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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/generic/realcalc
Initial commit
Diffstat (limited to 'macros/generic/realcalc')
-rw-r--r--macros/generic/realcalc/readme39
-rw-r--r--macros/generic/realcalc/realcalc.tex581
-rw-r--r--macros/generic/realcalc/realdemo.tex6
-rw-r--r--macros/generic/realcalc/realtest.tex291
4 files changed, 917 insertions, 0 deletions
diff --git a/macros/generic/realcalc/readme b/macros/generic/realcalc/readme
new file mode 100644
index 0000000000..aa152337fb
--- /dev/null
+++ b/macros/generic/realcalc/readme
@@ -0,0 +1,39 @@
+realcalc.tex
+
+(Copyright) Frank Buchholz, Jan. 1993
+e-mail: buchholz@lusty.informatik.uni-dortmund.de
+
+Real arithmetic with big values and high precision.
+Calculations are done with 9 decimal digits.
+Usable with TeX and LaTeX.
+
+Files:
+ readme This file
+ realcalc.tex You have to \input realcalc.tex to use it.
+ realdemo.tex Demo with LaTeX.
+ realtest.tex Demo with TeX (Type \test\bye after the prompt)
+
+Installation:
+ Put the file realcalc.tex where your TeX looks for inputs.
+ Name a copy realcalc.sty to use as a LaTeX style option,
+ or create a file realcalc.sty with the lines:
+ \input realcalc.tex
+ \endinput
+
+Documentation:
+ Use following command to extract the documentation:
+ grep %% realcalc.tex
+
+COPYING:
+ Copying of part or all of this file is allowed under the following
+ conditions only:
+ (1) You may freely distribute unchanged copies of the files. You have
+ to include this file when you do so.
+ (2) You may modify a renamed copy of the files, but only for personal
+ use or use within an organization.
+ (3) You may copy fragments from the files, for personal use or for
+ distribution, as long as credit is given where credit is due.
+
+ You are NOT ALLOWED to take money for the distribution or use of
+ this file or modified versions or fragments thereof, except for
+ a nominal charge for copying etc.
diff --git a/macros/generic/realcalc/realcalc.tex b/macros/generic/realcalc/realcalc.tex
new file mode 100644
index 0000000000..be46167fc4
--- /dev/null
+++ b/macros/generic/realcalc/realcalc.tex
@@ -0,0 +1,581 @@
+%% realcalc.tex
+%%
+%% (C) Frank Buchholz, Jan. 1993
+%% e-mail: buchholz@lusty.informatik.uni-dortmund.de
+% User documentation: All lines starting with two %
+% Try grep to extract these lines.
+%%
+%% Real arithmetic with big values and high precision.
+%% Calculations are done with 9 decimal digits.
+%% Usable with TeX and LaTeX.
+%%
+%% Parameter:
+%%
+%% <macro> Macro, witch catches the result.
+%% <value> String or macro witch expands to a value in the range
+%% from -2147483647.999999999 to 2147483647.999999999
+%% <precision> Number from 0 to 9
+%%
+%% Functions:
+%%
+
+% Don't read this file twice
+\ifx\Radd\undefined \else \endinput \fi
+
+% Make "@" be a letters
+\chardef\catamp=\the\catcode`\@
+\catcode`@=11
+
+\def\@Rversion{Version 1.0, Jan. 1993}
+\message{`Real arithmetic', \@Rversion (C) Frank Buchholz}
+
+% Allocation of temporary registers
+\newcount\@ta
+\newcount\@tb
+%
+\newcount\@xs % Sign of 1st value
+\newcount\@xi % Integer part of 1st value
+\newcount\@xf % Fractional part of 1st value
+%
+\newcount\@ys % Sign of 2nd value
+\newcount\@yi % Integer part of 2nd value
+\newcount\@yf % Fractional part of 2nd value
+%
+\newcount\@mil \@mil=1000000000 % 10^9
+%
+\countdef\@xa240
+\countdef\@xb241
+\countdef\@xc242
+\countdef\@xd243
+\countdef\@xe244
+\countdef\@ya245
+\countdef\@yb246
+\countdef\@yc247
+\countdef\@yd248
+\countdef\@ye249
+\let\@f=\@tb
+\let\@product=\@ta
+
+\chardef\@zero=0
+
+%% \Radd<macro><value><value> Addition
+\def\Radd#1#2#3{\@callc\@Radd#1{#2}{#3}}
+
+%% \Rsub<macro><value><value> Subtraction
+\def\Rsub#1#2#3{\@callc\@Radd#1{#2}{-#3}}
+
+\def\@Radd#1#2.#3.#4\relax#5.#6.#7\relax{%
+ % #1 Macro, witch gets the result
+ % #2 integer part of 1st value
+ % #3 fractional part of 1st value
+ % #4 dummy to swallow everthing after the 2nd '.'
