time33算法理解

Posted 2022-11-13 梦想田园

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.