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diff --git a/macros/generic/random/random-doc.tex b/macros/generic/random/random-doc.tex new file mode 100644 index 0000000000..59520b62b9 --- /dev/null +++ b/macros/generic/random/random-doc.tex @@ -0,0 +1,74 @@ +% plain TeX + +\def\cmd#1{\leavevmode\hbox{\tt\string#1}} +\edef\{{\string{} +\edef\}{\string}} + +\noindent{\bf RANDOM.TEX }\qquad\qquad ver 0.2 \qquad\qquad (Donald Arseneau) + +\bigskip + +\noindent Generating ``random'' numbers in \TeX. + +\medskip + + {\tt \string\setrannum \thinspace\{$\langle \it counter\rangle$\}\thinspace\{$\langle\it minimum\rangle$\}\thinspace\{$\langle\it maximum\rangle$\}} + + {\tt \string\setrandimen \thinspace\{$\langle \hbox{\it dimen-register}\rangle$\}\thinspace\{$\langle\it minimum\rangle$\}\thinspace\{$\langle\it maximum\rangle$\}} + +\medskip +\noindent This software is released to the public domain. +\bigskip +\noindent Random integers are generated in the range 1 to 2147483646 by the +macro \cmd\nextrandom. The result is returned in the counter \cmd\randomi. +Do not change \cmd\randomi\ except, perhaps, to initialize it at some +random (or specific) value. If you do not initialize it, it will be initialized +using the time and date. (This is a sparse initialization, giving +fewer than a million different starting values, but you should use +other sources of numbers if they are available---just remember that +most of the numbers available to \TeX\ are not at all random.) + +The \cmd\nextrandom\ command is not very useful by itself, unless you +have exactly 2147483646 things to choose from. Much more useful +is the \cmd\setrannum\ command which sets a given counter to a random +value within a specified range. There are three parameters: +\medskip +{\tt \string\setrannum \thinspace\{$\langle \it counter\rangle$\}\thinspace\{$\langle\it minimum\rangle$\}\thinspace\{$\langle\it maximum\rangle$\}} +\medskip +\noindent For example, to simulate a die-roll: +\medskip +{\tt \string\setrannum\{\string\die\}\{1\}\{6\} \string\ifcase\string\die...} +\medskip + +If you need random numbers that are not integers, you will have to +use dimen registers instead with \cmd\setrandimen. For example, to set a random +page width between 3 and 6.5 inches: +\medskip +\cmd\setrandimen \cmd\hsize{\tt\{3in\}\{6.5in\}} +\medskip\noindent +The ``\cmd\pointless'' macro +will remove the ``{\tt pt}'' that \TeX\ gives so you can use the dimensions +as pure ``real'' numbers. In that case, specify the range in {\tt pt} units. +For example, +\medskip + {\tt\string\setrandimen\string\answer\{2.71828pt\}\{3.14159pt\}} + \hfill\break\indent + {\tt The answer is \string\pointless\string\answer.} +\medskip + +The random number generator is the one by Lewis, Goodman, and Miller +(1969) and used as ``ran0'' in ``Numerical Recipies'' using Schrage's +method for avoiding overflows. The multiplier is 16807 ($7^5$), the +added constant is 0, and the modulus is 2147483647 ($2^{31}-1$). + +See CACM, Vol.~36, no. 7, (July 1993), p.~109. The original authors +Park and Miller have since concluded that a better multiplier is 48271, +rather than their original 16807. + +The range of integers generated is $1 - 2147483646$. A smaller range would +reduce the complexity of the macros a bit, but not much---most of the +code deals with initialization and type-conversion. On the other hand, +the large range may be wasted due to the sparse seed initialization. + + +\bye |