+ % #5 integer part of 2nd value
+ % #6 fractional part of 2nd value
+ % #7 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#2}{#3}%
+ \@readvalue\@ys\@yi\@yf{#5}{#6}%
+ %
+ % Add integer parts
+ \@ta=\@xi \advance\@ta\@yi%
+ %
+ % Add fractional parts if they are not zero
+ \ifnum\@xf=\@zero%
+ \ifnum\@yf=\@zero%
+ \@tb=\@zero%
+ \else%
+ \@longadd%
+ \fi%
+ \else%
+ \@longadd%
+ \fi%
+ %
+ % Store result
+ \@store#1\@ta\@tb%
+}
+
+\def\@longadd{%
+ % Propagate sign to fractional parts
+ \multiply\@xf\@xs \multiply\@yf\@ys%
+ %
+ % Add fractional parts
+ \@tb=\@xf \advance\@tb\@yf%
+ %
+ % Calculate carry
+ \ifnum\@tb<\@zero%
+ \ifnum\@tb<-\@mil \advance\@ta -\@ne \advance\@tb\@mil \fi%
+ \else%
+ \ifnum\@tb<\@mil \else \advance\@ta \@ne \advance\@tb-\@mil \fi%
+ \fi%
+}
+
+%% \Rmul<macro><value><value> Multiplication
+\def\Rmul#1#2#3{\@callc\@Rmul#1{#2}{#3}}
+
+\def\@Rmul#1#2.#3.#4\relax#5.#6.#7\relax{%
+ % #1 Macro, witch gets the result
+ % #2 integer part of 1st value
+ % #3 fractional part of 1st value
+ % #4 dummy to swallow everthing after the 2nd '.'
+ % #5 integer part of 2nd value
+ % #6 fractional part of 2nd value
+ % #7 dummy to swallow everthing after the 2nd '.'
+ %
+ % How to do real multiplications:
+ % Split values in various parts
+ % x y = 1234 567890 . 123 456 789
+ % -> xa xb xc xd xe
+ % -> ya yb yc yd ye
+ % Do 21 (!) integer multiplications if there are any fractional parts
+ % r = x * Y
+ % -> r = xi*yi
+ % + (xa*yc + xa*yc )*10^3
+ % + (xa*yd + xd*ya )*10^-0
+ % + (xa*ye + xe*ya + xb*yc + xc*yb)*10^-3
+ % + (xb*yd + xd*yb + xc*yc )*10^-6
+ % + (xb*ye + xe*yb + xc*yd + xd*yc)*10^-9
+ % + (xc*ye + xe*yc + xd*yd )*10^-12
+ % + (xd*ye + xe*yd )*10^-15
+ % + (xe*ye )*10^-18
+ %
+ % -> r = ((((( xe*ye / 1000
+ % + xd*ye + xe*yd ) / 1000
+ % + xc*ye + xe*yc + xd*yd ) / 1000
+ % + xb*ye + xe*yb + xc*yd + xd*yc ) / 1000
+ % + xb*yd + xd*yb + xc*yc ) / 1000
+ % + xa*ye + ye*xa + xb*yc + xc*yb ) / 1000
+ % + xa*yd + xd*ya + (xa*yc + ya*xc)*1000 + xi*yi
+ % The last three digigs are saved just before the divisions.
+ %
+ % Init
+ %
+ \@readvalue\@xs\@xi\@xf{#2}{#3}%
+ \@readvalue\@ys\@yi\@yf{#5}{#6}%
+ %
+ % Sign
+ \multiply\@xi\@xs%
+ \multiply\@yi\@ys%
+ \multiply\@xs\@ys%
+ %
+ \@product=\@zero%
+ %
+ \ifnum\@xf=\@zero%
+ \ifnum\@yf=\@zero%
+ % No fractional parts
+ \edef\@frac{000000000} % digits of fractional part
+ \else%
+ \@longmul % Long multiplication
+ \fi%
+ \else%
+ \@longmul % Long multiplication
+ \fi%
+ %
+ % Multiply integer parts
+ \count@=\@xi \multiply\count@\@yi%
+ \advance\@product\count@%
+ %
+ % Sign
+ \multiply\@product\@xs%
+ %
+ % Store result
+ \edef#1{\number\@product.\@frac}%
+}
+
+% Do long multiplication
+\def\@longmul{%
+ % Split values in pieces
+ \@f=1000000%
+ \count@=\@xi%
+ \divide\count@\@f \@xa=\count@%
+ \multiply\count@-\@f \advance\count@\@xi \@xb=\count@%
+ \count@=\@xf%
+ \divide\count@\@f \@xc=\count@%
+ \multiply\count@-\@f \advance\count@\@xf%
