a plain old ordinary +variable has, indeed, been scanned. + +@<Handle unusual cases that masquerade as variables...@>= +if ( post_head!=null ) { + @<Set up suffixed macro call and |goto restart|@>; +} +q=mp_link(pre_head); free_avail(pre_head); +if ( mp->cur_cmd==my_var_flag ) { + mp->cur_type=mp_token_list; mp->cur_exp=q; goto DONE; +} +p=mp_find_variable(mp, q); +if ( p!=null ) { + mp_make_exp_copy(mp, p); +} else { + mp_obliterated(mp, q); + mp->help_line[2]="While I was evaluating the suffix of this variable,"; + mp->help_line[1]="something was redefined, and it's no longer a variable!"; + mp->help_line[0]="In order to get back on my feet, I've inserted `0' instead."; + mp_put_get_flush_error(mp, 0); +} +mp_flush_node_list(mp, q); +goto DONE + +@ The only complication associated with macro calling is that the prefix +and ``at'' parameters must be packaged in an appropriate list of lists. + +@<Set up unsuffixed macro call and |goto restart|@>= +{ + p=mp_get_avail(mp); mp_info(pre_head)=mp_link(pre_head); mp_link(pre_head)=p; + mp_info(p)=t; mp_macro_call(mp, value(q),pre_head,null); + mp_get_x_next(mp); + goto RESTART; +} + +@ If the ``variable'' that turned out to be a suffixed macro no longer exists, +we don't care, because we have reserved a pointer (|macro_ref|) to its +token list. + +@<Set up suffixed macro call and |goto restart|@>= +{ + mp_back_input(mp); p=mp_get_avail(mp); q=mp_link(post_head); + mp_info(pre_head)=mp_link(pre_head); mp_link(pre_head)=post_head; + mp_info(post_head)=q; mp_link(post_head)=p; mp_info(p)=mp_link(q); mp_link(q)=null; + mp_macro_call(mp, macro_ref,pre_head,null); decr(ref_count(macro_ref)); + mp_get_x_next(mp); goto RESTART; +} + +@ Our remaining job is simply to make a copy of the value that has been +found. Some cases are harder than others, but complexity arises solely +because of the multiplicity of possible cases. + +@<Declare the procedure called |make_exp_copy|@>= +@<Declare subroutines needed by |make_exp_copy|@> +static void mp_make_exp_copy (MP mp,pointer p) { + pointer q,r,t; /* registers for list manipulation */ +RESTART: + mp->cur_type=mp_type(p); + switch (mp->cur_type) { + case mp_vacuous: case mp_boolean_type: case mp_known: + mp->cur_exp=value(p); break; + case unknown_types: + mp->cur_exp=mp_new_ring_entry(mp, p); + break; + case mp_string_type: + mp->cur_exp=value(p); add_str_ref(mp->cur_exp); + break; + case mp_picture_type: + mp->cur_exp=value(p);add_edge_ref(mp->cur_exp); + break; + case mp_pen_type: + mp->cur_exp=copy_pen(value(p)); + break; + case mp_path_type: + mp->cur_exp=mp_copy_path(mp, value(p)); + break; + case mp_transform_type: case mp_color_type: + case mp_cmykcolor_type: case mp_pair_type: + @<Copy the big node |p|@>; + break; + case mp_dependent: case mp_proto_dependent: + mp_encapsulate(mp, mp_copy_dep_list(mp, dep_list(p))); + break; + case mp_numeric_type: + new_indep(p); goto RESTART; + break; + case mp_independent: + q=mp_single_dependency(mp, p); + if ( q==mp->dep_final ){ + mp->cur_type=mp_known; mp->cur_exp=0; mp_free_node(mp, q,dep_node_size); + } else { + mp->cur_type=mp_dependent; mp_encapsulate(mp, q); + } + break; + default: + mp_confusion(mp, "copy"); +@:this can't happen copy}{\quad copy@> + break; + } +} + +@ The |encapsulate| subroutine assumes that |dep_final| is the +tail of dependency list~|p|. + +@<Declare subroutines needed by |make_exp_copy|@>= +static void mp_encapsulate (MP mp,pointer p) { + mp->cur_exp=mp_get_node(mp, value_node_size); mp_type(mp->cur_exp)=mp->cur_type; + mp_name_type(mp->cur_exp)=mp_capsule; mp_new_dep(mp, mp->cur_exp,p); +} + +@ The most tedious case arises when the user refers to a +\&{pair}, \&{color}, or \&{transform} variable; we must copy several fields, +each of which can be |independent|, |dependent|, |mp_proto_dependent|, +or |known|. + +@<Copy the big node |p|@>= +{ + if ( value(p)==null ) + mp_init_big_node(mp, p); + t=mp_get_node(mp, value_node_size); mp_name_type(t)=mp_capsule; mp_type(t)=mp->cur_type; + mp_init_big_node(mp, t); + q=value(p)+mp->big_node_size[mp->cur_type]; + r=value(t)+mp->big_node_size[mp->cur_type]; + do { + q=q-2; r=r-2; mp_install(mp, r,q); + } while (q!=value(p)); + mp->cur_exp=t; +} + +@ The |install| procedure copies a numeric field~|q| into field~|r| of +a big node that will be part of a capsule. + +@<Declare subroutines needed by |make_exp_copy|@>= +static void mp_install (MP mp,pointer r, pointer q) { + pointer p; /* temporary register */ + if ( mp_type(q)==mp_known ){ + value(r)=value(q); mp_type(r)=mp_known; + } else if ( mp_type(q)==mp_independent ) { + p=mp_single_dependency(mp, q); + if ( p==mp->dep_final ) { + mp_type(r)=mp_known; value(r)=0; mp_free_node(mp, p,dep_node_size); + } else { + mp_type(r)=mp_dependent; mp_new_dep(mp, r,p); + } + } else { + mp_type(r)=mp_type(q); mp_new_dep(mp, r,mp_copy_dep_list(mp, dep_list(q))); + } +} + +@ Expressions of the form `\.{a[b,c]}' are converted into +`\.{b+a*(c-b)}', without checking the types of \.b~or~\.c, +provided that \.a is numeric. + +@<Scan a mediation...@>= +{ + p=mp_stash_cur_exp(mp); mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_cmd!=comma ) { + @<Put the left bracket and the expression back...@>; + mp_unstash_cur_exp(mp, p); + } else { + q=mp_stash_cur_exp(mp); mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_cmd!=right_bracket ) { + mp_missing_err(mp, "]"); +@.Missing `]'@> + help3("I've scanned an expression of the form `a[b,c',", + "so a right bracket should have come next.", + "I shall pretend that one was there."); + mp_back_error(mp); + } + r=mp_stash_cur_exp(mp); mp_make_exp_copy(mp, q); + mp_do_binary(mp, r,minus); mp_do_binary(mp, p,times); + mp_do_binary(mp, q,plus); mp_get_x_next(mp); + } +} + +@ Here is a comparatively simple routine that is used to scan the +\&{suffix} parameters of a macro. + +@<Declare the basic parsing subroutines@>= +static void mp_scan_suffix (MP mp) { + pointer h,t; /* head and tail of the list being built */ + pointer p; /* temporary register */ + h=mp_get_avail(mp); t=h; + while (1) { + if ( mp->cur_cmd==left_bracket ) { + @<Scan a bracketed subscript and set |cur_cmd:=numeric_token|@>; + } + if ( mp->cur_cmd==numeric_token ) { + p=mp_new_num_tok(mp, mp->cur_mod); + } else if ((mp->cur_cmd==tag_token)||(mp->cur_cmd==internal_quantity) ) { + p=mp_get_avail(mp); mp_info(p)=mp->cur_sym; + } else { + break; + } + mp_link(t)=p; t=p; mp_get_x_next(mp); + } + mp->cur_exp=mp_link(h); free_avail(h); mp->cur_type=mp_token_list; +} + +@ @<Scan a bracketed subscript and set |cur_cmd:=numeric_token|@>= +{ + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ) mp_bad_subscript(mp); + if ( mp->cur_cmd!=right_bracket ) { + mp_missing_err(mp, "]"); +@.Missing `]'@> + help3("I've seen a `[' and a subscript value, in a suffix,", + "so a right bracket should have come next.", + "I shall pretend that one was there."); + mp_back_error(mp); + } + mp->cur_cmd=numeric_token; mp->cur_mod=mp->cur_exp; +} + +@* \[38] Parsing secondary and higher expressions. + +After the intricacies of |scan_primary|\kern-1pt, +the |scan_secondary| routine is +refreshingly simple. It's not trivial, but the operations are relatively +straightforward; the main difficulty is, again, that expressions and data +structures might change drastically every time we call |get_x_next|, so a +cautious approach is mandatory. For example, a macro defined by +\&{primarydef} might have disappeared by the time its second argument has +been scanned; we solve this by increasing the reference count of its token +list, so that the macro can be called even after it has been clobbered. + +@<Declare the basic parsing subroutines@>= +static void mp_scan_secondary (MP mp) { + pointer p; /* for list manipulation */ + halfword c,d; /* operation codes or modifiers */ + pointer mac_name; /* token defined with \&{primarydef} */ +RESTART: + if ((mp->cur_cmd<min_primary_command)|| + (mp->cur_cmd>max_primary_command) ) + mp_bad_exp(mp, "A secondary"); +@.A secondary expression...@> + mp_scan_primary(mp); +CONTINUE: + if ( mp->cur_cmd<=max_secondary_command && + mp->cur_cmd>=min_secondary_command ) { + p=mp_stash_cur_exp(mp); + c=mp->cur_mod; d=mp->cur_cmd; + if ( d==secondary_primary_macro ) { + mac_name=mp->cur_sym; + add_mac_ref(c); + } + mp_get_x_next(mp); + mp_scan_primary(mp); + if ( d!=secondary_primary_macro ) { + mp_do_binary(mp, p,c); + } else { + mp_back_input(mp); + mp_binary_mac(mp, p,c,mac_name); + decr(ref_count(c)); + mp_get_x_next(mp); + goto RESTART; + } + goto CONTINUE; + } +} + +@ The following procedure calls a macro that has two parameters, +|p| and |cur_exp|. + +@c +static void mp_binary_mac (MP mp,pointer p, pointer c, pointer n) { + pointer q,r; /* nodes in the parameter list */ + q=mp_get_avail(mp); r=mp_get_avail(mp); mp_link(q)=r; + mp_info(q)=p; mp_info(r)=mp_stash_cur_exp(mp); + mp_macro_call(mp, c,q,n); +} + +@ The next procedure, |scan_tertiary|, is pretty much the same deal. + +@<Declare the basic parsing subroutines@>= +static void mp_scan_tertiary (MP mp) { + pointer p; /* for list manipulation */ + halfword c,d; /* operation codes or modifiers */ + pointer mac_name; /* token defined with \&{secondarydef} */ +RESTART: + if ((mp->cur_cmd<min_primary_command)|| + (mp->cur_cmd>max_primary_command) ) + mp_bad_exp(mp, "A tertiary"); +@.A tertiary expression...@> + mp_scan_secondary(mp); +CONTINUE: + if ( mp->cur_cmd<=max_tertiary_command ) { + if ( mp->cur_cmd>=min_tertiary_command ) { + p=mp_stash_cur_exp(mp); c=mp->cur_mod; d=mp->cur_cmd; + if ( d==tertiary_secondary_macro ) { + mac_name=mp->cur_sym; add_mac_ref(c); + }; + mp_get_x_next(mp); mp_scan_secondary(mp); + if ( d!=tertiary_secondary_macro ) { + mp_do_binary(mp, p,c); + } else { + mp_back_input(mp); mp_binary_mac(mp, p,c,mac_name); + decr(ref_count(c)); mp_get_x_next(mp); + goto RESTART; + } + goto CONTINUE; + } + } +} + +@ Finally we reach the deepest level in our quartet of parsing routines. +This one is much like the others; but it has an extra complication from +paths, which materialize here. + +@d continue_path 25 /* a label inside of |scan_expression| */ +@d finish_path 26 /* another */ + +@<Declare the basic parsing subroutines@>= +static void mp_scan_expression (MP mp) { + pointer p,q,r,pp,qq; /* for list manipulation */ + halfword c,d; /* operation codes or modifiers */ + int my_var_flag; /* initial value of |var_flag| */ + pointer mac_name; /* token defined with \&{tertiarydef} */ + boolean cycle_hit; /* did a path expression just end with `\&{cycle}'? */ + scaled x,y; /* explicit coordinates or tension at a path join */ + int t; /* knot type following a path join */ + t=0; y=0; x=0; + my_var_flag=mp->var_flag; mac_name=null; +RESTART: + if ((mp->cur_cmd<min_primary_command)|| + (mp->cur_cmd>max_primary_command) ) + mp_bad_exp(mp, "An"); +@.An expression...@> + mp_scan_tertiary(mp); +CONTINUE: + if ( mp->cur_cmd<=max_expression_command ) + if ( mp->cur_cmd>=min_expression_command ) { + if ( (mp->cur_cmd!=equals)||(my_var_flag!=assignment) ) { + p=mp_stash_cur_exp(mp); c=mp->cur_mod; d=mp->cur_cmd; + if ( d==expression_tertiary_macro ) { + mac_name=mp->cur_sym; add_mac_ref(c); + } + if ( (d<ampersand)||((d==ampersand)&& + ((mp_type(p)==mp_pair_type)||(mp_type(p)==mp_path_type))) ) { + @<Scan a path construction operation; + but |return| if |p| has the wrong type@>; + } else { + mp_get_x_next(mp); mp_scan_tertiary(mp); + if ( d!=expression_tertiary_macro ) { + mp_do_binary(mp, p,c); + } else { + mp_back_input(mp); mp_binary_mac(mp, p,c,mac_name); + decr(ref_count(c)); mp_get_x_next(mp); + goto RESTART; + } + } + goto CONTINUE; + } + } +} + +@ The reader should review the data structure conventions for paths before +hoping to understand the next part of this code. + +@<Scan a path construction operation...@>= +{ + cycle_hit=false; + @<Convert the left operand, |p|, into a partial path ending at~|q|; + but |return| if |p| doesn't have a suitable type@>; +CONTINUE_PATH: + @<Determine the path join parameters; + but |goto finish_path| if there's only a direction specifier@>; + if ( mp->cur_cmd==cycle ) { + @<Get ready to close a cycle@>; + } else { + mp_scan_tertiary(mp); + @<Convert the right operand, |cur_exp|, + into a partial path from |pp| to~|qq|@>; + } + @<Join the partial paths and reset |p| and |q| to the head and tail + of the result@>; + if ( mp->cur_cmd>=min_expression_command ) + if ( mp->cur_cmd<=ampersand ) if ( ! cycle_hit ) goto CONTINUE_PATH; +FINISH_PATH: + @<Choose control points for the path and put the result into |cur_exp|@>; +} + +@ @<Convert the left operand, |p|, into a partial path ending at~|q|...@>= +{ + mp_unstash_cur_exp(mp, p); + if ( mp->cur_type==mp_pair_type ) p=mp_new_knot(mp); + else if ( mp->cur_type==mp_path_type ) p=mp->cur_exp; + else return; + q=p; + while ( mp_link(q)!=p ) q=mp_link(q); + if ( mp_left_type(p)!=mp_endpoint ) { /* open up a cycle */ + r=mp_copy_knot(mp, p); mp_link(q)=r; q=r; + } + mp_left_type(p)=mp_open; mp_right_type(q)=mp_open; +} + +@ A pair of numeric values is changed into a knot node for a one-point path +when \MP\ discovers that the pair is part of a path. + +@c +static pointer mp_new_knot (MP mp) { /* convert a pair to a knot with two endpoints */ + pointer q; /* the new node */ + q=mp_get_node(mp, knot_node_size); mp_left_type(q)=mp_endpoint; + mp_right_type(q)=mp_endpoint; mp_originator(q)=mp_metapost_user; mp_link(q)=q; + mp_known_pair(mp); mp_x_coord(q)=mp->cur_x; mp_y_coord(q)=mp->cur_y; + return q; +} + +@ The |known_pair| subroutine sets |cur_x| and |cur_y| to the components +of the current expression, assuming that the current expression is a +pair of known numerics. Unknown components are zeroed, and the +current expression is flushed. + +@<Declarations@>= +static void mp_known_pair (MP mp); + +@ @c +void mp_known_pair (MP mp) { + pointer p; /* the pair node */ + if ( mp->cur_type!=mp_pair_type ) { + exp_err("Undefined coordinates have been replaced by (0,0)"); +@.Undefined coordinates...@> + help5("I need x and y numbers for this part of the path.", + "The value I found (see above) was no good;", + "so I'll try to keep going by using zero instead.", + "(Chapter 27 of The METAFONTbook explains that", +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> + "you might want to type `I ??" "?' now.)"); + mp_put_get_flush_error(mp, 0); mp->cur_x=0; mp->cur_y=0; + } else { + p=value(mp->cur_exp); + @<Make sure that both |x| and |y| parts of |p| are known; + copy them into |cur_x| and |cur_y|@>; + mp_flush_cur_exp(mp, 0); + } +} + +@ @<Make sure that both |x| and |y| parts of |p| are known...@>= +if ( mp_type(x_part_loc(p))==mp_known ) { + mp->cur_x=value(x_part_loc(p)); +} else { + mp_disp_err(mp, x_part_loc(p), + "Undefined x coordinate has been replaced by 0"); +@.Undefined coordinates...@> + help5("I need a `known' x value for this part of the path.", + "The value I found (see above) was no good;", + "so I'll try to keep going by using zero instead.", + "(Chapter 27 of The METAFONTbook explains that", +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> + "you might want to type `I ??" "?' now.)"); + mp_put_get_error(mp); mp_recycle_value(mp, x_part_loc(p)); mp->cur_x=0; +} +if ( mp_type(y_part_loc(p))==mp_known ) { + mp->cur_y=value(y_part_loc(p)); +} else { + mp_disp_err(mp, y_part_loc(p), + "Undefined y coordinate has been replaced by 0"); + help5("I need a `known' y value for this part of the path.", + "The value I found (see above) was no good;", + "so I'll try to keep going by using zero instead.", + "(Chapter 27 of The METAFONTbook explains that", + "you might want to type `I ??" "?' now.)"); + mp_put_get_error(mp); mp_recycle_value(mp, y_part_loc(p)); mp->cur_y=0; +} + +@ At this point |cur_cmd| is either |ampersand|, |left_brace|, or |path_join|. + +@<Determine the path join parameters...@>= +if ( mp->cur_cmd==left_brace ) { + @<Put the pre-join direction information into node |q|@>; +} +d=mp->cur_cmd; +if ( d==path_join ) { + @<Determine the tension and/or control points@>; +} else if ( d!=ampersand ) { + goto FINISH_PATH; +} +mp_get_x_next(mp); +if ( mp->cur_cmd==left_brace ) { + @<Put the post-join direction information into |x| and |t|@>; +} else if ( mp_right_type(q)!=mp_explicit ) { + t=mp_open; x=0; +} + +@ The |scan_direction| subroutine looks at the directional information +that is enclosed in braces, and also scans ahead to the following character. +A type code is returned, either |open| (if the direction was $(0,0)$), +or |curl| (if the direction was a curl of known value |cur_exp|), or +|given| (if the direction is given by the |angle| value that now +appears in |cur_exp|). + +There's nothing difficult about this subroutine, but the program is rather +lengthy because a variety of potential errors need to be nipped in the bud. + +@c +static quarterword mp_scan_direction (MP mp) { + int t; /* the type of information found */ + scaled x; /* an |x| coordinate */ + mp_get_x_next(mp); + if ( mp->cur_cmd==curl_command ) { + @<Scan a curl specification@>; + } else { + @<Scan a given direction@>; + } + if ( mp->cur_cmd!=right_brace ) { + mp_missing_err(mp, "}"); +@.Missing `\char`\}'@> + help3("I've scanned a direction spec for part of a path,", + "so a right brace should have come next.", + "I shall pretend that one was there."); + mp_back_error(mp); + } + mp_get_x_next(mp); + return t; +} + +@ @<Scan a curl specification@>= +{ mp_get_x_next(mp); mp_scan_expression(mp); +if ( (mp->cur_type!=mp_known)||(mp->cur_exp<0) ){ + exp_err("Improper curl has been replaced by 1"); +@.Improper curl@> + help1("A curl must be a known, nonnegative number."); + mp_put_get_flush_error(mp, unity); +} +t=mp_curl; +} + +@ @<Scan a given direction@>= +{ mp_scan_expression(mp); + if ( mp->cur_type>mp_pair_type ) { + @<Get given directions separated by commas@>; + } else { + mp_known_pair(mp); + } + if ( (mp->cur_x==0)&&(mp->cur_y==0) ) t=mp_open; + else { t=mp_given; mp->cur_exp=mp_n_arg(mp, mp->cur_x,mp->cur_y);} +} + +@ @<Get given directions separated by commas@>= +{ + if ( mp->cur_type!=mp_known ) { + exp_err("Undefined x coordinate has been replaced by 0"); +@.Undefined coordinates...@> + help5("I need a `known' x value for this part of the path.", + "The value I found (see above) was no good;", + "so I'll try to keep going by using zero instead.", + "(Chapter 27 of The METAFONTbook explains that", +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> + "you might want to type `I ??" "?' now.)"); + mp_put_get_flush_error(mp, 0); + } + x=mp->cur_exp; + if ( mp->cur_cmd!=comma ) { + mp_missing_err(mp, ","); +@.Missing `,'@> + help2("I've got the x coordinate of a path direction;", + "will look for the y coordinate next."); + mp_back_error(mp); + } + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ) { + exp_err("Undefined y coordinate has been replaced by 0"); + help5("I need a `known' y value for this part of the path.", + "The value I found (see above) was no good;", + "so I'll try to keep going by using zero instead.", + "(Chapter 27 of The METAFONTbook explains that", + "you might want to type `I ??" "?' now.)"); + mp_put_get_flush_error(mp, 0); + } + mp->cur_y=mp->cur_exp; mp->cur_x=x; +} + +@ At this point |mp_right_type(q)| is usually |open|, but it may have been +set to some other value by a previous operation. We must maintain +the value of |mp_right_type(q)| in cases such as +`\.{..\{curl2\}z\{0,0\}..}'. + +@<Put the pre-join...@>= +{ + t=mp_scan_direction(mp); + if ( t!=mp_open ) { + mp_right_type(q)=t; right_given(q)=mp->cur_exp; + if ( mp_left_type(q)==mp_open ) { + mp_left_type(q)=t; left_given(q)=mp->cur_exp; + } /* note that |left_given(q)=left_curl(q)| */ + } +} + +@ Since |left_tension| and |mp_left_y| share the same position in knot nodes, +and since |left_given| is similarly equivalent to |mp_left_x|, we use +|x| and |y| to hold the given direction and tension information when +there are no explicit control points. + +@<Put the post-join...@>= +{ + t=mp_scan_direction(mp); + if ( mp_right_type(q)!=mp_explicit ) x=mp->cur_exp; + else t=mp_explicit; /* the direction information is superfluous */ +} + +@ @<Determine the tension and/or...@>= +{ + mp_get_x_next(mp); + if ( mp->cur_cmd==tension ) { + @<Set explicit tensions@>; + } else if ( mp->cur_cmd==controls ) { + @<Set explicit control points@>; + } else { + right_tension(q)=unity; y=unity; mp_back_input(mp); /* default tension */ + goto DONE; + }; + if ( mp->cur_cmd!=path_join ) { + mp_missing_err(mp, ".."); +@.Missing `..'@> + help1("A path join command should end with two dots."); + mp_back_error(mp); + } +DONE: + ; +} + +@ @<Set explicit tensions@>= +{ + mp_get_x_next(mp); y=mp->cur_cmd; + if ( mp->cur_cmd==at_least ) mp_get_x_next(mp); + mp_scan_primary(mp); + @<Make sure that the current expression is a valid tension setting@>; + if ( y==at_least ) negate(mp->cur_exp); + right_tension(q)=mp->cur_exp; + if ( mp->cur_cmd==and_command ) { + mp_get_x_next(mp); y=mp->cur_cmd; + if ( mp->cur_cmd==at_least ) mp_get_x_next(mp); + mp_scan_primary(mp); + @<Make sure that the current expression is a valid tension setting@>; + if ( y==at_least ) negate(mp->cur_exp); + } + y=mp->cur_exp; +} + +@ @d min_tension three_quarter_unit + +@<Make sure that the current expression is a valid tension setting@>= +if ( (mp->cur_type!=mp_known)||(mp->cur_exp<min_tension) ) { + exp_err("Improper tension has been set to 1"); +@.Improper tension@> + help1("The expression above should have been a number >=3/4."); + mp_put_get_flush_error(mp, unity); +} + +@ @<Set explicit control points@>= +{ + mp_right_type(q)=mp_explicit; t=mp_explicit; mp_get_x_next(mp); mp_scan_primary(mp); + mp_known_pair(mp); mp_right_x(q)=mp->cur_x; mp_right_y(q)=mp->cur_y; + if ( mp->cur_cmd!=and_command ) { + x=mp_right_x(q); y=mp_right_y(q); + } else { + mp_get_x_next(mp); mp_scan_primary(mp); + mp_known_pair(mp); x=mp->cur_x; y=mp->cur_y; + } +} + +@ @<Convert the right operand, |cur_exp|, into a partial path...@>= +{ + if ( mp->cur_type!=mp_path_type ) pp=mp_new_knot(mp); + else pp=mp->cur_exp; + qq=pp; + while ( mp_link(qq)!=pp ) qq=mp_link(qq); + if ( mp_left_type(pp)!=mp_endpoint ) { /* open up a cycle */ + r=mp_copy_knot(mp, pp); mp_link(qq)=r; qq=r; + } + mp_left_type(pp)=mp_open; mp_right_type(qq)=mp_open; +} + +@ If a person tries to define an entire path by saying `\.{(x,y)\&cycle}', +we silently change the specification to `\.{(x,y)..cycle}', since a cycle +shouldn't have length zero. + +@<Get ready to close a cycle@>= +{ + cycle_hit=true; mp_get_x_next(mp); pp=p; qq=p; + if ( d==ampersand ) if ( p==q ) { + d=path_join; right_tension(q)=unity; y=unity; + } +} + +@ @<Join the partial paths and reset |p| and |q|...@>= +{ +if ( d==ampersand ) { + if ( (mp_x_coord(q)!=mp_x_coord(pp))||(mp_y_coord(q)!=mp_y_coord(pp)) ) { + print_err("Paths don't touch; `&' will be changed to `..'"); +@.Paths don't touch@> + help3("When you join paths `p&q', the ending point of p", + "must be exactly equal to the starting point of q.", + "So I'm going to pretend that you said `p..q' instead."); + mp_put_get_error(mp); d=path_join; right_tension(q)=unity; y=unity; + } +} +@<Plug an opening in |mp_right_type(pp)|, if possible@>; +if ( d==ampersand ) { + @<Splice independent paths together@>; +} else { + @<Plug an opening in |mp_right_type(q)|, if possible@>; + mp_link(q)=pp; mp_left_y(pp)=y; + if ( t!=mp_open ) { mp_left_x(pp)=x; mp_left_type(pp)=t; }; +} +q=qq; +} + +@ @<Plug an opening in |mp_right_type(q)|...@>= +if ( mp_right_type(q)==mp_open ) { + if ( (mp_left_type(q)==mp_curl)||(mp_left_type(q)==mp_given) ) { + mp_right_type(q)=mp_left_type(q); right_given(q)=left_given(q); + } +} + +@ @<Plug an opening in |mp_right_type(pp)|...@>= +if ( mp_right_type(pp)==mp_open ) { + if ( (t==mp_curl)||(t==mp_given) ) { + mp_right_type(pp)=t; right_given(pp)=x; + } +} + +@ @<Splice independent paths together@>= +{ + if ( mp_left_type(q)==mp_open ) if ( mp_right_type(q)==mp_open ) { + mp_left_type(q)=mp_curl; left_curl(q)=unity; + } + if ( mp_right_type(pp)==mp_open ) if ( t==mp_open ) { + mp_right_type(pp)=mp_curl; right_curl(pp)=unity; + } + mp_right_type(q)=mp_right_type(pp); mp_link(q)=mp_link(pp); + mp_right_x(q)=mp_right_x(pp); mp_right_y(q)=mp_right_y(pp); + mp_free_node(mp, pp,knot_node_size); + if ( qq==pp ) qq=q; +} + +@ @<Choose control points for the path...@>= +if ( cycle_hit ) { + if ( d==ampersand ) p=q; +} else { + mp_left_type(p)=mp_endpoint; + if ( mp_right_type(p)==mp_open ) { + mp_right_type(p)=mp_curl; right_curl(p)=unity; + } + mp_right_type(q)=mp_endpoint; + if ( mp_left_type(q)==mp_open ) { + mp_left_type(q)=mp_curl; left_curl(q)=unity; + } + mp_link(q)=p; +} +mp_make_choices(mp, p); +mp->cur_type=mp_path_type; mp->cur_exp=p + +@ Finally, we sometimes need to scan an expression whose value is +supposed to be either |true_code| or |false_code|. + +@<Declare the basic parsing subroutines@>= +static void mp_get_boolean (MP mp) { + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_boolean_type ) { + exp_err("Undefined condition will be treated as `false'"); +@.Undefined condition...@> + help2("The expression shown above should have had a definite", + "true-or-false value. I'm changing it to `false'."); + mp_put_get_flush_error(mp, false_code); mp->cur_type=mp_boolean_type; + } +} + +@* \[39] Doing the operations. +The purpose of parsing is primarily to permit people to avoid piles of +parentheses. But the real work is done after the structure of an expression +has been recognized; that's when new expressions are generated. We +turn now to the guts of \MP, which handles individual operators that +have come through the parsing mechanism. + +We'll start with the easy ones that take no operands, then work our way +up to operators with one and ultimately two arguments. In other words, +we will write the three procedures |do_nullary|, |do_unary|, and |do_binary| +that are invoked periodically by the expression scanners. + +First let's make sure that all of the primitive operators are in the +hash table. Although |scan_primary| and its relatives made use of the +\\{cmd} code for these operators, the \\{do} routines base everything +on the \\{mod} code. For example, |do_binary| doesn't care whether the +operation it performs is a |primary_binary| or |secondary_binary|, etc. + +@<Put each...@>= +mp_primitive(mp, "true",nullary,true_code); +@:true_}{\&{true} primitive@> +mp_primitive(mp, "false",nullary,false_code); +@:false_}{\&{false} primitive@> +mp_primitive(mp, "nullpicture",nullary,null_picture_code); +@:null_picture_}{\&{nullpicture} primitive@> +mp_primitive(mp, "nullpen",nullary,null_pen_code); +@:null_pen_}{\&{nullpen} primitive@> +mp_primitive(mp, "jobname",nullary,job_name_op); +@:job_name_}{\&{jobname} primitive@> +mp_primitive(mp, "readstring",nullary,read_string_op); +@:read_string_}{\&{readstring} primitive@> +mp_primitive(mp, "pencircle",nullary,pen_circle); +@:pen_circle_}{\&{pencircle} primitive@> +mp_primitive(mp, "normaldeviate",nullary,normal_deviate); +@:normal_deviate_}{\&{normaldeviate} primitive@> +mp_primitive(mp, "readfrom",unary,read_from_op); +@:read_from_}{\&{readfrom} primitive@> +mp_primitive(mp, "closefrom",unary,close_from_op); +@:close_from_}{\&{closefrom} primitive@> +mp_primitive(mp, "odd",unary,odd_op); +@:odd_}{\&{odd} primitive@> +mp_primitive(mp, "known",unary,known_op); +@:known_}{\&{known} primitive@> +mp_primitive(mp, "unknown",unary,unknown_op); +@:unknown_}{\&{unknown} primitive@> +mp_primitive(mp, "not",unary,not_op); +@:not_}{\&{not} primitive@> +mp_primitive(mp, "decimal",unary,decimal); +@:decimal_}{\&{decimal} primitive@> +mp_primitive(mp, "reverse",unary,reverse); +@:reverse_}{\&{reverse} primitive@> +mp_primitive(mp, "makepath",unary,make_path_op); +@:make_path_}{\&{makepath} primitive@> +mp_primitive(mp, "makepen",unary,make_pen_op); +@:make_pen_}{\&{makepen} primitive@> +mp_primitive(mp, "oct",unary,oct_op); +@:oct_}{\&{oct} primitive@> +mp_primitive(mp, "hex",unary,hex_op); +@:hex_}{\&{hex} primitive@> +mp_primitive(mp, "ASCII",unary,ASCII_op); +@:ASCII_}{\&{ASCII} primitive@> +mp_primitive(mp, "char",unary,char_op); +@:char_}{\&{char} primitive@> +mp_primitive(mp, "length",unary,length_op); +@:length_}{\&{length} primitive@> +mp_primitive(mp, "turningnumber",unary,turning_op); +@:turning_number_}{\&{turningnumber} primitive@> +mp_primitive(mp, "xpart",unary,x_part); +@:x_part_}{\&{xpart} primitive@> +mp_primitive(mp, "ypart",unary,y_part); +@:y_part_}{\&{ypart} primitive@> +mp_primitive(mp, "xxpart",unary,xx_part); +@:xx_part_}{\&{xxpart} primitive@> +mp_primitive(mp, "xypart",unary,xy_part); +@:xy_part_}{\&{xypart} primitive@> +mp_primitive(mp, "yxpart",unary,yx_part); +@:yx_part_}{\&{yxpart} primitive@> +mp_primitive(mp, "yypart",unary,yy_part); +@:yy_part_}{\&{yypart} primitive@> +mp_primitive(mp, "redpart",unary,red_part); +@:red_part_}{\&{redpart} primitive@> +mp_primitive(mp, "greenpart",unary,green_part); +@:green_part_}{\&{greenpart} primitive@> +mp_primitive(mp, "bluepart",unary,blue_part); +@:blue_part_}{\&{bluepart} primitive@> +mp_primitive(mp, "cyanpart",unary,cyan_part); +@:cyan_part_}{\&{cyanpart} primitive@> +mp_primitive(mp, "magentapart",unary,magenta_part); +@:magenta_part_}{\&{magentapart} primitive@> +mp_primitive(mp, "yellowpart",unary,yellow_part); +@:yellow_part_}{\&{yellowpart} primitive@> +mp_primitive(mp, "blackpart",unary,black_part); +@:black_part_}{\&{blackpart} primitive@> +mp_primitive(mp, "greypart",unary,grey_part); +@:grey_part_}{\&{greypart} primitive@> +mp_primitive(mp, "colormodel",unary,color_model_part); +@:color_model_part_}{\&{colormodel} primitive@> +mp_primitive(mp, "fontpart",unary,font_part); +@:font_part_}{\&{fontpart} primitive@> +mp_primitive(mp, "textpart",unary,text_part); +@:text_part_}{\&{textpart} primitive@> +mp_primitive(mp, "pathpart",unary,path_part); +@:path_part_}{\&{pathpart} primitive@> +mp_primitive(mp, "penpart",unary,pen_part); +@:pen_part_}{\&{penpart} primitive@> +mp_primitive(mp, "dashpart",unary,dash_part); +@:dash_part_}{\&{dashpart} primitive@> +mp_primitive(mp, "sqrt",unary,sqrt_op); +@:sqrt_}{\&{sqrt} primitive@> +mp_primitive(mp, "mexp",unary,mp_m_exp_op); +@:m_exp_}{\&{mexp} primitive@> +mp_primitive(mp, "mlog",unary,mp_m_log_op); +@:m_log_}{\&{mlog} primitive@> +mp_primitive(mp, "sind",unary,sin_d_op); +@:sin_d_}{\&{sind} primitive@> +mp_primitive(mp, "cosd",unary,cos_d_op); +@:cos_d_}{\&{cosd} primitive@> +mp_primitive(mp, "floor",unary,floor_op); +@:floor_}{\&{floor} primitive@> +mp_primitive(mp, "uniformdeviate",unary,uniform_deviate); +@:uniform_deviate_}{\&{uniformdeviate} primitive@> +mp_primitive(mp, "charexists",unary,char_exists_op); +@:char_exists_}{\&{charexists} primitive@> +mp_primitive(mp, "fontsize",unary,font_size); +@:font_size_}{\&{fontsize} primitive@> +mp_primitive(mp, "llcorner",unary,ll_corner_op); +@:ll_corner_}{\&{llcorner} primitive@> +mp_primitive(mp, "lrcorner",unary,lr_corner_op); +@:lr_corner_}{\&{lrcorner} primitive@> +mp_primitive(mp, "ulcorner",unary,ul_corner_op); +@:ul_corner_}{\&{ulcorner} primitive@> +mp_primitive(mp, "urcorner",unary,ur_corner_op); +@:ur_corner_}{\&{urcorner} primitive@> +mp_primitive(mp, "arclength",unary,arc_length); +@:arc_length_}{\&{arclength} primitive@> +mp_primitive(mp, "angle",unary,angle_op); +@:angle_}{\&{angle} primitive@> +mp_primitive(mp, "cycle",cycle,cycle_op); +@:cycle_}{\&{cycle} primitive@> +mp_primitive(mp, "stroked",unary,stroked_op); +@:stroked_}{\&{stroked} primitive@> +mp_primitive(mp, "filled",unary,filled_op); +@:filled_}{\&{filled} primitive@> +mp_primitive(mp, "textual",unary,textual_op); +@:textual_}{\&{textual} primitive@> +mp_primitive(mp, "clipped",unary,clipped_op); +@:clipped_}{\&{clipped} primitive@> +mp_primitive(mp, "bounded",unary,bounded_op); +@:bounded_}{\&{bounded} primitive@> +mp_primitive(mp, "+",plus_or_minus,plus); +@:+ }{\.{+} primitive@> +mp_primitive(mp, "-",plus_or_minus,minus); +@:- }{\.{-} primitive@> +mp_primitive(mp, "*",secondary_binary,times); +@:* }{\.{*} primitive@> +mp_primitive(mp, "/",slash,over); mp->eqtb[frozen_slash]=mp->eqtb[mp->cur_sym]; +@:/ }{\.{/} primitive@> +mp_primitive(mp, "++",tertiary_binary,pythag_add); +@:++_}{\.{++} primitive@> +mp_primitive(mp, "+-+",tertiary_binary,pythag_sub); +@:+-+_}{\.{+-+} primitive@> +mp_primitive(mp, "or",tertiary_binary,or_op); +@:or_}{\&{or} primitive@> +mp_primitive(mp, "and",and_command,and_op); +@:and_}{\&{and} primitive@> +mp_primitive(mp, "<",expression_binary,less_than); +@:< }{\.{<} primitive@> +mp_primitive(mp, "<=",expression_binary,less_or_equal); +@:<=_}{\.{<=} primitive@> +mp_primitive(mp, ">",expression_binary,greater_than); +@:> }{\.{>} primitive@> +mp_primitive(mp, ">=",expression_binary,greater_or_equal); +@:>=_}{\.{>=} primitive@> +mp_primitive(mp, "=",equals,equal_to); +@:= }{\.{=} primitive@> +mp_primitive(mp, "<>",expression_binary,unequal_to); +@:<>_}{\.{<>} primitive@> +mp_primitive(mp, "substring",primary_binary,substring_of); +@:substring_}{\&{substring} primitive@> +mp_primitive(mp, "subpath",primary_binary,subpath_of); +@:subpath_}{\&{subpath} primitive@> +mp_primitive(mp, "directiontime",primary_binary,direction_time_of); +@:direction_time_}{\&{directiontime} primitive@> +mp_primitive(mp, "point",primary_binary,point_of); +@:point_}{\&{point} primitive@> +mp_primitive(mp, "precontrol",primary_binary,precontrol_of); +@:precontrol_}{\&{precontrol} primitive@> +mp_primitive(mp, "postcontrol",primary_binary,postcontrol_of); +@:postcontrol_}{\&{postcontrol} primitive@> +mp_primitive(mp, "penoffset",primary_binary,pen_offset_of); +@:pen_offset_}{\&{penoffset} primitive@> +mp_primitive(mp, "arctime",primary_binary,arc_time_of); +@:arc_time_of_}{\&{arctime} primitive@> +mp_primitive(mp, "mpversion",nullary,mp_version); +@:mp_verison_}{\&{mpversion} primitive@> +mp_primitive(mp, "&",ampersand,concatenate); +@:!!!}{\.{\&} primitive@> +mp_primitive(mp, "rotated",secondary_binary,rotated_by); +@:rotated_}{\&{rotated} primitive@> +mp_primitive(mp, "slanted",secondary_binary,slanted_by); +@:slanted_}{\&{slanted} primitive@> +mp_primitive(mp, "scaled",secondary_binary,scaled_by); +@:scaled_}{\&{scaled} primitive@> +mp_primitive(mp, "shifted",secondary_binary,shifted_by); +@:shifted_}{\&{shifted} primitive@> +mp_primitive(mp, "transformed",secondary_binary,transformed_by); +@:transformed_}{\&{transformed} primitive@> +mp_primitive(mp, "xscaled",secondary_binary,x_scaled); +@:x_scaled_}{\&{xscaled} primitive@> +mp_primitive(mp, "yscaled",secondary_binary,y_scaled); +@:y_scaled_}{\&{yscaled} primitive@> +mp_primitive(mp, "zscaled",secondary_binary,z_scaled); +@:z_scaled_}{\&{zscaled} primitive@> +mp_primitive(mp, "infont",secondary_binary,in_font); +@:in_font_}{\&{infont} primitive@> +mp_primitive(mp, "intersectiontimes",tertiary_binary,intersect); +@:intersection_times_}{\&{intersectiontimes} primitive@> +mp_primitive(mp, "envelope",primary_binary,envelope_of); +@:envelope_}{\&{envelope} primitive@> + +@ @<Cases of |print_cmd...