/* * This is the popular `times 33' hash algorithm which is used by * perl and also appears in Berkeley DB. This is one of the best * known hash functions for strings because it is both computed * very fast and distributes very well. * * The originator may be Dan Bernstein but the code in Berkeley DB * cites Chris Torek as the source. The best citation I have found * is "Chris Torek, Hash function for text in C, Usenet message * 27038@mimsy.umd.edu in comp.lang.c , October, 1990." in Rich * Salz's USENIX 1992 paper about INN which can be found at * . * * The magic of number 33, i.e. why it works better than many other * constants, prime or not, has never been adequately explained by * anyone. So I try an explanation: if one experimentally tests all * multipliers between 1 and 256 (as I did while writing a low-level * data structure library some time ago) one detects that even * numbers are not useable at all. The remaining 128 odd numbers * (except for the number 1) work more or less all equally well. * They all distribute in an acceptable way and this way fill a hash * table with an average percent of approx. 86%. * * If one compares the chi^2 html' target='_blank'>values of the variants (see * Bob Jenkins ``Hashing Frequently Asked Questions'' at * http://burtleburtle.net/bob/hash/hashfaq.html for a description * of chi^2), the number 33 not even has the best value. But the * number 33 and a few other equally good numbers like 17, 31, 63, * 127 and 129 have nevertheless a great advantage to the remaining * numbers in the large set of possible multipliers: their multiply * operation can be replaced by a faster operation based on just one * shift plus either a single addition or subtraction operation. And * because a hash function has to both distribute good _and_ has to * be very fast to compute, those few numbers should be preferred. * * -- Ralf S. Engelschall */