+ \@f=1000%
+ \@xe=\count@%
+ \divide\count@\@f \@xd=\count@%
+ \multiply\count@-\@f \advance\count@\@xe \@xe=\count@%
+ %
+ \@f=1000000%
+ \count@=\@yi%
+ \divide\count@\@f \@ya=\count@%
+ \multiply\count@-\@f \advance\count@\@yi \@yb=\count@%
+ \count@=\@yf%
+ \divide\count@\@f \@yc=\count@%
+ \multiply\count@-\@f \advance\count@\@yf%
+ \@f=1000%
+ \@ye=\count@%
+ \divide\count@\@f \@yd=\count@%
+ \multiply\count@-\@f \advance\count@\@ye \@ye=\count@%
+ %
+ \edef\@frac{} % digits of fractional part
+ %
+ \@mul ee \relax\@shift % 10^-18
+ \@mul de ed \relax\@shift % 10^-15
+ \@mul ce ec dd \relax\@shift % 10^-12
+ \@mul be eb cd dc \relax\@saveshift % 10^-9
+ \@mul bd db cc \relax\@saveshift % 10^-6
+ \@mul ae ea bc cb \relax\@saveshift % 10^-3
+ \multiply\@xa\@f \multiply\@xc\@f % 10^3
+ \@mul ad da ac ca \relax%
+}
+
+\def\@mul#1#2#3{%
+ \count@=\csname @x#1\endcsname%
+ \multiply\count@\csname @y#2\endcsname%
+ \advance\@product\count@%
+ %
+ \ifx#3\relax%
+ \let\next=\relax%
+ \else%
+ \let\next=\@mul%
+ \fi%
+ \next#3%
+}
+
+\def\@shift{%
+ \divide\@product\@f%
+}
+
+\def\@saveshift{%
+ % Save rightmost digits
+ \count@=\@product%
+ \divide\@product\@f%
+ \multiply\@product\@f%
+ \advance\count@-\@product%
+ \advance\count@\@f%
+ \edef\@frac{\expandafter\@ignorenext\number\count@\@frac}%
+ %
+ \divide\@product\@f%
+}
+
+%% \Rdiv<macro><value><value> Division
+\def\Rdiv#1#2#3{\@callc\@Radd#1{#2}{#3}}
+
+\def\@Rdiv#1#2.#3.#4\relax#5.#6.#7\relax{%
+ % #1 Macro, witch gets the result
+ % #2 integer part of 1st value
+ % #3 fractional part of 1st value
+ % #4 dummy to swallow everthing after the 2nd '.'
+ % #5 integer part of 2nd value
+ % #6 fractional part of 2nd value
+ % #7 dummy to swallow everthing after the 2nd '.'
+ %
+ \message{Error: Rdiv not ready}
+ %
+ \@readvalue\@xs\@xi\@xf{#2}{#3}%
+ \@readvalue\@ys\@yi\@yf{#5}{#6}%
+ %
+ \ifnum\@yi=\@zero
+ \@xi=\@zero
+ \else
+ \divide\@xi\@yi
+ \fi
+ %
+ \@store#1\@xi\@xf%
+}
+
+%% \Rneg<macro><value> Negation
+\def\Rneg#1#2{%
+ % Expand the value and split it into the integer and the fractional part
+ \edef\next{\noexpand\@Rneg\noexpand#1#2..\noexpand\relax}%
+ \next%
+}
+
+\def\@Rneg#1#2.#3.#4\relax{
+ % #1 Macro, witch gets the result
+ % #2 Integer part of value
+ % #3 Fractional part of value
+ % #4 Remaining tokens
+ %
+ \@readvalue\@xs\@xi\@xf{#2}{#3}%
+ %
+ % Change sign
+ \multiply\@xi-\@ne%
+ \multiply\@xf-\@xs%
+ %
+ % Store result
+ \@store#1\@xi\@xf%
+}
+
+%%
+%% \Rtrunc<macro><precision><value> Truncate value to specified precision
+\def\Rtrunc#1#2#3{%
+ % Expand parameter and split the value into the integer and fractional part
+ \edef\next{\noexpand\@Rtrunc\noexpand#1#2#3..\noexpand\relax}%
+ \next%
+}
+
+\def\@Rtrunc#1#2#3.#4.#5\relax{%
+ % #1 Macro, witch gets the result
+ % #2 Number of decimal places
+ % #3 Integer part of value
+ % #4 Fractional part of value
+ % #5 dummy to swallow everthing after the 2nd '.'
