Author: martin fierz
Date: 18:31:24 07/10/02
Go up one level in this thread
On July 09, 2002 at 17:59:17, Robert Hyatt wrote: >I have been running some tests after prompting by Bruce, and the results >have been interesting. > >The question posed by him was "how many hash collisions (signatures match >but positions do not) can we tolerate in a search without having serious >problems?" > >I did the following: I made my HashProbe() routine use the node counter, >and every N nodes, I would "match" a hash entry even if the signatures were >not the same, simulating a collision. I got all the way down to a collision >every 1000 nodes without seeing even a score change at the root, which was >surprising. > >I would like to ask others to try this as well. It only adds a couple of >lines to your HashProbe() code. I started at one "collision" every 100K >nodes, but that did nothing. Then one every 10K. And finally one every >1K. This seems surprising to me. I ran several positions, with and without >the "collision problem" and compared my logfile output. Scores did not change >at all. I used tactical positions like Kopec22, opening positions, and even >the classic fine #70. > >Seems that the search is far more resistant to such errors than anybody has >thought previously. It would be interesting to see if this is just a result >of Crafty, or if it holds for others. Particularly for someone that hashes >in the q-search, which I do not do... Note that I did not false match every >N calls to HashProbe() rather I false matched on the next call to HashProbe() >after having searched N nodes since the previous call. Sometimes this would >be less frequently than once per 1000 nodes obviously, since I could burn >several thousand nodes in the q-search and not do another false match until I >get back out of that mess and back into the normal non-qsearch part. i made a small experiment: my checkers program uses 2 32-bit numbers as hash signature, the first is used to compute the table position with number%hashtable size, the second is stored in the table for verification. i ran a test suite, 78 positions, each searched to depth 13 and depth 19. then i used only 10 bits of the 32-bit verification number to verify and did this thing again. result: out of 156 scores and moves, 3 scores were different, by a very small amount (0.02, 0.04 and 0.04) and the moves were the same, and in one instance the score was the same but the move different. i checked and the 10-bit move was actually an error. of course using 10 bits for verification purposes is ridiculously little. i repeated the experiment using 20 bits, and now all scores and all moves were identical, although the node counts sometimes were slightly different. anybody want to claim 32 bits is too little for a hash signature? :-) if my math doesnt let me down, this type of experiment actually should produce a fixed error rate: if you use 10 bits, the probability that you have the same number in your signature as the one in the table is 1/1024 (if you have a different position of course...). so you should be seeing 1 error in 1024 with this setup, if you have a single probe in the hashtable. implementation details: my program uses MTD(f) and has a bucket size of 2, i.e. it always probes two consecutive hashtable entries. so maybe my error rate was even higher than 1 in 1024 in the 10-bit-signature experiment. aloha martin
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