@>= +case nullary: +case unary: +case primary_binary: +case secondary_binary: +case tertiary_binary: +case expression_binary: +case cycle: +case plus_or_minus: +case slash: +case ampersand: +case equals: +case and_command: + mp_print_op(mp, m); + break; + +@ OK, let's look at the simplest \\{do} procedure first. + +@c @<Declare nullary action procedure@> +static void mp_do_nullary (MP mp,quarterword c) { + check_arith; + if ( mp->internal[mp_tracing_commands]>two ) + mp_show_cmd_mod(mp, nullary,c); + switch (c) { + case true_code: case false_code: + mp->cur_type=mp_boolean_type; mp->cur_exp=c; + break; + case null_picture_code: + mp->cur_type=mp_picture_type; + mp->cur_exp=mp_get_node(mp, edge_header_size); + mp_init_edges(mp, mp->cur_exp); + break; + case null_pen_code: + mp->cur_type=mp_pen_type; mp->cur_exp=mp_get_pen_circle(mp, 0); + break; + case normal_deviate: + mp->cur_type=mp_known; mp->cur_exp=mp_norm_rand(mp); + break; + case pen_circle: + mp->cur_type=mp_pen_type; mp->cur_exp=mp_get_pen_circle(mp, unity); + break; + case job_name_op: + if ( mp->job_name==NULL ) mp_open_log_file(mp); + mp->cur_type=mp_string_type; mp->cur_exp=rts(mp->job_name); + break; + case mp_version: + mp->cur_type=mp_string_type; + mp->cur_exp=intern(metapost_version) ; + break; + case read_string_op: + @<Read a string from the terminal@>; + break; + } /* there are no other cases */ + check_arith; +} + +@ @<Read a string...@>= +{ + if (mp->noninteractive || mp->interaction<=mp_nonstop_mode ) + mp_fatal_error(mp, "*** (cannot readstring in nonstop modes)"); + mp_begin_file_reading(mp); name=is_read; + limit=start; prompt_input(""); + mp_finish_read(mp); +} + +@ @<Declare nullary action procedure@>= +static void mp_finish_read (MP mp) { /* copy |buffer| line to |cur_exp| */ + size_t k; + str_room((int)mp->last-start); + for (k=(size_t)start;k<mp->last;k++) { + append_char(mp->buffer[k]); + } + mp_end_file_reading(mp); mp->cur_type=mp_string_type; + mp->cur_exp=mp_make_string(mp); +} + +@ Things get a bit more interesting when there's an operand. The +operand to |do_unary| appears in |cur_type| and |cur_exp|. + +@c @<Declare unary action procedures@> +static void mp_do_unary (MP mp,quarterword c) { + pointer p,q,r; /* for list manipulation */ + integer x; /* a temporary register */ + check_arith; + if ( mp->internal[mp_tracing_commands]>two ) + @<Trace the current unary operation@>; + switch (c) { + case plus: + if ( mp->cur_type<mp_color_type ) mp_bad_unary(mp, plus); + break; + case minus: + @<Negate the current expression@>; + break; + @<Additional cases of unary operators@>; + } /* there are no other cases */ + check_arith; +} + +@ The |nice_pair| function returns |true| if both components of a pair +are known. + +@<Declare unary action procedures@>= +static boolean mp_nice_pair (MP mp,integer p, quarterword t) { + if ( t==mp_pair_type ) { + p=value(p); + if ( mp_type(x_part_loc(p))==mp_known ) + if ( mp_type(y_part_loc(p))==mp_known ) + return true; + } + return false; +} + +@ The |nice_color_or_pair| function is analogous except that it also accepts +fully known colors. + +@<Declare unary action procedures@>= +static boolean mp_nice_color_or_pair (MP mp,integer p, quarterword t) { + pointer q,r; /* for scanning the big node */ + if ( (t!=mp_pair_type)&&(t!=mp_color_type)&&(t!=mp_cmykcolor_type) ) { + return false; + } else { + q=value(p); + r=q+mp->big_node_size[mp_type(p)]; + do { + r=r-2; + if ( mp_type(r)!=mp_known ) + return false; + } while (r!=q); + return true; + } +} + +@ @<Declare unary action...@>= +static void mp_print_known_or_unknown_type (MP mp,quarterword t, integer v) { + mp_print_char(mp, xord('(')); + if ( t>mp_known ) mp_print(mp, "unknown numeric"); + else { if ( (t==mp_pair_type)||(t==mp_color_type)||(t==mp_cmykcolor_type) ) + if ( ! mp_nice_color_or_pair(mp, v,t) ) mp_print(mp, "unknown "); + mp_print_type(mp, t); + } + mp_print_char(mp, xord(')')); +} + +@ @<Declare unary action...@>= +static void mp_bad_unary (MP mp,quarterword c) { + exp_err("Not implemented: "); mp_print_op(mp, c); +@.Not implemented...@> + mp_print_known_or_unknown_type(mp, mp->cur_type,mp->cur_exp); + help3("I'm afraid I don't know how to apply that operation to that", + "particular type. Continue, and I'll simply return the", + "argument (shown above) as the result of the operation."); + mp_put_get_error(mp); +} + +@ @<Trace the current unary operation@>= +{ + mp_begin_diagnostic(mp); mp_print_nl(mp, "{"); + mp_print_op(mp, c); mp_print_char(mp, xord('(')); + mp_print_exp(mp, null,0); /* show the operand, but not verbosely */ + mp_print(mp, ")}"); mp_end_diagnostic(mp, false); +} + +@ Negation is easy except when the current expression +is of type |independent|, or when it is a pair with one or more +|independent| components. + +It is tempting to argue that the negative of an independent variable +is an independent variable, hence we don't have to do anything when +negating it. The fallacy is that other dependent variables pointing +to the current expression must change the sign of their +coefficients if we make no change to the current expression. + +Instead, we work around the problem by copying the current expression +and recycling it afterwards (cf.~the |stash_in| routine). + +@<Negate the current expression@>= +switch (mp->cur_type) { +case mp_color_type: +case mp_cmykcolor_type: +case mp_pair_type: +case mp_independent: + q=mp->cur_exp; mp_make_exp_copy(mp, q); + if ( mp->cur_type==mp_dependent ) { + mp_negate_dep_list(mp, dep_list(mp->cur_exp)); + } else if ( mp->cur_type<=mp_pair_type ) { /* |mp_color_type| or |mp_pair_type| */ + p=value(mp->cur_exp); + r=p+mp->big_node_size[mp->cur_type]; + do { + r=r-2; + if ( mp_type(r)==mp_known ) negate(value(r)); + else mp_negate_dep_list(mp, dep_list(r)); + } while (r!=p); + } /* if |cur_type=mp_known| then |cur_exp=0| */ + mp_recycle_value(mp, q); mp_free_node(mp, q,value_node_size); + break; +case mp_dependent: +case mp_proto_dependent: + mp_negate_dep_list(mp, dep_list(mp->cur_exp)); + break; +case mp_known: + negate(mp->cur_exp); + break; +default: + mp_bad_unary(mp, minus); + break; +} + +@ @<Declare unary action...@>= +static void mp_negate_dep_list (MP mp,pointer p) { + while (1) { + negate(value(p)); + if ( mp_info(p)==null ) return; + p=mp_link(p); + } +} + +@ @<Additional cases of unary operators@>= +case not_op: + if ( mp->cur_type!=mp_boolean_type ) mp_bad_unary(mp, not_op); + else mp->cur_exp=true_code+false_code-mp->cur_exp; + break; + +@ @d three_sixty_units 23592960 /* that's |360*unity| */ +@d boolean_reset(A) if ( (A) ) mp->cur_exp=true_code; else mp->cur_exp=false_code + +@<Additional cases of unary operators@>= +case sqrt_op: +case mp_m_exp_op: +case mp_m_log_op: +case sin_d_op: +case cos_d_op: +case floor_op: +case uniform_deviate: +case odd_op: +case char_exists_op: + if ( mp->cur_type!=mp_known ) { + mp_bad_unary(mp, c); + } else { + switch (c) { + case sqrt_op:mp->cur_exp=mp_square_rt(mp, mp->cur_exp);break; + case mp_m_exp_op:mp->cur_exp=mp_m_exp(mp, mp->cur_exp);break; + case mp_m_log_op:mp->cur_exp=mp_m_log(mp, mp->cur_exp);break; + case sin_d_op: + case cos_d_op: + mp_n_sin_cos(mp, (mp->cur_exp % three_sixty_units)*16); + if ( c==sin_d_op ) mp->cur_exp=mp_round_fraction(mp, mp->n_sin); + else mp->cur_exp=mp_round_fraction(mp, mp->n_cos); + break; + case floor_op:mp->cur_exp=mp_floor_scaled(mp, mp->cur_exp);break; + case uniform_deviate:mp->cur_exp=mp_unif_rand(mp, mp->cur_exp);break; + case odd_op: + boolean_reset(odd(mp_round_unscaled(mp, mp->cur_exp))); + mp->cur_type=mp_boolean_type; + break; + case char_exists_op: + @<Determine if a character has been shipped out@>; + break; + } /* there are no other cases */ + } + break; + +@ @<Additional cases of unary operators@>= +case angle_op: + if ( mp_nice_pair(mp, mp->cur_exp,mp->cur_type) ) { + p=value(mp->cur_exp); + x=mp_n_arg(mp, value(x_part_loc(p)),value(y_part_loc(p))); + if ( x>=0 ) mp_flush_cur_exp(mp, (x+8)/ 16); + else mp_flush_cur_exp(mp, -((-x+8)/ 16)); + } else { + mp_bad_unary(mp, angle_op); + } + break; + +@ If the current expression is a pair, but the context wants it to +be a path, we call |pair_to_path|. + +@<Declare unary action...@>= +static void mp_pair_to_path (MP mp) { + mp->cur_exp=mp_new_knot(mp); + mp->cur_type=mp_path_type; +} + +@ +@d pict_color_type(A) ((mp_link(dummy_loc(mp->cur_exp))!=null) && + (has_color(mp_link(dummy_loc(mp->cur_exp)))) && + ((mp_color_model(mp_link(dummy_loc(mp->cur_exp)))==A) + || + ((mp_color_model(mp_link(dummy_loc(mp->cur_exp)))==mp_uninitialized_model) && + (mp->internal[mp_default_color_model]/unity)==(A)))) + +@<Additional cases of unary operators@>= +case x_part: +case y_part: + if ( (mp->cur_type==mp_pair_type)||(mp->cur_type==mp_transform_type) ) + mp_take_part(mp, c); + else if ( mp->cur_type==mp_picture_type ) mp_take_pict_part(mp, c); + else mp_bad_unary(mp, c); + break; +case xx_part: +case xy_part: +case yx_part: +case yy_part: + if ( mp->cur_type==mp_transform_type ) mp_take_part(mp, c); + else if ( mp->cur_type==mp_picture_type ) mp_take_pict_part(mp, c); + else mp_bad_unary(mp, c); + break; +case red_part: +case green_part: +case blue_part: + if ( mp->cur_type==mp_color_type ) mp_take_part(mp, c); + else if ( mp->cur_type==mp_picture_type ) { + if pict_color_type(mp_rgb_model) mp_take_pict_part(mp, c); + else mp_bad_color_part(mp, c); + } + else mp_bad_unary(mp, c); + break; +case cyan_part: +case magenta_part: +case yellow_part: +case black_part: + if ( mp->cur_type==mp_cmykcolor_type) mp_take_part(mp, c); + else if ( mp->cur_type==mp_picture_type ) { + if pict_color_type(mp_cmyk_model) mp_take_pict_part(mp, c); + else mp_bad_color_part(mp, c); + } + else mp_bad_unary(mp, c); + break; +case grey_part: + if ( mp->cur_type==mp_known ) mp->cur_exp=value(c); + else if ( mp->cur_type==mp_picture_type ) { + if pict_color_type(mp_grey_model) mp_take_pict_part(mp, c); + else mp_bad_color_part(mp, c); + } + else mp_bad_unary(mp, c); + break; +case color_model_part: + if ( mp->cur_type==mp_picture_type ) mp_take_pict_part(mp, c); + else mp_bad_unary(mp, c); + break; + +@ @<Declarations@>= +static void mp_bad_color_part(MP mp, quarterword c); + +@ @c +static void mp_bad_color_part(MP mp, quarterword c) { + pointer p; /* the big node */ + p=mp_link(dummy_loc(mp->cur_exp)); + exp_err("Wrong picture color model: "); mp_print_op(mp, c); +@.Wrong picture color model...@> + if (mp_color_model(p)==mp_grey_model) + mp_print(mp, " of grey object"); + else if (mp_color_model(p)==mp_cmyk_model) + mp_print(mp, " of cmyk object"); + else if (mp_color_model(p)==mp_rgb_model) + mp_print(mp, " of rgb object"); + else if (mp_color_model(p)==mp_no_model) + mp_print(mp, " of marking object"); + else + mp_print(mp," of defaulted object"); + help3("You can only ask for the redpart, greenpart, bluepart of a rgb object,", + "the cyanpart, magentapart, yellowpart or blackpart of a cmyk object, ", + "or the greypart of a grey object. No mixing and matching, please."); + mp_error(mp); + if (c==black_part) + mp_flush_cur_exp(mp,unity); + else + mp_flush_cur_exp(mp,0); +} + +@ In the following procedure, |cur_exp| points to a capsule, which points to +a big node. We want to delete all but one part of the big node. + +@<Declare unary action...@>= +static void mp_take_part (MP mp,quarterword c) { + pointer p; /* the big node */ + p=value(mp->cur_exp); value(temp_val)=p; mp_type(temp_val)=mp->cur_type; + mp_link(p)=temp_val; mp_free_node(mp, mp->cur_exp,value_node_size); + mp_make_exp_copy(mp, p+mp->sector_offset[c+mp_x_part_sector-x_part]); + mp_recycle_value(mp, temp_val); +} + +@ @<Initialize table entries...@>= +mp_name_type(temp_val)=mp_capsule; + +@ @<Additional cases of unary operators@>= +case font_part: +case text_part: +case path_part: +case pen_part: +case dash_part: + if ( mp->cur_type==mp_picture_type ) mp_take_pict_part(mp, c); + else mp_bad_unary(mp, c); + break; + +@ @<Declarations@>= +static void mp_scale_edges (MP mp); + +@ @<Declare unary action...@>= +static void mp_take_pict_part (MP mp,quarterword c) { + pointer p; /* first graphical object in |cur_exp| */ + p=mp_link(dummy_loc(mp->cur_exp)); + if ( p!=null ) { + switch (c) { + case x_part: case y_part: case xx_part: + case xy_part: case yx_part: case yy_part: + if ( mp_type(p)==mp_text_code ) mp_flush_cur_exp(mp, text_trans_part(p+c)); + else goto NOT_FOUND; + break; + case red_part: case green_part: case blue_part: + if ( has_color(p) ) mp_flush_cur_exp(mp, obj_color_part(p+c)); + else goto NOT_FOUND; + break; + case cyan_part: case magenta_part: case yellow_part: + case black_part: + if ( has_color(p) ) { + if ( mp_color_model(p)==mp_uninitialized_model && c==black_part) + mp_flush_cur_exp(mp, unity); + else + mp_flush_cur_exp(mp, obj_color_part(p+c+(red_part-cyan_part))); + } else goto NOT_FOUND; + break; + case grey_part: + if ( has_color(p) ) + mp_flush_cur_exp(mp, obj_color_part(p+c+(red_part-grey_part))); + else goto NOT_FOUND; + break; + case color_model_part: + if ( has_color(p) ) { + if ( mp_color_model(p)==mp_uninitialized_model ) + mp_flush_cur_exp(mp, mp->internal[mp_default_color_model]); + else + mp_flush_cur_exp(mp, mp_color_model(p)*unity); + } else goto NOT_FOUND; + break; + @<Handle other cases in |take_pict_part| or |goto not_found|@>; + } /* all cases have been enumerated */ + return; + }; +NOT_FOUND: + @<Convert the current expression to a null value appropriate + for |c|@>; +} + +@ @<Handle other cases in |take_pict_part| or |goto not_found|@>= +case text_part: + if ( mp_type(p)!=mp_text_code ) goto NOT_FOUND; + else { + mp_flush_cur_exp(mp, mp_text_p(p)); + add_str_ref(mp->cur_exp); + mp->cur_type=mp_string_type; + }; + break; +case font_part: + if ( mp_type(p)!=mp_text_code ) goto NOT_FOUND; + else { + mp_flush_cur_exp(mp, rts(mp->font_name[mp_font_n(p)])); + add_str_ref(mp->cur_exp); + mp->cur_type=mp_string_type; + }; + break; +case path_part: + if ( mp_type(p)==mp_text_code ) goto NOT_FOUND; + else if ( is_stop(p) ) mp_confusion(mp, "pict"); +@:this can't happen pict}{\quad pict@> + else { + mp_flush_cur_exp(mp, mp_copy_path(mp, mp_path_p(p))); + mp->cur_type=mp_path_type; + } + break; +case pen_part: + if ( ! has_pen(p) ) goto NOT_FOUND; + else { + if ( mp_pen_p(p)==null ) goto NOT_FOUND; + else { mp_flush_cur_exp(mp, copy_pen(mp_pen_p(p))); + mp->cur_type=mp_pen_type; + }; + } + break; +case dash_part: + if ( mp_type(p)!=mp_stroked_code ) goto NOT_FOUND; + else { if ( mp_dash_p(p)==null ) goto NOT_FOUND; + else { add_edge_ref(mp_dash_p(p)); + mp->se_sf=dash_scale(p); + mp->se_pic=mp_dash_p(p); + mp_scale_edges(mp); + mp_flush_cur_exp(mp, mp->se_pic); + mp->cur_type=mp_picture_type; + }; + } + break; + +@ Since |scale_edges| had to be declared |forward|, it had to be declared as a +parameterless procedure even though it really takes two arguments and updates +one of them. Hence the following globals are needed. + +@<Global...@>= +pointer se_pic; /* edge header used and updated by |scale_edges| */ +scaled se_sf; /* the scale factor argument to |scale_edges| */ + +@ @<Convert the current expression to a null value appropriate...@>= +switch (c) { +case text_part: case font_part: + mp_flush_cur_exp(mp, null_str); + mp->cur_type=mp_string_type; + break; +case path_part: + mp_flush_cur_exp(mp, mp_get_node(mp, knot_node_size)); + mp_left_type(mp->cur_exp)=mp_endpoint; + mp_right_type(mp->cur_exp)=mp_endpoint; + mp_link(mp->cur_exp)=mp->cur_exp; + mp_x_coord(mp->cur_exp)=0; + mp_y_coord(mp->cur_exp)=0; + mp_originator(mp->cur_exp)=mp_metapost_user; + mp->cur_type=mp_path_type; + break; +case pen_part: + mp_flush_cur_exp(mp, mp_get_pen_circle(mp, 0)); + mp->cur_type=mp_pen_type; + break; +case dash_part: + mp_flush_cur_exp(mp, mp_get_node(mp, edge_header_size)); + mp_init_edges(mp, mp->cur_exp); + mp->cur_type=mp_picture_type; + break; +default: + mp_flush_cur_exp(mp, 0); + break; +} + +@ @<Additional cases of unary...@>= +case char_op: + if ( mp->cur_type!=mp_known ) { + mp_bad_unary(mp, char_op); + } else { + mp->cur_exp=mp_round_unscaled(mp, mp->cur_exp) % 256; + mp->cur_type=mp_string_type; + if ( mp->cur_exp<0 ) mp->cur_exp=mp->cur_exp+256; + } + break; +case decimal: + if ( mp->cur_type!=mp_known ) { + mp_bad_unary(mp, decimal); + } else { + mp->old_setting=mp->selector; mp->selector=new_string; + mp_print_scaled(mp, mp->cur_exp); mp->cur_exp=mp_make_string(mp); + mp->selector=mp->old_setting; mp->cur_type=mp_string_type; + } + break; +case oct_op: +case hex_op: +case ASCII_op: + if ( mp->cur_type!=mp_string_type ) mp_bad_unary(mp, c); + else mp_str_to_num(mp, c); + break; +case font_size: + if ( mp->cur_type!=mp_string_type ) mp_bad_unary(mp, font_size); + else @<Find the design size of the font whose name is |cur_exp|@>; + break; + +@ @<Declare unary action...@>= +static void mp_str_to_num (MP mp,quarterword c) { /* converts a string to a number */ + integer n; /* accumulator */ + ASCII_code m; /* current character */ + pool_pointer k; /* index into |str_pool| */ + int b; /* radix of conversion */ + boolean bad_char; /* did the string contain an invalid digit? */ + if ( c==ASCII_op ) { + if ( length(mp->cur_exp)==0 ) n=-1; + else n=mp->str_pool[mp->str_start[mp->cur_exp]]; + } else { + if ( c==oct_op ) b=8; else b=16; + n=0; bad_char=false; + for (k=mp->str_start[mp->cur_exp];k<str_stop(mp->cur_exp);k++) { + m=mp->str_pool[k]; + if ( (m>='0')&&(m<='9') ) m=m-'0'; + else if ( (m>='A')&&(m<='F') ) m=m-'A'+10; + else if ( (m>='a')&&(m<='f') ) m=m-'a'+10; + else { bad_char=true; m=0; }; + if ( (int)m>=b ) { bad_char=true; m=0; }; + if ( n<32768 / b ) n=n*b+m; else n=32767; + } + @<Give error messages if |bad_char| or |n>=4096|@>; + } + mp_flush_cur_exp(mp, n*unity); +} + +@ @<Give error messages if |bad_char|...@>= +if ( bad_char ) { + exp_err("String contains illegal digits"); +@.String contains illegal digits@> + if ( c==oct_op ) { + help1("I zeroed out characters that weren't in the range 0..7."); + } else { + help1("I zeroed out characters that weren't hex digits."); + } + mp_put_get_error(mp); +} +if ( (n>4095) ) { + if ( mp->internal[mp_warning_check]>0 ) { + print_err("Number too large ("); + mp_print_int(mp, n); mp_print_char(mp, xord(')')); +@.Number too large@> + help2("I have trouble with numbers greater than 4095; watch out.", + "(Set warningcheck:=0 to suppress this message.)"); + mp_put_get_error(mp); + } +} + +@ The length operation is somewhat unusual in that it applies to a variety +of different types of operands. + +@<Additional cases of unary...@>= +case length_op: + switch (mp->cur_type) { + case mp_string_type: mp_flush_cur_exp(mp, length(mp->cur_exp)*unity); break; + case mp_path_type: mp_flush_cur_exp(mp, mp_path_length(mp)); break; + case mp_known: mp->cur_exp=abs(mp->cur_exp); break; + case mp_picture_type: mp_flush_cur_exp(mp, mp_pict_length(mp)); break; + default: + if ( mp_nice_pair(mp, mp->cur_exp,mp->cur_type) ) + mp_flush_cur_exp(mp, mp_pyth_add(mp, + value(x_part_loc(value(mp->cur_exp))), + value(y_part_loc(value(mp->cur_exp))))); + else mp_bad_unary(mp, c); + break; + } + break; + +@ @<Declare unary action...@>= +static scaled mp_path_length (MP mp) { /* computes the length of the current path */ + scaled n; /* the path length so far */ + pointer p; /* traverser */ + p=mp->cur_exp; + if ( mp_left_type(p)==mp_endpoint ) n=-unity; else n=0; + do { p=mp_link(p); n=n+unity; } while (p!=mp->cur_exp); + return n; +} + +@ @<Declare unary action...@>= +static scaled mp_pict_length (MP mp) { + /* counts interior components in picture |cur_exp| */ + scaled n; /* the count so far */ + pointer p; /* traverser */ + n=0; + p=mp_link(dummy_loc(mp->cur_exp)); + if ( p!=null ) { + if ( is_start_or_stop(p) ) + if ( mp_skip_1component(mp, p)==null ) p=mp_link(p); + while ( p!=null ) { + skip_component(p) return n; + n=n+unity; + } + } + return n; +} + +@ Implement |turningnumber| + +@<Additional cases of unary...@>= +case turning_op: + if ( mp->cur_type==mp_pair_type ) mp_flush_cur_exp(mp, 0); + else if ( mp->cur_type!=mp_path_type ) mp_bad_unary(mp, turning_op); + else if ( mp_left_type(mp->cur_exp)==mp_endpoint ) + mp_flush_cur_exp(mp, 0); /* not a cyclic path */ + else + mp_flush_cur_exp(mp, mp_turn_cycles_wrapper(mp, mp->cur_exp)); + break; + +@ The function |an_angle| returns the value of the |angle| primitive, or $0$ if the +argument is |origin|. + +@<Declare unary action...@>= +static angle mp_an_angle (MP mp,scaled xpar, scaled ypar) { + if ( (! ((xpar==0) && (ypar==0))) ) + return mp_n_arg(mp, xpar,ypar); + return 0; +} + + +@ The actual turning number is (for the moment) computed in a C function +that receives eight integers corresponding to the four controlling points, +and returns a single angle. Besides those, we have to account for discrete +moves at the actual points. + +@d mp_floor(a) ((a)>=0 ? (int)(a) : -(int)(-(a))) +@d bezier_error (720*(256*256*16))+1 +@d mp_sign(v) ((v)>0 ? 1 : ((v)<0 ? -1 : 0 )) +@d mp_out(A) (double)((A)/(256*256*16)) +@d divisor (256*256) +@d double2angle(a) (int)mp_floor(a*256.0*256.0*16.0) + +@<Declare unary action...@>= +static angle mp_bezier_slope(MP mp, integer AX,integer AY,integer BX,integer BY, + integer CX,integer CY,integer DX,integer DY); + +@ @c +static angle mp_bezier_slope(MP mp, integer AX,integer AY,integer BX,integer BY, + integer CX,integer CY,integer DX,integer DY) { + double a, b, c; + integer deltax,deltay; + double ax,ay,bx,by,cx,cy,dx,dy; + angle xi = 0, xo = 0, xm = 0; + double res = 0; + ax=(double)(AX/divisor); ay=(double)(AY/divisor); + bx=(double)(BX/divisor); by=(double)(BY/divisor); + cx=(double)(CX/divisor); cy=(double)(CY/divisor); + dx=(double)(DX/divisor); dy=(double)(DY/divisor); + + deltax = (BX-AX); deltay = (BY-AY); + if (deltax==0 && deltay == 0) { deltax=(CX-AX); deltay=(CY-AY); } + if (deltax==0 && deltay == 0) { deltax=(DX-AX); deltay=(DY-AY); } + xi = mp_an_angle(mp,deltax,deltay); + + deltax = (CX-BX); deltay = (CY-BY); + xm = mp_an_angle(mp,deltax,deltay); + + deltax = (DX-CX); deltay = (DY-CY); + if (deltax==0 && deltay == 0) { deltax=(DX-BX); deltay=(DY-BY); } + if (deltax==0 && deltay == 0) { deltax=(DX-AX); deltay=(DY-AY); } + xo = mp_an_angle(mp,deltax,deltay); + + a = (bx-ax)*(cy-by) - (cx-bx)*(by-ay); /* a = (bp-ap)x(cp-bp); */ + b = (bx-ax)*(dy-cy) - (by-ay)*(dx-cx);; /* b = (bp-ap)x(dp-cp);*/ + c = (cx-bx)*(dy-cy) - (dx-cx)*(cy-by); /* c = (cp-bp)x(dp-cp);*/ + + if ((a==0)&&(c==0)) { + res = (b==0 ? 0 : (mp_out(xo)-mp_out(xi))); + } else if ((a==0)||(c==0)) { + if ((mp_sign(b) == mp_sign(a)) || (mp_sign(b) == mp_sign(c))) { + res = mp_out(xo)-mp_out(xi); /* ? */ + if (res<-180.0) + res += 360.0; + else if (res>180.0) + res -= 360.0; + } else { + res = mp_out(xo)-mp_out(xi); /* ? */ + } + } else if ((mp_sign(a)*mp_sign(c))<0) { + res = mp_out(xo)-mp_out(xi); /* ? */ + if (res<-180.0) + res += 360.0; + else if (res>180.0) + res -= 360.0; + } else { + if (mp_sign(a) == mp_sign(b)) { + res = mp_out(xo)-mp_out(xi); /* ? */ + if (res<-180.0) + res += 360.0; + else if (res>180.0) + res -= 360.0; + } else { + if ((b*b) == (4*a*c)) { + res = (double)bezier_error; + } else if ((b*b) < (4*a*c)) { + res = mp_out(xo)-mp_out(xi); /* ? */ + if (res<=0.0 &&res>-180.0) + res += 360.0; + else if (res>=0.0 && res<180.0) + res -= 360.0; + } else { + res = mp_out(xo)-mp_out(xi); + if (res<-180.0) + res += 360.0; + else if (res>180.0) + res -= 360.0; + } + } + } + return double2angle(res); +} + +@ +@d p_nextnext mp_link(mp_link(p)) +@d p_next mp_link(p) +@d seven_twenty_deg 05500000000 /* $720\cdot2^{20}$, represents $720^\circ$ */ + +@<Declare unary action...@>= +static scaled mp_new_turn_cycles (MP mp,pointer c) { + angle res,ang; /* the angles of intermediate results */ + scaled turns; /* the turn counter */ + pointer p; /* for running around the path */ + integer xp,yp; /* coordinates of next point */ + integer x,y; /* helper coordinates */ + angle in_angle,out_angle; /* helper angles */ + unsigned old_setting; /* saved |selector| setting */ + res=0; + turns= 0; + p=c; + old_setting = mp->selector; mp->selector=term_only; + if ( mp->internal[mp_tracing_commands]>unity ) { + mp_begin_diagnostic(mp); + mp_print_nl(mp, ""); + mp_end_diagnostic(mp, false); + } + do { + xp = mp_x_coord(p_next); yp = mp_y_coord(p_next); + ang = mp_bezier_slope(mp,mp_x_coord(p), mp_y_coord(p), mp_right_x(p), mp_right_y(p), + mp_left_x(p_next), mp_left_y(p_next), xp, yp); + if ( ang>seven_twenty_deg ) { + print_err("Strange path"); + mp_error(mp); + mp->selector=old_setting; + return 0; + } + res = res + ang; + if ( res > one_eighty_deg ) { + res = res - three_sixty_deg; + turns = turns + unity; + } + if ( res <= -one_eighty_deg ) { + res = res + three_sixty_deg; + turns = turns - unity; + } + /* incoming angle at next point */ + x = mp_left_x(p_next); y = mp_left_y(p_next); + if ( (xp==x)&&(yp==y) ) { x = mp_right_x(p); y = mp_right_y(p); }; + if ( (xp==x)&&(yp==y) ) { x = mp_x_coord(p); y = mp_y_coord(p); }; + in_angle = mp_an_angle(mp, xp - x, yp - y); + /* outgoing angle at next point */ + x = mp_right_x(p_next); y = mp_right_y(p_next); + if ( (xp==x)&&(yp==y) ) { x = mp_left_x(p_nextnext); y = mp_left_y(p_nextnext); }; + if ( (xp==x)&&(yp==y) ) { x = mp_x_coord(p_nextnext); y = mp_y_coord(p_nextnext); }; + out_angle = mp_an_angle(mp, x - xp, y- yp); + ang = (out_angle - in_angle); + reduce_angle(ang); + if ( ang!=0 ) { + res = res + ang; + if ( res >= one_eighty_deg ) { + res = res - three_sixty_deg; + turns = turns + unity; + }; + if ( res <= -one_eighty_deg ) { + res = res + three_sixty_deg; + turns = turns - unity; + }; + }; + p = mp_link(p); + } while (p!=c); + mp->selector=old_setting; + return turns; +} + + +@ This code is based on Bogus\l{}av Jackowski's +|emergency_turningnumber| macro, with some minor changes by Taco +Hoekwater. The macro code looked more like this: +{\obeylines +vardef turning\_number primary p = +~~save res, ang, turns; +~~res := 0; +~~if length p <= 2: +~~~~if Angle ((point 0 of p) - (postcontrol 0 of p)) >= 0: 1 else: -1 fi +~~else: +~~~~for t = 0 upto length p-1 : +~~~~~~angc := Angle ((point t+1 of p) - (point t of p)) +~~~~~~~~- Angle ((point t of p) - (point t-1 of p)); +~~~~~~if angc > 180: angc := angc - 360; fi; +~~~~~~if angc < -180: angc := angc + 360; fi; +~~~~~~res := res + angc; +~~~~endfor; +~~res/360 +~~fi +enddef;} +The general idea is to calculate only the sum of the angles of +straight lines between the points, of a path, not worrying about cusps +or self-intersections in the segments at all. If the segment is not +well-behaved, the result is not necesarily correct. But the old code +was not always correct either, and worse, it sometimes failed for +well-behaved paths as well. All known bugs that were triggered by the +original code no longer occur with this code, and it runs roughly 3 +times as fast because the algorithm is much simpler. + +@ It is possible to overflow the return value of the |turn_cycles| +function when the path is sufficiently long and winding, but I am not +going to bother testing for that. In any case, it would only return +the looped result value, which is not a big problem. + +The macro code for the repeat loop was a bit nicer to look +at than the pascal code, because it could use |point -1 of p|. In +pascal, the fastest way to loop around the path is not to look +backward once, but forward twice. These defines help hide the trick. + +@d p_to mp_link(mp_link(p)) +@d p_here mp_link(p) +@d p_from p + +@<Declare unary action...@>= +static scaled mp_turn_cycles (MP mp,pointer c) { + angle res,ang; /* the angles of intermediate results */ + scaled turns; /* the turn counter */ + pointer p; /* for running around the path */ + res=0; turns= 0; p=c; + do { + ang = mp_an_angle (mp, mp_x_coord(p_to) - mp_x_coord(p_here), + mp_y_coord(p_to) - mp_y_coord(p_here)) + - mp_an_angle (mp, mp_x_coord(p_here) - mp_x_coord(p_from), + mp_y_coord(p_here) - mp_y_coord(p_from)); + reduce_angle(ang); + res = res + ang; + if ( res >= three_sixty_deg ) { + res = res - three_sixty_deg; + turns = turns + unity; + }; + if ( res <= -three_sixty_deg ) { + res = res + three_sixty_deg; + turns = turns - unity; + }; + p = mp_link(p); + } while (p!=c); + return turns; +} + +@ @<Declare unary action...@>= +static scaled mp_turn_cycles_wrapper (MP mp,pointer c) { + scaled nval,oval; + scaled saved_t_o; /* tracing\_online saved */ + if ( (mp_link(c)==c)||(mp_link(mp_link(c))==c) ) { + if ( mp_an_angle (mp, mp_x_coord(c) - mp_right_x(c), mp_y_coord(c) - mp_right_y(c)) > 0 ) + return unity; + else + return -unity; + } else { + nval = mp_new_turn_cycles(mp, c); + oval = mp_turn_cycles(mp, c); + if ( nval!=oval ) { + saved_t_o=mp->internal[mp_tracing_online]; + mp->internal[mp_tracing_online]=unity; + mp_begin_diagnostic(mp); + mp_print_nl (mp, "Warning: the turningnumber algorithms do not agree." + " The current computed value is "); + mp_print_scaled(mp, nval); + mp_print(mp, ", but the 'connect-the-dots' algorithm returned "); + mp_print_scaled(mp, oval); + mp_end_diagnostic(mp, false); + mp->internal[mp_tracing_online]=saved_t_o; + } + return nval; + } +} + +@ @d type_range(A,B) { + if ( (mp->cur_type>=(A)) && (mp->cur_type<=(B)) ) + mp_flush_cur_exp(mp, true_code); + else mp_flush_cur_exp(mp, false_code); + mp->cur_type=mp_boolean_type; + } +@d type_test(A) { + if ( mp->cur_type==(A) ) mp_flush_cur_exp(mp, true_code); + else mp_flush_cur_exp(mp, false_code); + mp->cur_type=mp_boolean_type; + } + +@<Additional cases of unary operators@>= +case mp_boolean_type: + type_range(mp_boolean_type,mp_unknown_boolean); break; +case mp_string_type: + type_range(mp_string_type,mp_unknown_string); break; +case mp_pen_type: + type_range(mp_pen_type,mp_unknown_pen); break; +case mp_path_type: + type_range(mp_path_type,mp_unknown_path); break; +case mp_picture_type: + type_range(mp_picture_type,mp_unknown_picture); break; +case mp_transform_type: case mp_color_type: case mp_cmykcolor_type: +case mp_pair_type: + type_test(c); break; +case mp_numeric_type: + type_range(mp_known,mp_independent); break; +case known_op: case unknown_op: + mp_test_known(mp, c); break; + +@ @<Declare unary action procedures@>= +static void mp_test_known (MP mp,quarterword c) { + int b; /* is the current expression known? */ + pointer p,q; /* locations in a big node */ + b=false_code; + switch (mp->cur_type) { + case mp_vacuous: case mp_boolean_type: case mp_string_type: + case mp_pen_type: case mp_path_type: case mp_picture_type: + case mp_known: + b=true_code; + break; + case mp_transform_type: + case mp_color_type: case mp_cmykcolor_type: case mp_pair_type: + p=value(mp->cur_exp); + q=p+mp->big_node_size[mp->cur_type]; + do { + q=q-2; + if ( mp_type(q)!=mp_known ) + goto DONE; + } while (q!=p); + b=true_code; + DONE: + break; + default: + break; + } + if ( c==known_op ) mp_flush_cur_exp(mp, b); + else mp_flush_cur_exp(mp, true_code+false_code-b); + mp->cur_type=mp_boolean_type; +} + +@ @<Additional cases of unary operators@>= +case cycle_op: + if ( mp->cur_type!=mp_path_type ) mp_flush_cur_exp(mp, false_code); + else if ( mp_left_type(mp->cur_exp)!=mp_endpoint ) mp_flush_cur_exp(mp, true_code); + else mp_flush_cur_exp(mp, false_code); + mp->cur_type=mp_boolean_type; + break; + +@ @<Additional cases of unary operators@>= +case arc_length: + if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + if ( mp->cur_type!=mp_path_type ) mp_bad_unary(mp, arc_length); + else mp_flush_cur_exp(mp, mp_get_arc_length(mp, mp->cur_exp)); + break; + +@ Here we use the fact that |c-filled_op+fill_code| is the desired graphical +object |type|. +@^data structure assumptions@> + +@<Additional cases of unary operators@>= +case filled_op: +case stroked_op: +case textual_op: +case clipped_op: +case bounded_op: + if ( mp->cur_type!=mp_picture_type ) mp_flush_cur_exp(mp, false_code); + else if ( mp_link(dummy_loc(mp->cur_exp))==null ) mp_flush_cur_exp(mp, false_code); + else if ( mp_type(mp_link(dummy_loc(mp->cur_exp)))==c+mp_fill_code-filled_op ) + mp_flush_cur_exp(mp, true_code); + else mp_flush_cur_exp(mp, false_code); + mp->cur_type=mp_boolean_type; + break; + +@ @<Additional cases of unary operators@>= +case make_pen_op: + if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + if ( mp->cur_type!=mp_path_type ) mp_bad_unary(mp, make_pen_op); + else { + mp->cur_type=mp_pen_type; + mp->cur_exp=mp_make_pen(mp, mp->cur_exp,true); + }; + break; +case make_path_op: + if ( mp->cur_type!=mp_pen_type ) mp_bad_unary(mp, make_path_op); + else { + mp->cur_type=mp_path_type; + mp_make_path(mp, mp->cur_exp); + }; + break; +case reverse: + if ( mp->cur_type==mp_path_type ) { + p=mp_htap_ypoc(mp, mp->cur_exp); + if ( mp_right_type(p)==mp_endpoint ) p=mp_link(p); + mp_toss_knot_list(mp, mp->cur_exp); mp->cur_exp=p; + } else if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + else mp_bad_unary(mp, reverse); + break; + +@ The |pair_value| routine changes the current expression to a +given ordered pair of values. + +@<Declare unary action procedures@>= +static void mp_pair_value (MP mp,scaled x, scaled y) { + pointer p; /* a pair node */ + p=mp_get_node(mp, value_node_size); + mp_flush_cur_exp(mp, p); mp->cur_type=mp_pair_type; + mp_type(p)=mp_pair_type; mp_name_type(p)=mp_capsule; mp_init_big_node(mp, p); + p=value(p); + mp_type(x_part_loc(p))=mp_known; value(x_part_loc(p))=x; + mp_type(y_part_loc(p))=mp_known; value(y_part_loc(p))=y; +} + +@ @<Additional cases of unary operators@>= +case ll_corner_op: + if ( ! mp_get_cur_bbox(mp) ) mp_bad_unary(mp, ll_corner_op); + else mp_pair_value(mp, mp_minx, mp_miny); + break; +case lr_corner_op: + if ( ! mp_get_cur_bbox(mp) ) mp_bad_unary(mp, lr_corner_op); + else mp_pair_value(mp, mp_maxx, mp_miny); + break; +case ul_corner_op: + if ( ! mp_get_cur_bbox(mp) ) mp_bad_unary(mp, ul_corner_op); + else mp_pair_value(mp, mp_minx, mp_maxy); + break; +case ur_corner_op: + if ( ! mp_get_cur_bbox(mp) ) mp_bad_unary(mp, ur_corner_op); + else mp_pair_value(mp, mp_maxx, mp_maxy); + break; + +@ Here is a function that sets |minx|, |maxx|, |miny|, |maxy| to the bounding +box of the current expression. The boolean result is |false| if the expression +has the wrong type. + +@<Declare unary action procedures@>= +static boolean mp_get_cur_bbox (MP mp) { + switch (mp->cur_type) { + case mp_picture_type: + mp_set_bbox(mp, mp->cur_exp,true); + if ( minx_val(mp->cur_exp)>maxx_val(mp->cur_exp) ) { + mp_minx=0; mp_maxx=0; mp_miny=0; mp_maxy=0; + } else { + mp_minx=minx_val(mp->cur_exp); + mp_maxx=maxx_val(mp->cur_exp); + mp_miny=miny_val(mp->cur_exp); + mp_maxy=maxy_val(mp->cur_exp); + } + break; + case mp_path_type: + mp_path_bbox(mp, mp->cur_exp); + break; + case mp_pen_type: + mp_pen_bbox(mp, mp->cur_exp); + break; + default: + return false; + } + return true; +} + +@ @<Additional cases of unary operators@>= +case read_from_op: +case close_from_op: + if ( mp->cur_type!=mp_string_type ) mp_bad_unary(mp, c); + else mp_do_read_or_close(mp,c); + break; + +@ Here is a routine that interprets |cur_exp| as a file name and tries to read +a line from the file or to close the file. + +@<Declare unary action procedures@>= +static void mp_do_read_or_close (MP mp,quarterword c) { + readf_index n,n0; /* indices for searching |rd_fname| */ + @<Find the |n| where |rd_fname[n]=cur_exp|; if |cur_exp| must be inserted, + call |start_read_input| and |goto found| or |not_found|@>; + mp_begin_file_reading(mp); + name=is_read; + if ( mp_input_ln(mp, mp->rd_file[n] ) ) + goto FOUND; + mp_end_file_reading(mp); +NOT_FOUND: + @<Record the end of file and set |cur_exp| to a dummy value@>; + return; +CLOSE_FILE: + mp_flush_cur_exp(mp, 0); mp->cur_type=mp_vacuous; + return; +FOUND: + mp_flush_cur_exp(mp, 0); + mp_finish_read(mp); +} + +@ Free slots in the |rd_file| and |rd_fname| arrays are marked with NULL's in +|rd_fname|. + +@<Find the |n| where |rd_fname[n]=cur_exp|...