+ %
+ \count@=#2%
+ \edef\next{\empty}%
+ \ifnum\count@>\@zero%
+ \expandafter\@@Rtrunc#4000000000\relax%
+ \fi%
+ \edef#1{#3\next}%
+}
+
+\def\@@Rtrunc#1#2#3#4#5#6#7#8#9{%
+ % #1...#9 fractional part, padded with trailing zeros
+ \edef\next{.#1%
+ \ifnum\count@>1 #2\fi%
+ \ifnum\count@>2 #3\fi%
+ \ifnum\count@>3 #4\fi%
+ \ifnum\count@>4 #5\fi%
+ \ifnum\count@>5 #6\fi%
+ \ifnum\count@>6 #7\fi%
+ \ifnum\count@>7 #8\fi%
+ \ifnum\count@>8 #9\fi%
+ }%
+ \@swallow%
+}
+
+%%
+%% \Rifle<value><value> Test v1 < v2
+\def\Rifle#1#2{\@callb\@Rifle{#1}{#2}}
+
+\def\@Rifle#1.#2.#3\relax#4.#5.#6\relax{%
+ % #1 integer part of 1st value
+ % #2 fractional part of 1st value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ % #4 integer part of 2nd value
+ % #5 fractional part of 2nd value
+ % #6 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ \@readvalue\@ys\@yi\@yf{#4}{#5}%
+ %
+ \ifnum\@xs<\@ys%
+ \Rtesttrue%
+ \else%
+ \ifnum\@xs>\@ys%
+ \Rtestfalse%
+ \else%
+ \Rtestfalse%
+ \ifnum\@xi<\@yi \Rtesttrue \fi%
+ \ifnum\@xi=\@yi%
+ \multiply\@xf\@xs \multiply\@yf\@ys%
+ \ifnum\@xf<\@yf \Rtesttrue \fi%
+ \fi%
+ \fi%
+ \fi%
+ %
+ \ifRtest%
+}
+
+%% \Rifeq<value><value> Test v1 = v2
+\def\Rifeq#1#2{\@callb\@Rifeq{#1}{#2}}
+
+\def\@Rifeq#1.#2.#3\relax#4.#5.#6\relax{%
+ % #1 integer part of 1st value
+ % #2 fractional part of 1st value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ % #4 integer part of 2nd value
+ % #5 fractional part of 2nd value
+ % #6 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ \@readvalue\@ys\@yi\@yf{#4}{#5}%
+ %
+ \Rtestfalse%
+ \ifnum\@xi=\@yi\ifnum\@xf=\@yf \Rtesttrue \fi\fi%
+ \ifRtest%
+}
+
+%% \Rifgt<value><value> Test v1 > v2
+\def\Rifgt#1#2{\@callb\@Rifgt{#1}{#2}}
+
+\def\@Rifgt#1.#2.#3\relax#4.#5.#6\relax{%
+ % #1 integer part of 1st value
+ % #2 fractional part of 1st value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ % #4 integer part of 2nd value
+ % #5 fractional part of 2nd value
+ % #6 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ \@readvalue\@ys\@yi\@yf{#4}{#5}%
+ %
+ \ifnum\@xs>\@ys%
+ \Rtesttrue%
+ \else%
+ \ifnum\@xs<\@ys%
+ \Rtestfalse%
+ \else%
+ \Rtestfalse%
+ \ifnum\@xi>\@yi \Rtesttrue \fi%
+ \ifnum\@xi=\@yi%
+ \multiply\@xf\@xs \multiply\@yf\@ys%
+ \ifnum\@xf>\@yf \Rtesttrue \fi%
+ \fi%
+ \fi%
+ \fi%
+ %
+ \ifRtest%
+}
+
+%% \Rifneg<value> Test v < 0
+\def\Rifneg#1{\@calla\@Rifneg{#1}}
+
+\def\@Rifneg#1.#2.#3\relax{%
+ % #1 Integer part of value
+ % #2 Fractional part of value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ %
+ \ifnum\@xs<0 \Rtesttrue \else \Rtestfalse \fi%
+ \ifRtest%
+ }
+
+%% \Rifzero<value> Test v = 0
+\def\Rifzero#1{\@calla\@Rifzero{#1}}
+
+\def\@Rifzero#1.#2.#3\relax{%
+ % #1 Integer part of value
+ % #2 Fractional part of value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ %
+ \Rtestfalse%
+ \ifnum\@xi=\@zero \ifnum\@xf=\@zero \Rtesttrue \fi \fi%
+ \ifRtest%
+}
+
+%% \Rifpos<value> Test v >= 0
+%% Take care to have a corresponding \fi
+\def\Rifpos#1{\@calla\@Rifpos{#1}}
+
+\def\@Rifpos#1.#2.#3\relax{%
+ % #1 Integer part of value
+ % #2 Fractional part of value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ %
+ \ifnum\@xs<0 \Rtestfalse \else \Rtesttrue \fi%
+ \ifRtest%
+}
+
+%% \Rifint<value> Test v is an integer value
+%% Take care to have a corresponding \fi
+\def\Rifint#1{\@calla\@Rifint{#1}}
+
+\def\@Rifint#1.#2.#3\relax{%
+ % #1 Integer part of value
+ % #2 Fractional part of value
+ % #3 dummy to swallow everthing after the 2nd '.'
