From: Eli Zaretskii <eliz AT is DOT elta DOT co DOT il>
Newsgroups: comp.os.msdos.djgpp
Subject: Re: randN
Date: Wed, 24 Nov 1999 15:41:35 +0200
Organization: NetVision Israel	
Lines: 32
Message-ID: <Pine.SUN.3.91.991124154011.4252I-100000@is>
References: <383904BA DOT AE45DCDE AT mpx DOT com DOT au> <81bigt$1i5 AT acp3bf DOT knirsch DOT de> <Pine DOT SUN DOT 3 DOT 91 DOT 991123091617 DOT 13225A-100000 AT is> <81dsi7$490 AT acp3bf DOT knirsch DOT de>
NNTP-Posting-Host: is.elta.co.il
Mime-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
X-Trace: news.netvision.net.il 943450803 6174 199.203.121.2 (24 Nov 1999 13:40:03 GMT)
X-Complaints-To: abuse AT netvision DOT net DOT il
NNTP-Posting-Date: 24 Nov 1999 13:40:03 GMT
X-Sender: eliz AT is
In-Reply-To: <81dsi7$490@acp3bf.knirsch.de>
To: djgpp AT delorie DOT com
DJ-Gateway: from newsgroup comp.os.msdos.djgpp
Reply-To: djgpp AT delorie DOT com
X-Mailing-List: djgpp AT delorie DOT com
X-Unsubscribes-To: listserv AT delorie DOT com
Precedence: bulk


On 23 Nov 1999, Hans-Bernhard Broeker wrote:

> > The
> > theory behind it is the well-known theorem which states that the sum
> > of a large number of independent random numbers approaches the normal
> > distribution.
> 
> Nice theory, but its application has a significant drawback: 6 is not
> 'large'. Not by any statistical definition I've seen. In the actual
> mathematical theorem, it's actually for 'infinitely' many terms only
> that the true gaussian is guaranteed to come out of the process.

As I said, this is good enough for the IMSL library, so it should be 
good enough for most of us.  I actually used this function in many 
simulations.  The results are usually indistinguishable from more 
complicated methods, as far as the simulation results go.

Of course, if you are doing a PhD thesis in random number generation,
don't dare to use it ;-)

> With a properly implemented inverse error function, or the 2D trick of
> transforming via polar coordinates posted here by someone else, the
> accuracy will be quite a lot better than that, usually. The only real
> justification for the sum-of-6 version would be speed, then. But that
> would only hold if the random number generator itself is significantly
> faster than, say a sin() or log() evaluation. For good RNGs, that
> won't usually hold.

Actually, modern uniform RNGs are lightning-fast, they involve only a
handful of arithmetic instructions and bit shifts.  See the RNGs
posted by Marsaglia a few months ago (Dejanews will find them).