@>= +{ + char *fn; + n=mp->read_files; + n0=mp->read_files; + fn = str(mp->cur_exp); + while (mp_xstrcmp(fn,mp->rd_fname[n])!=0) { + if ( n>0 ) { + decr(n); + } else if ( c==close_from_op ) { + goto CLOSE_FILE; + } else { + if ( n0==mp->read_files ) { + if ( mp->read_files<mp->max_read_files ) { + incr(mp->read_files); + } else { + void **rd_file; + char **rd_fname; + readf_index l,k; + l = mp->max_read_files + (mp->max_read_files/4); + rd_file = xmalloc((l+1), sizeof(void *)); + rd_fname = xmalloc((l+1), sizeof(char *)); + for (k=0;k<=l;k++) { + if (k<=mp->max_read_files) { + rd_file[k]=mp->rd_file[k]; + rd_fname[k]=mp->rd_fname[k]; + } else { + rd_file[k]=0; + rd_fname[k]=NULL; + } + } + xfree(mp->rd_file); xfree(mp->rd_fname); + mp->max_read_files = l; + mp->rd_file = rd_file; + mp->rd_fname = rd_fname; + } + } + n=n0; + if ( mp_start_read_input(mp,fn,n) ) + goto FOUND; + else + goto NOT_FOUND; + } + if ( mp->rd_fname[n]==NULL ) { n0=n; } + } + if ( c==close_from_op ) { + (mp->close_file)(mp,mp->rd_file[n]); + goto NOT_FOUND; + } +} + +@ @<Record the end of file and set |cur_exp| to a dummy value@>= +xfree(mp->rd_fname[n]); +mp->rd_fname[n]=NULL; +if ( n==mp->read_files-1 ) mp->read_files=n; +if ( c==close_from_op ) + goto CLOSE_FILE; +mp_flush_cur_exp(mp, mp->eof_line); +mp->cur_type=mp_string_type + +@ The string denoting end-of-file is a one-byte string at position zero, by definition + +@<Glob...@>= +str_number eof_line; + +@ @<Set init...@>= +mp->eof_line=0; + +@ Finally, we have the operations that combine a capsule~|p| +with the current expression. + +@d binary_return { mp_finish_binary(mp, old_p, old_exp); return; } + +@c @<Declare binary action procedures@> +static void mp_finish_binary (MP mp, pointer old_p, pointer old_exp ){ + check_arith; + @<Recycle any sidestepped |independent| capsules@>; +} +static void mp_do_binary (MP mp,pointer p, quarterword c) { + pointer q,r,rr; /* for list manipulation */ + pointer old_p,old_exp; /* capsules to recycle */ + integer v; /* for numeric manipulation */ + check_arith; + if ( mp->internal[mp_tracing_commands]>two ) { + @<Trace the current binary operation@>; + } + @<Sidestep |independent| cases in capsule |p|@>; + @<Sidestep |independent| cases in the current expression@>; + switch (c) { + case plus: case minus: + @<Add or subtract the current expression from |p|@>; + break; + @<Additional cases of binary operators@>; + }; /* there are no other cases */ + mp_recycle_value(mp, p); + mp_free_node(mp, p,value_node_size); /* |return| to avoid this */ + mp_finish_binary(mp, old_p, old_exp); +} + +@ @<Declare binary action...@>= +static void mp_bad_binary (MP mp,pointer p, quarterword c) { + mp_disp_err(mp, p,""); + exp_err("Not implemented: "); +@.Not implemented...@> + if ( c>=min_of ) mp_print_op(mp, c); + mp_print_known_or_unknown_type(mp, mp_type(p),p); + if ( c>=min_of ) mp_print(mp, "of"); else mp_print_op(mp, c); + mp_print_known_or_unknown_type(mp, mp->cur_type,mp->cur_exp); + help3("I'm afraid I don't know how to apply that operation to that", + "combination of types. Continue, and I'll return the second", + "argument (see above) as the result of the operation."); + mp_put_get_error(mp); +} +static void mp_bad_envelope_pen (MP mp) { + mp_disp_err(mp, null,""); + exp_err("Not implemented: envelope(elliptical pen)of(path)"); +@.Not implemented...@> + help3("I'm afraid I don't know how to apply that operation to that", + "combination of types. Continue, and I'll return the second", + "argument (see above) as the result of the operation."); + mp_put_get_error(mp); +} + +@ @<Trace the current binary operation@>= +{ + mp_begin_diagnostic(mp); mp_print_nl(mp, "{("); + mp_print_exp(mp,p,0); /* show the operand, but not verbosely */ + mp_print_char(mp,xord(')')); mp_print_op(mp,c); mp_print_char(mp,xord('(')); + mp_print_exp(mp,null,0); mp_print(mp,")}"); + mp_end_diagnostic(mp, false); +} + +@ Several of the binary operations are potentially complicated by the +fact that |independent| values can sneak into capsules. For example, +we've seen an instance of this difficulty in the unary operation +of negation. In order to reduce the number of cases that need to be +handled, we first change the two operands (if necessary) +to rid them of |independent| components. The original operands are +put into capsules called |old_p| and |old_exp|, which will be +recycled after the binary operation has been safely carried out. + +@<Recycle any sidestepped |independent| capsules@>= +if ( old_p!=null ) { + mp_recycle_value(mp, old_p); mp_free_node(mp, old_p,value_node_size); +} +if ( old_exp!=null ) { + mp_recycle_value(mp, old_exp); mp_free_node(mp, old_exp,value_node_size); +} + +@ A big node is considered to be ``tarnished'' if it contains at least one +independent component. We will define a simple function called `|tarnished|' +that returns |null| if and only if its argument is not tarnished. + +@<Sidestep |independent| cases in capsule |p|@>= +switch (mp_type(p)) { +case mp_transform_type: +case mp_color_type: +case mp_cmykcolor_type: +case mp_pair_type: + old_p=mp_tarnished(mp, p); + break; +case mp_independent: old_p=mp_void; break; +default: old_p=null; break; +} +if ( old_p!=null ) { + q=mp_stash_cur_exp(mp); old_p=p; mp_make_exp_copy(mp, old_p); + p=mp_stash_cur_exp(mp); mp_unstash_cur_exp(mp, q); +} + +@ @<Sidestep |independent| cases in the current expression@>= +switch (mp->cur_type) { +case mp_transform_type: +case mp_color_type: +case mp_cmykcolor_type: +case mp_pair_type: + old_exp=mp_tarnished(mp, mp->cur_exp); + break; +case mp_independent:old_exp=mp_void; break; +default: old_exp=null; break; +} +if ( old_exp!=null ) { + old_exp=mp->cur_exp; mp_make_exp_copy(mp, old_exp); +} + +@ @<Declare binary action...@>= +static pointer mp_tarnished (MP mp,pointer p) { + pointer q; /* beginning of the big node */ + pointer r; /* current position in the big node */ + q=value(p); r=q+mp->big_node_size[mp_type(p)]; + do { + r=r-2; + if ( mp_type(r)==mp_independent ) return mp_void; + } while (r!=q); + return null; +} + +@ @<Add or subtract the current expression from |p|@>= +if ( (mp->cur_type<mp_color_type)||(mp_type(p)<mp_color_type) ) { + mp_bad_binary(mp, p,c); +} else { + if ((mp->cur_type>mp_pair_type)&&(mp_type(p)>mp_pair_type) ) { + mp_add_or_subtract(mp, p,null,c); + } else { + if ( mp->cur_type!=mp_type(p) ) { + mp_bad_binary(mp, p,c); + } else { + q=value(p); r=value(mp->cur_exp); + rr=r+mp->big_node_size[mp->cur_type]; + while ( r<rr ) { + mp_add_or_subtract(mp, q,r,c); + q=q+2; r=r+2; + } + } + } +} + +@ The first argument to |add_or_subtract| is the location of a value node +in a capsule or pair node that will soon be recycled. The second argument +is either a location within a pair or transform node of |cur_exp|, +or it is null (which means that |cur_exp| itself should be the second +argument). The third argument is either |plus| or |minus|. + +The sum or difference of the numeric quantities will replace the second +operand. Arithmetic overflow may go undetected; users aren't supposed to +be monkeying around with really big values. +@^overflow in arithmetic@> + +@<Declare binary action...@>= +@<Declare the procedure called |dep_finish|@> +static void mp_add_or_subtract (MP mp,pointer p, pointer q, quarterword c) { + quarterword s,t; /* operand types */ + pointer r; /* list traverser */ + integer v; /* second operand value */ + if ( q==null ) { + t=mp->cur_type; + if ( t<mp_dependent ) v=mp->cur_exp; else v=dep_list(mp->cur_exp); + } else { + t=mp_type(q); + if ( t<mp_dependent ) v=value(q); else v=dep_list(q); + } + if ( t==mp_known ) { + if ( c==minus ) negate(v); + if ( mp_type(p)==mp_known ) { + v=mp_slow_add(mp, value(p),v); + if ( q==null ) mp->cur_exp=v; else value(q)=v; + return; + } + @<Add a known value to the constant term of |dep_list(p)|@>; + } else { + if ( c==minus ) mp_negate_dep_list(mp, v); + @<Add operand |p| to the dependency list |v|@>; + } +} + +@ @<Add a known value to the constant term of |dep_list(p)|@>= +r=dep_list(p); +while ( mp_info(r)!=null ) r=mp_link(r); +value(r)=mp_slow_add(mp, value(r),v); +if ( q==null ) { + q=mp_get_node(mp, value_node_size); mp->cur_exp=q; mp->cur_type=mp_type(p); + mp_name_type(q)=mp_capsule; +} +dep_list(q)=dep_list(p); mp_type(q)=mp_type(p); +prev_dep(q)=prev_dep(p); mp_link(prev_dep(p))=q; +mp_type(p)=mp_known; /* this will keep the recycler from collecting non-garbage */ + +@ We prefer |dependent| lists to |mp_proto_dependent| ones, because it is +nice to retain the extra accuracy of |fraction| coefficients. +But we have to handle both kinds, and mixtures too. + +@<Add operand |p| to the dependency list |v|@>= +if ( mp_type(p)==mp_known ) { + @<Add the known |value(p)| to the constant term of |v|@>; +} else { + s=mp_type(p); r=dep_list(p); + if ( t==mp_dependent ) { + if ( s==mp_dependent ) { + if ( mp_max_coef(mp, r)+mp_max_coef(mp, v)<coef_bound ) { + v=mp_p_plus_q(mp, v,r,mp_dependent); goto DONE; + } + } /* |fix_needed| will necessarily be false */ + t=mp_proto_dependent; + v=mp_p_over_v(mp, v,unity,mp_dependent,mp_proto_dependent); + } + if ( s==mp_proto_dependent ) v=mp_p_plus_q(mp, v,r,mp_proto_dependent); + else v=mp_p_plus_fq(mp, v,unity,r,mp_proto_dependent,mp_dependent); + DONE: + @<Output the answer, |v| (which might have become |known|)@>; +} + +@ @<Add the known |value(p)| to the constant term of |v|@>= +{ + while ( mp_info(v)!=null ) v=mp_link(v); + value(v)=mp_slow_add(mp, value(p),value(v)); +} + +@ @<Output the answer, |v| (which might have become |known|)@>= +if ( q!=null ) mp_dep_finish(mp, v,q,t); +else { mp->cur_type=t; mp_dep_finish(mp, v,null,t); } + +@ Here's the current situation: The dependency list |v| of type |t| +should either be put into the current expression (if |q=null|) or +into location |q| within a pair node (otherwise). The destination (|cur_exp| +or |q|) formerly held a dependency list with the same +final pointer as the list |v|. + +@<Declare the procedure called |dep_finish|@>= +static void mp_dep_finish (MP mp, pointer v, pointer q, quarterword t) { + pointer p; /* the destination */ + scaled vv; /* the value, if it is |known| */ + if ( q==null ) p=mp->cur_exp; else p=q; + dep_list(p)=v; mp_type(p)=t; + if ( mp_info(v)==null ) { + vv=value(v); + if ( q==null ) { + mp_flush_cur_exp(mp, vv); + } else { + mp_recycle_value(mp, p); mp_type(q)=mp_known; value(q)=vv; + } + } else if ( q==null ) { + mp->cur_type=t; + } + if ( mp->fix_needed ) mp_fix_dependencies(mp); +} + +@ Let's turn now to the six basic relations of comparison. + +@<Additional cases of binary operators@>= +case less_than: case less_or_equal: case greater_than: +case greater_or_equal: case equal_to: case unequal_to: + check_arith; /* at this point |arith_error| should be |false|? */ + if ( (mp->cur_type>mp_pair_type)&&(mp_type(p)>mp_pair_type) ) { + mp_add_or_subtract(mp, p,null,minus); /* |cur_exp:=(p)-cur_exp| */ + } else if ( mp->cur_type!=mp_type(p) ) { + mp_bad_binary(mp, p,c); goto DONE; + } else if ( mp->cur_type==mp_string_type ) { + mp_flush_cur_exp(mp, mp_str_vs_str(mp, value(p),mp->cur_exp)); + } else if ((mp->cur_type==mp_unknown_string)|| + (mp->cur_type==mp_unknown_boolean) ) { + @<Check if unknowns have been equated@>; + } else if ( (mp->cur_type<=mp_pair_type)&&(mp->cur_type>=mp_transform_type)) { + @<Reduce comparison of big nodes to comparison of scalars@>; + } else if ( mp->cur_type==mp_boolean_type ) { + mp_flush_cur_exp(mp, mp->cur_exp-value(p)); + } else { + mp_bad_binary(mp, p,c); goto DONE; + } + @<Compare the current expression with zero@>; +DONE: + mp->arith_error=false; /* ignore overflow in comparisons */ + break; + +@ @<Compare the current expression with zero@>= +if ( mp->cur_type!=mp_known ) { + if ( mp->cur_type<mp_known ) { + mp_disp_err(mp, p,""); + help1("The quantities shown above have not been equated.") + } else { + help2("Oh dear. I can\'t decide if the expression above is positive,", + "negative, or zero. So this comparison test won't be `true'."); + } + exp_err("Unknown relation will be considered false"); +@.Unknown relation...@> + mp_put_get_flush_error(mp, false_code); +} else { + switch (c) { + case less_than: boolean_reset(mp->cur_exp<0); break; + case less_or_equal: boolean_reset(mp->cur_exp<=0); break; + case greater_than: boolean_reset(mp->cur_exp>0); break; + case greater_or_equal: boolean_reset(mp->cur_exp>=0); break; + case equal_to: boolean_reset(mp->cur_exp==0); break; + case unequal_to: boolean_reset(mp->cur_exp!=0); break; + }; /* there are no other cases */ +} +mp->cur_type=mp_boolean_type + +@ When two unknown strings are in the same ring, we know that they are +equal. Otherwise, we don't know whether they are equal or not, so we +make no change. + +@<Check if unknowns have been equated@>= +{ + q=value(mp->cur_exp); + while ( (q!=mp->cur_exp)&&(q!=p) ) q=value(q); + if ( q==p ) mp_flush_cur_exp(mp, 0); +} + +@ @<Reduce comparison of big nodes to comparison of scalars@>= +{ + q=value(p); r=value(mp->cur_exp); + rr=r+mp->big_node_size[mp->cur_type]-2; + while (1) { mp_add_or_subtract(mp, q,r,minus); + if ( mp_type(r)!=mp_known ) break; + if ( value(r)!=0 ) break; + if ( r==rr ) break; + q=q+2; r=r+2; + } + mp_take_part(mp, mp_name_type(r)+x_part-mp_x_part_sector); +} + +@ Here we use the sneaky fact that |and_op-false_code=or_op-true_code|. + +@<Additional cases of binary operators@>= +case and_op: +case or_op: + if ( (mp_type(p)!=mp_boolean_type)||(mp->cur_type!=mp_boolean_type) ) + mp_bad_binary(mp, p,c); + else if ( value(p)==c+false_code-and_op ) mp->cur_exp=value(p); + break; + +@ @<Additional cases of binary operators@>= +case times: + if ( (mp->cur_type<mp_color_type)||(mp_type(p)<mp_color_type) ) { + mp_bad_binary(mp, p,times); + } else if ( (mp->cur_type==mp_known)||(mp_type(p)==mp_known) ) { + @<Multiply when at least one operand is known@>; + } else if ( (mp_nice_color_or_pair(mp, p,mp_type(p))&&(mp->cur_type>mp_pair_type)) + ||(mp_nice_color_or_pair(mp, mp->cur_exp,mp->cur_type)&& + (mp_type(p)>mp_pair_type)) ) { + mp_hard_times(mp, p); + binary_return; + } else { + mp_bad_binary(mp, p,times); + } + break; + +@ @<Multiply when at least one operand is known@>= +{ + if ( mp_type(p)==mp_known ) { + v=value(p); mp_free_node(mp, p,value_node_size); + } else { + v=mp->cur_exp; mp_unstash_cur_exp(mp, p); + } + if ( mp->cur_type==mp_known ) { + mp->cur_exp=mp_take_scaled(mp, mp->cur_exp,v); + } else if ( (mp->cur_type==mp_pair_type)|| + (mp->cur_type==mp_color_type)|| + (mp->cur_type==mp_cmykcolor_type) ) { + p=value(mp->cur_exp)+mp->big_node_size[mp->cur_type]; + do { + p=p-2; mp_dep_mult(mp, p,v,true); + } while (p!=value(mp->cur_exp)); + } else { + mp_dep_mult(mp, null,v,true); + } + binary_return; +} + +@ @<Declare binary action...@>= +static void mp_dep_mult (MP mp,pointer p, integer v, boolean v_is_scaled) { + pointer q; /* the dependency list being multiplied by |v| */ + quarterword s,t; /* its type, before and after */ + if ( p==null ) { + q=mp->cur_exp; + } else if ( mp_type(p)!=mp_known ) { + q=p; + } else { + if ( v_is_scaled ) value(p)=mp_take_scaled(mp, value(p),v); + else value(p)=mp_take_fraction(mp, value(p),v); + return; + }; + t=mp_type(q); q=dep_list(q); s=t; + if ( t==mp_dependent ) if ( v_is_scaled ) + if (mp_ab_vs_cd(mp, mp_max_coef(mp,q),abs(v),coef_bound-1,unity)>=0 ) + t=mp_proto_dependent; + q=mp_p_times_v(mp, q,v,s,t,v_is_scaled); + mp_dep_finish(mp, q,p,t); +} + +@ Here is a routine that is similar to |times|; but it is invoked only +internally, when |v| is a |fraction| whose magnitude is at most~1, +and when |cur_type>=mp_color_type|. + +@c +static void mp_frac_mult (MP mp,scaled n, scaled d) { + /* multiplies |cur_exp| by |n/d| */ + pointer p; /* a pair node */ + pointer old_exp; /* a capsule to recycle */ + fraction v; /* |n/d| */ + if ( mp->internal[mp_tracing_commands]>two ) { + @<Trace the fraction multiplication@>; + } + switch (mp->cur_type) { + case mp_transform_type: + case mp_color_type: + case mp_cmykcolor_type: + case mp_pair_type: + old_exp=mp_tarnished(mp, mp->cur_exp); + break; + case mp_independent: old_exp=mp_void; break; + default: old_exp=null; break; + } + if ( old_exp!=null ) { + old_exp=mp->cur_exp; mp_make_exp_copy(mp, old_exp); + } + v=mp_make_fraction(mp, n,d); + if ( mp->cur_type==mp_known ) { + mp->cur_exp=mp_take_fraction(mp, mp->cur_exp,v); + } else if ( mp->cur_type<=mp_pair_type ) { + p=value(mp->cur_exp)+mp->big_node_size[mp->cur_type]; + do { + p=p-2; + mp_dep_mult(mp, p,v,false); + } while (p!=value(mp->cur_exp)); + } else { + mp_dep_mult(mp, null,v,false); + } + if ( old_exp!=null ) { + mp_recycle_value(mp, old_exp); + mp_free_node(mp, old_exp,value_node_size); + } +} + +@ @<Trace the fraction multiplication@>= +{ + mp_begin_diagnostic(mp); + mp_print_nl(mp, "{("); mp_print_scaled(mp,n); mp_print_char(mp,xord('/')); + mp_print_scaled(mp,d); mp_print(mp,")*("); mp_print_exp(mp,null,0); + mp_print(mp,")}"); + mp_end_diagnostic(mp, false); +} + +@ The |hard_times| routine multiplies a nice color or pair by a dependency list. + +@<Declare binary action procedures@>= +static void mp_hard_times (MP mp,pointer p) { + pointer q; /* a copy of the dependent variable |p| */ + pointer r; /* a component of the big node for the nice color or pair */ + scaled v; /* the known value for |r| */ + if ( mp_type(p)<=mp_pair_type ) { + q=mp_stash_cur_exp(mp); mp_unstash_cur_exp(mp, p); p=q; + }; /* now |cur_type=mp_pair_type| or |cur_type=mp_color_type| */ + r=value(mp->cur_exp)+mp->big_node_size[mp->cur_type]; + while (1) { + r=r-2; + v=value(r); + mp_type(r)=mp_type(p); + if ( r==value(mp->cur_exp) ) + break; + mp_new_dep(mp, r,mp_copy_dep_list(mp, dep_list(p))); + mp_dep_mult(mp, r,v,true); + } + mp->mem[value_loc(r)]=mp->mem[value_loc(p)]; + mp_link(prev_dep(p))=r; + mp_free_node(mp, p,value_node_size); + mp_dep_mult(mp, r,v,true); +} + +@ @<Additional cases of binary operators@>= +case over: + if ( (mp->cur_type!=mp_known)||(mp_type(p)<mp_color_type) ) { + mp_bad_binary(mp, p,over); + } else { + v=mp->cur_exp; mp_unstash_cur_exp(mp, p); + if ( v==0 ) { + @<Squeal about division by zero@>; + } else { + if ( mp->cur_type==mp_known ) { + mp->cur_exp=mp_make_scaled(mp, mp->cur_exp,v); + } else if ( mp->cur_type<=mp_pair_type ) { + p=value(mp->cur_exp)+mp->big_node_size[mp->cur_type]; + do { + p=p-2; mp_dep_div(mp, p,v); + } while (p!=value(mp->cur_exp)); + } else { + mp_dep_div(mp, null,v); + } + } + binary_return; + } + break; + +@ @<Declare binary action...@>= +static void mp_dep_div (MP mp,pointer p, scaled v) { + pointer q; /* the dependency list being divided by |v| */ + quarterword s,t; /* its type, before and after */ + if ( p==null ) q=mp->cur_exp; + else if ( mp_type(p)!=mp_known ) q=p; + else { value(p)=mp_make_scaled(mp, value(p),v); return; }; + t=mp_type(q); q=dep_list(q); s=t; + if ( t==mp_dependent ) + if ( mp_ab_vs_cd(mp, mp_max_coef(mp,q),unity,coef_bound-1,abs(v))>=0 ) + t=mp_proto_dependent; + q=mp_p_over_v(mp, q,v,s,t); + mp_dep_finish(mp, q,p,t); +} + +@ @<Squeal about division by zero@>= +{ + exp_err("Division by zero"); +@.Division by zero@> + help2("You're trying to divide the quantity shown above the error", + "message by zero. I'm going to divide it by one instead."); + mp_put_get_error(mp); +} + +@ @<Additional cases of binary operators@>= +case pythag_add: +case pythag_sub: + if ( (mp->cur_type==mp_known)&&(mp_type(p)==mp_known) ) { + if ( c==pythag_add ) mp->cur_exp=mp_pyth_add(mp, value(p),mp->cur_exp); + else mp->cur_exp=mp_pyth_sub(mp, value(p),mp->cur_exp); + } else mp_bad_binary(mp, p,c); + break; + +@ The next few sections of the program deal with affine transformations +of coordinate data. + +@<Additional cases of binary operators@>= +case rotated_by: case slanted_by: +case scaled_by: case shifted_by: case transformed_by: +case x_scaled: case y_scaled: case z_scaled: + if ( mp_type(p)==mp_path_type ) { + path_trans(c,p); binary_return; + } else if ( mp_type(p)==mp_pen_type ) { + pen_trans(c,p); + mp->cur_exp=mp_convex_hull(mp, mp->cur_exp); + /* rounding error could destroy convexity */ + binary_return; + } else if ( (mp_type(p)==mp_pair_type)||(mp_type(p)==mp_transform_type) ) { + mp_big_trans(mp, p,c); + } else if ( mp_type(p)==mp_picture_type ) { + mp_do_edges_trans(mp, p,c); binary_return; + } else { + mp_bad_binary(mp, p,c); + } + break; + +@ Let |c| be one of the eight transform operators. The procedure call +|set_up_trans(c)| first changes |cur_exp| to a transform that corresponds to +|c| and the original value of |cur_exp|. (In particular, |cur_exp| doesn't +change at all if |c=transformed_by|.) + +Then, if all components of the resulting transform are |known|, they are +moved to the global variables |txx|, |txy|, |tyx|, |tyy|, |tx|, |ty|; +and |cur_exp| is changed to the known value zero. + +@<Declare binary action...@>= +static void mp_set_up_trans (MP mp,quarterword c) { + pointer p,q,r; /* list manipulation registers */ + if ( (c!=transformed_by)||(mp->cur_type!=mp_transform_type) ) { + @<Put the current transform into |cur_exp|@>; + } + @<If the current transform is entirely known, stash it in global variables; + otherwise |return|@>; +} + +@ @<Glob...@>= +scaled txx; +scaled txy; +scaled tyx; +scaled tyy; +scaled tx; +scaled ty; /* current transform coefficients */ + +@ @<Put the current transform...@>= +{ + p=mp_stash_cur_exp(mp); + mp->cur_exp=mp_id_transform(mp); + mp->cur_type=mp_transform_type; + q=value(mp->cur_exp); + switch (c) { + @<For each of the eight cases, change the relevant fields of |cur_exp| + and |goto done|; + but do nothing if capsule |p| doesn't have the appropriate type@>; + }; /* there are no other cases */ + mp_disp_err(mp, p,"Improper transformation argument"); +@.Improper transformation argument@> + help3("The expression shown above has the wrong type,", + "so I can\'t transform anything using it.", + "Proceed, and I'll omit the transformation."); + mp_put_get_error(mp); +DONE: + mp_recycle_value(mp, p); + mp_free_node(mp, p,value_node_size); +} + +@ @<If the current transform is entirely known, ...@>= +q=value(mp->cur_exp); r=q+transform_node_size; +do { + r=r-2; + if ( mp_type(r)!=mp_known ) return; +} while (r!=q); +mp->txx=value(xx_part_loc(q)); +mp->txy=value(xy_part_loc(q)); +mp->tyx=value(yx_part_loc(q)); +mp->tyy=value(yy_part_loc(q)); +mp->tx=value(x_part_loc(q)); +mp->ty=value(y_part_loc(q)); +mp_flush_cur_exp(mp, 0) + +@ @<For each of the eight cases...@>= +case rotated_by: + if ( mp_type(p)==mp_known ) + @<Install sines and cosines, then |goto done|@>; + break; +case slanted_by: + if ( mp_type(p)>mp_pair_type ) { + mp_install(mp, xy_part_loc(q),p); goto DONE; + }; + break; +case scaled_by: + if ( mp_type(p)>mp_pair_type ) { + mp_install(mp, xx_part_loc(q),p); mp_install(mp, yy_part_loc(q),p); + goto DONE; + }; + break; +case shifted_by: + if ( mp_type(p)==mp_pair_type ) { + r=value(p); mp_install(mp, x_part_loc(q),x_part_loc(r)); + mp_install(mp, y_part_loc(q),y_part_loc(r)); goto DONE; + }; + break; +case x_scaled: + if ( mp_type(p)>mp_pair_type ) { + mp_install(mp, xx_part_loc(q),p); goto DONE; + }; + break; +case y_scaled: + if ( mp_type(p)>mp_pair_type ) { + mp_install(mp, yy_part_loc(q),p); goto DONE; + }; + break; +case z_scaled: + if ( mp_type(p)==mp_pair_type ) + @<Install a complex multiplier, then |goto done|@>; + break; +case transformed_by: + break; + + +@ @<Install sines and cosines, then |goto done|@>= +{ mp_n_sin_cos(mp, (value(p) % three_sixty_units)*16); + value(xx_part_loc(q))=mp_round_fraction(mp, mp->n_cos); + value(yx_part_loc(q))=mp_round_fraction(mp, mp->n_sin); + value(xy_part_loc(q))=-value(yx_part_loc(q)); + value(yy_part_loc(q))=value(xx_part_loc(q)); + goto DONE; +} + +@ @<Install a complex multiplier, then |goto done|@>= +{ + r=value(p); + mp_install(mp, xx_part_loc(q),x_part_loc(r)); + mp_install(mp, yy_part_loc(q),x_part_loc(r)); + mp_install(mp, yx_part_loc(q),y_part_loc(r)); + if ( mp_type(y_part_loc(r))==mp_known ) negate(value(y_part_loc(r))); + else mp_negate_dep_list(mp, dep_list(y_part_loc(r))); + mp_install(mp, xy_part_loc(q),y_part_loc(r)); + goto DONE; +} + +@ Procedure |set_up_known_trans| is like |set_up_trans|, but it +insists that the transformation be entirely known. + +@<Declare binary action...@>= +static void mp_set_up_known_trans (MP mp,quarterword c) { + mp_set_up_trans(mp, c); + if ( mp->cur_type!=mp_known ) { + exp_err("Transform components aren't all known"); +@.Transform components...@> + help3("I'm unable to apply a partially specified transformation", + "except to a fully known pair or transform.", + "Proceed, and I'll omit the transformation."); + mp_put_get_flush_error(mp, 0); + mp->txx=unity; mp->txy=0; mp->tyx=0; mp->tyy=unity; + mp->tx=0; mp->ty=0; + } +} + +@ Here's a procedure that applies the transform |txx..ty| to a pair of +coordinates in locations |p| and~|q|. + +@<Declare binary action...@>= +static void mp_trans (MP mp,pointer p, pointer q) { + scaled v; /* the new |x| value */ + v=mp_take_scaled(mp, mp->mem[p].sc,mp->txx)+ + mp_take_scaled(mp, mp->mem[q].sc,mp->txy)+mp->tx; + mp->mem[q].sc=mp_take_scaled(mp, mp->mem[p].sc,mp->tyx)+ + mp_take_scaled(mp, mp->mem[q].sc,mp->tyy)+mp->ty; + mp->mem[p].sc=v; +} + +@ The simplest transformation procedure applies a transform to all +coordinates of a path. The |path_trans(c)(p)| macro applies +a transformation defined by |cur_exp| and the transform operator |c| +to the path~|p|. + +@d path_trans(A,B) { mp_set_up_known_trans(mp, (A)); + mp_unstash_cur_exp(mp, (B)); + mp_do_path_trans(mp, mp->cur_exp); } + +@<Declare binary action...@>= +static void mp_do_path_trans (MP mp,pointer p) { + pointer q; /* list traverser */ + q=p; + do { + if ( mp_left_type(q)!=mp_endpoint ) + mp_trans(mp, q+3,q+4); /* that's |mp_left_x| and |mp_left_y| */ + mp_trans(mp, q+1,q+2); /* that's |mp_x_coord| and |mp_y_coord| */ + if ( mp_right_type(q)!=mp_endpoint ) + mp_trans(mp, q+5,q+6); /* that's |mp_right_x| and |mp_right_y| */ +@^data structure assumptions@> + q=mp_link(q); + } while (q!=p); +} + +@ Transforming a pen is very similar, except that there are no |mp_left_type| +and |mp_right_type| fields. + +@d pen_trans(A,B) { mp_set_up_known_trans(mp, (A)); + mp_unstash_cur_exp(mp, (B)); + mp_do_pen_trans(mp, mp->cur_exp); } + +@<Declare binary action...@>= +static void mp_do_pen_trans (MP mp,pointer p) { + pointer q; /* list traverser */ + if ( pen_is_elliptical(p) ) { + mp_trans(mp, p+3,p+4); /* that's |mp_left_x| and |mp_left_y| */ + mp_trans(mp, p+5,p+6); /* that's |mp_right_x| and |mp_right_y| */ + }; + q=p; + do { + mp_trans(mp, q+1,q+2); /* that's |mp_x_coord| and |mp_y_coord| */ +@^data structure assumptions@> + q=mp_link(q); + } while (q!=p); +} + +@ The next transformation procedure applies to edge structures. It will do +any transformation, but the results may be substandard if the picture contains +text that uses downloaded bitmap fonts. The binary action procedure is +|do_edges_trans|, but we also need a function that just scales a picture. +That routine is |scale_edges|. Both it and the underlying routine |edges_trans| +should be thought of as procedures that update an edge structure |h|, except +that they have to return a (possibly new) structure because of the need to call +|private_edges|. + +@<Declare binary action...@>= +static pointer mp_edges_trans (MP mp, pointer h) { + pointer q; /* the object being transformed */ + pointer r,s; /* for list manipulation */ + scaled sx,sy; /* saved transformation parameters */ + scaled sqdet; /* square root of determinant for |dash_scale| */ + integer sgndet; /* sign of the determinant */ + scaled v; /* a temporary value */ + h=mp_private_edges(mp, h); + sqdet=mp_sqrt_det(mp, mp->txx,mp->txy,mp->tyx,mp->tyy); + sgndet=mp_ab_vs_cd(mp, mp->txx,mp->tyy,mp->txy,mp->tyx); + if ( dash_list(h)!=null_dash ) { + @<Try to transform the dash list of |h|@>; + } + @<Make the bounding box of |h| unknown if it can't be updated properly + without scanning the whole structure@>; + q=mp_link(dummy_loc(h)); + while ( q!=null ) { + @<Transform graphical object |q|@>; + q=mp_link(q); + } + return h; +} +static void mp_do_edges_trans (MP mp,pointer p, quarterword c) { + mp_set_up_known_trans(mp, c); + value(p)=mp_edges_trans(mp, value(p)); + mp_unstash_cur_exp(mp, p); +} +static void mp_scale_edges (MP mp) { + mp->txx=mp->se_sf; mp->tyy=mp->se_sf; + mp->txy=0; mp->tyx=0; mp->tx=0; mp->ty=0; + mp->se_pic=mp_edges_trans(mp, mp->se_pic); +} + +@ @<Try to transform the dash list of |h|@>= +if ( (mp->txy!=0)||(mp->tyx!=0)|| + (mp->ty!=0)||(abs(mp->txx)!=abs(mp->tyy))) { + mp_flush_dash_list(mp, h); +} else { + if ( mp->txx<0 ) { @<Reverse the dash list of |h|@>; } + @<Scale the dash list by |txx| and shift it by |tx|@>; + dash_y(h)=mp_take_scaled(mp, dash_y(h),abs(mp->tyy)); +} + +@ @<Reverse the dash list of |h|@>= +{ + r=dash_list(h); + dash_list(h)=null_dash; + while ( r!=null_dash ) { + s=r; r=mp_link(r); + v=start_x(s); start_x(s)=stop_x(s); stop_x(s)=v; + mp_link(s)=dash_list(h); + dash_list(h)=s; + } +} + +@ @<Scale the dash list by |txx| and shift it by |tx|@>= +r=dash_list(h); +while ( r!=null_dash ) { + start_x(r)=mp_take_scaled(mp, start_x(r),mp->txx)+mp->tx; + stop_x(r)=mp_take_scaled(mp, stop_x(r),mp->txx)+mp->tx; + r=mp_link(r); +} + +@ @<Make the bounding box of |h| unknown if it can't be updated properly...@>= +if ( (mp->txx==0)&&(mp->tyy==0) ) { + @<Swap the $x$ and $y$ parameters in the bounding box of |h|@>; +} else if ( (mp->txy!=0)||(mp->tyx!=0) ) { + mp_init_bbox(mp, h); + goto DONE1; +} +if ( minx_val(h)<=maxx_val(h) ) { + @<Scale the bounding box by |txx+txy| and |tyx+tyy|; then shift by + |(tx,ty)|@>; +} +DONE1: + + + +@ @<Swap the $x$ and $y$ parameters in the bounding box of |h|@>= +{ + v=minx_val(h); minx_val(h)=miny_val(h); miny_val(h)=v; + v=maxx_val(h); maxx_val(h)=maxy_val(h); maxy_val(h)=v; +} + +@ The sum ``|txx+txy|'' is whichever of |txx| or |txy| is nonzero. The other +sum is similar. + +@<Scale the bounding box by |txx+txy| and |tyx+tyy|; then shift...@>= +{ + minx_val(h)=mp_take_scaled(mp, minx_val(h),mp->txx+mp->txy)+mp->tx; + maxx_val(h)=mp_take_scaled(mp, maxx_val(h),mp->txx+mp->txy)+mp->tx; + miny_val(h)=mp_take_scaled(mp, miny_val(h),mp->tyx+mp->tyy)+mp->ty; + maxy_val(h)=mp_take_scaled(mp, maxy_val(h),mp->tyx+mp->tyy)+mp->ty; + if ( mp->txx+mp->txy<0 ) { + v=minx_val(h); minx_val(h)=maxx_val(h); maxx_val(h)=v; + } + if ( mp->tyx+mp->tyy<0 ) { + v=miny_val(h); miny_val(h)=maxy_val(h); maxy_val(h)=v; + } +} + +@ Now we ready for the main task of transforming the graphical objects in edge +structure~|h|. + +@<Transform graphical object |q|@>= +switch (mp_type(q)) { +case mp_fill_code: case mp_stroked_code: + mp_do_path_trans(mp, mp_path_p(q)); + @<Transform |mp_pen_p(q)|, making sure polygonal pens stay counter-clockwise@>; + break; +case mp_start_clip_code: case mp_start_bounds_code: + mp_do_path_trans(mp, mp_path_p(q)); + break; +case mp_text_code: + r=text_tx_loc(q); + @<Transform the compact transformation starting at |r|@>; + break; +case mp_stop_clip_code: case mp_stop_bounds_code: + break; +} /* there are no other cases */ + +@ Note that the shift parameters |(tx,ty)| apply only to the path being stroked. +The |dash_scale| has to be adjusted to scale the dash lengths in |mp_dash_p(q)| +since the \ps\ output procedures will try to compensate for the transformation +we are applying to |mp_pen_p(q)|. Since this compensation is based on the square +root of the determinant, |sqdet| is the appropriate factor. + +@<Transform |mp_pen_p(q)|, making sure...@>= +if ( mp_pen_p(q)!=null ) { + sx=mp->tx; sy=mp->ty; + mp->tx=0; mp->ty=0; + mp_do_pen_trans(mp, mp_pen_p(q)); + if ( ((mp_type(q)==mp_stroked_code)&&(mp_dash_p(q)!=null)) ) + dash_scale(q)=mp_take_scaled(mp, dash_scale(q),sqdet); + if ( ! pen_is_elliptical(mp_pen_p(q)) ) + if ( sgndet<0 ) + mp_pen_p(q)=mp_make_pen(mp, mp_copy_path(mp, mp_pen_p(q)),true); + /* this unreverses the pen */ + mp->tx=sx; mp->ty=sy; +} + +@ This uses the fact that transformations are stored in the order +|(tx,ty,txx,txy,tyx,tyy)|. +@^data structure assumptions@> + +@<Transform the compact transformation starting at |r|@>= +mp_trans(mp, r,r+1); +sx=mp->tx; sy=mp->ty; +mp->tx=0; mp->ty=0; +mp_trans(mp, r+2,r+4); +mp_trans(mp, r+3,r+5); +mp->tx=sx; mp->ty=sy + +@ The hard cases of transformation occur when big nodes are involved, +and when some of their components are unknown. + +@<Declare binary action...@>= +@<Declare subroutines needed by |big_trans|@> +static void mp_big_trans (MP mp,pointer p, quarterword c) { + pointer q,r,pp,qq; /* list manipulation registers */ + quarterword s; /* size of a big node */ + s=mp->big_node_size[mp_type(p)]; q=value(p); r=q+s; + do { + r=r-2; + if ( mp_type(r)!=mp_known ) { + @<Transform an unknown big node and |return|@>; + } + } while (r!=q); + @<Transform a known big node@>; +} /* node |p| will now be recycled by |do_binary| */ + +@ @<Transform an unknown big node and |return|@>= +{ + mp_set_up_known_trans(mp, c); mp_make_exp_copy(mp, p); + r=value(mp->cur_exp); + if ( mp->cur_type==mp_transform_type ) { + mp_bilin1(mp, yy_part_loc(r),mp->tyy,xy_part_loc(q),mp->tyx,0); + mp_bilin1(mp, yx_part_loc(r),mp->tyy,xx_part_loc(q),mp->tyx,0); + mp_bilin1(mp, xy_part_loc(r),mp->txx,yy_part_loc(q),mp->txy,0); + mp_bilin1(mp, xx_part_loc(r),mp->txx,yx_part_loc(q),mp->txy,0); + } + mp_bilin1(mp, y_part_loc(r),mp->tyy,x_part_loc(q),mp->tyx,mp->ty); + mp_bilin1(mp, x_part_loc(r),mp->txx,y_part_loc(q),mp->txy,mp->tx); + return; +} + +@ Let |p| point to a two-word value field inside a big node of |cur_exp|, +and let |q| point to a another value field. The |bilin1| procedure +replaces |p| by $p\cdot t+q\cdot u+\delta$. + +@<Declare subroutines needed by |big_trans|@>= +static void mp_bilin1 (MP mp, pointer p, scaled t, pointer q, + scaled u, scaled delta) { + pointer r; /* list traverser */ + if ( t!=unity ) mp_dep_mult(mp, p,t,true); + if ( u!=0 ) { + if ( mp_type(q)==mp_known ) { + delta+=mp_take_scaled(mp, value(q),u); + } else { + @<Ensure that |type(p)=mp_proto_dependent|@>; + dep_list(p)=mp_p_plus_fq(mp, dep_list(p),u,dep_list(q), + mp_proto_dependent,mp_type(q)); + } + } + if ( mp_type(p)==mp_known ) { + value(p)+=delta; + } else { + r=dep_list(p); + while ( mp_info(r)!=null ) r=mp_link(r); + delta+=value(r); + if ( r!=dep_list(p) ) value(r)=delta; + else { mp_recycle_value(mp, p); mp_type(p)=mp_known; value(p)=delta; }; + } + if ( mp->fix_needed ) mp_fix_dependencies(mp); +} + +@ @<Ensure that |type(p)=mp_proto_dependent|@>= +if ( mp_type(p)!