+ %
+ \@readvalue\@xs\@xi\@xf{#1}{#2}%
+ %
+ \ifnum\@xf=0 \Rtesttrue \else \Rtestfalse \fi%
+ \ifRtest%
+}
+
+% Utility macros
+
+\def\@calla#1#2{%
+ % #1 Macro to call
+ % #2 Value
+ % Expand the value and split them into the integer and the fractional part
+ \edef\next{\noexpand#1#2..\noexpand\relax}%
+ \next%
+}
+
+\def\@callb#1#2#3{%
+ % #1 Macro to call
+ % #2 1st value
+ % #3 2nd value
+ % Expand the values and split them into the integer and the fractional parts
+ \edef\next{\noexpand#1#2..\noexpand\relax#3..\noexpand\relax}%
+ \next%
+}
+
+\def\@callc#1#2#3#4{%
+ % #1 Macro to call
+ % #2 Macro, witch gets the result
+ % #3 1st value
+ % #4 2nd value
+ % Expand the values and split them into the integer and the fractional parts
+ \edef\next{\noexpand#1\noexpand#2#3..\noexpand\relax#4..\noexpand\relax}%
+ \next%
+}
+
+%% \ifRtest ... \else ... \fi Re-execute the last test
+\newif\ifRtest
+
+%
+% Read value
+%
+\def\@readvalue#1#2#3#4#5{%
+ % #1 macro to catch the sign ( -1 or 1 )
+ % #2 macro to catch the integer part (maybe negative)
+ % #3 macro to catch the fractional part (positive)
+ % #4.#5 value
+ %
+ % Regular expression [-...d]d...["."[d...]]
+ % Attention: There has to be at least one digit between "-" and "."!
+ %
+ % Integer part
+ \if !#4! #2=\@zero \else #2=#4 \fi%
+ %
+ % Sign
+ \ifnum#2<\@zero #1=-\@ne \else #1=\@ne \fi%
+ \ifnum#2=\@zero \ifnum #4#5<\@zero #1=-\@ne \fi \fi%
+ %
+ % Fractional part
+ \if !#5!%
+ #3=\@zero%
+ \else%
+ \@@setcount@#5000000000\relax%
+ #3=\count@%
+ \fi%
+}
+
+% Set count@ to fractional part with trailing zeros
+\def\@@setcount@#1#2#3#4#5#6#7#8#9{%
+ % #1...#9 fractional part, padded with '0'
+ \count@=#1#2#3#4#5#6#7#8#9%
+ \@swallow%
+}
+
+% Swallow everything up to next \relax
+\def\@swallow#1\relax{}
+
+%
+% Store result
+%
+\def\@store#1#2#3{%
+ % #1 marcro to catch the result
+ % #2 counter with integer part (maybe negative)
+ % #3 counter with fractional part (maybe negative}
+ %
+ % Sign
+ \edef#1{}%
+ \count@=#3%
+ \ifnum\count@<\@zero%
+ \count@=-\count@%
+ \ifnum#2=\@zero%
+ \edef#1{-}%
+ \fi%
+ \fi%
+ %
+ % Pad fractional part with leading zeros
+ \advance\count@\@mil%
+ %
+ % Store result
+ \edef#1{#1\number#2.\expandafter\@ignorenext\number\count@}%
+}
+
+% Ignore next token
+\def\@ignorenext#1{}
+
+% Restore catcode of "@"
+\catcode`\@=\catamp
diff --git a/macros/generic/realcalc/realdemo.tex b/macros/generic/realcalc/realdemo.tex
new file mode 100644
index 0000000000..fb4022cca1
--- /dev/null
+++ b/macros/generic/realcalc/realdemo.tex
@@ -0,0 +1,6 @@
+\documentstyle[]{article}
+\input{realcalc}
+\begin{document}
+\input{realtest}
+\test
+\end{document}
diff --git a/macros/generic/realcalc/realtest.tex b/macros/generic/realcalc/realtest.tex
new file mode 100644
index 0000000000..7b3a95ef45
--- /dev/null
