time33算法理解

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  • 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.

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