=mp_proto_dependent ) { + if ( mp_type(p)==mp_known ) + mp_new_dep(mp, p,mp_const_dependency(mp, value(p))); + else + dep_list(p)=mp_p_times_v(mp, dep_list(p),unity,mp_dependent, + mp_proto_dependent,true); + mp_type(p)=mp_proto_dependent; +} + +@ @<Transform a known big node@>= +mp_set_up_trans(mp, c); +if ( mp->cur_type==mp_known ) { + @<Transform known by known@>; +} else { + pp=mp_stash_cur_exp(mp); qq=value(pp); + mp_make_exp_copy(mp, p); r=value(mp->cur_exp); + if ( mp->cur_type==mp_transform_type ) { + mp_bilin2(mp, yy_part_loc(r),yy_part_loc(qq), + value(xy_part_loc(q)),yx_part_loc(qq),null); + mp_bilin2(mp, yx_part_loc(r),yy_part_loc(qq), + value(xx_part_loc(q)),yx_part_loc(qq),null); + mp_bilin2(mp, xy_part_loc(r),xx_part_loc(qq), + value(yy_part_loc(q)),xy_part_loc(qq),null); + mp_bilin2(mp, xx_part_loc(r),xx_part_loc(qq), + value(yx_part_loc(q)),xy_part_loc(qq),null); + }; + mp_bilin2(mp, y_part_loc(r),yy_part_loc(qq), + value(x_part_loc(q)),yx_part_loc(qq),y_part_loc(qq)); + mp_bilin2(mp, x_part_loc(r),xx_part_loc(qq), + value(y_part_loc(q)),xy_part_loc(qq),x_part_loc(qq)); + mp_recycle_value(mp, pp); mp_free_node(mp, pp,value_node_size); +} + +@ Let |p| be a |mp_proto_dependent| value whose dependency list ends +at |dep_final|. The following procedure adds |v| times another +numeric quantity to~|p|. + +@<Declare subroutines needed by |big_trans|@>= +static void mp_add_mult_dep (MP mp,pointer p, scaled v, pointer r) { + if ( mp_type(r)==mp_known ) { + value(mp->dep_final)+=mp_take_scaled(mp, value(r),v); + } else { + dep_list(p)=mp_p_plus_fq(mp, dep_list(p),v,dep_list(r), + mp_proto_dependent,mp_type(r)); + if ( mp->fix_needed ) mp_fix_dependencies(mp); + } +} + +@ The |bilin2| procedure is something like |bilin1|, but with known +and unknown quantities reversed. Parameter |p| points to a value field +within the big node for |cur_exp|; and |type(p)=mp_known|. Parameters +|t| and~|u| point to value fields elsewhere; so does parameter~|q|, +unless it is |null| (which stands for zero). Location~|p| will be +replaced by $p\cdot t+v\cdot u+q$. + +@<Declare subroutines needed by |big_trans|@>= +static void mp_bilin2 (MP mp,pointer p, pointer t, scaled v, + pointer u, pointer q) { + scaled vv; /* temporary storage for |value(p)| */ + vv=value(p); mp_type(p)=mp_proto_dependent; + mp_new_dep(mp, p,mp_const_dependency(mp, 0)); /* this sets |dep_final| */ + if ( vv!=0 ) + mp_add_mult_dep(mp, p,vv,t); /* |dep_final| doesn't change */ + if ( v!=0 ) mp_add_mult_dep(mp, p,v,u); + if ( q!=null ) mp_add_mult_dep(mp, p,unity,q); + if ( dep_list(p)==mp->dep_final ) { + vv=value(mp->dep_final); mp_recycle_value(mp, p); + mp_type(p)=mp_known; value(p)=vv; + } +} + +@ @<Transform known by known@>= +{ + mp_make_exp_copy(mp, p); r=value(mp->cur_exp); + if ( mp->cur_type==mp_transform_type ) { + mp_bilin3(mp, yy_part_loc(r),mp->tyy,value(xy_part_loc(q)),mp->tyx,0); + mp_bilin3(mp, yx_part_loc(r),mp->tyy,value(xx_part_loc(q)),mp->tyx,0); + mp_bilin3(mp, xy_part_loc(r),mp->txx,value(yy_part_loc(q)),mp->txy,0); + mp_bilin3(mp, xx_part_loc(r),mp->txx,value(yx_part_loc(q)),mp->txy,0); + } + mp_bilin3(mp, y_part_loc(r),mp->tyy,value(x_part_loc(q)),mp->tyx,mp->ty); + mp_bilin3(mp, x_part_loc(r),mp->txx,value(y_part_loc(q)),mp->txy,mp->tx); +} + +@ Finally, in |bilin3| everything is |known|. + +@<Declare subroutines needed by |big_trans|@>= +static void mp_bilin3 (MP mp,pointer p, scaled t, + scaled v, scaled u, scaled delta) { + if ( t!=unity ) + delta+=mp_take_scaled(mp, value(p),t); + else + delta+=value(p); + if ( u!=0 ) value(p)=delta+mp_take_scaled(mp, v,u); + else value(p)=delta; +} + +@ @<Additional cases of binary operators@>= +case concatenate: + if ( (mp->cur_type==mp_string_type)&&(mp_type(p)==mp_string_type) ) mp_cat(mp, p); + else mp_bad_binary(mp, p,concatenate); + break; +case substring_of: + if ( mp_nice_pair(mp, p,mp_type(p))&&(mp->cur_type==mp_string_type) ) + mp_chop_string(mp, value(p)); + else mp_bad_binary(mp, p,substring_of); + break; +case subpath_of: + if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + if ( mp_nice_pair(mp, p,mp_type(p))&&(mp->cur_type==mp_path_type) ) + mp_chop_path(mp, value(p)); + else mp_bad_binary(mp, p,subpath_of); + break; + +@ @<Declare binary action...@>= +static void mp_cat (MP mp,pointer p) { + str_number a,b; /* the strings being concatenated */ + integer k; /* run length */ + integer needed; + a=value(p); b=mp->cur_exp; k=length(a); + needed=mp->pool_ptr+k+length(b); + /* this will free some memory, hopefully */ + if (mp->pool_ptr>(11*mp->old_pool_size)/10) { + mp->old_pool_size = mp->pool_ptr; + mp_do_compaction(mp, mp->pool_size); + } + if ( needed > mp->max_pool_ptr ) { + if ( needed > mp->pool_size ) { + mp_reallocate_pool(mp,needed); + } + mp->max_pool_ptr=needed; + } + memcpy(mp->str_pool+mp->pool_ptr, mp->str_pool+mp->str_start[a],(size_t)k); + mp->pool_ptr+=k; + k=length(b); + memcpy(mp->str_pool+mp->pool_ptr, mp->str_pool+mp->str_start[b],(size_t)k); + mp->pool_ptr+=k; + mp->cur_exp=mp_make_string(mp); delete_str_ref(b); +} + +@ @<Declare binary action...@>= +static void mp_chop_string (MP mp,pointer p) { + integer a, b; /* start and stop points */ + integer l; /* length of the original string */ + integer k; /* runs from |a| to |b| */ + str_number s; /* the original string */ + boolean reversed; /* was |a>b|? */ + a=mp_round_unscaled(mp, value(x_part_loc(p))); + b=mp_round_unscaled(mp, value(y_part_loc(p))); + if ( a<=b ) reversed=false; + else { reversed=true; k=a; a=b; b=k; }; + s=mp->cur_exp; l=length(s); + if ( a<0 ) { + a=0; + if ( b<0 ) b=0; + } + if ( b>l ) { + b=l; + if ( a>l ) a=l; + } + str_room(b-a); + if ( reversed ) { + for (k=mp->str_start[s]+b-1;k>=mp->str_start[s]+a;k--) { + append_char(mp->str_pool[k]); + } + } else { + for (k=mp->str_start[s]+a;k<mp->str_start[s]+b;k++) { + append_char(mp->str_pool[k]); + } + } + mp->cur_exp=mp_make_string(mp); delete_str_ref(s); +} + +@ @<Declare binary action...@>= +static void mp_chop_path (MP mp,pointer p) { + pointer q; /* a knot in the original path */ + pointer pp,qq,rr,ss; /* link variables for copies of path nodes */ + scaled a,b,k,l; /* indices for chopping */ + boolean reversed; /* was |a>b|? */ + l=mp_path_length(mp); a=value(x_part_loc(p)); b=value(y_part_loc(p)); + if ( a<=b ) reversed=false; + else { reversed=true; k=a; a=b; b=k; }; + @<Dispense with the cases |a<0| and/or |b>l|@>; + q=mp->cur_exp; + while ( a>=unity ) { + q=mp_link(q); a=a-unity; b=b-unity; + } + if ( b==a ) { + @<Construct a path from |pp| to |qq| of length zero@>; + } else { + @<Construct a path from |pp| to |qq| of length $\lceil b\rceil$@>; + } + mp_left_type(pp)=mp_endpoint; mp_right_type(qq)=mp_endpoint; mp_link(qq)=pp; + mp_toss_knot_list(mp, mp->cur_exp); + if ( reversed ) { + mp->cur_exp=mp_link(mp_htap_ypoc(mp, pp)); mp_toss_knot_list(mp, pp); + } else { + mp->cur_exp=pp; + } +} + +@ @<Dispense with the cases |a<0| and/or |b>l|@>= +if ( a<0 ) { + if ( mp_left_type(mp->cur_exp)==mp_endpoint ) { + a=0; if ( b<0 ) b=0; + } else { + do { a=a+l; b=b+l; } while (a<0); /* a cycle always has length |l>0| */ + } +} +if ( b>l ) { + if ( mp_left_type(mp->cur_exp)==mp_endpoint ) { + b=l; if ( a>l ) a=l; + } else { + while ( a>=l ) { + a=a-l; b=b-l; + } + } +} + +@ @<Construct a path from |pp| to |qq| of length $\lceil b\rceil$@>= +{ + pp=mp_copy_knot(mp, q); qq=pp; + do { + q=mp_link(q); rr=qq; qq=mp_copy_knot(mp, q); mp_link(rr)=qq; b=b-unity; + } while (b>0); + if ( a>0 ) { + ss=pp; pp=mp_link(pp); + mp_split_cubic(mp, ss,a*010000); pp=mp_link(ss); + mp_free_node(mp, ss,knot_node_size); + if ( rr==ss ) { + b=mp_make_scaled(mp, b,unity-a); rr=pp; + } + } + if ( b<0 ) { + mp_split_cubic(mp, rr,(b+unity)*010000); + mp_free_node(mp, qq,knot_node_size); + qq=mp_link(rr); + } +} + +@ @<Construct a path from |pp| to |qq| of length zero@>= +{ + if ( a>0 ) { mp_split_cubic(mp, q,a*010000); q=mp_link(q); }; + pp=mp_copy_knot(mp, q); qq=pp; +} + +@ @<Additional cases of binary operators@>= +case point_of: case precontrol_of: case postcontrol_of: + if ( mp->cur_type==mp_pair_type ) + mp_pair_to_path(mp); + if ( (mp->cur_type==mp_path_type)&&(mp_type(p)==mp_known) ) + mp_find_point(mp, value(p),c); + else + mp_bad_binary(mp, p,c); + break; +case pen_offset_of: + if ( (mp->cur_type==mp_pen_type)&& mp_nice_pair(mp, p,mp_type(p)) ) + mp_set_up_offset(mp, value(p)); + else + mp_bad_binary(mp, p,pen_offset_of); + break; +case direction_time_of: + if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + if ( (mp->cur_type==mp_path_type)&& mp_nice_pair(mp, p,mp_type(p)) ) + mp_set_up_direction_time(mp, value(p)); + else + mp_bad_binary(mp, p,direction_time_of); + break; +case envelope_of: + if ( (mp_type(p) != mp_pen_type) || (mp->cur_type != mp_path_type) ) + mp_bad_binary(mp, p,envelope_of); + else + mp_set_up_envelope(mp, p); + break; + +@ @<Declare binary action...@>= +static void mp_set_up_offset (MP mp,pointer p) { + mp_find_offset(mp, value(x_part_loc(p)),value(y_part_loc(p)),mp->cur_exp); + mp_pair_value(mp, mp->cur_x,mp->cur_y); +} +static void mp_set_up_direction_time (MP mp,pointer p) { + mp_flush_cur_exp(mp, mp_find_direction_time(mp, value(x_part_loc(p)), + value(y_part_loc(p)),mp->cur_exp)); +} +static void mp_set_up_envelope (MP mp,pointer p) { + quarterword ljoin, lcap; + scaled miterlim; + pointer q = mp_copy_path(mp, mp->cur_exp); /* the original path */ + /* TODO: accept elliptical pens for straight paths */ + if (pen_is_elliptical(value(p))) { + mp_bad_envelope_pen(mp); + mp->cur_exp = q; + mp->cur_type = mp_path_type; + return; + } + if ( mp->internal[mp_linejoin]>unity ) ljoin=2; + else if ( mp->internal[mp_linejoin]>0 ) ljoin=1; + else ljoin=0; + if ( mp->internal[mp_linecap]>unity ) lcap=2; + else if ( mp->internal[mp_linecap]>0 ) lcap=1; + else lcap=0; + if ( mp->internal[mp_miterlimit]<unity ) + miterlim=unity; + else + miterlim=mp->internal[mp_miterlimit]; + mp->cur_exp = mp_make_envelope(mp, q, value(p), ljoin,lcap,miterlim); + mp->cur_type = mp_path_type; +} + +@ @<Declare binary action...@>= +static void mp_find_point (MP mp,scaled v, quarterword c) { + pointer p; /* the path */ + scaled n; /* its length */ + p=mp->cur_exp; + if ( mp_left_type(p)==mp_endpoint ) n=-unity; else n=0; + do { p=mp_link(p); n=n+unity; } while (p!=mp->cur_exp); + if ( n==0 ) { + v=0; + } else if ( v<0 ) { + if ( mp_left_type(p)==mp_endpoint ) v=0; + else v=n-1-((-v-1) % n); + } else if ( v>n ) { + if ( mp_left_type(p)==mp_endpoint ) v=n; + else v=v % n; + } + p=mp->cur_exp; + while ( v>=unity ) { p=mp_link(p); v=v-unity; }; + if ( v!=0 ) { + @<Insert a fractional node by splitting the cubic@>; + } + @<Set the current expression to the desired path coordinates@>; +} + +@ @<Insert a fractional node...@>= +{ mp_split_cubic(mp, p,v*010000); p=mp_link(p); } + +@ @<Set the current expression to the desired path coordinates...@>= +switch (c) { +case point_of: + mp_pair_value(mp, mp_x_coord(p),mp_y_coord(p)); + break; +case precontrol_of: + if ( mp_left_type(p)==mp_endpoint ) mp_pair_value(mp, mp_x_coord(p),mp_y_coord(p)); + else mp_pair_value(mp, mp_left_x(p),mp_left_y(p)); + break; +case postcontrol_of: + if ( mp_right_type(p)==mp_endpoint ) mp_pair_value(mp, mp_x_coord(p),mp_y_coord(p)); + else mp_pair_value(mp, mp_right_x(p),mp_right_y(p)); + break; +} /* there are no other cases */ + +@ @<Additional cases of binary operators@>= +case arc_time_of: + if ( mp->cur_type==mp_pair_type ) + mp_pair_to_path(mp); + if ( (mp->cur_type==mp_path_type)&&(mp_type(p)==mp_known) ) + mp_flush_cur_exp(mp, mp_get_arc_time(mp, mp->cur_exp,value(p))); + else + mp_bad_binary(mp, p,c); + break; + +@ @<Additional cases of bin...@>= +case intersect: + if ( mp_type(p)==mp_pair_type ) { + q=mp_stash_cur_exp(mp); mp_unstash_cur_exp(mp, p); + mp_pair_to_path(mp); p=mp_stash_cur_exp(mp); mp_unstash_cur_exp(mp, q); + }; + if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + if ( (mp->cur_type==mp_path_type)&&(mp_type(p)==mp_path_type) ) { + mp_path_intersection(mp, value(p),mp->cur_exp); + mp_pair_value(mp, mp->cur_t,mp->cur_tt); + } else { + mp_bad_binary(mp, p,intersect); + } + break; + +@ @<Additional cases of bin...@>= +case in_font: + if ( (mp->cur_type!=mp_string_type)||(mp_type(p)!=mp_string_type)) + mp_bad_binary(mp, p,in_font); + else { mp_do_infont(mp, p); binary_return; } + break; + +@ Function |new_text_node| owns the reference count for its second argument +(the text string) but not its first (the font name). + +@<Declare binary action...@>= +static void mp_do_infont (MP mp,pointer p) { + pointer q; + q=mp_get_node(mp, edge_header_size); + mp_init_edges(mp, q); + mp_link(obj_tail(q))=mp_new_text_node(mp,str(mp->cur_exp),value(p)); + obj_tail(q)=mp_link(obj_tail(q)); + mp_free_node(mp, p,value_node_size); + mp_flush_cur_exp(mp, q); + mp->cur_type=mp_picture_type; +} + +@* \[40] Statements and commands. +The chief executive of \MP\ is the |do_statement| routine, which +contains the master switch that causes all the various pieces of \MP\ +to do their things, in the right order. + +In a sense, this is the grand climax of the program: It applies all the +tools that we have worked so hard to construct. In another sense, this is +the messiest part of the program: It necessarily refers to other pieces +of code all over the place, so that a person can't fully understand what is +going on without paging back and forth to be reminded of conventions that +are defined elsewhere. We are now at the hub of the web. + +The structure of |do_statement| itself is quite simple. The first token +of the statement is fetched using |get_x_next|. If it can be the first +token of an expression, we look for an equation, an assignment, or a +title. Otherwise we use a \&{case} construction to branch at high speed to +the appropriate routine for various and sundry other types of commands, +each of which has an ``action procedure'' that does the necessary work. + +The program uses the fact that +$$\hbox{|min_primary_command=max_statement_command=type_name|}$$ +to interpret a statement that starts with, e.g., `\&{string}', +as a type declaration rather than a boolean expression. + +@c void mp_do_statement (MP mp) { /* governs \MP's activities */ + mp->cur_type=mp_vacuous; mp_get_x_next(mp); + if ( mp->cur_cmd>max_primary_command ) { + @<Worry about bad statement@>; + } else if ( mp->cur_cmd>max_statement_command ) { + @<Do an equation, assignment, title, or + `$\langle\,$expression$\,\rangle\,$\&{endgroup}'@>; + } else { + @<Do a statement that doesn't begin with an expression@>; + } + if ( mp->cur_cmd<semicolon ) + @<Flush unparsable junk that was found after the statement@>; + mp->error_count=0; +} + +@ @<Declarations@>= +@<Declare action procedures for use by |do_statement|@> + +@ The only command codes |>max_primary_command| that can be present +at the beginning of a statement are |semicolon| and higher; these +occur when the statement is null. + +@<Worry about bad statement@>= +{ + if ( mp->cur_cmd<semicolon ) { + print_err("A statement can't begin with `"); +@.A statement can't begin with x@> + mp_print_cmd_mod(mp, mp->cur_cmd,mp->cur_mod); mp_print_char(mp, xord('\'')); + help5("I was looking for the beginning of a new statement.", + "If you just proceed without changing anything, I'll ignore", + "everything up to the next `;'. Please insert a semicolon", + "now in front of anything that you don't want me to delete.", + "(See Chapter 27 of The METAFONTbook for an example.)"); +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> + mp_back_error(mp); mp_get_x_next(mp); + } +} + +@ The help message printed here says that everything is flushed up to +a semicolon, but actually the commands |end_group| and |stop| will +also terminate a statement. + +@<Flush unparsable junk that was found after the statement@>= +{ + print_err("Extra tokens will be flushed"); +@.Extra tokens will be flushed@> + help6("I've just read as much of that statement as I could fathom,", + "so a semicolon should have been next. It's very puzzling...", + "but I'll try to get myself back together, by ignoring", + "everything up to the next `;'. Please insert a semicolon", + "now in front of anything that you don't want me to delete.", + "(See Chapter 27 of The METAFONTbook for an example.)"); +@:METAFONTbook}{\sl The {\logos METAFONT\/}book@> + mp_back_error(mp); mp->scanner_status=flushing; + do { + get_t_next; + @<Decrease the string reference count...@>; + } while (! end_of_statement); /* |cur_cmd=semicolon|, |end_group|, or |stop| */ + mp->scanner_status=normal; +} + +@ If |do_statement| ends with |cur_cmd=end_group|, we should have +|cur_type=mp_vacuous| unless the statement was simply an expression; +in the latter case, |cur_type| and |cur_exp| should represent that +expression. + +@<Do a statement that doesn't...@>= +{ + if ( mp->internal[mp_tracing_commands]>0 ) + show_cur_cmd_mod; + switch (mp->cur_cmd ) { + case type_name:mp_do_type_declaration(mp); break; + case macro_def: + if ( mp->cur_mod>var_def ) mp_make_op_def(mp); + else if ( mp->cur_mod>end_def ) mp_scan_def(mp); + break; + @<Cases of |do_statement| that invoke particular commands@>; + } /* there are no other cases */ + mp->cur_type=mp_vacuous; +} + +@ The most important statements begin with expressions. + +@<Do an equation, assignment, title, or...@>= +{ + mp->var_flag=assignment; mp_scan_expression(mp); + if ( mp->cur_cmd<end_group ) { + if ( mp->cur_cmd==equals ) mp_do_equation(mp); + else if ( mp->cur_cmd==assignment ) mp_do_assignment(mp); + else if ( mp->cur_type==mp_string_type ) {@<Do a title@> ; } + else if ( mp->cur_type!=mp_vacuous ){ + exp_err("Isolated expression"); +@.Isolated expression@> + help3("I couldn't find an `=' or `:=' after the", + "expression that is shown above this error message,", + "so I guess I'll just ignore it and carry on."); + mp_put_get_error(mp); + } + mp_flush_cur_exp(mp, 0); mp->cur_type=mp_vacuous; + } +} + +@ @<Do a title@>= +{ + if ( mp->internal[mp_tracing_titles]>0 ) { + mp_print_nl(mp, ""); mp_print_str(mp, mp->cur_exp); update_terminal; + } +} + +@ Equations and assignments are performed by the pair of mutually recursive +@^recursion@> +routines |do_equation| and |do_assignment|. These routines are called when +|cur_cmd=equals| and when |cur_cmd=assignment|, respectively; the left-hand +side is in |cur_type| and |cur_exp|, while the right-hand side is yet +to be scanned. After the routines are finished, |cur_type| and |cur_exp| +will be equal to the right-hand side (which will normally be equal +to the left-hand side). + +@<Declarations@>= +@<Declare the procedure called |make_eq|@> +static void mp_do_equation (MP mp) ; + +@ @c +void mp_do_equation (MP mp) { + pointer lhs; /* capsule for the left-hand side */ + pointer p; /* temporary register */ + lhs=mp_stash_cur_exp(mp); mp_get_x_next(mp); + mp->var_flag=assignment; mp_scan_expression(mp); + if ( mp->cur_cmd==equals ) mp_do_equation(mp); + else if ( mp->cur_cmd==assignment ) mp_do_assignment(mp); + if ( mp->internal[mp_tracing_commands]>two ) + @<Trace the current equation@>; + if ( mp->cur_type==mp_unknown_path ) if ( mp_type(lhs)==mp_pair_type ) { + p=mp_stash_cur_exp(mp); mp_unstash_cur_exp(mp, lhs); lhs=p; + }; /* in this case |make_eq| will change the pair to a path */ + mp_make_eq(mp, lhs); /* equate |lhs| to |(cur_type,cur_exp)| */ +} + +@ And |do_assignment| is similar to |do_equation|: + +@<Declarations@>= +static void mp_do_assignment (MP mp); + +@ @c +void mp_do_assignment (MP mp) { + pointer lhs; /* token list for the left-hand side */ + pointer p; /* where the left-hand value is stored */ + pointer q; /* temporary capsule for the right-hand value */ + if ( mp->cur_type!=mp_token_list ) { + exp_err("Improper `:=' will be changed to `='"); +@.Improper `:='@> + help2("I didn't find a variable name at the left of the `:=',", + "so I'm going to pretend that you said `=' instead."); + mp_error(mp); mp_do_equation(mp); + } else { + lhs=mp->cur_exp; mp->cur_type=mp_vacuous; + mp_get_x_next(mp); mp->var_flag=assignment; mp_scan_expression(mp); + if ( mp->cur_cmd==equals ) mp_do_equation(mp); + else if ( mp->cur_cmd==assignment ) mp_do_assignment(mp); + if ( mp->internal[mp_tracing_commands]>two ) + @<Trace the current assignment@>; + if ( mp_info(lhs)>hash_end ) { + @<Assign the current expression to an internal variable@>; + } else { + @<Assign the current expression to the variable |lhs|@>; + } + mp_flush_node_list(mp, lhs); + } +} + +@ @<Trace the current equation@>= +{ + mp_begin_diagnostic(mp); mp_print_nl(mp, "{("); mp_print_exp(mp,lhs,0); + mp_print(mp,")=("); mp_print_exp(mp,null,0); + mp_print(mp,")}"); mp_end_diagnostic(mp, false); +} + +@ @<Trace the current assignment@>= +{ + mp_begin_diagnostic(mp); mp_print_nl(mp, "{"); + if ( mp_info(lhs)>hash_end ) + mp_print(mp, mp->int_name[mp_info(lhs)-(hash_end)]); + else + mp_show_token_list(mp, lhs,null,1000,0); + mp_print(mp, ":="); mp_print_exp(mp, null,0); + mp_print_char(mp, xord('}')); mp_end_diagnostic(mp, false); +} + +@ @<Assign the current expression to an internal variable@>= +if ( mp->cur_type==mp_known || mp->cur_type==mp_string_type ) { + if (mp->cur_type==mp_string_type) + add_str_ref(mp->cur_exp); + mp->internal[mp_info(lhs)-(hash_end)]=mp->cur_exp; +} else { + exp_err("Internal quantity `"); +@.Internal quantity...@> + mp_print(mp, mp->int_name[mp_info(lhs)-(hash_end)]); + mp_print(mp, "' must receive a known value"); + help2("I can\'t set an internal quantity to anything but a known", + "numeric value, so I'll have to ignore this assignment."); + mp_put_get_error(mp); +} + +@ @<Assign the current expression to the variable |lhs|@>= +{ + p=mp_find_variable(mp, lhs); + if ( p!=null ) { + q=mp_stash_cur_exp(mp); mp->cur_type=mp_und_type(mp, p); + mp_recycle_value(mp, p); + mp_type(p)=mp->cur_type; value(p)=null; mp_make_exp_copy(mp, p); + p=mp_stash_cur_exp(mp); mp_unstash_cur_exp(mp, q); mp_make_eq(mp, p); + } else { + mp_obliterated(mp, lhs); mp_put_get_error(mp); + } +} + + +@ And now we get to the nitty-gritty. The |make_eq| procedure is given +a pointer to a capsule that is to be equated to the current expression. + +@<Declare the procedure called |make_eq|@>= +static void mp_make_eq (MP mp,pointer lhs) ; + + +@ +@c void mp_make_eq (MP mp,pointer lhs) { + quarterword t; /* type of the left-hand side */ + pointer p,q; /* pointers inside of big nodes */ + integer v=0; /* value of the left-hand side */ +RESTART: + t=mp_type(lhs); + if ( t<=mp_pair_type ) v=value(lhs); + switch (t) { + @<For each type |t|, make an equation and |goto done| unless |cur_type| + is incompatible with~|t|@>; + } /* all cases have been listed */ + @<Announce that the equation cannot be performed@>; +DONE: + check_arith; mp_recycle_value(mp, lhs); + mp_free_node(mp, lhs,value_node_size); +} + +@ @<Announce that the equation cannot be performed@>= +mp_disp_err(mp, lhs,""); +exp_err("Equation cannot be performed ("); +@.Equation cannot be performed@> +if ( mp_type(lhs)<=mp_pair_type ) mp_print_type(mp, mp_type(lhs)); +else mp_print(mp, "numeric"); +mp_print_char(mp, xord('=')); +if ( mp->cur_type<=mp_pair_type ) mp_print_type(mp, mp->cur_type); +else mp_print(mp, "numeric"); +mp_print_char(mp, xord(')')); +help2("I'm sorry, but I don't know how to make such things equal.", + "(See the two expressions just above the error message.)"); +mp_put_get_error(mp) + +@ @<For each type |t|, make an equation and |goto done| unless...@>= +case mp_boolean_type: case mp_string_type: case mp_pen_type: +case mp_path_type: case mp_picture_type: + if ( mp->cur_type==t+unknown_tag ) { + mp_nonlinear_eq(mp, v,mp->cur_exp,false); + mp_unstash_cur_exp(mp, mp->cur_exp); goto DONE; + } else if ( mp->cur_type==t ) { + @<Report redundant or inconsistent equation and |goto done|@>; + } + break; +case unknown_types: + if ( mp->cur_type==t-unknown_tag ) { + mp_nonlinear_eq(mp, mp->cur_exp,lhs,true); goto DONE; + } else if ( mp->cur_type==t ) { + mp_ring_merge(mp, lhs,mp->cur_exp); goto DONE; + } else if ( mp->cur_type==mp_pair_type ) { + if ( t==mp_unknown_path ) { + mp_pair_to_path(mp); goto RESTART; + }; + } + break; +case mp_transform_type: case mp_color_type: +case mp_cmykcolor_type: case mp_pair_type: + if ( mp->cur_type==t ) { + @<Do multiple equations and |goto done|@>; + } + break; +case mp_known: case mp_dependent: +case mp_proto_dependent: case mp_independent: + if ( mp->cur_type>=mp_known ) { + mp_try_eq(mp, lhs,null); goto DONE; + }; + break; +case mp_vacuous: + break; + +@ @<Report redundant or inconsistent equation and |goto done|@>= +{ + if ( mp->cur_type<=mp_string_type ) { + if ( mp->cur_type==mp_string_type ) { + if ( mp_str_vs_str(mp, v,mp->cur_exp)!=0 ) { + goto NOT_FOUND; + } + } else if ( v!=mp->cur_exp ) { + goto NOT_FOUND; + } + @<Exclaim about a redundant equation@>; goto DONE; + } + print_err("Redundant or inconsistent equation"); +@.Redundant or inconsistent equation@> + help2("An equation between already-known quantities can't help.", + "But don't worry; continue and I'll just ignore it."); + mp_put_get_error(mp); goto DONE; +NOT_FOUND: + print_err("Inconsistent equation"); +@.Inconsistent equation@> + help2("The equation I just read contradicts what was said before.", + "But don't worry; continue and I'll just ignore it."); + mp_put_get_error(mp); goto DONE; +} + +@ @<Do multiple equations and |goto done|@>= +{ + p=v+mp->big_node_size[t]; + q=value(mp->cur_exp)+mp->big_node_size[t]; + do { + p=p-2; q=q-2; mp_try_eq(mp, p,q); + } while (p!=v); + goto DONE; +} + +@ The first argument to |try_eq| is the location of a value node +in a capsule that will soon be recycled. The second argument is +either a location within a pair or transform node pointed to by +|cur_exp|, or it is |null| (which means that |cur_exp| itself +serves as the second argument). The idea is to leave |cur_exp| unchanged, +but to equate the two operands. + +@<Declarations@>= +static void mp_try_eq (MP mp,pointer l, pointer r) ; + +@ +@c void mp_try_eq (MP mp,pointer l, pointer r) { + pointer p; /* dependency list for right operand minus left operand */ + int t; /* the type of list |p| */ + pointer q; /* the constant term of |p| is here */ + pointer pp; /* dependency list for right operand */ + int tt; /* the type of list |pp| */ + boolean copied; /* have we copied a list that ought to be recycled? */ + @<Remove the left operand from its container, negate it, and + put it into dependency list~|p| with constant term~|q|@>; + @<Add the right operand to list |p|@>; + if ( mp_info(p)==null ) { + @<Deal with redundant or inconsistent equation@>; + } else { + mp_linear_eq(mp, p,t); + if ( r==null ) if ( mp->cur_type!=mp_known ) { + if ( mp_type(mp->cur_exp)==mp_known ) { + pp=mp->cur_exp; mp->cur_exp=value(mp->cur_exp); mp->cur_type=mp_known; + mp_free_node(mp, pp,value_node_size); + } + } + } +} + +@ @<Remove the left operand from its container, negate it, and...@>= +t=mp_type(l); +if ( t==mp_known ) { + t=mp_dependent; p=mp_const_dependency(mp, -value(l)); q=p; +} else if ( t==mp_independent ) { + t=mp_dependent; p=mp_single_dependency(mp, l); negate(value(p)); + q=mp->dep_final; +} else { + p=dep_list(l); q=p; + while (1) { + negate(value(q)); + if ( mp_info(q)==null ) break; + q=mp_link(q); + } + mp_link(prev_dep(l))=mp_link(q); prev_dep(mp_link(q))=prev_dep(l); + mp_type(l)=mp_known; +} + +@ @<Deal with redundant or inconsistent equation@>= +{ + if ( abs(value(p))>64 ) { /* off by .001 or more */ + print_err("Inconsistent equation"); +@.Inconsistent equation@> + mp_print(mp, " (off by "); mp_print_scaled(mp, value(p)); + mp_print_char(mp, xord(')')); + help2("The equation I just read contradicts what was said before.", + "But don't worry; continue and I'll just ignore it."); + mp_put_get_error(mp); + } else if ( r==null ) { + @<Exclaim about a redundant equation@>; + } + mp_free_node(mp, p,dep_node_size); +} + +@ @<Add the right operand to list |p|@>= +if ( r==null ) { + if ( mp->cur_type==mp_known ) { + value(q)=value(q)+mp->cur_exp; goto DONE1; + } else { + tt=mp->cur_type; + if ( tt==mp_independent ) pp=mp_single_dependency(mp, mp->cur_exp); + else pp=dep_list(mp->cur_exp); + } +} else { + if ( mp_type(r)==mp_known ) { + value(q)=value(q)+value(r); goto DONE1; + } else { + tt=mp_type(r); + if ( tt==mp_independent ) pp=mp_single_dependency(mp, r); + else pp=dep_list(r); + } +} +if ( tt!=mp_independent ) copied=false; +else { copied=true; tt=mp_dependent; }; +@<Add dependency list |pp| of type |tt| to dependency list~|p| of type~|t|@>; +if ( copied ) mp_flush_node_list(mp, pp); +DONE1: + +@ @<Add dependency list |pp| of type |tt| to dependency list~|p| of type~|t|@>= +mp->watch_coefs=false; +if ( t==tt ) { + p=mp_p_plus_q(mp, p,pp,t); +} else if ( t==mp_proto_dependent ) { + p=mp_p_plus_fq(mp, p,unity,pp,mp_proto_dependent,mp_dependent); +} else { + q=p; + while ( mp_info(q)!=null ) { + value(q)=mp_round_fraction(mp, value(q)); q=mp_link(q); + } + t=mp_proto_dependent; p=mp_p_plus_q(mp, p,pp,t); +} +mp->watch_coefs=true; + +@ Our next goal is to process type declarations. For this purpose it's +convenient to have a procedure that scans a $\langle\,$declared +variable$\,\rangle$ and returns the corresponding token list. After the +following procedure has acted, the token after the declared variable +will have been scanned, so it will appear in |cur_cmd|, |cur_mod|, +and~|cur_sym|. + +@<Declarations@>= +static pointer mp_scan_declared_variable (MP mp) ; + +@ @c +pointer mp_scan_declared_variable (MP mp) { + pointer x; /* hash address of the variable's root */ + pointer h,t; /* head and tail of the token list to be returned */ + pointer l; /* hash address of left bracket */ + mp_get_symbol(mp); x=mp->cur_sym; + if ( mp->cur_cmd!=tag_token ) mp_clear_symbol(mp, x,false); + h=mp_get_avail(mp); mp_info(h)=x; t=h; + while (1) { + mp_get_x_next(mp); + if ( mp->cur_sym==0 ) break; + if ( mp->cur_cmd!=tag_token ) if ( mp->cur_cmd!=internal_quantity) { + if ( mp->cur_cmd==left_bracket ) { + @<Descend past a collective subscript@>; + } else { + break; + } + } + mp_link(t)=mp_get_avail(mp); t=mp_link(t); mp_info(t)=mp->cur_sym; + } + if ( (eq_type(x)%outer_tag)!=tag_token ) mp_clear_symbol(mp, x,false); + if ( equiv(x)==null ) mp_new_root(mp, x); + return h; +} + +@ If the subscript isn't collective, we don't accept it as part of the +declared variable. + +@<Descend past a collective subscript@>= +{ + l=mp->cur_sym; mp_get_x_next(mp); + if ( mp->cur_cmd!=right_bracket ) { + mp_back_input(mp); mp->cur_sym=l; mp->cur_cmd=left_bracket; break; + } else { + mp->cur_sym=collective_subscript; + } +} + +@ Type declarations are introduced by the following primitive operations. + +@<Put each...@>= +mp_primitive(mp, "numeric",type_name,mp_numeric_type); +@:numeric_}{\&{numeric} primitive@> +mp_primitive(mp, "string",type_name,mp_string_type); +@:string_}{\&{string} primitive@> +mp_primitive(mp, "boolean",type_name,mp_boolean_type); +@:boolean_}{\&{boolean} primitive@> +mp_primitive(mp, "path",type_name,mp_path_type); +@:path_}{\&{path} primitive@> +mp_primitive(mp, "pen",type_name,mp_pen_type); +@:pen_}{\&{pen} primitive@> +mp_primitive(mp, "picture",type_name,mp_picture_type); +@:picture_}{\&{picture} primitive@> +mp_primitive(mp, "transform",type_name,mp_transform_type); +@:transform_}{\&{transform} primitive@> +mp_primitive(mp, "color",type_name,mp_color_type); +@:color_}{\&{color} primitive@> +mp_primitive(mp, "rgbcolor",type_name,mp_color_type); +@:color_}{\&{rgbcolor} primitive@> +mp_primitive(mp, "cmykcolor",type_name,mp_cmykcolor_type); +@:color_}{\&{cmykcolor} primitive@> +mp_primitive(mp, "pair",type_name,mp_pair_type); +@:pair_}{\&{pair} primitive@> + +@ @<Cases of |print_cmd...@>= +case type_name: mp_print_type(mp, m); break; + +@ Now we are ready to handle type declarations, assuming that a +|type_name| has just been scanned. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_type_declaration (MP mp) ; + +@ @c +void mp_do_type_declaration (MP mp) { + quarterword t; /* the type being declared */ + pointer p; /* token list for a declared variable */ + pointer q; /* value node for the variable */ + if ( mp->cur_mod>=mp_transform_type ) + t=mp->cur_mod; + else + t=mp->cur_mod+unknown_tag; + do { + p=mp_scan_declared_variable(mp); + mp_flush_variable(mp, equiv(mp_info(p)),mp_link(p),false); + q=mp_find_variable(mp, p); + if ( q!=null ) { + mp_type(q)=t; value(q)=null; + } else { + print_err("Declared variable conflicts with previous vardef"); +@.Declared variable conflicts...@> + help2("You can't use, e.g., `numeric foo[]' after `vardef foo'.", + "Proceed, and I'll ignore the illegal redeclaration."); + mp_put_get_error(mp); + } + mp_flush_list(mp, p); + if ( mp->cur_cmd<comma ) { + @<Flush spurious symbols after the declared variable@>; + } + } while (! end_of_statement); +} + +@ @<Flush spurious symbols after the declared variable@>= +{ + print_err("Illegal suffix of declared variable will be flushed"); +@.Illegal suffix...flushed@> + help5("Variables in declarations must consist entirely of", + "names and collective subscripts, e.g., `x[]a'.", + "Are you trying to use a reserved word in a variable name?", + "I'm going to discard the junk I found here,", + "up to the next comma or the end of the declaration."); + if ( mp->cur_cmd==numeric_token ) + mp->help_line[2]="Explicit subscripts like `x15a' aren't permitted."; + mp_put_get_error(mp); mp->scanner_status=flushing; + do { + get_t_next; + @<Decrease the string reference count...@>; + } while (mp->cur_cmd<comma); /* either |end_of_statement| or |cur_cmd=comma| */ + mp->scanner_status=normal; +} + +@ \MP's |main_control| procedure just calls |do_statement| repeatedly +until coming to the end of the user's program. +Each execution of |do_statement| concludes with +|cur_cmd=semicolon|, |end_group|, or |stop|. + +@c +static void mp_main_control (MP mp) { + do { + mp_do_statement(mp); + if ( mp->cur_cmd==end_group ) { + print_err("Extra `endgroup'"); +@.Extra `endgroup'@> + help2("I'm not currently working on a `begingroup',", + "so I had better not try to end anything."); + mp_flush_error(mp, 0); + } + } while (mp->cur_cmd!=stop); +} +int mp_run (MP mp) { + if (mp->history < mp_fatal_error_stop ) { + xfree(mp->jump_buf); + mp->jump_buf = malloc(sizeof(jmp_buf)); + if (mp->jump_buf == NULL || setjmp(*(mp->jump_buf)) != 0) + return mp->history; + mp_main_control(mp); /* come to life */ + mp_final_cleanup(mp); /* prepare for death */ + mp_close_files_and_terminate(mp); + } + return mp->history; +} + +@ For |mp_execute|, we need to define a structure to store the +redirected input and output. This structure holds the five relevant +streams: the three informational output streams, the PostScript +generation stream, and the input stream. These streams have many +things in common, so it makes sense to give them their own structure +definition. + +\item{fptr} is a virtual file pointer +\item{data} is the data this stream holds +\item{cur} is a cursor pointing into |data| +\item{size} is the allocated length of the data stream +\item{used} is the actual length of the data stream + +There are small differences between input and output: |term_in| never +uses |used|, whereas the other four never use |cur|. + +@<Exported types@>= +typedef struct { + void * fptr; + char * data; + char * cur; + size_t size; + size_t used; +} mp_stream; + +typedef struct { + mp_stream term_out; + mp_stream error_out; + mp_stream log_out; + mp_stream ps_out; + mp_stream term_in; + struct mp_edge_object *edges; +} mp_run_data; + +@ We need a function to clear an output stream, this is called at the +beginning of |mp_execute|. We also need one for destroying an output +stream, this is called just before a stream is (re)opened. + +@c +static void mp_reset_stream(mp_stream *str) { + xfree(str->data); + str->cur = NULL; + str->size = 0; + str->used = 0; +} +static void mp_free_stream(mp_stream *str) { + xfree(str->fptr); + mp_reset_stream(str); +} + +@ @<Declarations@>= +static void mp_reset_stream(mp_stream *str); +static void mp_free_stream(mp_stream *str); + +@ The global instance contains a pointer instead of the actual structure +even though it is essentially static, because that makes it is easier to move +the object around. + +@<Global ...