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From: pokey@well.UUCP (Jef Poskanzer)
Newsgroups: sci.math,comp.sources.wanted
Subject: Re: random numbers
Summary: right for the wrong reason
Message-ID: <10708@well.UUCP>
Date: 14 Feb 89 09:43:56 GMT
References: <734@fcs280s.ncifcrf.gov>
Reply-To: Jef Poskanzer <jef@helios.ee.lbl.gov>
Distribution: na
Organization: Paratheo-Anametamystikhood Of Eris Esoteric, Ada Lovelace Cabal
Lines: 45

In the referenced message, toms@ncifcrf.gov (Tom Schneider) wrote:
}In article <10471@ut-emx.UUCP> ken@ut-emx.UUCP (kenneth Moore) writes:
}>I am looking for a program  to generate -Normal distributed
}> random numbers
}
}The simplest way to generate such numbers is to add together several
}flat distribution numbers.  This is very costly, and there is a better way.
}   theta = Un 2 pi
}   r     = sqrt(-2 ln(Un+1)) 
}then when these polar coordinates are converted to Cartesian
}coordinates, one gets two independent Normally distributed numbers

Excuse me, but for what meaning of the word "costly" is generating
several uniform numbers even SLIGHTLY more costly than generating
two uniform numbers and then doing a log, a square root, and a sine
or cosine??  Not to mention all those multiplies.

I prefer the polar method too (see below for an implementation in C,
straight out of Knuth), but not because of "cost".  I use it because
it's *correct*.  The "add up N uniforms" method is only an approximation.
---
Jef

            Jef Poskanzer   jef@helios.ee.lbl.gov   ...well!pokey
      "No wonder white people are going to Hell..." -- Andrew Purshottam

float
rndnor( mean, stddev )
float mean, stddev;
    {
    float v1, v2, z;

    do
        {
        v1 = -log( 1.0 - rnd() );
        v2 = -log( 1.0 - rnd() );
        }
    while ( 2.0 * v1 < ( (v2-1.0)*(v2-1.0) ) );

    if ( rnd() > 0.5 )
        z = 1.0;
    else
        z = -1.0;
    return stddev * z * v2 + mean;
    }