Author: Tim Foden
Date: 10:42:31 02/07/01
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On February 07, 2001 at 12:19:38, Andrew Dados 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 > > >You need about 800 random 64 bit values with maximized hamming distance >(different number of bits for each pair of 64 bit keys). According to my >experiments you can do much better then 32 (Why the perfect key should change >32? It should change as much as possible...). I managed to generate 800 keys >with hamming distance of 40 (so each key pair differ in exactly 40 bits); 41 >seem to hit some limits around 760 keys. > >-Andrew- That's impressive. I only managed to get a minimum hamming distance of 24. Here is a distribution for my 832 keys that took about 5 minutes to generate (min hamming distance of 23 only takes about 10 seconds): hamm 24, freq 9952 hamm 25, freq 2012 hamm 26, freq 22139 hamm 27, freq 3847 hamm 28, freq 38982 hamm 29, freq 5924 hamm 30, freq 53744 hamm 31, freq 7191 hamm 32, freq 60519 hamm 33, freq 7070 hamm 34, freq 52957 hamm 35, freq 5635 hamm 36, freq 37333 hamm 37, freq 3468 hamm 38, freq 20096 hamm 39, freq 1654 hamm 40, freq 8637 hamm 41, freq 588 hamm 42, freq 2837 hamm 43, freq 187 hamm 44, freq 717 hamm 45, freq 48 hamm 46, freq 131 hamm 47, freq 6 hamm 48, freq 19 hamm 49, freq 1 hamm 50, freq 1 hamm 51, freq 1 avg 31.9546 It just keeps generating keys randomly, and checks each new key against the rest. If the hamming distance is too small, it throws it away, and generates another one. I did think of also throwing away the key it clashed with, but I havn't tried it. How did you manage to get a min hamming distance of 40? Cheers, Tim.
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