@>= +mp_run_data run_data; + +@ Another type is needed: the indirection will overload some of the +file pointer objects in the instance (but not all). For clarity, an +indirect object is used that wraps a |FILE *|. + +@<Types ... @>= +typedef struct File { + FILE *f; +} File; + +@ Here are all of the functions that need to be overloaded for |mp_execute|. + +@<Declarations@>= +static void *mplib_open_file(MP mp, const char *fname, const char *fmode, int ftype); +static int mplib_get_char(void *f, mp_run_data * mplib_data); +static void mplib_unget_char(void *f, mp_run_data * mplib_data, int c); +static char *mplib_read_ascii_file(MP mp, void *ff, size_t * size); +static void mplib_write_ascii_file(MP mp, void *ff, const char *s); +static void mplib_read_binary_file(MP mp, void *ff, void **data, size_t * size); +static void mplib_write_binary_file(MP mp, void *ff, void *s, size_t size); +static void mplib_close_file(MP mp, void *ff); +static int mplib_eof_file(MP mp, void *ff); +static void mplib_flush_file(MP mp, void *ff); +static void mplib_shipout_backend(MP mp, int h); + +@ The |xmalloc(1,1)| calls make sure the stored indirection values are unique. + +@d reset_stream(a) do { + mp_reset_stream(&(a)); + if (!ff->f) { + ff->f = xmalloc(1,1); + (a).fptr = ff->f; + } } while (0) + +@c + +static void *mplib_open_file(MP mp, const char *fname, const char *fmode, int ftype) +{ + File *ff = xmalloc(1, sizeof(File)); + mp_run_data *run = mp_rundata(mp); + ff->f = NULL; + if (ftype == mp_filetype_terminal) { + if (fmode[0] == 'r') { + if (!ff->f) { + ff->f = xmalloc(1,1); + run->term_in.fptr = ff->f; + } + } else { + reset_stream(run->term_out); + } + } else if (ftype == mp_filetype_error) { + reset_stream(run->error_out); + } else if (ftype == mp_filetype_log) { + reset_stream(run->log_out); + } else if (ftype == mp_filetype_postscript) { + mp_free_stream(&(run->ps_out)); + ff->f = xmalloc(1,1); + run->ps_out.fptr = ff->f; + } else { + char realmode[3]; + char *f = (mp->find_file)(mp, fname, fmode, ftype); + if (f == NULL) + return NULL; + realmode[0] = *fmode; + realmode[1] = 'b'; + realmode[2] = 0; + ff->f = fopen(f, realmode); + free(f); + if ((fmode[0] == 'r') && (ff->f == NULL)) { + free(ff); + return NULL; + } + } + return ff; +} + +static int mplib_get_char(void *f, mp_run_data * run) +{ + int c; + if (f == run->term_in.fptr && run->term_in.data != NULL) { + if (run->term_in.size == 0) { + if (run->term_in.cur != NULL) { + run->term_in.cur = NULL; + } else { + xfree(run->term_in.data); + } + c = EOF; + } else { + run->term_in.size--; + c = *(run->term_in.cur)++; + } + } else { + c = fgetc(f); + } + return c; +} + +static void mplib_unget_char(void *f, mp_run_data * run, int c) +{ + if (f == run->term_in.fptr && run->term_in.cur != NULL) { + run->term_in.size++; + run->term_in.cur--; + } else { + ungetc(c, f); + } +} + + +static char *mplib_read_ascii_file(MP mp, void *ff, size_t * size) +{ + char *s = NULL; + if (ff != NULL) { + int c; + size_t len = 0, lim = 128; + mp_run_data *run = mp_rundata(mp); + FILE *f = ((File *) ff)->f; + if (f == NULL) + return NULL; + *size = 0; + c = mplib_get_char(f, run); + if (c == EOF) + return NULL; + s = malloc(lim); + if (s == NULL) + return NULL; + while (c != EOF && c != '\n' && c != '\r') { + if (len == lim) { + s = xrealloc(s, (lim + (lim >> 2)),1); + if (s == NULL) + return NULL; + lim += (lim >> 2); + } + s[len++] = c; + c = mplib_get_char(f, run); + } + if (c == '\r') { + c = mplib_get_char(f, run); + if (c != EOF && c != '\n') + mplib_unget_char(f, run, c); + } + s[len] = 0; + *size = len; + } + return s; +} + +static void mp_append_string (MP mp, mp_stream *a,const char *b) { + size_t l = strlen(b); + if ((a->used+l)>=a->size) { + a->size += 256+(a->size)/5+l; + a->data = xrealloc(a->data,a->size,1); + } + (void)strcpy(a->data+a->used,b); + a->used += l; +} + + +static void mplib_write_ascii_file(MP mp, void *ff, const char *s) +{ + if (ff != NULL) { + void *f = ((File *) ff)->f; + mp_run_data *run = mp_rundata(mp); + if (f != NULL) { + if (f == run->term_out.fptr) { + mp_append_string(mp,&(run->term_out), s); + } else if (f == run->error_out.fptr) { + mp_append_string(mp,&(run->error_out), s); + } else if (f == run->log_out.fptr) { + mp_append_string(mp,&(run->log_out), s); + } else if (f == run->ps_out.fptr) { + mp_append_string(mp,&(run->ps_out), s); + } else { + fprintf((FILE *) f, "%s", s); + } + } + } +} + +static void mplib_read_binary_file(MP mp, void *ff, void **data, size_t * size) +{ + (void) mp; + if (ff != NULL) { + size_t len = 0; + FILE *f = ((File *) ff)->f; + if (f != NULL) + len = fread(*data, 1, *size, f); + *size = len; + } +} + +static void mplib_write_binary_file(MP mp, void *ff, void *s, size_t size) +{ + (void) mp; + if (ff != NULL) { + FILE *f = ((File *) ff)->f; + if (f != NULL) + (void)fwrite(s, size, 1, f); + } +} + +static void mplib_close_file(MP mp, void *ff) +{ + if (ff != NULL) { + mp_run_data *run = mp_rundata(mp); + void *f = ((File *) ff)->f; + if (f != NULL) { + if (f != run->term_out.fptr + && f != run->error_out.fptr + && f != run->log_out.fptr + && f != run->ps_out.fptr + && f != run->term_in.fptr) { + fclose(f); + } + } + free(ff); + } +} + +static int mplib_eof_file(MP mp, void *ff) +{ + if (ff != NULL) { + mp_run_data *run = mp_rundata(mp); + FILE *f = ((File *) ff)->f; + if (f == NULL) + return 1; + if (f == run->term_in.fptr && run->term_in.data != NULL) { + return (run->term_in.size == 0); + } + return feof(f); + } + return 1; +} + +static void mplib_flush_file(MP mp, void *ff) +{ + (void) mp; + (void) ff; + return; +} + +static void mplib_shipout_backend(MP mp, int h) +{ + mp_edge_object *hh = mp_gr_export(mp, h); + if (hh) { + mp_run_data *run = mp_rundata(mp); + if (run->edges==NULL) { + run->edges = hh; + } else { + mp_edge_object *p = run->edges; + while (p->next!=NULL) { p = p->next; } + p->next = hh; + } + } +} + + +@ This is where we fill them all in. +@<Prepare function pointers for non-interactive use@>= +{ + mp->open_file = mplib_open_file; + mp->close_file = mplib_close_file; + mp->eof_file = mplib_eof_file; + mp->flush_file = mplib_flush_file; + mp->write_ascii_file = mplib_write_ascii_file; + mp->read_ascii_file = mplib_read_ascii_file; + mp->write_binary_file = mplib_write_binary_file; + mp->read_binary_file = mplib_read_binary_file; + mp->shipout_backend = mplib_shipout_backend; +} + +@ Perhaps this is the most important API function in the library. + +@<Exported function ...@>= +extern mp_run_data *mp_rundata (MP mp) ; + +@ @c +mp_run_data *mp_rundata (MP mp) { + return &(mp->run_data); +} + +@ @<Dealloc ...@>= +mp_free_stream(&(mp->run_data.term_in)); +mp_free_stream(&(mp->run_data.term_out)); +mp_free_stream(&(mp->run_data.log_out)); +mp_free_stream(&(mp->run_data.error_out)); +mp_free_stream(&(mp->run_data.ps_out)); + +@ @<Finish non-interactive use@>= +xfree(mp->term_out); +xfree(mp->term_in); +xfree(mp->err_out); + +@ @<Start non-interactive work@>= +@<Initialize the output routines@>; +mp->input_ptr=0; mp->max_in_stack=0; +mp->in_open=0; mp->open_parens=0; mp->max_buf_stack=0; +mp->param_ptr=0; mp->max_param_stack=0; +start = loc = iindex = 0; mp->first = 0; +line=0; name=is_term; +mp->mpx_name[0]=absent; +mp->force_eof=false; +t_open_in; +mp->scanner_status=normal; +if (mp->mem_ident==NULL) { + if ( ! mp_load_mem_file(mp) ) { + (mp->close_file)(mp, mp->mem_file); + mp->history = mp_fatal_error_stop; + return mp->history; + } + (mp->close_file)(mp, mp->mem_file); +} +mp_fix_date_and_time(mp); +if (mp->random_seed==0) + mp->random_seed = (mp->internal[mp_time] / unity)+mp->internal[mp_day]; +mp_init_randoms(mp, mp->random_seed); +@<Initialize the print |selector|...@>; +mp_open_log_file(mp); +mp_set_job_id(mp); +mp_init_map_file(mp, mp->troff_mode); +mp->history=mp_spotless; /* ready to go! */ +if (mp->troff_mode) { + mp->internal[mp_gtroffmode]=unity; + mp->internal[mp_prologues]=unity; +} +if ( mp->start_sym>0 ) { /* insert the `\&{everyjob}' symbol */ + mp->cur_sym=mp->start_sym; mp_back_input(mp); +} + +@ @c +int mp_execute (MP mp, char *s, size_t l) { + mp_reset_stream(&(mp->run_data.term_out)); + mp_reset_stream(&(mp->run_data.log_out)); + mp_reset_stream(&(mp->run_data.error_out)); + mp_reset_stream(&(mp->run_data.ps_out)); + if (mp->finished) { + return mp->history; + } else if (!mp->noninteractive) { + mp->history = mp_fatal_error_stop ; + return mp->history; + } + if (mp->history < mp_fatal_error_stop ) { + xfree(mp->jump_buf); + mp->jump_buf = malloc(sizeof(jmp_buf)); + if (mp->jump_buf == NULL || setjmp(*(mp->jump_buf)) != 0) { + return mp->history; + } + if (s==NULL) { /* this signals EOF */ + mp_final_cleanup(mp); /* prepare for death */ + mp_close_files_and_terminate(mp); + return mp->history; + } + mp->tally=0; + mp->term_offset=0; mp->file_offset=0; + /* Perhaps some sort of warning here when |data| is not + * yet exhausted would be nice ... this happens after errors + */ + if (mp->run_data.term_in.data) + xfree(mp->run_data.term_in.data); + mp->run_data.term_in.data = xstrdup(s); + mp->run_data.term_in.cur = mp->run_data.term_in.data; + mp->run_data.term_in.size = l; + if (mp->run_state == 0) { + mp->selector=term_only; + @<Start non-interactive work@>; + } + mp->run_state =1; + (void)mp_input_ln(mp,mp->term_in); + mp_firm_up_the_line(mp); + mp->buffer[limit]=xord('%'); + mp->first=(size_t)(limit+1); + loc=start; + do { + mp_do_statement(mp); + } while (mp->cur_cmd!=stop); + mp_final_cleanup(mp); + mp_close_files_and_terminate(mp); + } + return mp->history; +} + +@ This function cleans up +@c +int mp_finish (MP mp) { + int history = 0; + if (mp->finished || mp->history >= mp_fatal_error_stop) { + history = mp->history; + mp_free(mp); + return history; + } + xfree(mp->jump_buf); + mp->jump_buf = malloc(sizeof(jmp_buf)); + if (mp->jump_buf == NULL || setjmp(*(mp->jump_buf)) != 0) { + history = mp->history; + } else { + history = mp->history; + mp_final_cleanup(mp); /* prepare for death */ + } + mp_close_files_and_terminate(mp); + mp_free(mp); + return history; +} + +@ People may want to know the library version +@c +char * mp_metapost_version (void) { + return mp_strdup(metapost_version); +} + +@ @<Exported function headers@>= +int mp_run (MP mp); +int mp_execute (MP mp, char *s, size_t l); +int mp_finish (MP mp); +char * mp_metapost_version (void); + +@ @<Put each...@>= +mp_primitive(mp, "end",stop,0); +@:end_}{\&{end} primitive@> +mp_primitive(mp, "dump",stop,1); +@:dump_}{\&{dump} primitive@> + +@ @<Cases of |print_cmd...@>= +case stop: + if ( m==0 ) mp_print(mp, "end"); + else mp_print(mp, "dump"); + break; + +@* \[41] Commands. +Let's turn now to statements that are classified as ``commands'' because +of their imperative nature. We'll begin with simple ones, so that it +will be clear how to hook command processing into the |do_statement| routine; +then we'll tackle the tougher commands. + +Here's one of the simplest: + +@<Cases of |do_statement|...@>= +case mp_random_seed: mp_do_random_seed(mp); break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_random_seed (MP mp) ; + +@ @c void mp_do_random_seed (MP mp) { + mp_get_x_next(mp); + if ( mp->cur_cmd!=assignment ) { + mp_missing_err(mp, ":="); +@.Missing `:='@> + help1("Always say `randomseed:=<numeric expression>'."); + mp_back_error(mp); + }; + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ) { + exp_err("Unknown value will be ignored"); +@.Unknown value...ignored@> + help2("Your expression was too random for me to handle,", + "so I won't change the random seed just now."); + mp_put_get_flush_error(mp, 0); + } else { + @<Initialize the random seed to |cur_exp|@>; + } +} + +@ @<Initialize the random seed to |cur_exp|@>= +{ + mp_init_randoms(mp, mp->cur_exp); + if ( mp->selector>=log_only && mp->selector<write_file) { + mp->old_setting=mp->selector; mp->selector=log_only; + mp_print_nl(mp, "{randomseed:="); + mp_print_scaled(mp, mp->cur_exp); + mp_print_char(mp, xord('}')); + mp_print_nl(mp, ""); mp->selector=mp->old_setting; + } +} + +@ And here's another simple one (somewhat different in flavor): + +@<Cases of |do_statement|...@>= +case mode_command: + mp_print_ln(mp); mp->interaction=mp->cur_mod; + @<Initialize the print |selector| based on |interaction|@>; + if ( mp->log_opened ) mp->selector=mp->selector+2; + mp_get_x_next(mp); + break; + +@ @<Put each...@>= +mp_primitive(mp, "batchmode",mode_command,mp_batch_mode); +@:mp_batch_mode_}{\&{batchmode} primitive@> +mp_primitive(mp, "nonstopmode",mode_command,mp_nonstop_mode); +@:mp_nonstop_mode_}{\&{nonstopmode} primitive@> +mp_primitive(mp, "scrollmode",mode_command,mp_scroll_mode); +@:mp_scroll_mode_}{\&{scrollmode} primitive@> +mp_primitive(mp, "errorstopmode",mode_command,mp_error_stop_mode); +@:mp_error_stop_mode_}{\&{errorstopmode} primitive@> + +@ @<Cases of |print_cmd_mod|...@>= +case mode_command: + switch (m) { + case mp_batch_mode: mp_print(mp, "batchmode"); break; + case mp_nonstop_mode: mp_print(mp, "nonstopmode"); break; + case mp_scroll_mode: mp_print(mp, "scrollmode"); break; + default: mp_print(mp, "errorstopmode"); break; + } + break; + +@ The `\&{inner}' and `\&{outer}' commands are only slightly harder. + +@<Cases of |do_statement|...@>= +case protection_command: mp_do_protection(mp); break; + +@ @<Put each...@>= +mp_primitive(mp, "inner",protection_command,0); +@:inner_}{\&{inner} primitive@> +mp_primitive(mp, "outer",protection_command,1); +@:outer_}{\&{outer} primitive@> + +@ @<Cases of |print_cmd...@>= +case protection_command: + if ( m==0 ) mp_print(mp, "inner"); + else mp_print(mp, "outer"); + break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_protection (MP mp) ; + +@ @c void mp_do_protection (MP mp) { + int m; /* 0 to unprotect, 1 to protect */ + halfword t; /* the |eq_type| before we change it */ + m=mp->cur_mod; + do { + mp_get_symbol(mp); t=eq_type(mp->cur_sym); + if ( m==0 ) { + if ( t>=outer_tag ) + eq_type(mp->cur_sym)=t-outer_tag; + } else if ( t<outer_tag ) { + eq_type(mp->cur_sym)=t+outer_tag; + } + mp_get_x_next(mp); + } while (mp->cur_cmd==comma); +} + +@ \MP\ never defines the tokens `\.(' and `\.)' to be primitives, but +plain \MP\ begins with the declaration `\&{delimiters} \.{()}'. Such a +declaration assigns the command code |left_delimiter| to `\.{(}' and +|right_delimiter| to `\.{)}'; the |equiv| of each delimiter is the +hash address of its mate. + +@<Cases of |do_statement|...@>= +case delimiters: mp_def_delims(mp); break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_def_delims (MP mp) ; + +@ @c void mp_def_delims (MP mp) { + pointer l_delim,r_delim; /* the new delimiter pair */ + mp_get_clear_symbol(mp); l_delim=mp->cur_sym; + mp_get_clear_symbol(mp); r_delim=mp->cur_sym; + eq_type(l_delim)=left_delimiter; equiv(l_delim)=r_delim; + eq_type(r_delim)=right_delimiter; equiv(r_delim)=l_delim; + mp_get_x_next(mp); +} + +@ Here is a procedure that is called when \MP\ has reached a point +where some right delimiter is mandatory. + +@<Declarations@>= +static void mp_check_delimiter (MP mp,pointer l_delim, pointer r_delim); + +@ @c +void mp_check_delimiter (MP mp,pointer l_delim, pointer r_delim) { + if ( mp->cur_cmd==right_delimiter ) + if ( mp->cur_mod==l_delim ) + return; + if ( mp->cur_sym!=r_delim ) { + mp_missing_err(mp, str(text(r_delim))); +@.Missing `)'@> + help2("I found no right delimiter to match a left one. So I've", + "put one in, behind the scenes; this may fix the problem."); + mp_back_error(mp); + } else { + print_err("The token `"); mp_print_text(r_delim); +@.The token...delimiter@> + mp_print(mp, "' is no longer a right delimiter"); + help3("Strange: This token has lost its former meaning!", + "I'll read it as a right delimiter this time;", + "but watch out, I'll probably miss it later."); + mp_error(mp); + } +} + +@ The next four commands save or change the values associated with tokens. + +@<Cases of |do_statement|...@>= +case save_command: + do { + mp_get_symbol(mp); mp_save_variable(mp, mp->cur_sym); mp_get_x_next(mp); + } while (mp->cur_cmd==comma); + break; +case interim_command: mp_do_interim(mp); break; +case let_command: mp_do_let(mp); break; +case new_internal: mp_do_new_internal(mp); break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_statement (MP mp); +static void mp_do_interim (MP mp); + +@ @c void mp_do_interim (MP mp) { + mp_get_x_next(mp); + if ( mp->cur_cmd!=internal_quantity ) { + print_err("The token `"); +@.The token...quantity@> + if ( mp->cur_sym==0 ) mp_print(mp, "(%CAPSULE)"); + else mp_print_text(mp->cur_sym); + mp_print(mp, "' isn't an internal quantity"); + help1("Something like `tracingonline' should follow `interim'."); + mp_back_error(mp); + } else { + mp_save_internal(mp, mp->cur_mod); mp_back_input(mp); + } + mp_do_statement(mp); +} + +@ The following procedure is careful not to undefine the left-hand symbol +too soon, lest commands like `{\tt let x=x}' have a surprising effect. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_let (MP mp) ; + +@ @c void mp_do_let (MP mp) { + pointer l; /* hash location of the left-hand symbol */ + mp_get_symbol(mp); l=mp->cur_sym; mp_get_x_next(mp); + if ( mp->cur_cmd!=equals ) if ( mp->cur_cmd!=assignment ) { + mp_missing_err(mp, "="); +@.Missing `='@> + help3("You should have said `let symbol = something'.", + "But don't worry; I'll pretend that an equals sign", + "was present. The next token I read will be `something'."); + mp_back_error(mp); + } + mp_get_symbol(mp); + switch (mp->cur_cmd) { + case defined_macro: case secondary_primary_macro: + case tertiary_secondary_macro: case expression_tertiary_macro: + add_mac_ref(mp->cur_mod); + break; + default: + break; + } + mp_clear_symbol(mp, l,false); eq_type(l)=mp->cur_cmd; + if ( mp->cur_cmd==tag_token ) equiv(l)=null; + else equiv(l)=mp->cur_mod; + mp_get_x_next(mp); +} + +@ @<Declarations@>= +static void mp_do_new_internal (MP mp) ; + +@ @<Internal library ...@>= +void mp_grow_internals (MP mp, int l); + +@ @c +void mp_grow_internals (MP mp, int l) { + scaled *internal; + char * *int_name; + int k; + if ( hash_end+l>max_halfword ) { + mp_confusion(mp, "out of memory space"); /* can't be reached */ + } + int_name = xmalloc ((l+1),sizeof(char *)); + internal = xmalloc ((l+1),sizeof(scaled)); + for (k=0;k<=l; k++ ) { + if (k<=mp->max_internal) { + internal[k]=mp->internal[k]; + int_name[k]=mp->int_name[k]; + } else { + internal[k]=0; + int_name[k]=NULL; + } + } + xfree(mp->internal); xfree(mp->int_name); + mp->int_name = int_name; + mp->internal = internal; + mp->max_internal = l; +} + +void mp_do_new_internal (MP mp) { + do { + if ( mp->int_ptr==mp->max_internal ) { + mp_grow_internals(mp, (mp->max_internal + (mp->max_internal/4))); + } + mp_get_clear_symbol(mp); incr(mp->int_ptr); + eq_type(mp->cur_sym)=internal_quantity; + equiv(mp->cur_sym)=mp->int_ptr; + if(mp->int_name[mp->int_ptr]!=NULL) + xfree(mp->int_name[mp->int_ptr]); + mp->int_name[mp->int_ptr]=str(text(mp->cur_sym)); + mp->internal[mp->int_ptr]=0; + mp_get_x_next(mp); + } while (mp->cur_cmd==comma); +} + +@ @<Dealloc variables@>= +for (k=0;k<=mp->max_internal;k++) { + xfree(mp->int_name[k]); +} +xfree(mp->internal); +xfree(mp->int_name); + + +@ The various `\&{show}' commands are distinguished by modifier fields +in the usual way. + +@d show_token_code 0 /* show the meaning of a single token */ +@d show_stats_code 1 /* show current memory and string usage */ +@d show_code 2 /* show a list of expressions */ +@d show_var_code 3 /* show a variable and its descendents */ +@d show_dependencies_code 4 /* show dependent variables in terms of independents */ + +@<Put each...@>= +mp_primitive(mp, "showtoken",show_command,show_token_code); +@:show_token_}{\&{showtoken} primitive@> +mp_primitive(mp, "showstats",show_command,show_stats_code); +@:show_stats_}{\&{showstats} primitive@> +mp_primitive(mp, "show",show_command,show_code); +@:show_}{\&{show} primitive@> +mp_primitive(mp, "showvariable",show_command,show_var_code); +@:show_var_}{\&{showvariable} primitive@> +mp_primitive(mp, "showdependencies",show_command,show_dependencies_code); +@:show_dependencies_}{\&{showdependencies} primitive@> + +@ @<Cases of |print_cmd...@>= +case show_command: + switch (m) { + case show_token_code:mp_print(mp, "showtoken"); break; + case show_stats_code:mp_print(mp, "showstats"); break; + case show_code:mp_print(mp, "show"); break; + case show_var_code:mp_print(mp, "showvariable"); break; + default: mp_print(mp, "showdependencies"); break; + } + break; + +@ @<Cases of |do_statement|...@>= +case show_command:mp_do_show_whatever(mp); break; + +@ The value of |cur_mod| controls the |verbosity| in the |print_exp| routine: +if it's |show_code|, complicated structures are abbreviated, otherwise +they aren't. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_show (MP mp) ; + +@ @c void mp_do_show (MP mp) { + do { + mp_get_x_next(mp); mp_scan_expression(mp); + mp_print_nl(mp, ">> "); +@.>>@> + mp_print_exp(mp, null,2); mp_flush_cur_exp(mp, 0); + } while (mp->cur_cmd==comma); +} + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_disp_token (MP mp) ; + +@ @c void mp_disp_token (MP mp) { + mp_print_nl(mp, "> "); +@.>\relax@> + if ( mp->cur_sym==0 ) { + @<Show a numeric or string or capsule token@>; + } else { + mp_print_text(mp->cur_sym); mp_print_char(mp, xord('=')); + if ( eq_type(mp->cur_sym)>=outer_tag ) mp_print(mp, "(outer) "); + mp_print_cmd_mod(mp, mp->cur_cmd,mp->cur_mod); + if ( mp->cur_cmd==defined_macro ) { + mp_print_ln(mp); mp_show_macro(mp, mp->cur_mod,null,100000); + } /* this avoids recursion between |show_macro| and |print_cmd_mod| */ +@^recursion@> + } +} + +@ @<Show a numeric or string or capsule token@>= +{ + if ( mp->cur_cmd==numeric_token ) { + mp_print_scaled(mp, mp->cur_mod); + } else if ( mp->cur_cmd==capsule_token ) { + mp_print_capsule(mp,mp->cur_mod); + } else { + mp_print_char(mp, xord('"')); + mp_print_str(mp, mp->cur_mod); mp_print_char(mp, xord('"')); + delete_str_ref(mp->cur_mod); + } +} + +@ The following cases of |print_cmd_mod| might arise in connection +with |disp_token|, although they don't necessarily correspond to +primitive tokens. + +@<Cases of |print_cmd_...@>= +case left_delimiter: +case right_delimiter: + if ( c==left_delimiter ) mp_print(mp, "left"); + else mp_print(mp, "right"); + mp_print(mp, " delimiter that matches "); + mp_print_text(m); + break; +case tag_token: + if ( m==null ) mp_print(mp, "tag"); + else mp_print(mp, "variable"); + break; +case defined_macro: + mp_print(mp, "macro:"); + break; +case secondary_primary_macro: +case tertiary_secondary_macro: +case expression_tertiary_macro: + mp_print_cmd_mod(mp, macro_def,c); + mp_print(mp, "'d macro:"); + mp_print_ln(mp); mp_show_token_list(mp, mp_link(mp_link(m)),null,1000,0); + break; +case repeat_loop: + mp_print(mp, "[repeat the loop]"); + break; +case internal_quantity: + mp_print(mp, mp->int_name[m]); + break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_show_token (MP mp) ; + +@ @c void mp_do_show_token (MP mp) { + do { + get_t_next; mp_disp_token(mp); + mp_get_x_next(mp); + } while (mp->cur_cmd==comma); +} + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_show_stats (MP mp) ; + +@ @c void mp_do_show_stats (MP mp) { + mp_print_nl(mp, "Memory usage "); +@.Memory usage...@> + mp_print_int(mp, mp->var_used); mp_print_char(mp, xord('&')); mp_print_int(mp, mp->dyn_used); + mp_print(mp, " ("); mp_print_int(mp, mp->hi_mem_min-mp->lo_mem_max-1); + mp_print(mp, " still untouched)"); mp_print_ln(mp); + mp_print_nl(mp, "String usage "); + mp_print_int(mp, mp->strs_in_use-mp->init_str_use); + mp_print_char(mp, xord('&')); mp_print_int(mp, mp->pool_in_use-mp->init_pool_ptr); + mp_print(mp, " ("); + mp_print_int(mp, mp->max_strings-1-mp->strs_used_up); mp_print_char(mp, xord('&')); + mp_print_int(mp, mp->pool_size-mp->pool_ptr); + mp_print(mp, " now untouched)"); mp_print_ln(mp); + mp_get_x_next(mp); +} + +@ Here's a recursive procedure that gives an abbreviated account +of a variable, for use by |do_show_var|. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_disp_var (MP mp,pointer p) ; + +@ @c void mp_disp_var (MP mp,pointer p) { + pointer q; /* traverses attributes and subscripts */ + int n; /* amount of macro text to show */ + if ( mp_type(p)==mp_structured ) { + @<Descend the structure@>; + } else if ( mp_type(p)>=mp_unsuffixed_macro ) { + @<Display a variable macro@>; + } else if ( mp_type(p)!=undefined ){ + mp_print_nl(mp, ""); mp_print_variable_name(mp, p); + mp_print_char(mp, xord('=')); + mp_print_exp(mp, p,0); + } +} + +@ @<Descend the structure@>= +{ + q=attr_head(p); + do { mp_disp_var(mp, q); q=mp_link(q); } while (q!=end_attr); + q=subscr_head(p); + while ( mp_name_type(q)==mp_subscr ) { + mp_disp_var(mp, q); q=mp_link(q); + } +} + +@ @<Display a variable macro@>= +{ + mp_print_nl(mp, ""); mp_print_variable_name(mp, p); + if ( mp_type(p)>mp_unsuffixed_macro ) + mp_print(mp, "@@#"); /* |suffixed_macro| */ + mp_print(mp, "=macro:"); + if ( (int)mp->file_offset>=mp->max_print_line-20 ) n=5; + else n=mp->max_print_line-mp->file_offset-15; + mp_show_macro(mp, value(p),null,n); +} + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_show_var (MP mp) ; + +@ @c void mp_do_show_var (MP mp) { + do { + get_t_next; + if ( mp->cur_sym>0 ) if ( mp->cur_sym<=hash_end ) + if ( mp->cur_cmd==tag_token ) if ( mp->cur_mod!=null ) { + mp_disp_var(mp, mp->cur_mod); goto DONE; + } + mp_disp_token(mp); + DONE: + mp_get_x_next(mp); + } while (mp->cur_cmd==comma); +} + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_show_dependencies (MP mp) ; + +@ @c void mp_do_show_dependencies (MP mp) { + pointer p; /* link that runs through all dependencies */ + p=mp_link(dep_head); + while ( p!=dep_head ) { + if ( mp_interesting(mp, p) ) { + mp_print_nl(mp, ""); mp_print_variable_name(mp, p); + if ( mp_type(p)==mp_dependent ) mp_print_char(mp, xord('=')); + else mp_print(mp, " = "); /* extra spaces imply proto-dependency */ + mp_print_dependency(mp, dep_list(p),mp_type(p)); + } + p=dep_list(p); + while ( mp_info(p)!=null ) p=mp_link(p); + p=mp_link(p); + } + mp_get_x_next(mp); +} + +@ Finally we are ready for the procedure that governs all of the +show commands. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_show_whatever (MP mp) ; + +@ @c void mp_do_show_whatever (MP mp) { + if ( mp->interaction==mp_error_stop_mode ) wake_up_terminal; + switch (mp->cur_mod) { + case show_token_code:mp_do_show_token(mp); break; + case show_stats_code:mp_do_show_stats(mp); break; + case show_code:mp_do_show(mp); break; + case show_var_code:mp_do_show_var(mp); break; + case show_dependencies_code:mp_do_show_dependencies(mp); break; + } /* there are no other cases */ + if ( mp->internal[mp_showstopping]>0 ){ + print_err("OK"); +@.OK@> + if ( mp->interaction<mp_error_stop_mode ) { + help0; decr(mp->error_count); + } else { + help1("This isn't an error message; I'm just showing something."); + } + if ( mp->cur_cmd==semicolon ) mp_error(mp); + else mp_put_get_error(mp); + } +} + +@ The `\&{addto}' command needs the following additional primitives: + +@d double_path_code 0 /* command modifier for `\&{doublepath}' */ +@d contour_code 1 /* command modifier for `\&{contour}' */ +@d also_code 2 /* command modifier for `\&{also}' */ + +@ Pre and postscripts need two new identifiers: + +@d with_mp_pre_script 11 +@d with_mp_post_script 13 + +@<Put each...@>= +mp_primitive(mp, "doublepath",thing_to_add,double_path_code); +@:double_path_}{\&{doublepath} primitive@> +mp_primitive(mp, "contour",thing_to_add,contour_code); +@:contour_}{\&{contour} primitive@> +mp_primitive(mp, "also",thing_to_add,also_code); +@:also_}{\&{also} primitive@> +mp_primitive(mp, "withpen",with_option,mp_pen_type); +@:with_pen_}{\&{withpen} primitive@> +mp_primitive(mp, "dashed",with_option,mp_picture_type); +@:dashed_}{\&{dashed} primitive@> +mp_primitive(mp, "withprescript",with_option,with_mp_pre_script); +@:with_mp_pre_script_}{\&{withprescript} primitive@> +mp_primitive(mp, "withpostscript",with_option,with_mp_post_script); +@:with_mp_post_script_}{\&{withpostscript} primitive@> +mp_primitive(mp, "withoutcolor",with_option,mp_no_model); +@:with_color_}{\&{withoutcolor} primitive@> +mp_primitive(mp, "withgreyscale",with_option,mp_grey_model); +@:with_color_}{\&{withgreyscale} primitive@> +mp_primitive(mp, "withcolor",with_option,mp_uninitialized_model); +@:with_color_}{\&{withcolor} primitive@> +/* \&{withrgbcolor} is an alias for \&{withcolor} */ +mp_primitive(mp, "withrgbcolor",with_option,mp_rgb_model); +@:with_color_}{\&{withrgbcolor} primitive@> +mp_primitive(mp, "withcmykcolor",with_option,mp_cmyk_model); +@:with_color_}{\&{withcmykcolor} primitive@> + +@ @<Cases of |print_cmd...@>= +case thing_to_add: + if ( m==contour_code ) mp_print(mp, "contour"); + else if ( m==double_path_code ) mp_print(mp, "doublepath"); + else mp_print(mp, "also"); + break; +case with_option: + if ( m==mp_pen_type ) mp_print(mp, "withpen"); + else if ( m==with_mp_pre_script ) mp_print(mp, "withprescript"); + else if ( m==with_mp_post_script ) mp_print(mp, "withpostscript"); + else if ( m==mp_no_model ) mp_print(mp, "withoutcolor"); + else if ( m==mp_rgb_model ) mp_print(mp, "withrgbcolor"); + else if ( m==mp_uninitialized_model ) mp_print(mp, "withcolor"); + else if ( m==mp_cmyk_model ) mp_print(mp, "withcmykcolor"); + else if ( m==mp_grey_model ) mp_print(mp, "withgreyscale"); + else mp_print(mp, "dashed"); + break; + +@ The |scan_with_list| procedure parses a $\langle$with list$\rangle$ and +updates the list of graphical objects starting at |p|. Each $\langle$with +clause$\rangle$ updates all graphical objects whose |type| is compatible. +Other objects are ignored. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_scan_with_list (MP mp,pointer p) ; + +@ @c void mp_scan_with_list (MP mp,pointer p) { + quarterword t; /* |cur_mod| of the |with_option| (should match |cur_type|) */ + pointer q; /* for list manipulation */ + unsigned old_setting; /* saved |selector| setting */ + pointer k; /* for finding the near-last item in a list */ + str_number s; /* for string cleanup after combining */ + pointer cp,pp,dp,ap,bp; + /* objects being updated; |void| initially; |null| to suppress update */ + cp=mp_void; pp=mp_void; dp=mp_void; ap=mp_void; bp=mp_void; + k=0; + while ( mp->cur_cmd==with_option ){ + t=mp->cur_mod; + mp_get_x_next(mp); + if ( t!=mp_no_model ) mp_scan_expression(mp); + if (((t==with_mp_pre_script)&&(mp->cur_type!=mp_string_type))|| + ((t==with_mp_post_script)&&(mp->cur_type!=mp_string_type))|| + ((t==mp_uninitialized_model)&& + ((mp->cur_type!=mp_cmykcolor_type)&&(mp->cur_type!=mp_color_type) + &&(mp->cur_type!=mp_known)&&(mp->cur_type!=mp_boolean_type)))|| + ((t==mp_cmyk_model)&&(mp->cur_type!=mp_cmykcolor_type))|| + ((t==mp_rgb_model)&&(mp->cur_type!=mp_color_type))|| + ((t==mp_grey_model)&&(mp->cur_type!=mp_known))|| + ((t==mp_pen_type)&&(mp->cur_type!=t))|| + ((t==mp_picture_type)&&(mp->cur_type!=t)) ) { + @<Complain about improper type@>; + } else if ( t==mp_uninitialized_model ) { + if ( cp==mp_void ) @<Make |cp| a colored object in object list~|p|@>; + if ( cp!=null ) + @<Transfer a color from the current expression to object~|cp|@>; + mp_flush_cur_exp(mp, 0); + } else if ( t==mp_rgb_model ) { + if ( cp==mp_void ) @<Make |cp| a colored object in object list~|p|@>; + if ( cp!=null ) + @<Transfer a rgbcolor from the current expression to object~|cp|@>; + mp_flush_cur_exp(mp, 0); + } else if ( t==mp_cmyk_model ) { + if ( cp==mp_void ) @<Make |cp| a colored object in object list~|p|@>; + if ( cp!=null ) + @<Transfer a cmykcolor from the current expression to object~|cp|@>; + mp_flush_cur_exp(mp, 0); + } else if ( t==mp_grey_model ) { + if ( cp==mp_void ) @<Make |cp| a colored object in object list~|p|@>; + if ( cp!=null ) + @<Transfer a greyscale from the current expression to object~|cp|@>; + mp_flush_cur_exp(mp, 0); + } else if ( t==mp_no_model ) { + if ( cp==mp_void ) @<Make |cp| a colored object in object list~|p|@>; + if ( cp!=null ) + @<Transfer a noncolor from the current expression to object~|cp|@>; + } else if ( t==mp_pen_type ) { + if ( pp==mp_void ) @<Make |pp| an object in list~|p| that needs a pen@>; + if ( pp!=null ) { + if ( mp_pen_p(pp)!=null ) mp_toss_knot_list(mp, mp_pen_p(pp)); + mp_pen_p(pp)=mp->cur_exp; mp->cur_type=mp_vacuous; + } + } else if ( t==with_mp_pre_script ) { + if ( ap==mp_void ) + ap=p; + while ( (ap!=null)&&(! has_color(ap)) ) + ap=mp_link(ap); + if ( ap!=null ) { + if ( mp_pre_script(ap)!=null ) { /* build a new,combined string */ + s=mp_pre_script(ap); + old_setting=mp->selector; + mp->selector=new_string; + str_room(length(mp_pre_script(ap))+length(mp->cur_exp)+2); + mp_print_str(mp, mp->cur_exp); + append_char(13); /* a forced \ps\ newline */ + mp_print_str(mp, mp_pre_script(ap)); + mp_pre_script(ap)=mp_make_string(mp); + delete_str_ref(s); + mp->selector=old_setting; + } else { + mp_pre_script(ap)=mp->cur_exp; + } + mp->cur_type=mp_vacuous; + } + } else if ( t==with_mp_post_script ) { + if ( bp==mp_void ) + k=p; + bp=k; + while ( mp_link(k)!=null ) { + k=mp_link(k); + if ( has_color(k) ) bp=k; + } + if ( bp!=null ) { + if ( mp_post_script(bp)!=null ) { + s=mp_post_script(bp); + old_setting=mp->selector; + mp->selector=new_string; + str_room(length(mp_post_script(bp))+length(mp->cur_exp)+2); + mp_print_str(mp, mp_post_script(bp)); + append_char(13); /* a forced \ps\ newline */ + mp_print_str(mp, mp->cur_exp); + mp_post_script(bp)=mp_make_string(mp); + delete_str_ref(s); + mp->selector=old_setting; + } else { + mp_post_script(bp)=mp->cur_exp; + } + mp->cur_type=mp_vacuous; + } + } else { + if ( dp==mp_void ) { + @<Make |dp| a stroked node in list~|p|@>; + } + if ( dp!=null ) { + if ( mp_dash_p(dp)!