G'day rootcho,

There may be a better algorithm; however, just rearranging your code, without changing the basic logic, produced significant speed improvements: more than 30% for 8 bits and almost 50% for 64 bits. Here's my version of your subroutine:

sub hd_Ken {
    my ($diff, $bits, $count, $mask) = ($_[0] ^ $_[1], $_[2] || 8, 0);

    $mask = 1 << $_, $diff & $mask && ++$count for 0 .. $bits - 1;

    $count;
}
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As you can see, I've eliminated a number of variables completely ($d1, $d2 and $b) and declared the reminder only once; there's less assignments and the return has been removed. Here's my test and benchmark code:

#!/usr/bin/env perl

use strict;
use warnings;

use Benchmark qw{cmpthese};

my $x = 1 << 0;                             
my $y = 1 << 1 ^ 1 << 4 ^ 1 << 7 ^ 1 << 15 ^ 1 << 31 ^ 1 << 63;

my @test_results = (
    hd_OP($x, $y),
    hd_Ken($x, $y),
    hd_OP($x, $y, 16),
    hd_Ken($x, $y, 16),
    hd_OP($x, $y, 32),
    hd_Ken($x, $y, 32),
    hd_OP($x, $y, 64),
    hd_Ken($x, $y, 64),
);
print "Test results: @test_results\n";

cmpthese(-1, {
    hd_OP_8 => sub { hd_OP($x, $y) },
    hd_Ken_8 => sub { hd_Ken($x, $y) },
});

cmpthese(-1, {
    hd_OP_16 => sub { hd_OP($x, $y, 16) },
    hd_Ken_16 => sub { hd_Ken($x, $y, 16) },
});

cmpthese(-1, {
    hd_OP_32 => sub { hd_OP($x, $y, 32) },
    hd_Ken_32 => sub { hd_Ken($x, $y, 32) },
});

cmpthese(-1, {
    hd_OP_64 => sub { hd_OP($x, $y, 64) },
    hd_Ken_64 => sub { hd_Ken($x, $y, 64) },
});

sub hd_Ken {
    my ($diff, $bits, $count, $mask) = ($_[0] ^ $_[1], $_[2] || 8, 0);

    $mask = 1 << $_, $diff & $mask && ++$count for 0 .. $bits - 1;

    $count;
}

sub hd_OP {
   my ($d1,$d2,$bits) = @_;
   $bits ||= 8;
   my $diff = $d1 ^ $d2;
   my $count = 0;
   for my $b ( 0 .. $bits-1 ) {
      my $mask = 1 << $b;
      ++ $count if $diff & $mask
   }
   return $count
}
[download]

Obviously, you'll want to run that on your system. I usually run benchmarks several times to identify outliers; here's a fairly representative result:

$ pm_hamming.pl
Test results: 4 4 5 5 6 6 7 7
             Rate  hd_OP_8 hd_Ken_8
hd_OP_8  344926/s       --     -24%
hd_Ken_8 454209/s      32%       --
              Rate  hd_OP_16 hd_Ken_16
hd_OP_16  231849/s        --      -26%
hd_Ken_16 314139/s       35%        --
              Rate  hd_OP_32 hd_Ken_32
hd_OP_32  139183/s        --      -30%
hd_Ken_32 198422/s       43%        --
              Rate  hd_OP_64 hd_Ken_64
hd_OP_64   77282/s        --      -32%
hd_Ken_64 113551/s       47%        --
[download]