summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/source/latex/l3kernel/l3fp-random.dtx
blob: 565c61dbcc84297ea47012890b1f07bee9bdc5ce (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
% \iffalse meta-comment
%
%% File: l3fp-random.dtx Copyright (C) 2016-2018 The LaTeX3 Project
%
% It may be distributed and/or modified under the conditions of the
% LaTeX Project Public License (LPPL), either version 1.3c of this
% license or (at your option) any later version.  The latest version
% of this license is in the file
%
%    https://www.latex-project.org/lppl.txt
%
% This file is part of the "l3kernel bundle" (The Work in LPPL)
% and all files in that bundle must be distributed together.
%
% -----------------------------------------------------------------------
%
% The development version of the bundle can be found at
%
%    https://github.com/latex3/latex3
%
% for those people who are interested.
%
%<*driver>
\documentclass[full,kernel]{l3doc}
\begin{document}
  \DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
% \title{The \textsf{l3fp-random} package\\
%   Floating point random numbers}
% \author{^^A
%  The \LaTeX3 Project\thanks
%    {^^A
%      E-mail:
%        \href{mailto:latex-team@latex-project.org}
%          {latex-team@latex-project.org}^^A
%    }^^A
% }
% \date{Released 2018/03/05}
%
% \maketitle
%
% \begin{documentation}
%
% \end{documentation}
%
% \begin{implementation}
%
% \section{\pkg{l3fp-random} Implementation}
%
%    \begin{macrocode}
%<*initex|package>
%    \end{macrocode}
%
%    \begin{macrocode}
%<@@=fp>
%    \end{macrocode}
%
% \begin{macro}[EXP]{\@@_parse_word_rand:N , \@@_parse_word_randint:N}
%   Those functions may receive a variable number of arguments.  We
%   won't use the argument~|?|.
%    \begin{macrocode}
\cs_new:Npn \@@_parse_word_rand:N
  { \@@_parse_function:NNN \@@_rand_o:Nw ? }
\cs_new:Npn \@@_parse_word_randint:N
  { \@@_parse_function:NNN \@@_randint_o:Nw ? }
%    \end{macrocode}
% \end{macro}
%
% \subsection{Engine support}
%
% At present, \XeTeX{}, \pTeX{} and \upTeX{} do not provide random
% numbers, while \LuaTeX{} and \pdfTeX{} provide the primitive
% \cs{pdftex_uniformdeviate:D} (\tn{pdfuniformdeviate} in \pdfTeX{} and
% \tn{uniformdeviate} in \LuaTeX{}).  We write the test twice simply in
% order to write the \texttt{false} branch first.
%    \begin{macrocode}
\cs_if_exist:NF \pdftex_uniformdeviate:D
  {
    \__kernel_msg_new:nnn { kernel } { fp-no-random }
      { Random~numbers~unavailable }
    \cs_new:Npn \@@_rand_o:Nw ? #1 @
      {
        \__kernel_msg_expandable_error:nn { kernel } { fp-no-random }
        \exp_after:wN \c_nan_fp
      }
    \cs_new_eq:NN \@@_randint_o:Nw \@@_rand_o:Nw
  }
\cs_if_exist:NT \pdftex_uniformdeviate:D
  {
%    \end{macrocode}
%
% \begin{macro}[EXP]{\@@_rand_uniform:}
% \begin{variable}
%   {
%     \c_@@_rand_size_int,
%     \c_@@_rand_four_int,
%     \c_@@_rand_eight_int,
%   }
%   The \cs{pdftex_uniformdeviate:D} primitive gives a pseudo-random
%   integer in a range $[0,n-1]$ of the user's choice.  This number is
%   meant to be uniformly distributed, but is produced by rescaling a
%   uniform pseudo-random integer in $[0,2^{28}-1]$.  For instance,
%   setting~$n$ to (any multiple of) $2^{29}$ gives only even values.
%   Thus it is only safe to call \cs{pdftex_uniformdeviate:D} with
%   argument $2^{28}$.  This integer is also used in the implementation
%   of \cs{int_rand:nn}.  We also use variants of this number
%   rounded down to multiples of $10^4$ and $10^8$.