=null ) delete_edge_ref(mp_dash_p(dp)); + mp_dash_p(dp)=mp_make_dashes(mp, mp->cur_exp); + dash_scale(dp)=unity; + mp->cur_type=mp_vacuous; + } + } + } + @<Copy the information from objects |cp|, |pp|, and |dp| into the rest + of the list@>; +} + +@ @<Complain about improper type@>= +{ exp_err("Improper type"); +@.Improper type@> +help2("Next time say `withpen <known pen expression>';", + "I'll ignore the bad `with' clause and look for another."); +if ( t==with_mp_pre_script ) + mp->help_line[1]="Next time say `withprescript <known string expression>';"; +else if ( t==with_mp_post_script ) + mp->help_line[1]="Next time say `withpostscript <known string expression>';"; +else if ( t==mp_picture_type ) + mp->help_line[1]="Next time say `dashed <known picture expression>';"; +else if ( t==mp_uninitialized_model ) + mp->help_line[1]="Next time say `withcolor <known color expression>';"; +else if ( t==mp_rgb_model ) + mp->help_line[1]="Next time say `withrgbcolor <known color expression>';"; +else if ( t==mp_cmyk_model ) + mp->help_line[1]="Next time say `withcmykcolor <known cmykcolor expression>';"; +else if ( t==mp_grey_model ) + mp->help_line[1]="Next time say `withgreyscale <known numeric expression>';";; +mp_put_get_flush_error(mp, 0); +} + +@ Forcing the color to be between |0| and |unity| here guarantees that no +picture will ever contain a color outside the legal range for \ps\ graphics. + +@<Transfer a color from the current expression to object~|cp|@>= +{ if ( mp->cur_type==mp_color_type ) + @<Transfer a rgbcolor from the current expression to object~|cp|@> +else if ( mp->cur_type==mp_cmykcolor_type ) + @<Transfer a cmykcolor from the current expression to object~|cp|@> +else if ( mp->cur_type==mp_known ) + @<Transfer a greyscale from the current expression to object~|cp|@> +else if ( mp->cur_exp==false_code ) + @<Transfer a noncolor from the current expression to object~|cp|@>; +} + +@ @<Transfer a rgbcolor from the current expression to object~|cp|@>= +{ q=value(mp->cur_exp); +cyan_val(cp)=0; +magenta_val(cp)=0; +yellow_val(cp)=0; +black_val(cp)=0; +red_val(cp)=value(red_part_loc(q)); +green_val(cp)=value(green_part_loc(q)); +blue_val(cp)=value(blue_part_loc(q)); +mp_color_model(cp)=mp_rgb_model; +if ( red_val(cp)<0 ) red_val(cp)=0; +if ( green_val(cp)<0 ) green_val(cp)=0; +if ( blue_val(cp)<0 ) blue_val(cp)=0; +if ( red_val(cp)>unity ) red_val(cp)=unity; +if ( green_val(cp)>unity ) green_val(cp)=unity; +if ( blue_val(cp)>unity ) blue_val(cp)=unity; +} + +@ @<Transfer a cmykcolor from the current expression to object~|cp|@>= +{ q=value(mp->cur_exp); +cyan_val(cp)=value(cyan_part_loc(q)); +magenta_val(cp)=value(magenta_part_loc(q)); +yellow_val(cp)=value(yellow_part_loc(q)); +black_val(cp)=value(black_part_loc(q)); +mp_color_model(cp)=mp_cmyk_model; +if ( cyan_val(cp)<0 ) cyan_val(cp)=0; +if ( magenta_val(cp)<0 ) magenta_val(cp)=0; +if ( yellow_val(cp)<0 ) yellow_val(cp)=0; +if ( black_val(cp)<0 ) black_val(cp)=0; +if ( cyan_val(cp)>unity ) cyan_val(cp)=unity; +if ( magenta_val(cp)>unity ) magenta_val(cp)=unity; +if ( yellow_val(cp)>unity ) yellow_val(cp)=unity; +if ( black_val(cp)>unity ) black_val(cp)=unity; +} + +@ @<Transfer a greyscale from the current expression to object~|cp|@>= +{ q=mp->cur_exp; +cyan_val(cp)=0; +magenta_val(cp)=0; +yellow_val(cp)=0; +black_val(cp)=0; +grey_val(cp)=q; +mp_color_model(cp)=mp_grey_model; +if ( grey_val(cp)<0 ) grey_val(cp)=0; +if ( grey_val(cp)>unity ) grey_val(cp)=unity; +} + +@ @<Transfer a noncolor from the current expression to object~|cp|@>= +{ +cyan_val(cp)=0; +magenta_val(cp)=0; +yellow_val(cp)=0; +black_val(cp)=0; +grey_val(cp)=0; +mp_color_model(cp)=mp_no_model; +} + +@ @<Make |cp| a colored object in object list~|p|@>= +{ cp=p; + while ( cp!=null ){ + if ( has_color(cp) ) break; + cp=mp_link(cp); + } +} + +@ @<Make |pp| an object in list~|p| that needs a pen@>= +{ pp=p; + while ( pp!=null ) { + if ( has_pen(pp) ) break; + pp=mp_link(pp); + } +} + +@ @<Make |dp| a stroked node in list~|p|@>= +{ dp=p; + while ( dp!=null ) { + if ( mp_type(dp)==mp_stroked_code ) break; + dp=mp_link(dp); + } +} + +@ @<Copy the information from objects |cp|, |pp|, and |dp| into...@>= +@<Copy |cp|'s color into the colored objects linked to~|cp|@>; +if ( pp>mp_void ) { + @<Copy |mp_pen_p(pp)| into stroked and filled nodes linked to |pp|@>; +} +if ( dp>mp_void ) { + @<Make stroked nodes linked to |dp| refer to |mp_dash_p(dp)|@>; +} + + +@ @<Copy |cp|'s color into the colored objects linked to~|cp|@>= +{ q=mp_link(cp); + while ( q!=null ) { + if ( has_color(q) ) { + red_val(q)=red_val(cp); + green_val(q)=green_val(cp); + blue_val(q)=blue_val(cp); + black_val(q)=black_val(cp); + mp_color_model(q)=mp_color_model(cp); + } + q=mp_link(q); + } +} + +@ @<Copy |mp_pen_p(pp)| into stroked and filled nodes linked to |pp|@>= +{ q=mp_link(pp); + while ( q!=null ) { + if ( has_pen(q) ) { + if ( mp_pen_p(q)!=null ) mp_toss_knot_list(mp, mp_pen_p(q)); + mp_pen_p(q)=copy_pen(mp_pen_p(pp)); + } + q=mp_link(q); + } +} + +@ @<Make stroked nodes linked to |dp| refer to |mp_dash_p(dp)|@>= +{ q=mp_link(dp); + while ( q!=null ) { + if ( mp_type(q)==mp_stroked_code ) { + if ( mp_dash_p(q)!=null ) delete_edge_ref(mp_dash_p(q)); + mp_dash_p(q)=mp_dash_p(dp); + dash_scale(q)=unity; + if ( mp_dash_p(q)!=null ) add_edge_ref(mp_dash_p(q)); + } + q=mp_link(q); + } +} + +@ One of the things we need to do when we've parsed an \&{addto} or +similar command is find the header of a supposed \&{picture} variable, given +a token list for that variable. Since the edge structure is about to be +updated, we use |private_edges| to make sure that this is possible. + +@<Declare action procedures for use by |do_statement|@>= +static pointer mp_find_edges_var (MP mp, pointer t) ; + +@ @c pointer mp_find_edges_var (MP mp, pointer t) { + pointer p; + pointer cur_edges; /* the return value */ + p=mp_find_variable(mp, t); cur_edges=null; + if ( p==null ) { + mp_obliterated(mp, t); mp_put_get_error(mp); + } else if ( mp_type(p)!=mp_picture_type ) { + print_err("Variable "); mp_show_token_list(mp, t,null,1000,0); +@.Variable x is the wrong type@> + mp_print(mp, " is the wrong type ("); + mp_print_type(mp, mp_type(p)); mp_print_char(mp, xord(')')); + help2("I was looking for a \"known\" picture variable.", + "So I'll not change anything just now."); + mp_put_get_error(mp); + } else { + value(p)=mp_private_edges(mp, value(p)); + cur_edges=value(p); + } + mp_flush_node_list(mp, t); + return cur_edges; +} + +@ @<Cases of |do_statement|...@>= +case add_to_command: mp_do_add_to(mp); break; +case bounds_command:mp_do_bounds(mp); break; + +@ @<Put each...@>= +mp_primitive(mp, "clip",bounds_command,mp_start_clip_code); +@:clip_}{\&{clip} primitive@> +mp_primitive(mp, "setbounds",bounds_command,mp_start_bounds_code); +@:set_bounds_}{\&{setbounds} primitive@> + +@ @<Cases of |print_cmd...@>= +case bounds_command: + if ( m==mp_start_clip_code ) mp_print(mp, "clip"); + else mp_print(mp, "setbounds"); + break; + +@ The following function parses the beginning of an \&{addto} or \&{clip} +command: it expects a variable name followed by a token with |cur_cmd=sep| +and then an expression. The function returns the token list for the variable +and stores the command modifier for the separator token in the global variable +|last_add_type|. We must be careful because this variable might get overwritten +any time we call |get_x_next|. + +@<Glob...@>= +quarterword last_add_type; + /* command modifier that identifies the last \&{addto} command */ + +@ @<Declare action procedures for use by |do_statement|@>= +static pointer mp_start_draw_cmd (MP mp,quarterword sep) ; + +@ @c pointer mp_start_draw_cmd (MP mp,quarterword sep) { + pointer lhv; /* variable to add to left */ + quarterword add_type=0; /* value to be returned in |last_add_type| */ + lhv=null; + mp_get_x_next(mp); mp->var_flag=sep; mp_scan_primary(mp); + if ( mp->cur_type!=mp_token_list ) { + @<Abandon edges command because there's no variable@>; + } else { + lhv=mp->cur_exp; add_type=mp->cur_mod; + mp->cur_type=mp_vacuous; mp_get_x_next(mp); mp_scan_expression(mp); + } + mp->last_add_type=add_type; + return lhv; +} + +@ @<Abandon edges command because there's no variable@>= +{ exp_err("Not a suitable variable"); +@.Not a suitable variable@> + help4("At this point I needed to see the name of a picture variable.", + "(Or perhaps you have indeed presented me with one; I might", + "have missed it, if it wasn't followed by the proper token.)", + "So I'll not change anything just now."); + mp_put_get_flush_error(mp, 0); +} + +@ Here is an example of how to use |start_draw_cmd|. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_bounds (MP mp) ; + +@ @c void mp_do_bounds (MP mp) { + pointer lhv,lhe; /* variable on left, the corresponding edge structure */ + pointer p; /* for list manipulation */ + integer m; /* initial value of |cur_mod| */ + m=mp->cur_mod; + lhv=mp_start_draw_cmd(mp, to_token); + if ( lhv!=null ) { + lhe=mp_find_edges_var(mp, lhv); + if ( lhe==null ) { + mp_flush_cur_exp(mp, 0); + } else if ( mp->cur_type!=mp_path_type ) { + exp_err("Improper `clip'"); +@.Improper `addto'@> + help2("This expression should have specified a known path.", + "So I'll not change anything just now."); + mp_put_get_flush_error(mp, 0); + } else if ( mp_left_type(mp->cur_exp)==mp_endpoint ) { + @<Complain about a non-cycle@>; + } else { + @<Make |cur_exp| into a \&{setbounds} or clipping path and add it to |lhe|@>; + } + } +} + +@ @<Complain about a non-cycle@>= +{ print_err("Not a cycle"); +@.Not a cycle@> + help2("That contour should have ended with `..cycle' or `&cycle'.", + "So I'll not change anything just now."); mp_put_get_error(mp); +} + +@ @<Make |cur_exp| into a \&{setbounds} or clipping path and add...@>= +{ p=mp_new_bounds_node(mp, mp->cur_exp,m); + mp_link(p)=mp_link(dummy_loc(lhe)); + mp_link(dummy_loc(lhe))=p; + if ( obj_tail(lhe)==dummy_loc(lhe) ) obj_tail(lhe)=p; + p=mp_get_node(mp, mp->gr_object_size[stop_type(m)]); + mp_type(p)=stop_type(m); + mp_link(obj_tail(lhe))=p; + obj_tail(lhe)=p; + mp_init_bbox(mp, lhe); +} + +@ The |do_add_to| procedure is a little like |do_clip| but there are a lot more +cases to deal with. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_add_to (MP mp) ; + +@ @c void mp_do_add_to (MP mp) { + pointer lhv,lhe; /* variable on left, the corresponding edge structure */ + pointer p; /* the graphical object or list for |scan_with_list| to update */ + pointer e; /* an edge structure to be merged */ + quarterword add_type; /* |also_code|, |contour_code|, or |double_path_code| */ + lhv=mp_start_draw_cmd(mp, thing_to_add); add_type=mp->last_add_type; + if ( lhv!=null ) { + if ( add_type==also_code ) { + @<Make sure the current expression is a suitable picture and set |e| and |p| + appropriately@>; + } else { + @<Create a graphical object |p| based on |add_type| and the current + expression@>; + } + mp_scan_with_list(mp, p); + @<Use |p|, |e|, and |add_type| to augment |lhv| as requested@>; + } +} + +@ Setting |p:=null| causes the $\langle$with list$\rangle$ to be ignored; +setting |e:=null| prevents anything from being added to |lhe|. + +@ @<Make sure the current expression is a suitable picture and set |e|...@>= +{ + p=null; e=null; + if ( mp->cur_type!=mp_picture_type ) { + exp_err("Improper `addto'"); +@.Improper `addto'@> + help2("This expression should have specified a known picture.", + "So I'll not change anything just now."); + mp_put_get_flush_error(mp, 0); + } else { + e=mp_private_edges(mp, mp->cur_exp); mp->cur_type=mp_vacuous; + p=mp_link(dummy_loc(e)); + } +} + +@ In this case |add_type<>also_code| so setting |p:=null| suppresses future +attempts to add to the edge structure. + +@<Create a graphical object |p| based on |add_type| and the current...@>= +{ e=null; p=null; + if ( mp->cur_type==mp_pair_type ) mp_pair_to_path(mp); + if ( mp->cur_type!=mp_path_type ) { + exp_err("Improper `addto'"); +@.Improper `addto'@> + help2("This expression should have specified a known path.", + "So I'll not change anything just now."); + mp_put_get_flush_error(mp, 0); + } else if ( add_type==contour_code ) { + if ( mp_left_type(mp->cur_exp)==mp_endpoint ) { + @<Complain about a non-cycle@>; + } else { + p=mp_new_fill_node(mp, mp->cur_exp); + mp->cur_type=mp_vacuous; + } + } else { + p=mp_new_stroked_node(mp, mp->cur_exp); + mp->cur_type=mp_vacuous; + } +} + +@ @<Use |p|, |e|, and |add_type| to augment |lhv| as requested@>= +lhe=mp_find_edges_var(mp, lhv); +if ( lhe==null ) { + if ( (e==null)&&(p!=null) ) e=mp_toss_gr_object(mp, p); + if ( e!=null ) delete_edge_ref(e); +} else if ( add_type==also_code ) { + if ( e!=null ) { + @<Merge |e| into |lhe| and delete |e|@>; + } else { + do_nothing; + } +} else if ( p!=null ) { + mp_link(obj_tail(lhe))=p; + obj_tail(lhe)=p; + if ( add_type==double_path_code ) + if ( mp_pen_p(p)==null ) + mp_pen_p(p)=mp_get_pen_circle(mp, 0); +} + +@ @<Merge |e| into |lhe| and delete |e|@>= +{ if ( mp_link(dummy_loc(e))!=null ) { + mp_link(obj_tail(lhe))=mp_link(dummy_loc(e)); + obj_tail(lhe)=obj_tail(e); + obj_tail(e)=dummy_loc(e); + mp_link(dummy_loc(e))=null; + mp_flush_dash_list(mp, lhe); + } + mp_toss_edges(mp, e); +} + +@ @<Cases of |do_statement|...@>= +case ship_out_command: mp_do_ship_out(mp); break; + +@ @<Declare action procedures for use by |do_statement|@>= +@<Declare the \ps\ output procedures@> +static void mp_do_ship_out (MP mp) ; + +@ @c void mp_do_ship_out (MP mp) { + integer c; /* the character code */ + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_picture_type ) { + @<Complain that it's not a known picture@>; + } else { + c=mp_round_unscaled(mp, mp->internal[mp_char_code]) % 256; + if ( c<0 ) c=c+256; + @<Store the width information for character code~|c|@>; + mp_ship_out(mp, mp->cur_exp); + mp_flush_cur_exp(mp, 0); + } +} + +@ @<Complain that it's not a known picture@>= +{ + exp_err("Not a known picture"); + help1("I can only output known pictures."); + mp_put_get_flush_error(mp, 0); +} + +@ The \&{everyjob} command simply assigns a nonzero value to the global variable +|start_sym|. + +@<Cases of |do_statement|...@>= +case every_job_command: + mp_get_symbol(mp); mp->start_sym=mp->cur_sym; mp_get_x_next(mp); + break; + +@ @<Glob...@>= +halfword start_sym; /* a symbolic token to insert at beginning of job */ + +@ @<Set init...@>= +mp->start_sym=0; + +@ Finally, we have only the ``message'' commands remaining. + +@d message_code 0 +@d err_message_code 1 +@d err_help_code 2 +@d filename_template_code 3 +@d print_with_leading_zeroes(A) g = mp->pool_ptr; + mp_print_int(mp, (A)); g = mp->pool_ptr-g; + if ( f>g ) { + mp->pool_ptr = mp->pool_ptr - g; + while ( f>g ) { + mp_print_char(mp, xord('0')); + decr(f); + }; + mp_print_int(mp, (A)); + }; + f = 0 + +@<Put each...@>= +mp_primitive(mp, "message",message_command,message_code); +@:message_}{\&{message} primitive@> +mp_primitive(mp, "errmessage",message_command,err_message_code); +@:err_message_}{\&{errmessage} primitive@> +mp_primitive(mp, "errhelp",message_command,err_help_code); +@:err_help_}{\&{errhelp} primitive@> +mp_primitive(mp, "filenametemplate",message_command,filename_template_code); +@:filename_template_}{\&{filenametemplate} primitive@> + +@ @<Cases of |print_cmd...@>= +case message_command: + if ( m<err_message_code ) mp_print(mp, "message"); + else if ( m==err_message_code ) mp_print(mp, "errmessage"); + else if ( m==filename_template_code ) mp_print(mp, "filenametemplate"); + else mp_print(mp, "errhelp"); + break; + +@ @<Cases of |do_statement|...@>= +case message_command: mp_do_message(mp); break; + +@ @<Declare action procedures for use by |do_statement|@>= +@<Declare a procedure called |no_string_err|@> +static void mp_do_message (MP mp) ; + +@ +@c void mp_do_message (MP mp) { + int m; /* the type of message */ + m=mp->cur_mod; mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_string_type ) + mp_no_string_err(mp, "A message should be a known string expression."); + else { + switch (m) { + case message_code: + mp_print_nl(mp, ""); mp_print_str(mp, mp->cur_exp); + break; + case err_message_code: + @<Print string |cur_exp| as an error message@>; + break; + case err_help_code: + @<Save string |cur_exp| as the |err_help|@>; + break; + case filename_template_code: + @<Save the filename template@>; + break; + } /* there are no other cases */ + } + mp_flush_cur_exp(mp, 0); +} + +@ @<Declare a procedure called |no_string_err|@>= +static void mp_no_string_err (MP mp, const char *s) { + exp_err("Not a string"); +@.Not a string@> + help1(s); + mp_put_get_error(mp); +} + +@ The global variable |err_help| is zero when the user has most recently +given an empty help string, or if none has ever been given. + +@<Save string |cur_exp| as the |err_help|@>= +{ + if ( mp->err_help!=0 ) delete_str_ref(mp->err_help); + if ( length(mp->cur_exp)==0 ) mp->err_help=0; + else { mp->err_help=mp->cur_exp; add_str_ref(mp->err_help); } +} + +@ If \&{errmessage} occurs often in |mp_scroll_mode|, without user-defined +\&{errhelp}, we don't want to give a long help message each time. So we +give a verbose explanation only once. + +@<Glob...@>= +boolean long_help_seen; /* has the long \.{\\errmessage} help been used? */ + +@ @<Set init...@>=mp->long_help_seen=false; + +@ @<Print string |cur_exp| as an error message@>= +{ + print_err(""); mp_print_str(mp, mp->cur_exp); + if ( mp->err_help!=0 ) { + mp->use_err_help=true; + } else if ( mp->long_help_seen ) { + help1("(That was another `errmessage'.)") ; + } else { + if ( mp->interaction<mp_error_stop_mode ) mp->long_help_seen=true; + help4("This error message was generated by an `errmessage'", + "command, so I can\'t give any explicit help.", + "Pretend that you're Miss Marple: Examine all clues,", +@^Marple, Jane@> + "and deduce the truth by inspired guesses."); + } + mp_put_get_error(mp); mp->use_err_help=false; +} + +@ @<Cases of |do_statement|...@>= +case write_command: mp_do_write(mp); break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_write (MP mp) ; + +@ @c void mp_do_write (MP mp) { + str_number t; /* the line of text to be written */ + write_index n,n0; /* for searching |wr_fname| and |wr_file| arrays */ + unsigned old_setting; /* for saving |selector| during output */ + mp_get_x_next(mp); + mp_scan_expression(mp); + if ( mp->cur_type!=mp_string_type ) { + mp_no_string_err(mp, "The text to be written should be a known string expression"); + } else if ( mp->cur_cmd!=to_token ) { + print_err("Missing `to' clause"); + help1("A write command should end with `to <filename>'"); + mp_put_get_error(mp); + } else { + t=mp->cur_exp; mp->cur_type=mp_vacuous; + mp_get_x_next(mp); + mp_scan_expression(mp); + if ( mp->cur_type!=mp_string_type ) + mp_no_string_err(mp, "I can\'t write to that file name. It isn't a known string"); + else { + @<Write |t| to the file named by |cur_exp|@>; + } + delete_str_ref(t); + } + mp_flush_cur_exp(mp, 0); +} + +@ @<Write |t| to the file named by |cur_exp|@>= +{ + @<Find |n| where |wr_fname[n]=cur_exp| and call |open_write_file| if + |cur_exp| must be inserted@>; + if ( mp_str_vs_str(mp, t,mp->eof_line)==0 ) { + @<Record the end of file on |wr_file[n]|@>; + } else { + old_setting=mp->selector; + mp->selector=n+write_file; + mp_print_str(mp, t); mp_print_ln(mp); + mp->selector = old_setting; + } +} + +@ @<Find |n| where |wr_fname[n]=cur_exp| and call |open_write_file| if...@>= +{ + char *fn = str(mp->cur_exp); + n=mp->write_files; + n0=mp->write_files; + while (mp_xstrcmp(fn,mp->wr_fname[n])!=0) { + if ( n==0 ) { /* bottom reached */ + if ( n0==mp->write_files ) { + if ( mp->write_files<mp->max_write_files ) { + incr(mp->write_files); + } else { + void **wr_file; + char **wr_fname; + write_index l,k; + l = mp->max_write_files + (mp->max_write_files/4); + wr_file = xmalloc((l+1),sizeof(void *)); + wr_fname = xmalloc((l+1),sizeof(char *)); + for (k=0;k<=l;k++) { + if (k<=mp->max_write_files) { + wr_file[k]=mp->wr_file[k]; + wr_fname[k]=mp->wr_fname[k]; + } else { + wr_file[k]=0; + wr_fname[k]=NULL; + } + } + xfree(mp->wr_file); xfree(mp->wr_fname); + mp->max_write_files = l; + mp->wr_file = wr_file; + mp->wr_fname = wr_fname; + } + } + n=n0; + mp_open_write_file(mp, fn ,n); + } else { + decr(n); + if ( mp->wr_fname[n]==NULL ) n0=n; + } + } +} + +@ @<Record the end of file on |wr_file[n]|@>= +{ (mp->close_file)(mp,mp->wr_file[n]); + xfree(mp->wr_fname[n]); + if ( n==mp->write_files-1 ) mp->write_files=n; +} + + +@* \[42] Writing font metric data. +\TeX\ gets its knowledge about fonts from font metric files, also called +\.{TFM} files; the `\.T' in `\.{TFM}' stands for \TeX, +but other programs know about them too. One of \MP's duties is to +write \.{TFM} files so that the user's fonts can readily be +applied to typesetting. +@:TFM files}{\.{TFM} files@> +@^font metric files@> + +The information in a \.{TFM} file appears in a sequence of 8-bit bytes. +Since the number of bytes is always a multiple of~4, we could +also regard the file as a sequence of 32-bit words, but \MP\ uses the +byte interpretation. The format of \.{TFM} files was designed by +Lyle Ramshaw in 1980. The intent is to convey a lot of different kinds +@^Ramshaw, Lyle Harold@> +of information in a compact but useful form. + +@<Glob...@>= +void * tfm_file; /* the font metric output goes here */ +char * metric_file_name; /* full name of the font metric file */ + +@ The first 24 bytes (6 words) of a \.{TFM} file contain twelve 16-bit +integers that give the lengths of the various subsequent portions +of the file. These twelve integers are, in order: +$$\vbox{\halign{\hfil#&$\null=\null$#\hfil\cr +|lf|&length of the entire file, in words;\cr +|lh|&length of the header data, in words;\cr +|bc|&smallest character code in the font;\cr +|ec|&largest character code in the font;\cr +|nw|&number of words in the width table;\cr +|nh|&number of words in the height table;\cr +|nd|&number of words in the depth table;\cr +|ni|&number of words in the italic correction table;\cr +|nl|&number of words in the lig/kern table;\cr +|nk|&number of words in the kern table;\cr +|ne|&number of words in the extensible character table;\cr +|np|&number of font parameter words.\cr}}$$ +They are all nonnegative and less than $2^{15}$. We must have |bc-1<=ec<=255|, +|ne<=256|, and +$$\hbox{|lf=6+lh+(ec-bc+1)+nw+nh+nd+ni+nl+nk+ne+np|.}$$ +Note that a font may contain as many as 256 characters (if |bc=0| and |ec=255|), +and as few as 0 characters (if |bc=ec+1|). + +Incidentally, when two or more 8-bit bytes are combined to form an integer of +16 or more bits, the most significant bytes appear first in the file. +This is called BigEndian order. +@^BigEndian order@> + +@ The rest of the \.{TFM} file may be regarded as a sequence of ten data +arrays. + +The most important data type used here is a |fix_word|, which is +a 32-bit representation of a binary fraction. A |fix_word| is a signed +quantity, with the two's complement of the entire word used to represent +negation. Of the 32 bits in a |fix_word|, exactly 12 are to the left of the +binary point; thus, the largest |fix_word| value is $2048-2^{-20}$, and +the smallest is $-2048$. We will see below, however, that all but two of +the |fix_word| values must lie between $-16$ and $+16$. + +@ The first data array is a block of header information, which contains +general facts about the font. The header must contain at least two words, +|header[0]| and |header[1]|, whose meaning is explained below. Additional +header information of use to other software routines might also be +included, and \MP\ will generate it if the \.{headerbyte} command occurs. +For example, 16 more words of header information are in use at the Xerox +Palo Alto Research Center; the first ten specify the character coding +scheme used (e.g., `\.{XEROX TEXT}' or `\.{TEX MATHSY}'), the next five +give the font family name (e.g., `\.{HELVETICA}' or `\.{CMSY}'), and the +last gives the ``face byte.'' + +\yskip\hang|header[0]| is a 32-bit check sum that \MP\ will copy into +the \.{GF} output file. This helps ensure consistency between files, +since \TeX\ records the check sums from the \.{TFM}'s it reads, and these +should match the check sums on actual fonts that are used. The actual +relation between this check sum and the rest of the \.{TFM} file is not +important; the check sum is simply an identification number with the +property that incompatible fonts almost always have distinct check sums. +@^check sum@> + +\yskip\hang|header[1]| is a |fix_word| containing the design size of the +font, in units of \TeX\ points. This number must be at least 1.0; it is +fairly arbitrary, but usually the design size is 10.0 for a ``10 point'' +font, i.e., a font that was designed to look best at a 10-point size, +whatever that really means. When a \TeX\ user asks for a font `\.{at} +$\delta$ \.{pt}', the effect is to override the design size and replace it +by $\delta$, and to multiply the $x$ and~$y$ coordinates of the points in +the font image by a factor of $\delta$ divided by the design size. {\sl +All other dimensions in the\/ \.{TFM} file are |fix_word|\kern-1pt\ +numbers in design-size units.} Thus, for example, the value of |param[6]|, +which defines the \.{em} unit, is often the |fix_word| value $2^{20}=1.0$, +since many fonts have a design size equal to one em. The other dimensions +must be less than 16 design-size units in absolute value; thus, +|header[1]| and |param[1]| are the only |fix_word| entries in the whole +\.{TFM} file whose first byte might be something besides 0 or 255. +@^design size@> + +@ Next comes the |char_info| array, which contains one |char_info_word| +per character. Each word in this part of the file contains six fields +packed into four bytes as follows. + +\yskip\hang first byte: |width_index| (8 bits)\par +\hang second byte: |height_index| (4 bits) times 16, plus |depth_index| + (4~bits)\par +\hang third byte: |italic_index| (6 bits) times 4, plus |tag| + (2~bits)\par +\hang fourth byte: |remainder| (8 bits)\par +\yskip\noindent +The actual width of a character is \\{width}|[width_index]|, in design-size +units; this is a device for compressing information, since many characters +have the same width. Since it is quite common for many characters +to have the same height, depth, or italic correction, the \.{TFM} format +imposes a limit of 16 different heights, 16 different depths, and +64 different italic corrections. + +Incidentally, the relation $\\{width}[0]=\\{height}[0]=\\{depth}[0]= +\\{italic}[0]=0$ should always hold, so that an index of zero implies a +value of zero. The |width_index| should never be zero unless the +character does not exist in the font, since a character is valid if and +only if it lies between |bc| and |ec| and has a nonzero |width_index|. + +@ The |tag| field in a |char_info_word| has four values that explain how to +interpret the |remainder| field. + +\yskip\hang|tag=0| (|no_tag|) means that |remainder| is unused.\par +\hang|tag=1| (|lig_tag|) means that this character has a ligature/kerning +program starting at location |remainder| in the |lig_kern| array.\par +\hang|tag=2| (|list_tag|) means that this character is part of a chain of +characters of ascending sizes, and not the largest in the chain. The +|remainder| field gives the character code of the next larger character.\par +\hang|tag=3| (|ext_tag|) means that this character code represents an +extensible character, i.e., a character that is built up of smaller pieces +so that it can be made arbitrarily large. The pieces are specified in +|exten[remainder]|.\par +\yskip\noindent +Characters with |tag=2| and |tag=3| are treated as characters with |tag=0| +unless they are used in special circumstances in math formulas. For example, +\TeX's \.{\\sum} operation looks for a |list_tag|, and the \.{\\left} +operation looks for both |list_tag| and |ext_tag|. + +@d no_tag 0 /* vanilla character */ +@d lig_tag 1 /* character has a ligature/kerning program */ +@d list_tag 2 /* character has a successor in a charlist */ +@d ext_tag 3 /* character is extensible */ + +@ The |lig_kern| array contains instructions in a simple programming language +that explains what to do for special letter pairs. Each word in this array is a +|lig_kern_command| of four bytes. + +\yskip\hang first byte: |skip_byte|, indicates that this is the final program + step if the byte is 128 or more, otherwise the next step is obtained by + skipping this number of intervening steps.\par +\hang second byte: |next_char|, ``if |next_char| follows the current character, + then perform the operation and stop, otherwise continue.''\par +\hang third byte: |op_byte|, indicates a ligature step if less than~128, + a kern step otherwise.\par +\hang fourth byte: |remainder|.\par +\yskip\noindent +In a kern step, an +additional space equal to |kern[256*(op_byte-128)+remainder]| is inserted +between the current character and |next_char|. This amount is +often negative, so that the characters are brought closer together +by kerning; but it might be positive. + +There are eight kinds of ligature steps, having |op_byte| codes $4a+2b+c$ where +$0\le a\le b+c$ and $0\le b,c\le1$. The character whose code is +|remainder| is inserted between the current character and |next_char|; +then the current character is deleted if $b=0$, and |next_char| is +deleted if $c=0$; then we pass over $a$~characters to reach the next +current character (which may have a ligature/kerning program of its own). + +If the very first instruction of the |lig_kern| array has |skip_byte=255|, +the |next_char| byte is the so-called right boundary character of this font; +the value of |next_char| need not lie between |bc| and~|ec|. +If the very last instruction of the |lig_kern| array has |skip_byte=255|, +there is a special ligature/kerning program for a left boundary character, +beginning at location |256*op_byte+remainder|. +The interpretation is that \TeX\ puts implicit boundary characters +before and after each consecutive string of characters from the same font. +These implicit characters do not appear in the output, but they can affect +ligatures and kerning. + +If the very first instruction of a character's |lig_kern| program has +|skip_byte>128|, the program actually begins in location +|256*op_byte+remainder|. This feature allows access to large |lig_kern| +arrays, because the first instruction must otherwise +appear in a location |<=255|. + +Any instruction with |skip_byte>128| in the |lig_kern| array must satisfy +the condition +$$\hbox{|256*op_byte+remainder<nl|.}$$ +If such an instruction is encountered during +normal program execution, it denotes an unconditional halt; no ligature +command is performed. + +@d stop_flag (128) + /* value indicating `\.{STOP}' in a lig/kern program */ +@d kern_flag (128) /* op code for a kern step */ +@d skip_byte(A) mp->lig_kern[(A)].b0 +@d next_char(A) mp->lig_kern[(A)].b1 +@d op_byte(A) mp->lig_kern[(A)].b2 +@d rem_byte(A) mp->lig_kern[(A)].b3 + +@ Extensible characters are specified by an |extensible_recipe|, which +consists of four bytes called |top|, |mid|, |bot|, and |rep| (in this +order). These bytes are the character codes of individual pieces used to +build up a large symbol. If |top|, |mid|, or |bot| are zero, they are not +present in the built-up result. For example, an extensible vertical line is +like an extensible bracket, except that the top and bottom pieces are missing. + +Let $T$, $M$, $B$, and $R$ denote the respective pieces, or an empty box +if the piece isn't present. Then the extensible characters have the form +$TR^kMR^kB$ from top to bottom, for some |k>=0|, unless $M$ is absent; +in the latter case we can have $TR^kB$ for both even and odd values of~|k|. +The width of the extensible character is the width of $R$; and the +height-plus-depth is the sum of the individual height-plus-depths of the +components used, since the pieces are butted together in a vertical list. + +@d ext_top(A) mp->exten[(A)].b0 /* |top| piece in a recipe */ +@d ext_mid(A) mp->exten[(A)].b1 /* |mid| piece in a recipe */ +@d ext_bot(A) mp->exten[(A)].b2 /* |bot| piece in a recipe */ +@d ext_rep(A) mp->exten[(A)].b3 /* |rep| piece in a recipe */ + +@ The final portion of a \.{TFM} file is the |param| array, which is another +sequence of |fix_word| values. + +\yskip\hang|param[1]=slant| is the amount of italic slant, which is used +to help position accents. For example, |slant=.25| means that when you go +up one unit, you also go .25 units to the right. The |slant| is a pure +number; it is the only |fix_word| other than the design size itself that is +not scaled by the design size. +@^design size@> + +\hang|param[2]=space| is the normal spacing between words in text. +Note that character 040 in the font need not have anything to do with +blank spaces. + +\hang|param[3]=space_stretch| is the amount of glue stretching between words. + +\hang|param[4]=space_shrink| is the amount of glue shrinking between words. + +\hang|param[5]=x_height| is the size of one ex in the font; it is also +the height of letters for which accents don't have to be raised or lowered. + +\hang|param[6]=quad| is the size of one em in the font. + +\hang|param[7]=extra_space| is the amount added to |param[2]| at the +ends of sentences. + +\yskip\noindent +If fewer than seven parameters are present, \TeX\ sets the missing parameters +to zero. + +@d slant_code 1 +@d space_code 2 +@d space_stretch_code 3 +@d space_shrink_code 4 +@d x_height_code 5 +@d quad_code 6 +@d extra_space_code 7 + +@ So that is what \.{TFM} files hold. One of \MP's duties is to output such +information, and it does this all at once at the end of a job. +In order to prepare for such frenetic activity, it squirrels away the +necessary facts in various arrays as information becomes available. + +Character dimensions (\&{charwd}, \&{charht}, \&{chardp}, and \&{charic}) +are stored respectively in |tfm_width|, |tfm_height|, |tfm_depth|, and +|tfm_ital_corr|. Other information about a character (e.g., about +its ligatures or successors) is accessible via the |char_tag| and +|char_remainder| arrays. Other information about the font as a whole +is kept in additional arrays called |header_byte|, |lig_kern|, +|kern|, |exten|, and |param|. + +@d max_tfm_int 32510 +@d undefined_label max_tfm_int /* an undefined local label */ + +@<Glob...@>= +#define TFM_ITEMS 257 +eight_bits bc; +eight_bits ec; /* smallest and largest character codes shipped out */ +scaled tfm_width[TFM_ITEMS]; /* \&{charwd} values */ +scaled tfm_height[TFM_ITEMS]; /* \&{charht} values */ +scaled tfm_depth[TFM_ITEMS]; /* \&{chardp} values */ +scaled tfm_ital_corr[TFM_ITEMS]; /* \&{charic} values */ +boolean char_exists[TFM_ITEMS]; /* has this code been shipped out? */ +int char_tag[TFM_ITEMS]; /* |remainder| category */ +int char_remainder[TFM_ITEMS]; /* the |remainder| byte */ +char *header_byte; /* bytes of the \.{TFM} header */ +int header_last; /* last initialized \.{TFM} header byte */ +int header_size; /* size of the \.{TFM} header */ +four_quarters *lig_kern; /* the ligature/kern table */ +short nl; /* the number of ligature/kern steps so far */ +scaled *kern; /* distinct kerning amounts */ +short nk; /* the number of distinct kerns so far */ +four_quarters exten[TFM_ITEMS]; /* extensible character recipes */ +short ne; /* the number of extensible characters so far */ +scaled *param; /* \&{fontinfo} parameters */ +short np; /* the largest \&{fontinfo} parameter specified so far */ +short nw;short nh;short nd;short ni; /* sizes of \.{TFM} subtables */ +short skip_table[TFM_ITEMS]; /* local label status */ +boolean lk_started; /* has there been a lig/kern step in this command yet? */ +integer bchar; /* right boundary character */ +short bch_label; /* left boundary starting location */ +short ll;short lll; /* registers used for lig/kern processing */ +short label_loc[257]; /* lig/kern starting addresses */ +eight_bits label_char[257]; /* characters for |label_loc| */ +short label_ptr; /* highest position occupied in |label_loc| */ + +@ @<Allocate or initialize ...@>= +mp->header_last=7; +mp->header_size = 128; /* just for init */ +mp->header_byte = xmalloc(mp->header_size, sizeof(char)); + +@ @<Dealloc variables@>= +xfree(mp->header_byte); +xfree(mp->lig_kern); +xfree(mp->kern); +xfree(mp->param); + +@ @<Set init...