Re: [eigen] Vectorized Hamming distance

[Mark Borgerding <mark@xxxxxxxxxxxxxx>]

On 11/25/2009 06:37 AM, rodrigo benenson wrote:
> The hamming distance consists on doing XOR between two vectors and
> then counting the number of bits in the resulting vector.
>
> Any suggestion on how to do this ?
>    

The easy way:
In SSE4.2, there is a POPCNT (population count) instruction that counts 
the set bits.


The hard way:
On processors that lack a popcnt instruction, you can add the bits in 
parallel.
Conceptually:
* use bitwise AND to mask a word into two words: one with even bits [ 
.... b4 0 b2 0 b0 ] and one with odd [ ... b3 0 b1 0 ]
* shift one of the words right one bit so their LSBs line up
* add the one-bit numbers in parallel with integer addition
* mask the 2-bit words,right shift by 2,and add the 2-bit numbers in 
parallel (creating half as many 3 bit numbers)
* mask the 3 bit words,right shift by 4 and add the 3-bit numbers in 
parallel
* mask the 4-bit words,right shift by 8 and add the 4-bit numbers in 
parallel.  Each of these 4 bit numbers represents the number of set bits 
in each byte.
* continue as many more rounds as your word length requires


This could be extended to 128 bit words or beyond.

There is an implementation for 32 bit words at
http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel