```From: Jim Weigang To: apl-l@hermes.csd.unb.ca (comp.lang.apl) Date: Wed, 25 Mar 1998 21:25:06 -0500 (EST) Subject: Re: Monadic Roll and generating normal distributions in APL Tony Corso wrote on March 23: > I find myself in need of generating a bunch of numbers from a normal > distribution with mean = 0 and std. dev. = 1. And I need to do it in APL. Here's an APL program that does this (and actually works): (Note: The program assumes #IO is 1. Localize and set #IO if you're in the habit of fiddling with the index origin.) As Tony deduced, uniform random numbers in a range such as [0..1] or [-1..1] are produced by arithmetically transforming the results of roll. The technical detail he didn't know was that the roll algorithm used by most APL systems works with 32-bit signed integers, so the finest resolution for floating randoms can be obtained by transforming ?M, where M is the largest integer value, (2*31)-1. For an explanation of why APL's roll function works well (and the significance of 16807), see the article "How the Roll Function Works", by E. E. McDonnell, in Quote Quad vol. 8 no. 3 [1978]. Another interesting article is "Merrily We Roll Along", by J. O. Shallit, in the the APL83 Conference Proceedings. He describes a way of using the current value of #RL to figure out how many random numbers have been generated. In the first appendix, I was surprised to find a description of the infamous Chinese Remainder Theorem (of ACM ball clock puzzler fame). Jim ``` Note: The APL code on this page can be extracted without you having to retype it. See "Downloading Code" for instructions. JimW's Home Page