Author: Dieter Buerssner
Date: 13:52:14 08/17/02
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On August 17, 2002 at 03:38:04, Daniel Clausen wrote: Some comments to Daniel, some other comments to various points made in this tread. >The Crafty-sources contain a reference to a very good random generator. I have no doubt, that the lagged Fibonacci generator used by Crafty is more than adequate for Zorbrist hashing. However, I would not call it a good pseudo random number generator. (Almost) all lagged Fibonacci generators have at least one serious and well known flaw - they totally fail Marsaglia's duplicate birthday test - the failure can be statistically very significant be seen even with rather few calls to the generator. So certainly, for serious statistical simulation (which more or less is done by the mentioned test), they should be handled with very much care - or better avoided when not combined with another algorithm. It is some time ago, when I tried various generators for zorbrist hashing. I could not detect any systematic difference in test positions. Of course, the very worst PRNGs must be avoided. For example some (i.e. one used in some Unix systems) only toggle the lowest significant bit, and when one naivly combines several calls to such a PRNG to create one 64 bit random number, one will have several basically useless bits. For slightly serious PRNGs, I see no problem to combine several calls to get a 64 bit number. Another point: it is to my knowledge not clear at all, that good randomness of the keys is needed for Zorbrist hashing. Also, it at least seems doubtful, that having a very large mininimal Hammond distance is needed or especially good (we combine more than 2 of those keys ...). Regards, Dieter
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