@>= +for (k=0;k<= 255;k++ ) { + mp->tfm_width[k]=0; mp->tfm_height[k]=0; mp->tfm_depth[k]=0; mp->tfm_ital_corr[k]=0; + mp->char_exists[k]=false; mp->char_tag[k]=no_tag; mp->char_remainder[k]=0; + mp->skip_table[k]=undefined_label; +} +memset(mp->header_byte,0,(size_t)mp->header_size); +mp->bc=255; mp->ec=0; mp->nl=0; mp->nk=0; mp->ne=0; mp->np=0; +mp->internal[mp_boundary_char]=-unity; +mp->bch_label=undefined_label; +mp->label_loc[0]=-1; mp->label_ptr=0; + +@ @<Declarations@>= +static scaled mp_tfm_check (MP mp,quarterword m) ; + +@ @c +static scaled mp_tfm_check (MP mp,quarterword m) { + if ( abs(mp->internal[m])>=fraction_half ) { + print_err("Enormous "); mp_print(mp, mp->int_name[m]); +@.Enormous charwd...@> +@.Enormous chardp...@> +@.Enormous charht...@> +@.Enormous charic...@> +@.Enormous designsize...@> + mp_print(mp, " has been reduced"); + help1("Font metric dimensions must be less than 2048pt."); + mp_put_get_error(mp); + if ( mp->internal[m]>0 ) return (fraction_half-1); + else return (1-fraction_half); + } else { + return mp->internal[m]; + } +} + +@ @<Store the width information for character code~|c|@>= +if ( c<mp->bc ) mp->bc=(eight_bits)c; +if ( c>mp->ec ) mp->ec=(eight_bits)c; +mp->char_exists[c]=true; +mp->tfm_width[c]=mp_tfm_check(mp,mp_char_wd); +mp->tfm_height[c]=mp_tfm_check(mp, mp_char_ht); +mp->tfm_depth[c]=mp_tfm_check(mp, mp_char_dp); +mp->tfm_ital_corr[c]=mp_tfm_check(mp, mp_char_ic) + +@ Now let's consider \MP's special \.{TFM}-oriented commands. + +@<Cases of |do_statement|...@>= +case tfm_command: mp_do_tfm_command(mp); break; + +@ @d char_list_code 0 +@d lig_table_code 1 +@d extensible_code 2 +@d header_byte_code 3 +@d font_dimen_code 4 + +@<Put each...@>= +mp_primitive(mp, "charlist",tfm_command,char_list_code); +@:char_list_}{\&{charlist} primitive@> +mp_primitive(mp, "ligtable",tfm_command,lig_table_code); +@:lig_table_}{\&{ligtable} primitive@> +mp_primitive(mp, "extensible",tfm_command,extensible_code); +@:extensible_}{\&{extensible} primitive@> +mp_primitive(mp, "headerbyte",tfm_command,header_byte_code); +@:header_byte_}{\&{headerbyte} primitive@> +mp_primitive(mp, "fontdimen",tfm_command,font_dimen_code); +@:font_dimen_}{\&{fontdimen} primitive@> + +@ @<Cases of |print_cmd...@>= +case tfm_command: + switch (m) { + case char_list_code:mp_print(mp, "charlist"); break; + case lig_table_code:mp_print(mp, "ligtable"); break; + case extensible_code:mp_print(mp, "extensible"); break; + case header_byte_code:mp_print(mp, "headerbyte"); break; + default: mp_print(mp, "fontdimen"); break; + } + break; + +@ @<Declare action procedures for use by |do_statement|@>= +static eight_bits mp_get_code (MP mp) ; + +@ @c eight_bits mp_get_code (MP mp) { /* scans a character code value */ + integer c; /* the code value found */ + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type==mp_known ) { + c=mp_round_unscaled(mp, mp->cur_exp); + if ( c>=0 ) if ( c<256 ) return (eight_bits)c; + } else if ( mp->cur_type==mp_string_type ) { + if ( length(mp->cur_exp)==1 ) { + c=mp->str_pool[mp->str_start[mp->cur_exp]]; + return (eight_bits)c; + } + } + exp_err("Invalid code has been replaced by 0"); +@.Invalid code...@> + help2("I was looking for a number between 0 and 255, or for a", + "string of length 1. Didn't find it; will use 0 instead."); + mp_put_get_flush_error(mp, 0); c=0; + return (eight_bits)c; +} + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_set_tag (MP mp,halfword c, quarterword t, halfword r) ; + +@ @c void mp_set_tag (MP mp,halfword c, quarterword t, halfword r) { + if ( mp->char_tag[c]==no_tag ) { + mp->char_tag[c]=t; mp->char_remainder[c]=r; + if ( t==lig_tag ){ + incr(mp->label_ptr); mp->label_loc[mp->label_ptr]=r; + mp->label_char[mp->label_ptr]=(eight_bits)c; + } + } else { + @<Complain about a character tag conflict@>; + } +} + +@ @<Complain about a character tag conflict@>= +{ + print_err("Character "); + if ( (c>' ')&&(c<127) ) mp_print_char(mp,xord(c)); + else if ( c==256 ) mp_print(mp, "||"); + else { mp_print(mp, "code "); mp_print_int(mp, c); }; + mp_print(mp, " is already "); +@.Character c is already...@> + switch (mp->char_tag[c]) { + case lig_tag: mp_print(mp, "in a ligtable"); break; + case list_tag: mp_print(mp, "in a charlist"); break; + case ext_tag: mp_print(mp, "extensible"); break; + } /* there are no other cases */ + help2("It's not legal to label a character more than once.", + "So I'll not change anything just now."); + mp_put_get_error(mp); +} + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_tfm_command (MP mp) ; + +@ @c void mp_do_tfm_command (MP mp) { + int c,cc; /* character codes */ + int k; /* index into the |kern| array */ + int j; /* index into |header_byte| or |param| */ + switch (mp->cur_mod) { + case char_list_code: + c=mp_get_code(mp); + /* we will store a list of character successors */ + while ( mp->cur_cmd==colon ) { + cc=mp_get_code(mp); mp_set_tag(mp, c,list_tag,cc); c=cc; + }; + break; + case lig_table_code: + if (mp->lig_kern==NULL) + mp->lig_kern = xmalloc((max_tfm_int+1),sizeof(four_quarters)); + if (mp->kern==NULL) + mp->kern = xmalloc((max_tfm_int+1),sizeof(scaled)); + @<Store a list of ligature/kern steps@>; + break; + case extensible_code: + @<Define an extensible recipe@>; + break; + case header_byte_code: + case font_dimen_code: + c=mp->cur_mod; mp_get_x_next(mp); + mp_scan_expression(mp); + if ( (mp->cur_type!=mp_known)||(mp->cur_exp<half_unit) ) { + exp_err("Improper location"); +@.Improper location@> + help2("I was looking for a known, positive number.", + "For safety's sake I'll ignore the present command."); + mp_put_get_error(mp); + } else { + j=mp_round_unscaled(mp, mp->cur_exp); + if ( mp->cur_cmd!=colon ) { + mp_missing_err(mp, ":"); +@.Missing `:'@> + help1("A colon should follow a headerbyte or fontinfo location."); + mp_back_error(mp); + } + if ( c==header_byte_code ) { + @<Store a list of header bytes@>; + } else { + if (mp->param==NULL) + mp->param = xmalloc((max_tfm_int+1),sizeof(scaled)); + @<Store a list of font dimensions@>; + } + } + break; + } /* there are no other cases */ +} + +@ @<Store a list of ligature/kern steps@>= +{ + mp->lk_started=false; +CONTINUE: + mp_get_x_next(mp); + if ((mp->cur_cmd==skip_to)&& mp->lk_started ) + @<Process a |skip_to| command and |goto done|@>; + if ( mp->cur_cmd==bchar_label ) { c=256; mp->cur_cmd=colon; } + else { mp_back_input(mp); c=mp_get_code(mp); }; + if ((mp->cur_cmd==colon)||(mp->cur_cmd==double_colon)) { + @<Record a label in a lig/kern subprogram and |goto continue|@>; + } + if ( mp->cur_cmd==lig_kern_token ) { + @<Compile a ligature/kern command@>; + } else { + print_err("Illegal ligtable step"); +@.Illegal ligtable step@> + help1("I was looking for `=:' or `kern' here."); + mp_back_error(mp); next_char(mp->nl)=qi(0); + op_byte(mp->nl)=qi(0); rem_byte(mp->nl)=qi(0); + skip_byte(mp->nl)=stop_flag+1; /* this specifies an unconditional stop */ + } + if ( mp->nl==max_tfm_int) mp_fatal_error(mp, "ligtable too large"); + incr(mp->nl); + if ( mp->cur_cmd==comma ) goto CONTINUE; + if ( skip_byte(mp->nl-1)<stop_flag ) skip_byte(mp->nl-1)=stop_flag; +} +DONE: + +@ @<Put each...@>= +mp_primitive(mp, "=:",lig_kern_token,0); +@:=:_}{\.{=:} primitive@> +mp_primitive(mp, "=:|",lig_kern_token,1); +@:=:/_}{\.{=:\char'174} primitive@> +mp_primitive(mp, "=:|>",lig_kern_token,5); +@:=:/>_}{\.{=:\char'174>} primitive@> +mp_primitive(mp, "|=:",lig_kern_token,2); +@:=:/_}{\.{\char'174=:} primitive@> +mp_primitive(mp, "|=:>",lig_kern_token,6); +@:=:/>_}{\.{\char'174=:>} primitive@> +mp_primitive(mp, "|=:|",lig_kern_token,3); +@:=:/_}{\.{\char'174=:\char'174} primitive@> +mp_primitive(mp, "|=:|>",lig_kern_token,7); +@:=:/>_}{\.{\char'174=:\char'174>} primitive@> +mp_primitive(mp, "|=:|>>",lig_kern_token,11); +@:=:/>_}{\.{\char'174=:\char'174>>} primitive@> +mp_primitive(mp, "kern",lig_kern_token,128); +@:kern_}{\&{kern} primitive@> + +@ @<Cases of |print_cmd...@>= +case lig_kern_token: + switch (m) { + case 0:mp_print(mp, "=:"); break; + case 1:mp_print(mp, "=:|"); break; + case 2:mp_print(mp, "|=:"); break; + case 3:mp_print(mp, "|=:|"); break; + case 5:mp_print(mp, "=:|>"); break; + case 6:mp_print(mp, "|=:>"); break; + case 7:mp_print(mp, "|=:|>"); break; + case 11:mp_print(mp, "|=:|>>"); break; + default: mp_print(mp, "kern"); break; + } + break; + +@ Local labels are implemented by maintaining the |skip_table| array, +where |skip_table[c]| is either |undefined_label| or the address of the +most recent lig/kern instruction that skips to local label~|c|. In the +latter case, the |skip_byte| in that instruction will (temporarily) +be zero if there were no prior skips to this label, or it will be the +distance to the prior skip. + +We may need to cancel skips that span more than 127 lig/kern steps. + +@d cancel_skips(A) mp->ll=(A); + do { + mp->lll=qo(skip_byte(mp->ll)); + skip_byte(mp->ll)=stop_flag; mp->ll=mp->ll-mp->lll; + } while (mp->lll!=0) +@d skip_error(A) { print_err("Too far to skip"); +@.Too far to skip@> + help1("At most 127 lig/kern steps can separate skipto1 from 1::."); + mp_error(mp); cancel_skips((A)); + } + +@<Process a |skip_to| command and |goto done|@>= +{ + c=mp_get_code(mp); + if ( mp->nl-mp->skip_table[c]>128 ) { + skip_error(mp->skip_table[c]); mp->skip_table[c]=undefined_label; + } + if ( mp->skip_table[c]==undefined_label ) skip_byte(mp->nl-1)=qi(0); + else skip_byte(mp->nl-1)=qi(mp->nl-mp->skip_table[c]-1); + mp->skip_table[c]=mp->nl-1; goto DONE; +} + +@ @<Record a label in a lig/kern subprogram and |goto continue|@>= +{ + if ( mp->cur_cmd==colon ) { + if ( c==256 ) mp->bch_label=mp->nl; + else mp_set_tag(mp, c,lig_tag,mp->nl); + } else if ( mp->skip_table[c]<undefined_label ) { + mp->ll=mp->skip_table[c]; mp->skip_table[c]=undefined_label; + do { + mp->lll=qo(skip_byte(mp->ll)); + if ( mp->nl-mp->ll>128 ) { + skip_error(mp->ll); goto CONTINUE; + } + skip_byte(mp->ll)=qi(mp->nl-mp->ll-1); mp->ll=mp->ll-mp->lll; + } while (mp->lll!=0); + } + goto CONTINUE; +} + +@ @<Compile a ligature/kern...@>= +{ + next_char(mp->nl)=qi(c); skip_byte(mp->nl)=qi(0); + if ( mp->cur_mod<128 ) { /* ligature op */ + op_byte(mp->nl)=qi(mp->cur_mod); rem_byte(mp->nl)=qi(mp_get_code(mp)); + } else { + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ) { + exp_err("Improper kern"); +@.Improper kern@> + help2("The amount of kern should be a known numeric value.", + "I'm zeroing this one. Proceed, with fingers crossed."); + mp_put_get_flush_error(mp, 0); + } + mp->kern[mp->nk]=mp->cur_exp; + k=0; + while ( mp->kern[k]!=mp->cur_exp ) incr(k); + if ( k==mp->nk ) { + if ( mp->nk==max_tfm_int ) mp_fatal_error(mp, "too many TFM kerns"); + incr(mp->nk); + } + op_byte(mp->nl)=kern_flag+(k / 256); + rem_byte(mp->nl)=qi((k % 256)); + } + mp->lk_started=true; +} + +@ @d missing_extensible_punctuation(A) + { mp_missing_err(mp, (A)); +@.Missing `\char`\#'@> + help1("I'm processing `extensible c: t,m,b,r'."); mp_back_error(mp); + } + +@<Define an extensible recipe@>= +{ + if ( mp->ne==256 ) mp_fatal_error(mp, "too many extensible recipies"); + c=mp_get_code(mp); mp_set_tag(mp, c,ext_tag,mp->ne); + if ( mp->cur_cmd!=colon ) missing_extensible_punctuation(":"); + ext_top(mp->ne)=qi(mp_get_code(mp)); + if ( mp->cur_cmd!=comma ) missing_extensible_punctuation(","); + ext_mid(mp->ne)=qi(mp_get_code(mp)); + if ( mp->cur_cmd!=comma ) missing_extensible_punctuation(","); + ext_bot(mp->ne)=qi(mp_get_code(mp)); + if ( mp->cur_cmd!=comma ) missing_extensible_punctuation(","); + ext_rep(mp->ne)=qi(mp_get_code(mp)); + incr(mp->ne); +} + +@ The header could contain ASCII zeroes, so can't use |strdup|. + +@<Store a list of header bytes@>= +do { + if ( j>=mp->header_size ) { + size_t l = (size_t)(mp->header_size + (mp->header_size/4)); + char *t = xmalloc(l,1); + memset(t,0,l); + memcpy(t,mp->header_byte,(size_t)mp->header_size); + xfree (mp->header_byte); + mp->header_byte = t; + mp->header_size = (int)l; + } + mp->header_byte[j]=(char)mp_get_code(mp); + incr(j); incr(mp->header_last); +} while (mp->cur_cmd==comma) + +@ @<Store a list of font dimensions@>= +do { + if ( j>max_tfm_int ) mp_fatal_error(mp, "too many fontdimens"); + while ( j>mp->np ) { incr(mp->np); mp->param[mp->np]=0; }; + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_known ){ + exp_err("Improper font parameter"); +@.Improper font parameter@> + help1("I'm zeroing this one. Proceed, with fingers crossed."); + mp_put_get_flush_error(mp, 0); + } + mp->param[j]=mp->cur_exp; incr(j); +} while (mp->cur_cmd==comma) + +@ OK: We've stored all the data that is needed for the \.{TFM} file. +All that remains is to output it in the correct format. + +An interesting problem needs to be solved in this connection, because +the \.{TFM} format allows at most 256~widths, 16~heights, 16~depths, +and 64~italic corrections. If the data has more distinct values than +this, we want to meet the necessary restrictions by perturbing the +given values as little as possible. + +\MP\ solves this problem in two steps. First the values of a given +kind (widths, heights, depths, or italic corrections) are sorted; +then the list of sorted values is perturbed, if necessary. + +The sorting operation is facilitated by having a special node of +essentially infinite |value| at the end of the current list. + +@<Initialize table entries...@>= +value(inf_val)=fraction_four; + +@ Straight linear insertion is good enough for sorting, since the lists +are usually not terribly long. As we work on the data, the current list +will start at |mp_link(temp_head)| and end at |inf_val|; the nodes in this +list will be in increasing order of their |value| fields. + +Given such a list, the |sort_in| function takes a value and returns a pointer +to where that value can be found in the list. The value is inserted in +the proper place, if necessary. + +At the time we need to do these operations, most of \MP's work has been +completed, so we will have plenty of memory to play with. The value nodes +that are allocated for sorting will never be returned to free storage. + +@d clear_the_list mp_link(temp_head)=inf_val + +@c +static pointer mp_sort_in (MP mp,scaled v) { + pointer p,q,r; /* list manipulation registers */ + p=temp_head; + while (1) { + q=mp_link(p); + if ( v<=value(q) ) break; + p=q; + } + if ( v<value(q) ) { + r=mp_get_node(mp, value_node_size); value(r)=v; mp_link(r)=q; mp_link(p)=r; + } + return mp_link(p); +} + +@ Now we come to the interesting part, where we reduce the list if necessary +until it has the required size. The |min_cover| routine is basic to this +process; it computes the minimum number~|m| such that the values of the +current sorted list can be covered by |m|~intervals of width~|d|. It +also sets the global value |perturbation| to the smallest value $d'>d$ +such that the covering found by this algorithm would be different. + +In particular, |min_cover(0)| returns the number of distinct values in the +current list and sets |perturbation| to the minimum distance between +adjacent values. + +@c +static integer mp_min_cover (MP mp,scaled d) { + pointer p; /* runs through the current list */ + scaled l; /* the least element covered by the current interval */ + integer m; /* lower bound on the size of the minimum cover */ + m=0; p=mp_link(temp_head); mp->perturbation=el_gordo; + while ( p!=inf_val ){ + incr(m); l=value(p); + do { p=mp_link(p); } while (value(p)<=l+d); + if ( value(p)-l<mp->perturbation ) + mp->perturbation=value(p)-l; + } + return m; +} + +@ @<Glob...@>= +scaled perturbation; /* quantity related to \.{TFM} rounding */ +integer excess; /* the list is this much too long */ + +@ The smallest |d| such that a given list can be covered with |m| intervals +is determined by the |threshold| routine, which is sort of an inverse +to |min_cover|. The idea is to increase the interval size rapidly until +finding the range, then to go sequentially until the exact borderline has +been discovered. + +@c +static scaled mp_threshold (MP mp,integer m) { + scaled d; /* lower bound on the smallest interval size */ + mp->excess=mp_min_cover(mp, 0)-m; + if ( mp->excess<=0 ) { + return 0; + } else { + do { + d=mp->perturbation; + } while (mp_min_cover(mp, d+d)>m); + while ( mp_min_cover(mp, d)>m ) + d=mp->perturbation; + return d; + } +} + +@ The |skimp| procedure reduces the current list to at most |m| entries, +by changing values if necessary. It also sets |mp_info(p):=k| if |value(p)| +is the |k|th distinct value on the resulting list, and it sets +|perturbation| to the maximum amount by which a |value| field has +been changed. The size of the resulting list is returned as the +value of |skimp|. + +@c +static integer mp_skimp (MP mp,integer m) { + scaled d; /* the size of intervals being coalesced */ + pointer p,q,r; /* list manipulation registers */ + scaled l; /* the least value in the current interval */ + scaled v; /* a compromise value */ + d=mp_threshold(mp, m); mp->perturbation=0; + q=temp_head; m=0; p=mp_link(temp_head); + while ( p!=inf_val ) { + incr(m); l=value(p); mp_info(p)=m; + if ( value(mp_link(p))<=l+d ) { + @<Replace an interval of values by its midpoint@>; + } + q=p; p=mp_link(p); + } + return m; +} + +@ @<Replace an interval...@>= +{ + do { + p=mp_link(p); mp_info(p)=m; + decr(mp->excess); if ( mp->excess==0 ) d=0; + } while (value(mp_link(p))<=l+d); + v=l+halfp(value(p)-l); + if ( value(p)-v>mp->perturbation ) + mp->perturbation=value(p)-v; + r=q; + do { + r=mp_link(r); value(r)=v; + } while (r!=p); + mp_link(q)=p; /* remove duplicate values from the current list */ +} + +@ A warning message is issued whenever something is perturbed by +more than 1/16\thinspace pt. + +@c +static void mp_tfm_warning (MP mp,quarterword m) { + mp_print_nl(mp, "(some "); + mp_print(mp, mp->int_name[m]); +@.some charwds...@> +@.some chardps...@> +@.some charhts...@> +@.some charics...@> + mp_print(mp, " values had to be adjusted by as much as "); + mp_print_scaled(mp, mp->perturbation); mp_print(mp, "pt)"); +} + +@ Here's an example of how we use these routines. +The width data needs to be perturbed only if there are 256 distinct +widths, but \MP\ must check for this case even though it is +highly unusual. + +An integer variable |k| will be defined when we use this code. +The |dimen_head| array will contain pointers to the sorted +lists of dimensions. + +@<Massage the \.{TFM} widths@>= +clear_the_list; +for (k=mp->bc;k<=mp->ec;k++) { + if ( mp->char_exists[k] ) + mp->tfm_width[k]=mp_sort_in(mp, mp->tfm_width[k]); +} +mp->nw=mp_skimp(mp, 255)+1; mp->dimen_head[1]=mp_link(temp_head); +if ( mp->perturbation>=010000 ) mp_tfm_warning(mp, mp_char_wd) + +@ @<Glob...@>= +pointer dimen_head[5]; /* lists of \.{TFM} dimensions */ + +@ Heights, depths, and italic corrections are different from widths +not only because their list length is more severely restricted, but +also because zero values do not need to be put into the lists. + +@<Massage the \.{TFM} heights, depths, and italic corrections@>= +clear_the_list; +for (k=mp->bc;k<=mp->ec;k++) { + if ( mp->char_exists[k] ) { + if ( mp->tfm_height[k]==0 ) mp->tfm_height[k]=zero_val; + else mp->tfm_height[k]=mp_sort_in(mp, mp->tfm_height[k]); + } +} +mp->nh=mp_skimp(mp, 15)+1; mp->dimen_head[2]=mp_link(temp_head); +if ( mp->perturbation>=010000 ) mp_tfm_warning(mp, mp_char_ht); +clear_the_list; +for (k=mp->bc;k<=mp->ec;k++) { + if ( mp->char_exists[k] ) { + if ( mp->tfm_depth[k]==0 ) mp->tfm_depth[k]=zero_val; + else mp->tfm_depth[k]=mp_sort_in(mp, mp->tfm_depth[k]); + } +} +mp->nd=mp_skimp(mp, 15)+1; mp->dimen_head[3]=mp_link(temp_head); +if ( mp->perturbation>=010000 ) mp_tfm_warning(mp, mp_char_dp); +clear_the_list; +for (k=mp->bc;k<=mp->ec;k++) { + if ( mp->char_exists[k] ) { + if ( mp->tfm_ital_corr[k]==0 ) mp->tfm_ital_corr[k]=zero_val; + else mp->tfm_ital_corr[k]=mp_sort_in(mp, mp->tfm_ital_corr[k]); + } +} +mp->ni=mp_skimp(mp, 63)+1; mp->dimen_head[4]=mp_link(temp_head); +if ( mp->perturbation>=010000 ) mp_tfm_warning(mp, mp_char_ic) + +@ @<Initialize table entries...@>= +value(zero_val)=0; mp_info(zero_val)=0; + +@ Bytes 5--8 of the header are set to the design size, unless the user has +some crazy reason for specifying them differently. +@^design size@> + +Error messages are not allowed at the time this procedure is called, +so a warning is printed instead. + +The value of |max_tfm_dimen| is calculated so that +$$\hbox{|make_scaled(16*max_tfm_dimen,internal[mp_design_size])|} + < \\{three\_bytes}.$$ + +@d three_bytes 0100000000 /* $2^{24}$ */ + +@c +static void mp_fix_design_size (MP mp) { + scaled d; /* the design size */ + d=mp->internal[mp_design_size]; + if ( (d<unity)||(d>=fraction_half) ) { + if ( d!=0 ) + mp_print_nl(mp, "(illegal design size has been changed to 128pt)"); +@.illegal design size...@> + d=040000000; mp->internal[mp_design_size]=d; + } + if ( mp->header_byte[4]==0 && mp->header_byte[5]==0 && + mp->header_byte[6]==0 && mp->header_byte[7]==0 ) { + mp->header_byte[4]=d / 04000000; + mp->header_byte[5]=(d / 4096) % 256; + mp->header_byte[6]=(d / 16) % 256; + mp->header_byte[7]=(d % 16)*16; + } + mp->max_tfm_dimen=16*mp->internal[mp_design_size]-1-mp->internal[mp_design_size] / 010000000; + if ( mp->max_tfm_dimen>=fraction_half ) mp->max_tfm_dimen=fraction_half-1; +} + +@ The |dimen_out| procedure computes a |fix_word| relative to the +design size. If the data was out of range, it is corrected and the +global variable |tfm_changed| is increased by~one. + +@c +static integer mp_dimen_out (MP mp,scaled x) { + if ( abs(x)>mp->max_tfm_dimen ) { + incr(mp->tfm_changed); + if ( x>0 ) x=mp->max_tfm_dimen; else x=-mp->max_tfm_dimen; + } + x=mp_make_scaled(mp, x*16,mp->internal[mp_design_size]); + return x; +} + +@ @<Glob...@>= +scaled max_tfm_dimen; /* bound on widths, heights, kerns, etc. */ +integer tfm_changed; /* the number of data entries that were out of bounds */ + +@ If the user has not specified any of the first four header bytes, +the |fix_check_sum| procedure replaces them by a ``check sum'' computed +from the |tfm_width| data relative to the design size. +@^check sum@> + +@c +static void mp_fix_check_sum (MP mp) { + eight_bits k; /* runs through character codes */ + eight_bits B1,B2,B3,B4; /* bytes of the check sum */ + integer x; /* hash value used in check sum computation */ + if ( mp->header_byte[0]==0 && mp->header_byte[1]==0 && + mp->header_byte[2]==0 && mp->header_byte[3]==0 ) { + @<Compute a check sum in |(b1,b2,b3,b4)|@>; + mp->header_byte[0]=(char)B1; mp->header_byte[1]=(char)B2; + mp->header_byte[2]=(char)B3; mp->header_byte[3]=(char)B4; + return; + } +} + +@ @<Compute a check sum in |(b1,b2,b3,b4)|@>= +B1=mp->bc; B2=mp->ec; B3=mp->bc; B4=mp->ec; mp->tfm_changed=0; +for (k=mp->bc;k<=mp->ec;k++) { + if ( mp->char_exists[k] ) { + x=mp_dimen_out(mp, value(mp->tfm_width[k]))+(k+4)*020000000; /* this is positive */ + B1=(eight_bits)((B1+B1+x) % 255); + B2=(eight_bits)((B2+B2+x) % 253); + B3=(eight_bits)((B3+B3+x) % 251); + B4=(eight_bits)((B4+B4+x) % 247); + } + if (k==mp->ec) break; +} + +@ Finally we're ready to actually write the \.{TFM} information. +Here are some utility routines for this purpose. + +@d tfm_out(A) do { /* output one byte to |tfm_file| */ + unsigned char s=(unsigned char)(A); + (mp->write_binary_file)(mp,mp->tfm_file,(void *)&s,1); + } while (0) + +@c +static void mp_tfm_two (MP mp,integer x) { /* output two bytes to |tfm_file| */ + tfm_out(x / 256); tfm_out(x % 256); +} +static void mp_tfm_four (MP mp,integer x) { /* output four bytes to |tfm_file| */ + if ( x>=0 ) tfm_out(x / three_bytes); + else { + x=x+010000000000; /* use two's complement for negative values */ + x=x+010000000000; + tfm_out((x / three_bytes) + 128); + }; + x=x % three_bytes; tfm_out(x / unity); + x=x % unity; tfm_out(x / 0400); + tfm_out(x % 0400); +} +static void mp_tfm_qqqq (MP mp,four_quarters x) { /* output four quarterwords to |tfm_file| */ + tfm_out(qo(x.b0)); tfm_out(qo(x.b1)); + tfm_out(qo(x.b2)); tfm_out(qo(x.b3)); +} + +@ @<Finish the \.{TFM} file@>= +if ( mp->job_name==NULL ) mp_open_log_file(mp); +mp_pack_job_name(mp, ".tfm"); +while ( ! mp_b_open_out(mp, &mp->tfm_file, mp_filetype_metrics) ) + mp_prompt_file_name(mp, "file name for font metrics",".tfm"); +mp->metric_file_name=xstrdup(mp->name_of_file); +@<Output the subfile sizes and header bytes@>; +@<Output the character information bytes, then + output the dimensions themselves@>; +@<Output the ligature/kern program@>; +@<Output the extensible character recipes and the font metric parameters@>; + if ( mp->internal[mp_tracing_stats]>0 ) + @<Log the subfile sizes of the \.{TFM} file@>; +mp_print_nl(mp, "Font metrics written on "); +mp_print(mp, mp->metric_file_name); mp_print_char(mp, xord('.')); +@.Font metrics written...@> +(mp->close_file)(mp,mp->tfm_file) + +@ Integer variables |lh|, |k|, and |lk_offset| will be defined when we use +this code. + +@<Output the subfile sizes and header bytes@>= +k=mp->header_last; +LH=(k+4) / 4; /* this is the number of header words */ +if ( mp->bc>mp->ec ) mp->bc=1; /* if there are no characters, |ec=0| and |bc=1| */ +@<Compute the ligature/kern program offset and implant the + left boundary label@>; +mp_tfm_two(mp,6+LH+(mp->ec-mp->bc+1)+mp->nw+mp->nh+mp->nd+mp->ni+mp->nl + +lk_offset+mp->nk+mp->ne+mp->np); + /* this is the total number of file words that will be output */ +mp_tfm_two(mp, LH); mp_tfm_two(mp, mp->bc); mp_tfm_two(mp, mp->ec); +mp_tfm_two(mp, mp->nw); mp_tfm_two(mp, mp->nh); +mp_tfm_two(mp, mp->nd); mp_tfm_two(mp, mp->ni); mp_tfm_two(mp, mp->nl+lk_offset); +mp_tfm_two(mp, mp->nk); mp_tfm_two(mp, mp->ne); +mp_tfm_two(mp, mp->np); +for (k=0;k< 4*LH;k++) { + tfm_out(mp->header_byte[k]); +} + +@ @<Output the character information bytes...@>= +for (k=mp->bc;k<=mp->ec;k++) { + if ( ! mp->char_exists[k] ) { + mp_tfm_four(mp, 0); + } else { + tfm_out(mp_info(mp->tfm_width[k])); /* the width index */ + tfm_out((mp_info(mp->tfm_height[k]))*16+mp_info(mp->tfm_depth[k])); + tfm_out((mp_info(mp->tfm_ital_corr[k]))*4+mp->char_tag[k]); + tfm_out(mp->char_remainder[k]); + }; +} +mp->tfm_changed=0; +for (k=1;k<=4;k++) { + mp_tfm_four(mp, 0); p=mp->dimen_head[k]; + while ( p!=inf_val ) { + mp_tfm_four(mp, mp_dimen_out(mp, value(p))); p=mp_link(p); + } +} + + +@ We need to output special instructions at the beginning of the +|lig_kern| array in order to specify the right boundary character +and/or to handle starting addresses that exceed 255. The |label_loc| +and |label_char| arrays have been set up to record all the +starting addresses; we have $-1=|label_loc|[0]<|label_loc|[1]\le\cdots +\le|label_loc|[|label_ptr]|$. + +@<Compute the ligature/kern program offset...@>= +mp->bchar=mp_round_unscaled(mp, mp->internal[mp_boundary_char]); +if ((mp->bchar<0)||(mp->bchar>255)) { + mp->bchar=-1; mp->lk_started=false; lk_offset=0; +} else { + mp->lk_started=true; lk_offset=1; +} +@<Find the minimum |lk_offset| and adjust all remainders@>; +if ( mp->bch_label<undefined_label ) + { skip_byte(mp->nl)=qi(255); next_char(mp->nl)=qi(0); + op_byte(mp->nl)=qi(((mp->bch_label+lk_offset)/ 256)); + rem_byte(mp->nl)=qi(((mp->bch_label+lk_offset)% 256)); + incr(mp->nl); /* possibly |nl=lig_table_size+1| */ + } + +@ @<Find the minimum |lk_offset|...@>= +k=mp->label_ptr; /* pointer to the largest unallocated label */ +if ( mp->label_loc[k]+lk_offset>255 ) { + lk_offset=0; mp->lk_started=false; /* location 0 can do double duty */ + do { + mp->char_remainder[mp->label_char[k]]=lk_offset; + while ( mp->label_loc[k-1]==mp->label_loc[k] ) { + decr(k); mp->char_remainder[mp->label_char[k]]=lk_offset; + } + incr(lk_offset); decr(k); + } while (! (lk_offset+mp->label_loc[k]<256)); + /* N.B.: |lk_offset=256| satisfies this when |k=0| */ +} +if ( lk_offset>0 ) { + while ( k>0 ) { + mp->char_remainder[mp->label_char[k]] + =mp->char_remainder[mp->label_char[k]]+lk_offset; + decr(k); + } +} + +@ @<Output the ligature/kern program@>= +for (k=0;k<= 255;k++ ) { + if ( mp->skip_table[k]<undefined_label ) { + mp_print_nl(mp, "(local label "); mp_print_int(mp, k); mp_print(mp, ":: was missing)"); +@.local label l:: was missing@> + cancel_skips(mp->skip_table[k]); + } +} +if ( mp->lk_started ) { /* |lk_offset=1| for the special |bchar| */ + tfm_out(255); tfm_out(mp->bchar); mp_tfm_two(mp, 0); +} else { + for (k=1;k<=lk_offset;k++) {/* output the redirection specs */ + mp->ll=mp->label_loc[mp->label_ptr]; + if ( mp->bchar<0 ) { tfm_out(254); tfm_out(0); } + else { tfm_out(255); tfm_out(mp->bchar); }; + mp_tfm_two(mp, mp->ll+lk_offset); + do { + decr(mp->label_ptr); + } while (! (mp->label_loc[mp->label_ptr]<mp->ll)); + } +} +for (k=0;k<mp->nl;k++) mp_tfm_qqqq(mp, mp->lig_kern[k]); +for (k=0;k<mp->nk;k++) mp_tfm_four(mp, mp_dimen_out(mp, mp->kern[k])) + +@ @<Output the extensible character recipes...@>= +for (k=0;k<mp->ne;k++) + mp_tfm_qqqq(mp, mp->exten[k]); +for (k=1;k<=mp->np;k++) { + if ( k==1 ) { + if ( abs(mp->param[1])<fraction_half ) { + mp_tfm_four(mp, mp->param[1]*16); + } else { + incr(mp->tfm_changed); + if ( mp->param[1]>0 ) mp_tfm_four(mp, el_gordo); + else mp_tfm_four(mp, -el_gordo); + } + } else { + mp_tfm_four(mp, mp_dimen_out(mp, mp->param[k])); + } +} +if ( mp->tfm_changed>0 ) { + if ( mp->tfm_changed==1 ) mp_print_nl(mp, "(a font metric dimension"); +@.a font metric dimension...@> + else { + mp_print_nl(mp, "("); mp_print_int(mp, mp->tfm_changed); +@.font metric dimensions...@> + mp_print(mp, " font metric dimensions"); + } + mp_print(mp, " had to be decreased)"); +} + +@ @<Log the subfile sizes of the \.{TFM} file@>= +{ + char s[200]; + wlog_ln(" "); + if ( mp->bch_label<undefined_label ) decr(mp->nl); + mp_snprintf(s,128,"(You used %iw,%ih,%id,%ii,%il,%ik,%ie,%ip metric file positions)", + mp->nw, mp->nh, mp->nd, mp->ni, mp->nl, mp->nk, mp->ne,mp->np); + wlog_ln(s); +} + +@* \[43] Reading font metric data. + +\MP\ isn't a typesetting program but it does need to find the bounding box +of a sequence of typeset characters. Thus it needs to read \.{TFM} files as +well as write them. + +@<Glob...@>= +void * tfm_infile; + +@ All the width, height, and depth information is stored in an array called +|font_info|. This array is allocated sequentially and each font is stored +as a series of |char_info| words followed by the width, height, and depth +tables. Since |font_name| entries are permanent, their |str_ref| values are +set to |max_str_ref|. + +@<Types...@>= +typedef unsigned int font_number; /* |0..font_max| */ + +@ The |font_info| array is indexed via a group directory arrays. +For example, the |char_info| data for character~|c| in font~|f| will be +in |font_info[char_base[f]+c].qqqq|. + +@<Glob...@>= +font_number font_max; /* maximum font number for included text fonts */ +size_t font_mem_size; /* number of words for \.{TFM} information for text fonts */ +memory_word *font_info; /* height, width, and depth data */ +char **font_enc_name; /* encoding names, if any */ +boolean *font_ps_name_fixed; /* are the postscript names fixed already? */ +size_t next_fmem; /* next unused entry in |font_info| */ +font_number last_fnum; /* last font number used so far */ +scaled *font_dsize; /* 16 times the ``design'' size in \ps\ points */ +char **font_name; /* name as specified in the \&{infont} command */ +char **font_ps_name; /* PostScript name for use when |internal[mp_prologues]>0| */ +font_number last_ps_fnum; /* last valid |font_ps_name| index */ +eight_bits *font_bc; +eight_bits *font_ec; /* first and last character code */ +int *char_base; /* base address for |char_info| */ +int *width_base; /* index for zeroth character width */ +int *height_base; /* index for zeroth character height */ +int *depth_base; /* index for zeroth character depth */ +pointer *font_sizes; + +@ @<Allocate or initialize ...@>= +mp->font_mem_size = 10000; +mp->font_info = xmalloc ((mp->font_mem_size+1),sizeof(memory_word)); +memset (mp->font_info,0,sizeof(memory_word)*(mp->font_mem_size+1)); +mp->last_fnum = null_font; + +@ @<Dealloc variables@>= +for (k=1;k<=(int)mp->last_fnum;k++) { + xfree(mp->font_enc_name[k]); + xfree(mp->font_name[k]); + xfree(mp->font_ps_name[k]); +} +xfree(mp->font_info); +xfree(mp->font_enc_name); +xfree(mp->font_ps_name_fixed); +xfree(mp->font_dsize); +xfree(mp->font_name); +xfree(mp->font_ps_name); +xfree(mp->font_bc); +xfree(mp->font_ec); +xfree(mp->char_base); +xfree(mp->width_base); +xfree(mp->height_base); +xfree(mp->depth_base); +xfree(mp->font_sizes); + +@ +@c +void mp_reallocate_fonts (MP mp, font_number l) { + font_number f; + XREALLOC(mp->font_enc_name, l, char *); + XREALLOC(mp->font_ps_name_fixed, l, boolean); + XREALLOC(mp->font_dsize, l, scaled); + XREALLOC(mp->font_name, l, char *); + XREALLOC(mp->font_ps_name, l, char *); + XREALLOC(mp->font_bc, l, eight_bits); + XREALLOC(mp->font_ec, l, eight_bits); + XREALLOC(mp->char_base, l, int); + XREALLOC(mp->width_base, l, int); + XREALLOC(mp->height_base, l, int); + XREALLOC(mp->depth_base, l, int); + XREALLOC(mp->font_sizes, l, pointer); + for (f=(mp->last_fnum+1);f<=l;f++) { + mp->font_enc_name[f]=NULL; + mp->font_ps_name_fixed[f] = false; + mp->font_name[f]=NULL; + mp->font_ps_name[f]=NULL; + mp->font_sizes[f]=null; + } + mp->font_max = l; +} + +@ @<Internal library declarations@>= +void mp_reallocate_fonts (MP mp, font_number l); + + +@ A |null_font| containing no characters is useful for error recovery. Its +|font_name| entry starts out empty but is reset each time an erroneous font is +found. This helps to cut down on the number of duplicate error messages without +wasting a lot of space. + +@d null_font 0 /* the |font_number| for an empty font */ + +@<Set initial...@>= +mp->font_dsize[null_font]=0; +mp->font_bc[null_font]=1; +mp->font_ec[null_font]=0; +mp->char_base[null_font]=0; +mp->width_base[null_font]=0; +mp->height_base[null_font]=0; +mp->depth_base[null_font]=0; +mp->next_fmem=0; +mp->last_fnum=null_font; +mp->last_ps_fnum=null_font; +mp->font_name[null_font]=(char *)"nullfont"; +mp->font_ps_name[null_font]=(char *)""; +mp->font_ps_name_fixed[null_font] = false; +mp->font_enc_name[null_font]=NULL; +mp->font_sizes[null_font]=null; + +@ Each |char_info| word is of type |four_quarters|. The |b0| field contains +the |width index|; the |b1| field contains the height +index; the |b2| fields contains the depth index, and the |b3| field used only +for temporary storage. (It is used to keep track of which characters occur in +an edge structure that is being shipped out.) +The corresponding words in the width, height, and depth tables are stored as +|scaled| values in units of \ps\ points. + +With the macros below, the |char_info| word for character~|c| in font~|f| is +|char_mp_info(f,c)| and the width is +$$\hbox{|char_width(f,char_mp_info(f,c)).sc|.}$$ + +@d char_mp_info(A,B) mp->font_info[mp->char_base[(A)]+(B)].qqqq +@d char_width(A,B) mp->font_info[mp->width_base[(A)]+(B).b0].sc +@d char_height(A,B) mp->font_info[mp->height_base[(A)]+(B).b1].sc +@d char_depth(A,B) mp->font_info[mp->depth_base[(A)]+(B).b2].sc +@d ichar_exists(A) ((A).b0>0) + +@ When we have a font name and we don't know whether it has been loaded yet, +we scan the |font_name| array before calling |read_font_info|. + +@<Declarations@>= +static font_number mp_find_font (MP mp, char *f) ; + +@ @c +font_number mp_find_font (MP mp, char *f) { + font_number n; + for (n=0;n<=mp->last_fnum;n++) { + if (mp_xstrcmp(f,mp->font_name[n])==0 ) { + mp_xfree(f); + return n; + } + } + n = mp_read_font_info(mp, f); + mp_xfree(f); + return n; +} + +@ This is an interface function for getting the width of character, +as a double in ps units + +@c double mp_get_char_dimension (MP mp, char *fname, int c, int t) { + unsigned n; + four_quarters cc; + font_number f = 0; + double w = -1.0; + for (n=0;n<=mp->last_fnum;n++) { + if (mp_xstrcmp(fname,mp->font_name[n])==0 ) { + f = n; + break; + } + } + if (f==0) + return 0.0; + cc = char_mp_info(f,c); + if (! ichar_exists(cc) ) + return 0.0; + if (t=='w') + w = (double)char_width(f,cc); + else if (t=='h') + w = (double)char_height(f,cc); + else if (t=='d') + w = (double)char_depth(f,cc); + return w/655.35*(72.27/72); +} + +@ @<Exported function ...