Newsgroups: sci.stat.math,sci.math,sci.math.num-analysis Path: bga.com!news.sprintlink.net!news.onramp.net!convex!cs.utexas.edu!swrinde!ihnp4.ucsd.edu!agate!library.ucla.edu!csulb.edu!csus.edu!netcom.com!deleyd From: deleyd@netcom.com Subject: Random Numbers - Request for feedback Message-ID: <deleydCsIB28.KEI@netcom.com> Organization: NETCOM On-line Communication Services (408 261-4700 guest) Date: Wed, 6 Jul 1994 06:51:43 GMT Lines: 43 Xref: bga.com sci.stat.math:1315 sci.math:15353 sci.math.num-analysis:3354 RE: Computer Generated Random Numbers A few closing comments and requests for further information: 1. All my tests on random number generators were performed on VAX/VMS computers. VAX uses a 32-bit architecture, so the random number generators I tested were ones which used a word size of 32 bits or less. I would be interested in anybody's test results of a random number generator utilizing a larger word size, such as xrand() using SIZE=63. 2. Anyone know of some good references on primitive polynomials mod 2 and their applications? They're used in additive congruential random number generators like the xrand() one tested here. They're also used by file transfer programs such as xmodem to insure error free transmission, and they're used in cryptography too. Anyone know of a good book on Abstract Algebra? (The ones I have just briefly touch the topic and then move on.) 3. Resolution: Usually the random number generator is set up to return a floating point value between 0 and 1. A typical floating point variable R can only represent a finite number of different values between 0 and 1. If you magnify the result too much the discreetness of the floating point datum will become obvious. For example, in VAX architecture the F-floating datum has a precision of approximately one part in 2**23. Multiplying R by a very large number N to create a random variable between 0 and N will fail if N is too large because some of the values between 0 and N have no corresponding R value which maps to them (i.e. the mapping is no longer a surjection or onto map). For an F_floating datum, N above 2**23 is obviously too large. But even below 2**23 there's still a problem of some bins having 2 R values which map to them while other bins have only 1. We need to get N small enough so that the number of R values which maps to any bin is about the same, close enough so that differences aren't noticed when we test the random number generator. -David Deley deleyd@netcom.com