TIP #310: Add a New Pseudo-Random Number Generator

Abstract

This TIP proposes to add a new expr function: a random number generator with a longer sequence than the one currently in the core.

Rationale

The expr command has used a straightforward implementation of a pseudo-random number generator via the rand() function for many years. This has a number of desirable properties, but better ones (e.g. with a longer sequence) have been known for a long time. This TIP proposes a new function as an alternative PRNG.

PRNGs with different properties can be important for Monte Carlo simulations and other algorithms that require large amounts of random numbers without having to worry about the sequence length.

Proposal

Introduce a new function, randM(), as an alternative PRNG to the expr command. This function is based on work by George Marsaglia and implementations in many different languages are available on the Internet. There will be a corresponding seed function srandM(x).

The new function is not a replacement of the original rand() function.

Implementation

With the new tcl::mathfunc mechanism (TIP #232) it should be simple to add this function to the core.

An example implementation in Tcl is given below:

 # marsaglia.tcl --
 #     Implementation of a PRNG according to George Marsaglia
 #
 namespace eval ::PRNG {
     variable mod [expr {wide(256)*wide(256)*wide(256)*wide(256)-5}]
     variable fac [expr {wide(256)*wide(32)}]
     variable x1 [expr {wide($mod*rand())}]
     variable x2 [expr {wide($mod*rand())}]
     variable x3 [expr {wide($mod*rand())}]

     puts $mod
 }

 proc ::PRNG::marsaglia {} {
     variable mod
     variable fac
     variable x1
     variable x2
     variable x3

     set xn [expr {($fac*($x3+$x2+$x1))%$mod}]

     set x1 $x2
     set x2 $x3
     set x3 $xn

     return [expr {$xn/double($mod)}]
 }

Copyright

This document is placed in the public domain

[Index] [History] [HTML Format] [Source Format] [LaTeX Format] [Text Format] [XML Format] [*roff Format (experimental)] [RTF Format (experimental)]