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From: johnk@megaron.UUCP
Newsgroups: sci.math
Subject: Algorithm Description
Message-ID: <1266@megaron.UUCP>
Date: Thu, 30-Oct-86 11:28:56 EST
Article-I.D.: megaron.1266
Posted: Thu Oct 30 11:28:56 1986
Date-Received: Fri, 31-Oct-86 20:00:38 EST
References: <146@helm.UUCP> <9700056@uiucdcsb>
Organization: Dept of CS, U of Arizona, Tucson
Lines: 32


	I'm always amazed at the manner in which mathematicians describe
algorithms.  In a recent discussion on the generation of variates from a
normal distribution, one of the most interesting presentations of the
Box-Muller-Marsaglia algorithm was the following:
 
 	V1 = 2*RND - 1 <--------+
 	V2 = 2*RND - 1          |
 	S = V1*V1 + V2*V2       |
 	IF S >= 1 THEN GOTO ----+
 	X1 = V1 * SQRT (-2 * LOG(S) / S)
 	X2 = V2 * SQRT (-2 * LOG(S) / S)
 
While this is a clever improvement on the ghastly "step 1", "step 2", "go to
step i" style, why not simply

	repeat {
		v1 = 2*rand() - 1
		v2 = 2*rand() - 1
		s = v1^2 + v2^2
	} until ( s < 1 )
	x1 = v1 * sqrt(-2 * ln(s) / s)
	x2 = v2 * sqrt(-2 * ln(s) / s)

Admittedly, this algorithm is trivial; here the manner of presentation
makes little difference.  I think the computer scientist most
mathematicians know of is Knuth, and by presenting the algorithms of his
_The_Art_of_Computer_Programming_ in the numbered step form, he legitimized
a style which should, in our enlightened age, be obsolete.
-- 
John Kececioglu / arizona!johnk
"Chess, like love, like music, has the power to make men happy." -- S. Tarrasch