Re^3: Mersenne Twister

May I ask why in particular you're interested in the Mersenne Twister? I mean, they do claim that the Mersenne Twister is the "most popular" pseudorandom number generator today, but... the C library, for example, (and any program such as Perl that uses the standard C library) uses the Lehmer random number generator. It's very simple:

SEED = ( SEED * A + B ) MOD C

...where A, B, and C are some fractions, although in the C library, the value of B is set to 1.

Look here https://blogs.mathworks.com/cleve/2015/04/17/random-number-generator-mersenne-twister/ This page has a well documented source code. And maybe here as well https://en.wikipedia.org/wiki/List_of_random_number_generators which shows a list of random number generators.

Comment on Re^3: Mersenne Twister

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Re^4: Mersenne Twister by swl (Prior) on Jan 05, 2024 at 23:42 UTC
The Mersenne Twister is a popular pseudo-random number generator (PRNG) because it has good distribution properties and a long period length (2^19937 - 1) before the sequence repeats. It passes all the diehard tests of randomness, and nearly all of the TestUO1 tests. (Wikipedia is a reasonable source of info for this: https://en.wikipedia.org/wiki/Mersenne_Twister). The algorithm you describe is a Linear Congruential Generator (LCG). These have global correlation structures that cause issues at the square root or cubed root of the period length. Perl's `rand()` uses the drand48 algorithm on all operating systems since 5.20 (https://metacpan.org/release/RJBS/perl-5.20.0/view/pod/perldelta.pod#rand-now-uses-a-consistent-random-number-generator). This has a longer period length (2^48) than the standard ANSI C rand (2^31) but is still an LCG and thus has issues with correlation structures. Some useful illustrations are at https://wellington.pm.org/archive/200704/randomness/index.html, for example slide7, slide8 and slide 14. Whether all the above matters depends on the application. If it is just selecting from a small pool of items a small number of times then the choice of PRNG is unlikely to be an issue. Applications with larger data sets require better quality PRNGs.	[reply] [d/l]
Re^5: Mersenne Twister by harangzsolt33 (Deacon) on Jan 06, 2024 at 00:44 UTC
"since 5.20" Hmm... Interesting. That's good to know... I have been using TinyPerl 5.8 mostly. When plotting random lines, I did notice that there is a visible difference or should I say "resemblance of a pattern" visible with what you mentioned, LCG, but when I plotted lines with Mersenne Twister, the lines appeared completely random.	[reply]