time33算法理解

This is Daniel J. Bernstein's popular `times 33' hash function as  posted by him years ago on comp.lang.c. It basically uses a function  like ``hash(i) = hash(i-1) * 33 + str[i]''. This is one of the best  known hash functions for strings. Because it is both computed very  fast and distributes very well.  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 RSE did now) 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 values of the variants, 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 and seems to be the reason why Daniel J.  Bernstein also preferred it.