Re: Randomness tests

[jonathan <johnscpg@googlemail.com>]

On Jul 16, 8:41 pm, Gautier write-only <gautier_niou...@hotmail.com>
wrote:
> Does someone have some randomness checking sources in Ada ?
> I am evaluating a fast random generator (published long time ago in
> the Ada letters), alternative to GNAT's implementation.
> Probably the most obvious test is to check that it is well uniformly
> distributed.
> _________________________________________________________
> Gautier's Ada programming --http://sf.net/users/gdemont/
> NB: For a direct answer, e-mail address on the Web site!

You can find several basic tests at

http://web.am.qub.ac.uk/users/j.parker/miscellany

 in the subdirectory: disorderly

see for example:

  gcd_4bytes_1.adb
  gcd_6bytes_1.adb
  rank_tst_2.adb
  bday_tst_1.adb
  gorilla_tst_demo_2.adb


(To use gcd_6bytes_1.adb, concatenate 2 of the
24 bit words generated by Marsaglia's Universal
generator.)

The greatest-common-divisor test, gcd_6bytes_1.adb
and gorilla tests are from the Marsaglia,
Tsang updated diehard suite. To find their paper
google for

"Some difficult-to-pass tests of
randomness", Marsaglia, Tsang.

The birthday test is a variant of
Marsaglia's birthday test. I include
the birthday test (bday_tst_1.adb) because the
present GNAT generator fails this. (It has to.
All short period generators fail this test.)

I include Marsaglia's rank test (rank_tst_2.adb)
because it easily breaks the Mersenne Twister.
(It has to. The Mersenne Twister is full-period
and linear; they all fail this test catastrophically.)
I would still prefer the Mersenne Twister over
the Marsaglia Universal generator though .. it
does quite a bit more bit-mixing between outputs
than the Marsaglia Universal generator.

The site given above contains my own version of
the way I think Random Number Generators ought
to be done:  disorderly.ads. Generator Disorderly
is really just a non-linear 61-bit version
of Marsaglia's KISS generator. KISS appeared
about a decade after his Universal generator.
The KISS generator is a combination generator
that uses linear component generators.
Disorderly includes a non-linear
component generator: X_{n+1} = X_n**2 mod M.
The X_{n+1} = X_n**2 mod M component in Disorderly
was inspired by GNAT's generator. The GNAT
generator is a combination generator made from
2 of these non-linear component generators.
(If you use just the least significant bit of
each word output by the GNAT generator, then
its called the Blum-Blum-Schub generator.)

A fast linear version of Disorderly is included;
seemed to be about 3 times faster than the GNAT
generator .. produces 61 bits per call.

Here is the start of the README:

1. directory Disorderly contains

  a package of new Random Number Generators (package
  Disorderly.Random) along with some test/demo
  routines.

  a package of Random Deviates (package
  Disorderly.Random.Deviates) with the following distributions:

    Uniform, Normal (Gaussian), Exponential, Lorentzian (Cauchy),
    Poissonian, Binomial, Negative Binomial, Weibull, Rayleigh,
    Student_t, Beta, Gamma, Chi_Squared, Log_Normal,
    Multivariate_Normal.

   procedure Deviates_Demo_1 tests
     and demonstrates usage of random deviates (variates).
     The procedure tests package Disorderly.Random.Deviates.

   procedure Basic_Deviates_Demo_1 tests
     and demonstrates usage of random deviates:
     Disorderly.Basic_Rand.Deviates.
     Uses Disorderly.Basic_Rand.
     and demonstrates usage of random deviates (variates).

Jonathan