%    \begin{macrocode}
\cs_new:Npn \@@_rand_uniform:
  { \pdftex_uniformdeviate:D \c_@@_rand_size_int }
\int_const:Nn \c_@@_rand_size_int   { 268 435 456 }
\int_const:Nn \c_@@_rand_four_int   { 268 430 000 }
\int_const:Nn \c_@@_rand_eight_int  { 200 000 000 }
%    \end{macrocode}
% \end{variable}
% \end{macro}
%
% \begin{macro}[EXP]{\@@_rand_myriads:n}
% \begin{macro}[EXP]
%   {
%     \@@_rand_myriads_loop:nn,
%     \@@_rand_myriads_get:w,
%     \@@_rand_myriads_last:,
%     \@@_rand_myriads_last:w,
%   }
%   Used as \cs{@@_rand_myriads:n} |{XXX}| with one input character per
%   block of four digit we want.  Given a pseudo-random integer from the
%   primitive, we extract $2$ blocks of digits if possible, namely if
%   the integer is less than $2\times 10^8$.  If that's not possible,
%   we try to extract $1$~block, which succeeds in the range $[2\times
%   10^8, 26843\times 10^4)$.  For the $5456$ remaining possible values
%   we just throw away the random integer and get a new one.  Depending
%   on whether we got $2$, $1$, or~$0$ blocks, remove the same number of
%   characters from the input stream with \cs{use_i:nnn}, \cs{use_i:nn}
%   or nothing.
%    \begin{macrocode}
\cs_new:Npn \@@_rand_myriads:n #1
  {
    \@@_rand_myriads_loop:nn #1
      { ? \use_i_delimit_by_q_stop:nw \@@_rand_myriads_last: }
      { ? \use_none_delimit_by_q_stop:w } \q_stop
  }
\cs_new:Npn \@@_rand_myriads_loop:nn #1#2
  {
    \use_none:n #2
    \exp_after:wN \@@_rand_myriads_get:w
    \__int_value:w \@@_rand_uniform: ; {#1}{#2}
  }
\cs_new:Npn \@@_rand_myriads_get:w #1 ;
  {
    \if_int_compare:w #1 < \c_@@_rand_eight_int
      \exp_after:wN \use_none:n
      \__int_value:w \__int_eval:w
        \c_@@_rand_eight_int + #1 \__int_eval_end:
      \exp_after:wN \use_i:nnn
    \else:
      \if_int_compare:w #1 < \c_@@_rand_four_int
        \exp_after:wN \use_none:nnnnn
        \__int_value:w \__int_eval:w
          \c_@@_rand_four_int + #1 \__int_eval_end:
        \exp_after:wN \exp_after:wN \exp_after:wN \use_i:nn
      \fi:
    \fi:
    \@@_rand_myriads_loop:nn
  }
\cs_new:Npn \@@_rand_myriads_last:
  {
    \exp_after:wN \@@_rand_myriads_last:w
    \__int_value:w \@@_rand_uniform: ;
  }
\cs_new:Npn \@@_rand_myriads_last:w #1 ;
  {
    \if_int_compare:w #1 < \c_@@_rand_four_int
      \exp_after:wN \use_none:nnnnn
      \__int_value:w \__int_eval:w
        \c_@@_rand_four_int + #1 \__int_eval_end:
    \else:
      \exp_after:wN \@@_rand_myriads_last:
    \fi:
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Random floating point}
%
% \begin{macro}[EXP]{\@@_rand_o:Nw}
% \begin{macro}[EXP]{\@@_rand_o:, \@@_rand_o:w}
%   First we check that |random| was called without argument.  Then get
%   four blocks of four digits.
%    \begin{macrocode}
\cs_new:Npn \@@_rand_o:Nw ? #1 @
  {
    \tl_if_empty:nTF {#1}
      { \@@_rand_o: }
      {
        \__kernel_msg_expandable_error:nnnnn
          { kernel } { fp-num-args } { rand() } { 0 } { 0 }
        \exp_after:wN \c_nan_fp
      }
  }
\cs_new:Npn \@@_rand_o:
  { \@@_parse_o:n { . \@@_rand_myriads:n { xxxx } } }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Random integer}
%
% \begin{macro}[EXP]{\@@_randint_o:Nw}
% \begin{macro}[EXP]
%   {
%     \@@_randint_default:w,
%     \@@_randint_badarg:w,
%     \@@_randint_o:w,
%     \@@_randint_e:wnn,
%     \@@_randint_e:wwNnn,
%     \@@_randint_e:wwwNnn,
%     \@@_randint_narrow_e:nnnn,
%     \@@_randint_wide_e:nnnn,
%     \@@_randint_wide_e:wnnn,
%   }
%     Enforce that there is one argument (then add first argument~$1$)
%     or two arguments.  Enforce that they are integers in
%     $(-10^{16},10^{16})$ and ordered.  We distinguish narrow ranges
%     (less than $2^{28}$) from wider ones.
