% \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