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From: braner@batcomputer.UUCP
Newsgroups: sci.math,sci.physics,sci.crypt,sci.math.stat
Subject: Re: Do you use RANDOM NUMBERS?
Message-ID: <464@batcomputer.tn.cornell.edu>
Date: Fri, 20-Mar-87 16:14:25 EST
Article-I.D.: batcompu.464
Posted: Fri Mar 20 16:14:25 1987
Date-Received: Thu, 26-Mar-87 04:40:04 EST
References: <5712@reed.UUCP>
Reply-To: braner@batcomputer.UUCP (braner)
Organization: Theory Center, Cornell University, Ithaca NY
Lines: 28
Keywords: Random numbers, leprechauns
Xref: utgpu sci.math:761 sci.physics:950 sci.crypt:256 sci.math.stat:83
Summary: Autocorr's is what worries me. I use my own AL routine.

[]

In some simulations I do I need _MANY_ random numbers (say 1E8 numbers...),
and calculating them _IS_ a major portion of the program run time
(especially if I need nonuniform numbers, e.g. lognormal).  I worry mostly
about them being autocorrelated, a common flaw in simple-minded generators.

I currently use home-made assembly-language routines (for the 68000 chip).
My basic uniform generator yields a 32-bit random integer in about 36
microsec (_including_ the overhead of calling from a high-level language
and returning the value into a variable in that language).  Other AL
routines return floating-point results that are either uniform (60 usec),
approximately normal, exponential, or lognormal (about 100-200 usec for
these).  (All timings with an 8 Mhz CPU.)

My generator has limited resolution (32 bits), hence not very good in the
extreme tails.  And the transcendental functions are implemented using
look-up tables, for speed rather than accuracy.  But the basic generator
passed all the uniformity and autocorrelation tests I could devise.

I recommend using integer rather than FP randoms in simulations whenever
possible, for speed.  E.g., to simulate an event that happens with prob p
(a constant), calculate "intp = (integer) (K*p)" _outside_ the loop, and
use "if random() < intp then do it" inside the loop.  (K is 2^32, or whatever
fits your _integer_ random() generator.)  (Those of you for whom all this
is boring, obvious, old-hat stuff, please forgive me...)

- Moshe Braner