+++ b/macros/generic/realcalc/realtest.tex
@@ -0,0 +1,291 @@
+% realcalc.tex
+%
+% (C) Frank Buchholz, Jan. 1993
+% e-mail: buchholz@lusty.informatik.uni-dortmund.de
+%%
+%% Type \test\bye
+%%
+
+\input realcalc
+
+% Test
+
+\catcode`@=11
+
+\def\traceon{%
+ \tracingonline \@ne
+ \tracincommands \tw@
+ \tracingstats \tw@
+ \tracingpages \@ne
+ \tracingoutput \@ne
+ \tracinglostchars \@ne
+ \tracingmacros \tw@
+ \tracingparagraphs \@ne
+ \tracingrestores \@ne
+ \showboxbreadth \maxdimen
+ \showboxdepth \maxdimen
+}
+
+\def\traceoff{%
+ \tracingonline \@zero
+ \tracingcommands \@zero
+ \tracingstats \@zero
+ \tracingpages \@zero
+ \tracingoutput \@zero
+ \tracinglostchars \@zero
+ \tracingmacros \@zero
+ \tracingparagraphs \@zero
+ \tracingrestores \@zero
+ \showboxbreadth \maxdimen
+ \showboxdepth \maxdimen
+}
+
+\errorstopmode
+
+\let\sl=\showlists
+\let\st=\showthe
+\let\s=\show
+\def\e{\par \vfill \supereject}
+
+\def\test{%
+ \message{Test REALCALC.TEX \@Rversion:}
+ Test REALCALC.TEX \@Rversion\par\medskip
+ \testadd\medskip
+ \testsub\medskip
+ \testmul\medskip
+ \testdiv\medskip
+ \testneg\medskip
+ \testtrunc\medskip
+ \testifle\medskip
+ \testifeq\medskip
+ \testifgt\medskip
+ \testifneg\medskip
+ \testifzero\medskip
+ \testifpos\medskip
+ \testifint\medskip
+}
+
+\def\testadd{%
+ \message{Radd}
+ Test: Radd\par
+ \def\a{1234.5678}
+ \def\b{4321.8765}
+ \Radd\r{123456789.987654321}{4321.123456789}
+ \r={123461111.111111110}\par
+ \Radd\r\a\b \r={5556.4443}\par
+ \Radd\r{-\a}\b \r={3087.3087}\par
+ \Radd\r\a{-\b} \r={-3087.3087}\par
+ \Radd\r{-\a}{-\b} \r={-5556.4443}\par
+}
+
+\def\testsub{%
+ \message{Rsub}
+ Test: Rsub\par
+ \def\a{1234.5678}
+ \def\b{4321.8765}
+ \Rsub\r\a{-\b} \r={5556.4443}\par
+ \Rsub\r{-\a}{-\b} \r={3087.3087}\par
+ \Rsub\r\a\b \r={-3087.3087}\par
+ \Rsub\r{-\a}\b \r={-5556.4443}\par
+}
+
+\def\testmul{%
+ \message{Rmul}
+ Test: Rmul\par
+ \def\a{1234}
+ \def\b{4321}
+ \Rmul\r{\a}{\b} \Rtrunc\r0\r \r={5332114}\par
+ \Rmul\r{-\a}{\b} \Rtrunc\r0\r \r={-5332114}\par
+ \Rmul\r{\a}{-\b} \Rtrunc\r0\r \r={-5332114}\par
+ \Rmul\r{-\a}{-\b} \Rtrunc\r0\r \r={5332114}\par
+ \Rmul\r\a0 \Rtrunc\r0\r \r={0}\par
+ \Rmul\r0\a \Rtrunc\r0\r \r={0}\par
+ \Rmul\r00 \Rtrunc\r0\r \r={0}\par
+ \Rmul\r\a1 \Rtrunc\r0\r \r={\a}\par
+ \Rmul\r1\a \Rtrunc\r0\r \r={\a}\par
+ \Rmul\r11 \Rtrunc\r0\r \r={1}\par
+ \Rmul\r\a{-1} \Rtrunc\r0\r \r={-\a}\par
+ \Rmul\r{-1}\a \Rtrunc\r0\r \r={-\a}\par
+ \Rmul\r{-1}{-1} \Rtrunc\r0\r \r={1}\par
+
+ \Rmul\r{46340.123456789}{10.123456789}\r={469122.2374}\par
+ \Rmul\r{46340.123456789}{1}\r={46340.123456789}\par
+ \Rmul\r{46340.123456789}{100}\r={4634012.3456789}\par
+ \Rmul\r{0.5}{0.5} \r={0.25}\par
+ \Rmul\r\r\r \r={0.0625}\par
+ \Rmul\r\r\r \r={0.00390625}\par
+ \Rmul\r\r\r \r={0.000015258}\par
+ \Rmul\r\r\r \r={0}\par
+ \Rmul\r{1.6}{1.6} \r={2.56}\par