%
%     For narrow ranges, compute the number~$n$ of possible outputs as
%     an integer using \cs{fp_to_int:n}, and reduce a pseudo-random
%     $28$-bit integer~$r$ modulo~$n$.  On its own, this is not uniform
%     when $[0,2^{28}-1]$ does not divide evenly into intervals of
%     size~$n$.  The auxiliary \cs{@@_randint_e:wwwNnn} discards the
%     pseudo-random integer if it lies in an incomplete interval, and
%     repeats.
%
%     For wide ranges we use the same code except for the last eight
%     digits which use \cs{@@_rand_myriads:n}.  It is not safe to
%     combine the first digits with the last eight as a single string of
%     digits, as this may exceed $16$~digits and be rounded.  Instead,
%     we first add the first few digits (times $10^8$) to the lower
%     bound.  The result is compared to the upper bound and the process
%     repeats if needed.
%    \begin{macrocode}
\cs_new:Npn \@@_randint_o:Nw ?
  {
    \@@_parse_function_one_two:nnw
      { randint }
      { \@@_randint_default:w \@@_randint_o:w }
  }
\cs_new:Npn \@@_randint_default:w #1 { \exp_after:wN #1 \c_one_fp }
\cs_new:Npn \@@_randint_badarg:w \s_@@ \@@_chk:w #1#2#3;
  {
    \@@_int:wTF \s_@@ \@@_chk:w #1#2#3;
      {
        \if_meaning:w 1 #1
          \if_int_compare:w
            \use_i_delimit_by_q_stop:nw #3 \q_stop > \c_@@_prec_int
            1 \exp_stop_f:
          \fi:
        \fi:
      }
      { 1 \exp_stop_f: }
  }
\cs_new:Npn \@@_randint_o:w #1; #2; @
  {
    \if_case:w
        \@@_randint_badarg:w #1;
        \@@_randint_badarg:w #2;
        \fp_compare:nNnTF { #1; } > { #2; } { 1 } { 0 } \exp_stop_f:
      \exp_after:wN \exp_after:wN \exp_after:wN \@@_randint_e:wnn
        \@@_parse:n { #2; - #1; } { #1; } { #2; }
    \or:
      \@@_invalid_operation_tl_o:ff
        { randint } { \@@_array_to_clist:n { #1; #2; } }
      \exp:w
    \fi:
    \exp_after:wN \exp_end:
  }
\cs_new:Npn \@@_randint_e:wnn #1;
  {
    \exp_after:wN \@@_randint_e:wwNnn
    \__int_value:w \@@_rand_uniform: \exp_after:wN ;
    \exp:w \exp_end_continue_f:w
      \fp_compare:nNnTF { #1 ; } < \c_@@_rand_size_int
        { \fp_to_int:n { #1 ; + 1 } ; \@@_randint_narrow_e:nnnn }
        { \fp_to_int:n { floor(#1 ; * 1e-8 + 1) } ; \@@_randint_wide_e:nnnn }
  }
\cs_new:Npn \@@_randint_e:wwNnn #1 ; #2 ;
  {
    \exp_after:wN \@@_randint_e:wwwNnn
    \__int_value:w \int_mod:nn {#1} {#2} ; #1 ; #2 ;
  }
\cs_new:Npn \@@_randint_e:wwwNnn #1 ; #2 ; #3 ; #4
  {
    \int_compare:nNnTF { #2 - #1 + #3 } > \c_@@_rand_size_int
      {
        \exp_after:wN \@@_randint_e:wwNnn
          \__int_value:w \@@_rand_uniform: ; #3 ; #4
      }
      { #4 {#1} {#3} }
  }
\cs_new:Npn \@@_randint_narrow_e:nnnn #1#2#3#4
  { \@@_parse_o:n { #3 + #1 } \exp:w }
\cs_new:Npn \@@_randint_wide_e:nnnn #1#2#3#4
  {
    \exp_after:wN \exp_after:wN
    \exp_after:wN \@@_randint_wide_e:wnnn
      \@@_parse:n { #3 + #1e8 + \@@_rand_myriads:n { xx } }
      {#2} {#3} {#4}
  }
\cs_new:Npn \@@_randint_wide_e:wnnn #1 ; #2#3#4
  {
    \fp_compare:nNnTF { #1 ; } > {#4}
      {
        \exp_after:wN \@@_randint_e:wwNnn
          \__int_value:w \@@_rand_uniform: ; #2 ;
          \@@_randint_wide_e:nnnn {#3} {#4}
      }
      { \@@_exp_after_o:w #1 ; \exp:w }
  }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% End the initial conditional that ensures these commands are only
% defined in \pdfTeX{} and \LuaTeX{}.
%    \begin{macrocode}
  }
%    \end{macrocode}
%
%    \begin{macrocode}
%</initex|package>
%    \end{macrocode}
%
% \end{implementation}
%
% \PrintChanges
%
% \PrintIndex