Author: Ricardo Gibert
Date: 16:50:08 02/09/01
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On February 09, 2001 at 19:34:03, Ricardo Gibert wrote: >On February 09, 2001 at 19:04:45, David Rasmussen wrote: > >>On February 09, 2001 at 10:39:09, Pat King wrote: >> >>>On February 07, 2001 at 10:59:31, Pat King wrote: >>> >>>>I have seen it written here that with 64 bit Zobrist hashing, the perfect key >>>>should change 32 bits. When I had what I thought to be hashing problems, I >>>>captured some stats on my hash keys. I found that most of them changed 28-36 >>>>bits (within 4) with a few outliers as far as 13 bits from "perfection". I also >>>>checked that I was not generating duplicate keys. How good or bad is this? >>>>Should I work on the average, or the outliers? Any comments appreciated :) >>>> >>>>Pat >>>Thanks to all for your thoughtful replies. For what it's worth, the only change >>>I've made is to generate a key set with hamming distance 31-33, with a >>>significant improvement in hash performance (thanks to Ricardo for providing a >>>reasonable argument to justify the 32 bit standard). I have yet to compare this >>>set with Rob's 16 bit criteria for XORing any 2 keys. >>> >>>Pat >> >>But 32 isn't optimal. As high as possible is optimal. > > >So far the conclusions I've come up with are: > >(1) A Key = 0 should be excluded, since positions with a particular piece on a >particular square will produce the same hash signature as the same position >without that piece. >(2) Keys with a close hamming distance to zero should be also be excluded. >(3) Pairs of keys of the form x and ~x, since 2 such pairs will XOR to zero. >(4) Pairs with a close hamming distance to x and ~x should also be excluded. >(5) A key set with a hamming distance > 21 and < 43 with respect to each other 43 should be 45 above. >*and* to zero should satisfy (1)-(4) above can be quickly produced within the >program without having to read in a file with the keys. Just use the same random >number seed. > >I'm trying to find sources on the net to verify these conclusions, but so far no >luck. What do you think?
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