+ \Rmul\r\r\r \r={6.5536}\par
+ \Rmul\r\r\r \r={42.94967296}\par
+ \Rmul\r\r\r \r={1844.674407}\par
+ \Rmul\r\r\r \r={3402823.669}\par
+}
+
+\def\testdiv{%
+ \message{Rdiv}
+ Test: Rdiv\par
+ not ready\par
+}
+
+\def\testneg{%
+ \message{Rneg}
+ Test: Rneg\par
+ -\ 0 = \Rneg\r{0}\r\par
+ -\ -1 = \Rneg\r{-1}\r\par
+ -\ 1 = \Rneg\r{1}\r\par
+ -\ 0.5 = \Rneg\r{0.5}\r\par
+ -\ -0.5 = \Rneg\r{-0.5}\r\par
+ -\ -1234.5678 = \Rneg\r{-1234.5678}\r\par
+ -\ 1234.5678 = \Rneg\r{1234.5678}\r\par
+}
+
+\def\testtrunc{%
+ \message{Rtrunc}
+ Test: Rtrunc\par
+ \def\a{12345.123456789012345}
+ 0:\ \Rtrunc\r0\a\r\ \Rtrunc\r00\r\par
+ 1:\ \Rtrunc\r1\a\r\ \Rtrunc\r10\r\par
+ 2:\ \Rtrunc\r2\a\r\ \Rtrunc\r20\r\par
+ 3:\ \Rtrunc\r3\a\r\ \Rtrunc\r30\r\par
+ 4:\ \Rtrunc\r4\a\r\ \Rtrunc\r40\r\par
+ 5:\ \Rtrunc\r5\a\r\ \Rtrunc\r50\r\par
+ 6:\ \Rtrunc\r6\a\r\ \Rtrunc\r60\r\par
+ 7:\ \Rtrunc\r7\a\r\ \Rtrunc\r70\r\par
+ 8:\ \Rtrunc\r8\a\r\ \Rtrunc\r80\r\par
+ 9:\ \Rtrunc\r9\a\r\ \Rtrunc\r90\r\par
+}
+
+\def\testifle{%
+ \message{Rifle}
+ Test: Rifle\par
+ 0 $<$ 0 \Rifle{0}{0} fehler\else ok\fi\par
+ 0 $<$ 1 \Rifle{0}{1} ok\else fehler\fi\par
+ 1 $<$ 0 \Rifle{1}{0} fehler\else ok\fi\par
+ 1 $<$ 1 \Rifle{1}{1} fehler\else ok\fi\par
+ 1 $<$ 2 \Rifle{1}{2} ok\else fehler\fi\par
+ 2 $<$ 1 \Rifle{2}{1} fehler\else ok\fi\par
+ 0 $<$ -1 \Rifle{0}{-1} fehler\else ok\fi\par
+ -1 $<$ 0 \Rifle{-1}{0} ok\else fehler\fi\par
+ -1 $<$ -1 \Rifle{-1}{-1} fehler\else ok\fi\par
+ -1 $<$ -2 \Rifle{-1}{-2} fehler\else ok\fi\par
+ -2 $<$ -1 \Rifle{-2}{-1} ok\else fehler\fi\par
+
+ 1 $<$ 1.2 \Rifle{1}{1.2} ok\else fehler\fi\par
+ 1.2 $<$ 1 \Rifle{1.2}{1} fehler\else ok\fi\par
+ -1 $<$ -1.2 \Rifle{-1}{-1.2} fehler\else ok\fi\par
+ -1.2 $<$ -1 \Rifle{-1.2}{-1} ok\else fehler\fi\par
+
+ 0.1 $<$ 0.1 \Rifle{0.1}{0.1} fehler\else ok\fi\par
+ 0.1 $<$ 0.2 \Rifle{0.1}{0.2} ok\else fehler\fi\par
+ 0.2 $<$ 0.1 \Rifle{0.2}{0.1} fehler\else ok\fi\par
+ -0.1 $<$ -0.2 \Rifle{-0.1}{-0.2} fehler\else ok\fi\par
+ -0.1 $<$ -0.1 \Rifle{-0.1}{-0.1} fehler\else ok\fi\par
+ -0.2 $<$ -0.1 \Rifle{-0.2}{-0.1} ok\else fehler\fi\par
+}
+
+\def\testifeq{%
+ \message{Rifeq}
+ Test: Rifeq\par
+ 0 = 0 \Rifeq{0}{0} ok\else fehler\fi\par
+ 0 = 1 \Rifeq{0}{1} fehler\else ok\fi\par
+ 1 = 0 \Rifeq{1}{0} fehler\else ok\fi\par
+ 1 = 1 \Rifeq{1}{1} ok\else fehler\fi\par
+ 1 = 2 \Rifeq{1}{2} fehler\else ok\fi\par
+ 2 = 1 \Rifeq{2}{1} fehler\else ok\fi\par
+ 0 = -1 \Rifeq{0}{-1} fehler\else ok\fi\par
+ -1 = 0 \Rifeq{-1}{0} fehler\else ok\fi\par
+ -1 = -1 \Rifeq{-1}{-1} ok\else fehler\fi\par
+ -1 = -2 \Rifeq{-1}{-2} fehler\else ok\fi\par
+ -2 = -1 \Rifeq{-2}{-1} fehler\else ok\fi\par
+
+ 1 = 1.2 \Rifeq{1}{1.2} fehler\else ok\fi\par
+ 1.2 = 1 \Rifeq{1.2}{1} fehler\else ok\fi\par
+ -1 = -1.2 \Rifeq{-1}{-1.2} fehler\else ok\fi\par
+ -1.2 = -1 \Rifeq{-1.2}{-1} fehler\else ok\fi\par
+
