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Merge #10577: Add an explanation of quickly hashing onto a non-power of two range.

dd869c6 Add an explanation of quickly hashing onto a non-power of two range. (Gregory Maxwell)

Tree-SHA512: 8b362e396206a4ee2e825908dcff6fe4525c12b9c85a6e6ed809d75f03d42edcfba5e460a002e5d17cc70c103792f84d99693563b638057e4e97946dd1d800b2
tags/v0.15.1
Wladimir J. van der Laan 3 years ago
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      src/cuckoocache.h

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src/cuckoocache.h View File

@@ -206,6 +206,37 @@ private:
/** compute_hashes is convenience for not having to write out this
* expression everywhere we use the hash values of an Element.
*
* We need to map the 32-bit input hash onto a hash bucket in a range [0, size) in a
* manner which preserves as much of the hash's uniformity as possible. Ideally
* this would be done by bitmasking but the size is usually not a power of two.
*
* The naive approach would be to use a mod -- which isn't perfectly uniform but so
* long as the hash is much larger than size it is not that bad. Unfortunately,
* mod/division is fairly slow on ordinary microprocessors (e.g. 90-ish cycles on
* haswell, ARM doesn't even have an instruction for it.); when the divisor is a
* constant the compiler will do clever tricks to turn it into a multiply+add+shift,
* but size is a run-time value so the compiler can't do that here.
*
* One option would be to implement the same trick the compiler uses and compute the
* constants for exact division based on the size, as described in "{N}-bit Unsigned
* Division via {N}-bit Multiply-Add" by Arch D. Robison in 2005. But that code is
* somewhat complicated and the result is still slower than other options:
*
* Instead we treat the 32-bit random number as a Q32 fixed-point number in the range
* [0,1) and simply multiply it by the size. Then we just shift the result down by
* 32-bits to get our bucket number. The results has non-uniformity the same as a
* mod, but it is much faster to compute. More about this technique can be found at
* http://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
*
* The resulting non-uniformity is also more equally distributed which would be
* advantageous for something like linear probing, though it shouldn't matter
* one way or the other for a cuckoo table.
*
* The primary disadvantage of this approach is increased intermediate precision is
* required but for a 32-bit random number we only need the high 32 bits of a
* 32*32->64 multiply, which means the operation is reasonably fast even on a
* typical 32-bit processor.
*
* @param e the element whose hashes will be returned
* @returns std::array<uint32_t, 8> of deterministic hashes derived from e
*/

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