mt19937 large integers, was: Re: RANDOM() and RANDOM(FALSE) problem

Hi Ray,

I am looking at CMUCL rand-mt19937.lisp and I see that large
integers are generated by overlapping 3 bits of several 
random chunks (32 bits). In addition 10 extra bits are generated
and thrown away. This approach was present in the previous 
CMUCL rng, rand.lisp.

I don't think this is necessary for MT19937. A page 
(http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/efaq.html)
at Matsumoto's web site says to concatenate 32-bit words
to get 64 bits. The source code at his web site
(http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c)
constructs double floats by concatenating 26 and 27 bits without
overlap to get 53.

Maybe we would wish to drop the overlap & extra bits --
(1) A simpler method makes the rng more comprehensible and more
comparable to other implementations. (2) The overlap & extra
bits method suggests some knowledge about the properties of MT19937
which aren't otherwise in evidence.

I have reviewed the Matsumoto & Nishimura paper 
(http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/earticles.html)
and I wish that I could divine the properties of concatenated
integers from it, but I can't. Maybe someone else can weigh in.

For what it's worth,
Robert Dodier


		
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