+ 0.1 = 0.1 \Rifeq{0.1}{0.1} ok\else fehler\fi\par
+ 0.1 = 0.2 \Rifeq{0.1}{0.2} fehler\else ok\fi\par
+ 0.2 = 0.1 \Rifeq{0.2}{0.1} fehler\else ok\fi\par
+ -0.1 = -0.2 \Rifeq{-0.1}{-0.2} fehler\else ok\fi\par
+ -0.1 = -0.1 \Rifeq{-0.1}{-0.1} ok\else fehler\fi\par
+ -0.2 = -0.1 \Rifeq{-0.2}{-0.1} fehler\else ok\fi\par
+}
+
+\def\testifgt{%
+ \message{Rifgt}
+ Test: Rifgt\par
+ 0 $>$ 0 \Rifgt{0}{0} fehler\else ok\fi\par
+ 0 $>$ 1 \Rifgt{0}{1} fehler\else ok\fi\par
+ 1 $>$ 0 \Rifgt{1}{0} ok\else fehler\fi\par
+ 1 $>$ 1 \Rifgt{1}{1} fehler\else ok\fi\par
+ 1 $>$ 2 \Rifgt{1}{2} fehler\else ok\fi\par
+ 2 $>$ 1 \Rifgt{2}{1} ok\else fehler\fi\par
+ 0 $>$ -1 \Rifgt{0}{-1} ok\else fehler\fi\par
+ -1 $>$ 0 \Rifgt{-1}{0} fehler\else ok\fi\par
+ -1 $>$ -1 \Rifgt{-1}{-1} fehler\else ok\fi\par
+ -1 $>$ -2 \Rifgt{-1}{-2} ok\else fehler\fi\par
+ -2 $>$ -1 \Rifgt{-2}{-1} fehler\else ok\fi\par
+
+ 1 $>$ 1.2 \Rifgt{1}{1.2} fehler\else ok\fi\par
+ 1.2 $>$ 1 \Rifgt{1.2}{1} ok\else fehler\fi\par
+ -1 $>$ -1.2 \Rifgt{-1}{-1.2} ok\else fehler\fi\par
+ -1.2 $>$ -1 \Rifgt{-1.2}{-1} fehler\else ok\fi\par
+
+ 0.1 $>$ 0.1 \Rifgt{0.1}{0.1} fehler\else ok\fi\par
+ 0.1 $>$ 0.2 \Rifgt{0.1}{0.2} fehler\else ok\fi\par
+ 0.2 $>$ 0.1 \Rifgt{0.2}{0.1} ok\else fehler\fi\par
+ -0.1 $>$ -0.2 \Rifgt{-0.1}{-0.2} ok\else fehler\fi\par
+ -0.1 $>$ -0.1 \Rifgt{-0.1}{-0.1} fehler\else ok\fi\par
+ -0.2 $>$ -0.1 \Rifgt{-0.2}{-0.1} fehler\else ok\fi\par
+}
+
+\def\testifneg{%
+ \message{Rifneg}
+ Test: Rifneg\par
+ 0: \Rifneg{0} fehler\else ok\fi\par
+ 0.5: \Rifneg{0.5} fehler\else ok\fi\par
+ .5: \Rifneg{.5} fehler\else ok\fi\par
+ 1: \Rifneg{1} fehler\else ok\fi\par
+ -0: \Rifneg{-0} fehler\else ok\fi\par
+ -0.5: \Rifneg{-0.5} ok\else fehler\fi\par
+ -1: \Rifneg{-1} ok\else fehler\fi\par
+}
+
+\def\testifzero{%
+ \message{Rifzero}
+ Test: Rifzero\par
+ 0: \Rifzero{0} ok\else fehler\fi\par
+ 0.5: \Rifzero{0.5} fehler\else ok\fi\par
+ .5: \Rifzero{.5} fehler\else ok\fi\par
+ 1: \Rifzero{1} fehler\else ok\fi\par
+ -0: \Rifzero{-0} ok\else fehler\fi\par
+ -0.5: \Rifzero{-0.5} fehler\else ok\fi\par
+ -1: \Rifzero{-1} fehler\else ok\fi\par
+}
+
+\def\testifpos{%
+ \message{Rifpos}
+ Test: Rifpos\par
+ 0: \Rifpos{0} ok\else fehler\fi\par
+ 0.5: \Rifpos{0.5} ok\else fehler\fi\par
+ .5: \Rifpos{.5} ok\else fehler\fi\par
+ 1: \Rifpos{1} ok\else fehler\fi\par
+ -0: \Rifpos{-0} ok\else fehler\fi\par
+ -0.5: \Rifpos{-0.5} fehler\else ok\fi\par
+ -1: \Rifpos{-1} fehler\else ok\fi\par
+}
+
+\def\testifint{%
+ \message{Rifint}
+ Test: Rifint\par
+ 0: \Rifint{0} ok\else fehler\fi\par
+ -0: \Rifint{-0} ok\else fehler\fi\par
+ 1: \Rifint{1} ok\else fehler\fi\par
+ -1: \Rifint{-1} ok\else fehler\fi\par
+ 0.5: \Rifint{0.5} fehler\else ok\fi\par
+ -0.5: \Rifint{-0.5} fehler\else ok\fi\par
+ 1.5: \Rifint{1.5} fehler\else ok\fi\par
+ -1.5: \Rifint{-1.5} fehler\else ok\fi\par
+}