@>= +double mp_get_char_dimension (MP mp, char *fname, int n, int t); + + +@ One simple application of |find_font| is the implementation of the |font_size| +operator that gets the design size for a given font name. + +@<Find the design size of the font whose name is |cur_exp|@>= +mp_flush_cur_exp(mp, (mp->font_dsize[mp_find_font(mp, str(mp->cur_exp))]+8) / 16) + +@ If we discover that the font doesn't have a requested character, we omit it +from the bounding box computation and expect the \ps\ interpreter to drop it. +This routine issues a warning message if the user has asked for it. + +@<Declarations@>= +static void mp_lost_warning (MP mp,font_number f, pool_pointer k); + +@ @c +void mp_lost_warning (MP mp,font_number f, pool_pointer k) { + if ( mp->internal[mp_tracing_lost_chars]>0 ) { + mp_begin_diagnostic(mp); + if ( mp->selector==log_only ) incr(mp->selector); + mp_print_nl(mp, "Missing character: There is no "); +@.Missing character@> + mp_print_str(mp, mp->str_pool[k]); + mp_print(mp, " in font "); + mp_print(mp, mp->font_name[f]); mp_print_char(mp, xord('!')); + mp_end_diagnostic(mp, false); + } +} + +@ The whole purpose of saving the height, width, and depth information is to be +able to find the bounding box of an item of text in an edge structure. The +|set_text_box| procedure takes a text node and adds this information. + +@<Declarations@>= +static void mp_set_text_box (MP mp,pointer p); + +@ @c +void mp_set_text_box (MP mp,pointer p) { + font_number f; /* |mp_font_n(p)| */ + ASCII_code bc,ec; /* range of valid characters for font |f| */ + pool_pointer k,kk; /* current character and character to stop at */ + four_quarters cc; /* the |char_info| for the current character */ + scaled h,d; /* dimensions of the current character */ + width_val(p)=0; + height_val(p)=-el_gordo; + depth_val(p)=-el_gordo; + f=(font_number)mp_font_n(p); + bc=mp->font_bc[f]; + ec=mp->font_ec[f]; + kk=str_stop(mp_text_p(p)); + k=mp->str_start[mp_text_p(p)]; + while ( k<kk ) { + @<Adjust |p|'s bounding box to contain |str_pool[k]|; advance |k|@>; + } + @<Set the height and depth to zero if the bounding box is empty@>; +} + +@ @<Adjust |p|'s bounding box to contain |str_pool[k]|; advance |k|@>= +{ + if ( (mp->str_pool[k]<bc)||(mp->str_pool[k]>ec) ) { + mp_lost_warning(mp, f,k); + } else { + cc=char_mp_info(f,mp->str_pool[k]); + if ( ! ichar_exists(cc) ) { + mp_lost_warning(mp, f,k); + } else { + width_val(p)=width_val(p)+char_width(f,cc); + h=char_height(f,cc); + d=char_depth(f,cc); + if ( h>height_val(p) ) height_val(p)=h; + if ( d>depth_val(p) ) depth_val(p)=d; + } + } + incr(k); +} + +@ Let's hope modern compilers do comparisons correctly when the difference would +overflow. + +@<Set the height and depth to zero if the bounding box is empty@>= +if ( height_val(p)<-depth_val(p) ) { + height_val(p)=0; + depth_val(p)=0; +} + +@ The new primitives fontmapfile and fontmapline. + +@<Declare action procedures for use by |do_statement|@>= +static void mp_do_mapfile (MP mp) ; +static void mp_do_mapline (MP mp) ; + +@ @c +static void mp_do_mapfile (MP mp) { + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_string_type ) { + @<Complain about improper map operation@>; + } else { + mp_map_file(mp,mp->cur_exp); + } +} +static void mp_do_mapline (MP mp) { + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_string_type ) { + @<Complain about improper map operation@>; + } else { + mp_map_line(mp,mp->cur_exp); + } +} + +@ @<Complain about improper map operation@>= +{ + exp_err("Unsuitable expression"); + help1("Only known strings can be map files or map lines."); + mp_put_get_error(mp); +} + +@ To print |scaled| value to PDF output we need some subroutines to ensure +accurary. + +@d max_integer 0x7FFFFFFF /* $2^{31}-1$ */ + +@<Glob...@>= +scaled one_bp; /* scaled value corresponds to 1bp */ +scaled one_hundred_bp; /* scaled value corresponds to 100bp */ +scaled one_hundred_inch; /* scaled value corresponds to 100in */ +integer ten_pow[10]; /* $10^0..10^9$ */ +integer scaled_out; /* amount of |scaled| that was taken out in |divide_scaled| */ + +@ @<Set init...@>= +mp->one_bp = 65782; /* 65781.76 */ +mp->one_hundred_bp = 6578176; +mp->one_hundred_inch = 473628672; +mp->ten_pow[0] = 1; +for (i = 1;i<= 9; i++ ) { + mp->ten_pow[i] = 10*mp->ten_pow[i - 1]; +} + +@ The following function divides |s| by |m|. |dd| is number of decimal digits. + +@c scaled mp_divide_scaled (MP mp,scaled s, scaled m, integer dd) { + scaled q,r; + integer sign,i; + sign = 1; + if ( s < 0 ) { sign = -sign; s = -s; } + if ( m < 0 ) { sign = -sign; m = -m; } + if ( m == 0 ) + mp_confusion(mp, "arithmetic: divided by zero"); + else if ( m >= (max_integer / 10) ) + mp_confusion(mp, "arithmetic: number too big"); + q = s / m; + r = s % m; + for (i = 1;i<=dd;i++) { + q = 10*q + (10*r) / m; + r = (10*r) % m; + } + if ( 2*r >= m ) { incr(q); r = r - m; } + mp->scaled_out = sign*(s - (r / mp->ten_pow[dd])); + return (sign*q); +} + +@* \[44] Shipping pictures out. +The |ship_out| procedure, to be described below, is given a pointer to +an edge structure. Its mission is to output a file containing the \ps\ +description of an edge structure. + +@ Each time an edge structure is shipped out we write a new \ps\ output +file named according to the current \&{charcode}. +@:char_code_}{\&{charcode} primitive@> + +This is the only backend function that remains in the main |mpost.w| file. +There are just too many variable accesses needed for status reporting +etcetera to make it worthwile to move the code to |psout.w|. + +@<Internal library declarations@>= +void mp_open_output_file (MP mp) ; + +@ @c +static char *mp_set_output_file_name (MP mp, integer c) { + char *ss = NULL; /* filename extension proposal */ + char *nn = NULL; /* temp string for str() */ + unsigned old_setting; /* previous |selector| setting */ + pool_pointer i; /* indexes into |filename_template| */ + integer cc; /* a temporary integer for template building */ + integer f,g=0; /* field widths */ + if ( mp->job_name==NULL ) mp_open_log_file(mp); + if ( mp->internal[mp_output_template]==0) { + char *s; /* a file extension derived from |c| */ + if ( c<0 ) + s=xstrdup(".ps"); + else + @<Use |c| to compute the file extension |s|@>; + mp_pack_job_name(mp, s); + free(s); + ss = xstrdup(mp->name_of_file); + } else { /* initializations */ + str_number s, n; /* a file extension derived from |c| */ + old_setting=mp->selector; + mp->selector=new_string; + f = 0; + i = mp->str_start[mp->internal[mp_output_template]]; + n = null_str; /* initialize */ + while ( i<str_stop(mp->internal[mp_output_template]) ) { + if ( mp->str_pool[i]=='%' ) { + CONTINUE: + incr(i); + if ( i<str_stop(mp->internal[mp_output_template]) ) { + if ( mp->str_pool[i]=='j' ) { + mp_print(mp, mp->job_name); + } else if ( mp->str_pool[i]=='o' ) { + { char *s; + s = str(mp->internal[mp_output_format]); + mp_print(mp, s); + mp_xfree(s); + } + } else if ( mp->str_pool[i]=='d' ) { + cc= mp_round_unscaled(mp, mp->internal[mp_day]); + print_with_leading_zeroes(cc); + } else if ( mp->str_pool[i]=='m' ) { + cc= mp_round_unscaled(mp, mp->internal[mp_month]); + print_with_leading_zeroes(cc); + } else if ( mp->str_pool[i]=='y' ) { + cc= mp_round_unscaled(mp, mp->internal[mp_year]); + print_with_leading_zeroes(cc); + } else if ( mp->str_pool[i]=='H' ) { + cc= mp_round_unscaled(mp, mp->internal[mp_time]) / 60; + print_with_leading_zeroes(cc); + } else if ( mp->str_pool[i]=='M' ) { + cc= mp_round_unscaled(mp, mp->internal[mp_time]) % 60; + print_with_leading_zeroes(cc); + } else if ( mp->str_pool[i]=='c' ) { + if ( c<0 ) mp_print(mp, "ps"); + else print_with_leading_zeroes(c); + } else if ( (mp->str_pool[i]>='0') && + (mp->str_pool[i]<='9') ) { + if ( (f<10) ) + f = (f*10) + mp->str_pool[i]-'0'; + goto CONTINUE; + } else { + mp_print_str(mp, mp->str_pool[i]); + } + } + } else { + if ( mp->str_pool[i]=='.' ) + if (length(n)==0) + n = mp_make_string(mp); + mp_print_str(mp, mp->str_pool[i]); + }; + incr(i); + } + s = mp_make_string(mp); + mp->selector= old_setting; + if (length(n)==0) { + n=s; + s=null_str; + } + ss = str(s); + nn = str(n); + mp_pack_file_name(mp, nn,"",ss); + free(nn); + delete_str_ref(n); + delete_str_ref(s); + } + return ss; +} + +static char * mp_get_output_file_name (MP mp) { + char *f; + char *saved_name; /* saved |name_of_file| */ + saved_name = xstrdup(mp->name_of_file); + f = xstrdup(mp_set_output_file_name(mp, mp_round_unscaled(mp, mp->internal[mp_char_code]))); + mp_pack_file_name(mp, saved_name,NULL,NULL); + free(saved_name); + return f; +} + +void mp_open_output_file (MP mp) { + char *ss; /* filename extension proposal */ + integer c; /* \&{charcode} rounded to the nearest integer */ + c=mp_round_unscaled(mp, mp->internal[mp_char_code]); + ss = mp_set_output_file_name(mp, c); + while ( ! mp_a_open_out(mp, (void *)&mp->output_file, mp_filetype_postscript) ) + mp_prompt_file_name(mp, "file name for output",ss); + xfree(ss); + @<Store the true output file name if appropriate@>; +} + +@ The file extension created here could be up to five characters long in +extreme cases so it may have to be shortened on some systems. +@^system dependencies@> + +@<Use |c| to compute the file extension |s|@>= +{ + s = xmalloc(7,1); + mp_snprintf(s,7,".%i",(int)c); +} + +@ The user won't want to see all the output file names so we only save the +first and last ones and a count of how many there were. For this purpose +files are ordered primarily by \&{charcode} and secondarily by order of +creation. +@:char_code_}{\&{charcode} primitive@> + +@<Store the true output file name if appropriate@>= +if ((c<mp->first_output_code)&&(mp->first_output_code>=0)) { + mp->first_output_code=c; + xfree(mp->first_file_name); + mp->first_file_name=xstrdup(mp->name_of_file); +} +if ( c>=mp->last_output_code ) { + mp->last_output_code=c; + xfree(mp->last_file_name); + mp->last_file_name=xstrdup(mp->name_of_file); +} + +@ @<Glob...@>= +char * first_file_name; +char * last_file_name; /* full file names */ +integer first_output_code;integer last_output_code; /* rounded \&{charcode} values */ +@:char_code_}{\&{charcode} primitive@> +integer total_shipped; /* total number of |ship_out| operations completed */ + +@ @<Set init...@>= +mp->first_file_name=xstrdup(""); +mp->last_file_name=xstrdup(""); +mp->first_output_code=32768; +mp->last_output_code=-32768; +mp->total_shipped=0; + +@ @<Dealloc variables@>= +xfree(mp->first_file_name); +xfree(mp->last_file_name); + +@ @<Begin the progress report for the output of picture~|c|@>= +if ( (int)mp->term_offset>mp->max_print_line-6 ) mp_print_ln(mp); +else if ( (mp->term_offset>0)||(mp->file_offset>0) ) mp_print_char(mp, xord(' ')); +mp_print_char(mp, xord('[')); +if ( c>=0 ) mp_print_int(mp, c) + +@ @<End progress report@>= +mp_print_char(mp, xord(']')); +update_terminal; +incr(mp->total_shipped) + +@ @<Explain what output files were written@>= +if ( mp->total_shipped>0 ) { + mp_print_nl(mp, ""); + mp_print_int(mp, mp->total_shipped); + if (mp->noninteractive) { + mp_print(mp, " figure"); + if ( mp->total_shipped>1 ) mp_print_char(mp, xord('s')); + mp_print(mp, " created."); + } else { + mp_print(mp, " output file"); + if ( mp->total_shipped>1 ) mp_print_char(mp, xord('s')); + mp_print(mp, " written: "); + mp_print(mp, mp->first_file_name); + if ( mp->total_shipped>1 ) { + if ( 31+strlen(mp->first_file_name)+ + strlen(mp->last_file_name)> (unsigned)mp->max_print_line) + mp_print_ln(mp); + mp_print(mp, " .. "); + mp_print(mp, mp->last_file_name); + } + } +} + +@ @<Internal library declarations@>= +boolean mp_has_font_size(MP mp, font_number f ); + +@ @c +boolean mp_has_font_size(MP mp, font_number f ) { + return (mp->font_sizes[f]!=null); +} + +@ The \&{special} command saves up lines of text to be printed during the next +|ship_out| operation. The saved items are stored as a list of capsule tokens. + +@<Glob...@>= +pointer last_pending; /* the last token in a list of pending specials */ + +@ @<Set init...@>= +mp->last_pending=spec_head; + +@ @<Cases of |do_statement|...@>= +case special_command: + if ( mp->cur_mod==0 ) mp_do_special(mp); else + if ( mp->cur_mod==1 ) mp_do_mapfile(mp); else + mp_do_mapline(mp); + break; + +@ @<Declare action procedures for use by |do_statement|@>= +static void mp_do_special (MP mp) ; + +@ @c void mp_do_special (MP mp) { + mp_get_x_next(mp); mp_scan_expression(mp); + if ( mp->cur_type!=mp_string_type ) { + @<Complain about improper special operation@>; + } else { + mp_link(mp->last_pending)=mp_stash_cur_exp(mp); + mp->last_pending=mp_link(mp->last_pending); + mp_link(mp->last_pending)=null; + } +} + +@ @<Complain about improper special operation@>= +{ + exp_err("Unsuitable expression"); + help1("Only known strings are allowed for output as specials."); + mp_put_get_error(mp); +} + +@ On the export side, we need an extra object type for special strings. + +@<Graphical object codes@>= +mp_special_code=8, + +@ @<Export pending specials@>= +p=mp_link(spec_head); +while ( p!=null ) { + mp_special_object *tp; + tp = (mp_special_object *)mp_new_graphic_object(mp,mp_special_code); + gr_pre_script(tp) = str(value(p)); + if (hh->body==NULL) hh->body = (mp_graphic_object *)tp; + else gr_link(hp) = (mp_graphic_object *)tp; + hp = (mp_graphic_object *)tp; + p=mp_link(p); +} +mp_flush_token_list(mp, mp_link(spec_head)); +mp_link(spec_head)=null; +mp->last_pending=spec_head + +@ We are now ready for the main output procedure. Note that the |selector| +setting is saved in a global variable so that |begin_diagnostic| can access it. + +@<Declare the \ps\ output procedures@>= +static void mp_ship_out (MP mp, pointer h) ; + +@ Once again, the |gr_XXXX| macros are defined in |mppsout.h| + +@d export_color(q,p) + if ( mp_color_model(p)==mp_uninitialized_model ) { + gr_color_model(q) = (unsigned char)(mp->internal[mp_default_color_model]/65536); + gr_cyan_val(q) = 0; + gr_magenta_val(q) = 0; + gr_yellow_val(q) = 0; + gr_black_val(q) = (gr_color_model(q)==mp_cmyk_model ? unity : 0); + } else { + gr_color_model(q) = (unsigned char)mp_color_model(p); + gr_cyan_val(q) = cyan_val(p); + gr_magenta_val(q) = magenta_val(p); + gr_yellow_val(q) = yellow_val(p); + gr_black_val(q) = black_val(p); + } + +@d export_scripts(q,p) + if (mp_pre_script(p)!=null) gr_pre_script(q) = str(mp_pre_script(p)); + if (mp_post_script(p)!=null) gr_post_script(q) = str(mp_post_script(p)); + +@c +struct mp_edge_object *mp_gr_export(MP mp, pointer h) { + pointer p; /* the current graphical object */ + integer t; /* a temporary value */ + integer c; /* a rounded charcode */ + scaled d_width; /* the current pen width */ + mp_edge_object *hh; /* the first graphical object */ + mp_graphic_object *hq; /* something |hp| points to */ + mp_text_object *tt; + mp_fill_object *tf; + mp_stroked_object *ts; + mp_clip_object *tc; + mp_bounds_object *tb; + mp_graphic_object *hp = NULL; /* the current graphical object */ + mp_set_bbox(mp, h, true); + hh = xmalloc(1,sizeof(mp_edge_object)); + hh->body = NULL; + hh->next = NULL; + hh->parent = mp; + hh->minx = minx_val(h); + hh->miny = miny_val(h); + hh->maxx = maxx_val(h); + hh->maxy = maxy_val(h); + hh->filename = mp_get_output_file_name(mp); + c = mp_round_unscaled(mp,mp->internal[mp_char_code]); + hh->charcode = c; + hh->width = mp->internal[mp_char_wd]; + hh->height = mp->internal[mp_char_ht]; + hh->depth = mp->internal[mp_char_dp]; + hh->ital_corr = mp->internal[mp_char_ic]; + @<Export pending specials@>; + p=mp_link(dummy_loc(h)); + while ( p!=null ) { + hq = mp_new_graphic_object(mp,mp_type(p)); + switch (mp_type(p)) { + case mp_fill_code: + tf = (mp_fill_object *)hq; + gr_pen_p(tf) = mp_export_knot_list(mp,mp_pen_p(p)); + d_width = mp_get_pen_scale(mp, mp_pen_p(p)); + if ((mp_pen_p(p)==null) || pen_is_elliptical(mp_pen_p(p))) { + gr_path_p(tf) = mp_export_knot_list(mp,mp_path_p(p)); + } else { + pointer pc, pp; + pc = mp_copy_path(mp, mp_path_p(p)); + pp = mp_make_envelope(mp, pc, mp_pen_p(p),ljoin_val(p),0,miterlim_val(p)); + gr_path_p(tf) = mp_export_knot_list(mp,pp); + mp_toss_knot_list(mp, pp); + pc = mp_htap_ypoc(mp, mp_path_p(p)); + pp = mp_make_envelope(mp, pc, mp_pen_p(p),ljoin_val(p),0,miterlim_val(p)); + gr_htap_p(tf) = mp_export_knot_list(mp,pp); + mp_toss_knot_list(mp, pp); + } + export_color(tf,p) ; + export_scripts(tf,p); + gr_ljoin_val(tf) = (unsigned char)ljoin_val(p); + gr_miterlim_val(tf) = miterlim_val(p); + break; + case mp_stroked_code: + ts = (mp_stroked_object *)hq; + gr_pen_p(ts) = mp_export_knot_list(mp,mp_pen_p(p)); + d_width = mp_get_pen_scale(mp, mp_pen_p(p)); + if (pen_is_elliptical(mp_pen_p(p))) { + gr_path_p(ts) = mp_export_knot_list(mp,mp_path_p(p)); + } else { + pointer pc; + pc=mp_copy_path(mp, mp_path_p(p)); + t=lcap_val(p); + if ( mp_left_type(pc)!=mp_endpoint ) { + mp_left_type(mp_insert_knot(mp, pc,mp_x_coord(pc),mp_y_coord(pc)))=mp_endpoint; + mp_right_type(pc)=mp_endpoint; + pc=mp_link(pc); + t=1; + } + pc=mp_make_envelope(mp,pc,mp_pen_p(p),ljoin_val(p),t,miterlim_val(p)); + gr_path_p(ts) = mp_export_knot_list(mp,pc); + mp_toss_knot_list(mp, pc); + } + export_color(ts,p) ; + export_scripts(ts,p); + gr_ljoin_val(ts) = (unsigned char)ljoin_val(p); + gr_miterlim_val(ts) = miterlim_val(p); + gr_lcap_val(ts) = (unsigned char)lcap_val(p); + gr_dash_p(ts) = mp_export_dashes(mp,p,&d_width); + break; + case mp_text_code: + tt = (mp_text_object *)hq; + gr_text_p(tt) = str(mp_text_p(p)); + gr_text_l(tt) = (size_t)length(mp_text_p(p)); + gr_font_n(tt) = (unsigned int)mp_font_n(p); + gr_font_name(tt) = mp_xstrdup(mp,mp->font_name[mp_font_n(p)]); + gr_font_dsize(tt) = (unsigned int)mp->font_dsize[mp_font_n(p)]; + export_color(tt,p) ; + export_scripts(tt,p); + gr_width_val(tt) = width_val(p); + gr_height_val(tt) = height_val(p); + gr_depth_val(tt) = depth_val(p); + gr_tx_val(tt) = tx_val(p); + gr_ty_val(tt) = ty_val(p); + gr_txx_val(tt) = txx_val(p); + gr_txy_val(tt) = txy_val(p); + gr_tyx_val(tt) = tyx_val(p); + gr_tyy_val(tt) = tyy_val(p); + break; + case mp_start_clip_code: + tc = (mp_clip_object *)hq; + gr_path_p(tc) = mp_export_knot_list(mp,mp_path_p(p)); + break; + case mp_start_bounds_code: + tb = (mp_bounds_object *)hq; + gr_path_p(tb) = mp_export_knot_list(mp,mp_path_p(p)); + break; + case mp_stop_clip_code: + case mp_stop_bounds_code: + /* nothing to do here */ + break; + } + if (hh->body==NULL) hh->body=hq; else gr_link(hp) = hq; + hp = hq; + p=mp_link(p); + } + return hh; +} + +@ @<Declarations@>= +static struct mp_edge_object *mp_gr_export(MP mp, int h); + +@ This function is now nearly trivial. + +@c +void mp_ship_out (MP mp, pointer h) { /* output edge structure |h| */ + integer c; /* \&{charcode} rounded to the nearest integer */ + c=mp_round_unscaled(mp, mp->internal[mp_char_code]); + @<Begin the progress report for the output of picture~|c|@>; + (mp->shipout_backend) (mp, h); + @<End progress report@>; + if ( mp->internal[mp_tracing_output]>0 ) + mp_print_edges(mp, h," (just shipped out)",true); +} + +@ @<Declarations@>= +static void mp_shipout_backend (MP mp, pointer h); + +@ +@c +void mp_shipout_backend (MP mp, pointer h) { + char *s; + mp_edge_object *hh; /* the first graphical object */ + hh = mp_gr_export(mp,h); + s = NULL; + if (mp->internal[mp_output_format]>0) + s = str(mp->internal[mp_output_format]); + if (s && strcmp(s,"svg")==0) { + (void)mp_svg_gr_ship_out (hh, + (mp->internal[mp_prologues]/65536), + false); + } else { + (void)mp_gr_ship_out (hh, + (mp->internal[mp_prologues]/65536), + (mp->internal[mp_procset]/65536), + false); + } + mp_gr_toss_objects(hh); +} + +@ @<Exported types@>= +typedef void (*mp_backend_writer)(MP, int); + +@ @<Option variables@>= +mp_backend_writer shipout_backend; + +@ Now that we've finished |ship_out|, let's look at the other commands +by which a user can send things to the \.{GF} file. + +@ @<Determine if a character has been shipped out@>= +{ + mp->cur_exp=mp_round_unscaled(mp, mp->cur_exp) % 256; + if ( mp->cur_exp<0 ) mp->cur_exp=mp->cur_exp+256; + boolean_reset(mp->char_exists[mp->cur_exp]); + mp->cur_type=mp_boolean_type; +} + +@ @<Glob...@>= +psout_data ps; +svgout_data svg; + +@ @<Allocate or initialize ...@>= +mp_ps_backend_initialize(mp); +mp_svg_backend_initialize(mp); + +@ @<Dealloc...@>= +mp_ps_backend_free(mp); +mp_svg_backend_free(mp); + + +@* \[45] Dumping and undumping the tables. +After \.{INIMP} has seen a collection of macros, it +can write all the necessary information on an auxiliary file so +that production versions of \MP\ are able to initialize their +memory at high speed. The present section of the program takes +care of such output and input. We shall consider simultaneously +the processes of storing and restoring, +so that the inverse relation between them is clear. +@.INIMP@> + +The global variable |mem_ident| is a string that is printed right +after the |banner| line when \MP\ is ready to start. For \.{INIMP} this +string says simply `\.{(INIMP)}'; for other versions of \MP\ it says, +for example, `\.{(mem=plain 1990.4.14)}', showing the year, +month, and day that the mem file was created. We have |mem_ident=0| +before \MP's tables are loaded. + +@<Glob...@>= +char * mem_ident; +void * mem_file; /* for input or output of mem information */ + +@ @<Set init...@>= +mp->mem_ident=NULL; + +@ @<Initialize table entries...@>= +mp->mem_ident=xstrdup(" (INIMP)"); + +@ @<Declarations@>= +extern void mp_store_mem_file (MP mp) ; +extern boolean mp_load_mem_file (MP mp); +extern int mp_undump_constants (MP mp); + +@ @<Dealloc variables@>= +xfree(mp->mem_ident); + + +@* \[46] The main program. +This is it: the part of \MP\ that executes all those procedures we have +written. + +Well---almost. We haven't put the parsing subroutines into the +program yet; and we'd better leave space for a few more routines that may +have been forgotten. + +@c @<Declare the basic parsing subroutines@> +@<Declare miscellaneous procedures that were declared |forward|@> + +@ We've noted that there are two versions of \MP. One, called \.{INIMP}, +@.INIMP@> +has to be run first; it initializes everything from scratch, without +reading a mem file, and it has the capability of dumping a mem file. +The other one is called `\.{VIRMP}'; it is a ``virgin'' program that needs +@.VIRMP@> +to input a mem file in order to get started. \.{VIRMP} typically has +a bit more memory capacity than \.{INIMP}, because it does not need the +space consumed by the dumping/undumping routines and the numerous calls on +|primitive|, etc. + +The \.{VIRMP} program cannot read a mem file instantaneously, of course; +the best implementations therefore allow for production versions of \MP\ that +not only avoid the loading routine for object code, they also have +a mem file pre-loaded. + +@ @<Option variables@>= +int ini_version; /* are we iniMP? */ + +@ @<Set |ini_version|@>= +mp->ini_version = (opt->ini_version ? true : false); + +@ The code below make the final chosen hash size the next larger +multiple of 2 from the requested size, and this array is a list of +suitable prime numbers to go with such values. + +The top limit is chosen such that it is definately lower than +|max_halfword-3*param_size|, because |param_size| cannot be larger +than |max_halfword/sizeof(pointer)|. + +@<Declarations@>= +static int mp_prime_choices[] = + { 12289, 24593, 49157, 98317, + 196613, 393241, 786433, 1572869, + 3145739, 6291469, 12582917, 25165843, + 50331653, 100663319 }; + +@ @<Find constant sizes@>= +if (mp->ini_version) { + unsigned i = 14; + set_value(mp->mem_top,opt->main_memory,5000); + mp->mem_max = mp->mem_top; + set_value(mp->param_size,opt->param_size,150); + set_value(mp->max_in_open,opt->max_in_open,10); + if (opt->hash_size>0x8000000) + opt->hash_size=0x8000000; + if (opt->hash_size>0) { + set_value(mp->hash_size,(2*opt->hash_size-1),16384); + } else { + mp->hash_size = 16384; + } + mp->hash_size = mp->hash_size>>i; + while (mp->hash_size>=2) { + mp->hash_size /= 2; + i++; + } + mp->hash_size = mp->hash_size << i; + if (mp->hash_size>0x8000000) + mp->hash_size=0x8000000; + mp->hash_prime=mp_prime_choices[(i-14)]; +} else { + int i = -1; + if (mp->mem_name == NULL) { + mp->mem_name = mp_xstrdup(mp,"plain"); + } + if (mp_open_mem_file(mp)) { + i = mp_undump_constants(mp); + if (i != metapost_magic) + goto OFF_BASE; + set_value(mp->mem_max,opt->main_memory,mp->mem_top); + goto DONE; +OFF_BASE: + wterm_ln("(Fatal mem file error; "); + wterm((mp->find_file)(mp, mp->mem_name, "r", mp_filetype_memfile)); + if (i>metapost_old_magic && i<metapost_magic) { + wterm(" was written by an older version)\n"); + } else { + wterm(" appears not to be a mem file)\n"); + } + } + mp->history = mp_fatal_error_stop; + mp_jump_out(mp); +} +DONE: + + +@ Here we do whatever is needed to complete \MP's job gracefully on the +local operating system. The code here might come into play after a fatal +error; it must therefore consist entirely of ``safe'' operations that +cannot produce error messages. For example, it would be a mistake to call +|str_room| or |make_string| at this time, because a call on |overflow| +might lead to an infinite loop. +@^system dependencies@> + +This program doesn't bother to close the input files that may still be open. + +@ @c +void mp_close_files_and_terminate (MP mp) { + integer k; /* all-purpose index */ + integer LH; /* the length of the \.{TFM} header, in words */ + int lk_offset; /* extra words inserted at beginning of |lig_kern| array */ + pointer p; /* runs through a list of \.{TFM} dimensions */ + if (mp->finished) + return; + @<Close all open files in the |rd_file| and |wr_file| arrays@>; + if ( mp->internal[mp_tracing_stats]>0 ) + @<Output statistics about this job@>; + wake_up_terminal; + @<Do all the finishing work on the \.{TFM} file@>; + @<Explain what output files were written@>; + if ( mp->log_opened && ! mp->noninteractive ){ + wlog_cr; + (mp->close_file)(mp,mp->log_file); + mp->selector=mp->selector-2; + if ( mp->selector==term_only ) { + mp_print_nl(mp, "Transcript written on "); +@.Transcript written...@> + mp_print(mp, mp->log_name); mp_print_char(mp, xord('.')); + } + } + mp_print_ln(mp); + mp->finished = true; +} + +@ @<Declarations@>= +static void mp_close_files_and_terminate (MP mp) ; + +@ @<Close all open files in the |rd_file| and |wr_file| arrays@>= +if (mp->rd_fname!=NULL) { + for (k=0;k<(int)mp->read_files;k++ ) { + if ( mp->rd_fname[k]!=NULL ) { + (mp->close_file)(mp,mp->rd_file[k]); + xfree(mp->rd_fname[k]); + } + } +} +if (mp->wr_fname!=NULL) { + for (k=0;k<(int)mp->write_files;k++) { + if ( mp->wr_fname[k]!=NULL ) { + (mp->close_file)(mp,mp->wr_file[k]); + xfree(mp->wr_fname[k]); + } + } +} + +@ @<Dealloc ...@>= +for (k=0;k<(int)mp->max_read_files;k++ ) { + if ( mp->rd_fname[k]!=NULL ) { + (mp->close_file)(mp,mp->rd_file[k]); + xfree(mp->rd_fname[k]); + } +} +xfree(mp->rd_file); +xfree(mp->rd_fname); +for (k=0;k<(int)mp->max_write_files;k++) { + if ( mp->wr_fname[k]!=NULL ) { + (mp->close_file)(mp,mp->wr_file[k]); + xfree(mp->wr_fname[k]); + } +} +xfree(mp->wr_file); +xfree(mp->wr_fname); + + +@ We want to produce a \.{TFM} file if and only if |mp_fontmaking| is positive. + +We reclaim all of the variable-size memory at this point, so that +there is no chance of another memory overflow after the memory capacity +has already been exceeded. + +@<Do all the finishing work on the \.{TFM} file@>= +if ( mp->internal[mp_fontmaking]>0 ) { + @<Make the dynamic memory into one big available node@>; + @<Massage the \.{TFM} widths@>; + mp_fix_design_size(mp); mp_fix_check_sum(mp); + @<Massage the \.{TFM} heights, depths, and italic corrections@>; + mp->internal[mp_fontmaking]=0; /* avoid loop in case of fatal error */ + @<Finish the \.{TFM} file@>; +} + +@ @<Make the dynamic memory into one big available node@>= +mp->rover=lo_mem_stat_max+1; mp_link(mp->rover)=empty_flag; mp->lo_mem_max=mp->hi_mem_min-1; +if ( mp->lo_mem_max-mp->rover>max_halfword ) mp->lo_mem_max=max_halfword+mp->rover; +node_size(mp->rover)=mp->lo_mem_max-mp->rover; +lmp_link(mp->rover)=mp->rover; rmp_link(mp->rover)=mp->rover; +mp_link(mp->lo_mem_max)=null; mp_info(mp->lo_mem_max)=null + +@ The present section goes directly to the log file instead of using +|print| commands, because there's no need for these strings to take +up |str_pool| memory when a non-{\bf stat} version of \MP\ is being used. + +@<Output statistics...@>= +if ( mp->log_opened ) { + char s[128]; + wlog_ln(" "); + wlog_ln("Here is how much of MetaPost's memory you used:"); +@.Here is how much...@> + mp_snprintf(s,128," %i string%s out of %i",(int)mp->max_strs_used-mp->init_str_use, + (mp->max_strs_used!=mp->init_str_use+1 ? "s" : ""), + (int)(mp->max_strings-1-mp->init_str_use)); + wlog_ln(s); + mp_snprintf(s,128," %i string characters out of %i", + (int)mp->max_pl_used-mp->init_pool_ptr, + (int)mp->pool_size-mp->init_pool_ptr); + wlog_ln(s); + mp_snprintf(s,128," %i words of memory out of %i", + (int)mp->lo_mem_max+mp->mem_end-mp->hi_mem_min+2, + (int)mp->mem_end); + wlog_ln(s); + mp_snprintf(s,128," %i symbolic tokens out of %i", (int)mp->st_count, (int)mp->hash_size); + wlog_ln(s); + mp_snprintf(s,128," %ii,%in,%ip,%ib,%if stack positions out of %ii,%in,%ip,%ib,%if", + (int)mp->max_in_stack,(int)mp->int_ptr, + (int)mp->max_param_stack,(int)mp->max_buf_stack+1,(int)mp->in_open_max, + (int)mp->stack_size,(int)mp->max_internal,(int)mp->param_size, + (int)mp->buf_size,(int)mp->max_in_open); + wlog_ln(s); + mp_snprintf(s,128," %i string compactions (moved %i characters, %i strings)", + (int)mp->pact_count,(int)mp->pact_chars,(int)mp->pact_strs); + wlog_ln(s); +} + +@ It is nice to have have some of the stats available from the API. + +@<Exported function ...@>= +int mp_memory_usage (MP mp ); +int mp_hash_usage (MP mp ); +int mp_param_usage (MP mp ); +int mp_open_usage (MP mp ); + +@ @c +int mp_memory_usage (MP mp ) { + return (int)mp->lo_mem_max+mp->mem_end-mp->hi_mem_min+2; +} +int mp_hash_usage (MP mp ) { + return (int)mp->st_count; +} +int mp_param_usage (MP mp ) { + return (int)mp->max_param_stack; +} +int mp_open_usage (MP mp ) { + return (int)mp->max_in_stack; +} + +@ We get to the |final_cleanup| routine when \&{end} or \&{dump} has +been scanned. + +@c +void mp_final_cleanup (MP mp) { + quarterword c; /* 0 for \&{end}, 1 for \&{dump} */ + c=mp->cur_mod; + if ( mp->job_name==NULL ) mp_open_log_file(mp); + while ( mp->input_ptr>0 ) { + if ( token_state ) mp_end_token_list(mp); + else mp_end_file_reading(mp); + } + while ( mp->loop_ptr!=null ) mp_stop_iteration(mp); + while ( mp->open_parens>0 ) { + mp_print(mp, " )"); decr(mp->open_parens); + }; + while ( mp->cond_ptr!=null ) { + mp_print_nl(mp, "(end occurred when "); +@.end occurred...@> + mp_print_cmd_mod(mp, fi_or_else,mp->cur_if); + /* `\.{if}' or `\.{elseif}' or `\.{else}' */ + if ( mp->if_line!=0 ) { + mp_print(mp, " on line "); mp_print_int(mp, mp->if_line); + } + mp_print(mp, " was incomplete)"); + mp->if_line=if_line_field(mp->cond_ptr); + mp->cur_if=mp_name_type(mp->cond_ptr); mp->cond_ptr=mp_link(mp->cond_ptr); + } + if ( mp->history!=mp_spotless ) + if ( ((mp->history==mp_warning_issued)||(mp->interaction<mp_error_stop_mode)) ) + if ( mp->selector==term_and_log ) { + mp->selector=term_only; + mp_print_nl(mp, "(see the transcript file for additional information)"); +@.see the transcript file...@> + mp->selector=term_and_log; + } + if ( c==1 ) { + if (mp->ini_version) { + mp_store_mem_file(mp); return; + } + mp_print_nl(mp, "(dump is performed only by INIMP)"); return; +@.dump...only by INIMP@> + } +} + +@ @<Declarations@>= +static void mp_final_cleanup (MP mp) ; +static void mp_init_prim (MP mp) ; +static void mp_init_tab (MP mp) ; + +@ @c +void mp_init_prim (MP mp) { /* initialize all the primitives */ + @<Put each...@>; +} +@# +void mp_init_tab (MP mp) { /* initialize other tables */ + integer k; /* all-purpose index */ + @<Initialize table entries (done by \.{INIMP} only)@>; +} + + +@ When we begin the following code, \MP's tables may still contain garbage; +thus we must proceed cautiously to get bootstrapped in. + +But when we finish this part of the program, \MP\ is ready to call on the +|main_control| routine to do its work. + +@<Get the first line...@>= +{ + @<Initialize the input routines@>; + if (mp->mem_ident==NULL) { + if ( ! mp_load_mem_file(mp) ) { + (mp->close_file)(mp, mp->mem_file); + mp->history = mp_fatal_error_stop; + return mp; + } + (mp->close_file)(mp, mp->mem_file); + } + @<Initializations following first line@>; +} + +@ @<Initializations following first line@>= + mp->buffer[limit]=(ASCII_code)'%'; + mp_fix_date_and_time(mp); + if (mp->random_seed==0) + mp->random_seed = (mp->internal[mp_time] / unity)+mp->internal[mp_day]; + mp_init_randoms(mp, mp->random_seed); + @<Initialize the print |selector|...@>; + if ( loc<limit ) if ( mp->buffer[loc]!='\\' ) + mp_start_input(mp); /* \&{input} assumed */ + +@ @<Run inimpost commands@>= +{ + mp_get_strings_started(mp); + mp_init_tab(mp); /* initialize the tables */ + mp_init_prim(mp); /* call |primitive| for each primitive */ + mp->init_str_use=mp->max_str_ptr=mp->str_ptr; + mp->init_pool_ptr=mp->max_pool_ptr=mp->pool_ptr; + mp_fix_date_and_time(mp); +} + +@ Saving the filename template + +@<Save the filename template@>= +{ + delete_str_ref(mp->internal[mp_output_template]); + if ( length(mp->cur_exp)==0 ) { + mp->internal[mp_output_template] = rts("%j.%c"); + } else { + mp->internal[mp_output_template]=mp->cur_exp; + add_str_ref(mp->internal[mp_output_template]); + } +} + +@* \[47] Debugging. + + +@* \[48] System-dependent changes. +This section should be replaced, if necessary, by any special +modification of the program +that are necessary to make \MP\ work at a particular installation. +It is usually best to design your change file so that all changes to +previous sections preserve the section numbering; then everybody's version +will be consistent with the published program. More extensive changes, +which introduce new sections, can be inserted here; then only the index +itself will get a new section number. +@^system dependencies@> + +@* \[49] Index. +Here is where you can find all uses of each identifier in the program, +with underlined entries pointing to where the identifier was defined. +If the identifier is only one letter long, however, you get to see only +the underlined entries. {\sl All references are to section numbers instead of +page numbers.} + +This index also lists error messages and other aspects of the program +that you might want to look up some day. For example, the entry +for ``system dependencies'' lists all sections that should receive +special attention from people who are installing \MP\ in a new +operating environment. A list of various things that can't happen appears +under ``this can't happen''. +Approximately 25 sections are listed under ``inner loop''; these account +for more than 60\pct! of \MP's running time, exclusive of input and output. |