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diff --git a/Master/texmf-dist/tex/latex/fp/fp-random.sty b/Master/texmf-dist/tex/latex/fp/fp-random.sty new file mode 100644 index 00000000000..72bf17f1f10 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-random.sty @@ -0,0 +1,120 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-random}[1995/02/23] + +% Version information +\def\FP@randomversion{1.0a} +\message{% + `Fixed Point Random,% + \space\space\space\space\space\space% + \space\space\space\space\space\space\space% + Version \FP@randomversion% + \space(C) Denis Girou (CNRS/IDRIS)% + \space\space\space% +} + +% Resolve dependencies +\RequirePackage{fp-basic} + +% Uniform random value + +\newcount\FPseed % Seed value + +\def\FPrandom#1{% + % #1 macro, which gets the result + % + % Uniform random number generator (numbers between 0 and 1) + % + % Algorithm reproduce from a very old Fortran program (unknown origin!) + % + % double precision function RANF() + % + % integer SEED + % common /COMSEED/SEED + % * + % integer A,M,Q,R + % parameter(A=16807,M=2147483647,Q=127773,R=2836) + % * + % integer LO,HI,TEST + % * + % HI = SEED/Q + % LO = SEED-HI*Q + % TEST = A*LO-R*HI + % if(TEST.gt.0) then + % SEED = TEST + % else + % SEED = TEST+M + % endif + % * + % RANF = DFLOAT(SEED)/DFLOAT(M) + % * + % end + % + % The macro used a seed value, defined by the counter \FPseed. + % If it's unknown at first call, we used an arbitrary value. + % + % We verify that we obtain the same results as in Fortran + % + % The algorithm seems fairly good. With the Fortran version, we obtain + % typically something like 49954 numbers between 0 and 0.5 and 50046 between + % 0.5 and 1 for 100000 random numbers, depending of the seed value used. + % + % To generate a "pseudo-random" seed, you can consider to use the \time + % macro, to intialize the random numbers generator according to the time. + % Something like: + % \FPseed=\the\time + % \multiply\FPseed\the\day + % \multiply\FPseed\the\month + % \multiply\FPseed\the\year + % + % Of course, it is very slow comparing to "standard" programming + % languages. On a RS 6000 370, it's take 51s to generate 100 numbers, + % loading time of the test program included (and 0.2s for the Fortran + % version ... for 100000 numbers!) + % But you must also notice that Hans van der Meer published in TUGboat + % Vol. 15, 1, March 1994, pages 57-58, an article on "Random bit generator + % in TeX". In fact, he doesn't give a complete solution to generate uniform + % random numbers, but at least give some interesting ideas, and also the + % code of a simple but powerful macro \SRtest{choice 1}{choice 2}, which + % allow to execute the instructions of "choice 1" or those of "choice 2" + % with a probability of 1/2 each. As his method is based on shifts of bits + % with almost no computations, it's very fast (around 1000 faster than to do + % the same thing that \SRtest with \FPrandom.) + % + {\FP@beginmessage{RANDOM}% + % + \ifnum\FPseed=0% + \FPseed=123456789% + \FP@debug{random: seed value undefined! We will used \the\FPseed.^^J% + Define it if you want to generate a different sequence of random% + numbers.}% + \else% + \FP@debug{random: seed value used: \the\FPseed}% + \fi% + % + \FP@xia=\FPseed% + \divide\FP@xia by 127773% + \FP@xib=\FP@xia% + \multiply\FP@xib by 127773% + \advance\FP@xib by -\FPseed% + \FP@xib=-\FP@xib% + \multiply\FP@xia by 2836% + \FPseed=\FP@xib% + \multiply\FPseed by 16807% + \advance\FPseed by -\FP@xia% + % + \ifnum\FPseed>0% + \else% + \advance\FPseed by 2147483647% + \fi% + \FPdiv\FP@tmpa{\the\FPseed}{2147483647}% + \global\let\FP@tmp\FP@tmpa% + \global\FPseed=\FPseed% + \FP@debug{random: random number: \FP@tmp\space% + (new seed value: \the\FPseed)}% + % + \FP@endmessage{}% + }% + \let#1\FP@tmp% +} + +\endinput |