That's interesting, but there are reasons other than performance for wanting fix-width integer semantics.

Try coding this with GMP (or any arbitrary precision math):

#! perl -slw
use strict;
use Math::Int128 qw[int128 uint128];

my $ZERO = uint128( 0 );
my $ONE  = uint128( 1 );
my $ALLONES = ~ $ZERO;
my $MASK1 = $ALLONES / 3;
my $MASK2 = $ALLONES / 15 * 3;
my $MASK3 = $ALLONES / 255;
my $MASK4 = $MASK3 * 15;

sub bcount {
    my $v = shift;
    $v = $v - ( ( $v >> 1 ) & $MASK1 );
    $v = ( $v & $MASK2 ) + ( ( $v >> 2 ) & $MASK2 );
    $v = ( $v + ( $v >> 4 ) ) &  $MASK4;
    my $c = ( $v * ( $MASK3 ) ) >> 120;
    return $c;
}

my $bits = uint128( 0 );

## set every 3rd bit
$bits |= $ONE << $_ for map $_*3+1, 0 .. 42;
print $bits;

## count the bits (43)
print bcount( $bits );

## now invert them and count again. (85)
print bcount( ~$bits );

__END__
c:\test>m128.pl
194447066811964836264785489961010406546
43
85
[download]

Note: I would have supplied a GMPz version, but I couldn't work out how to do it from the docs. There seem to be a million ways to initialise a number; a million ways to divide two numbers etc, But not so much when it comes to doing bitwise math.

Update: Here's my attempt at a GMP version of the above. Note that it doesn't just produce the wrong results, but it does so silently:

#! perl -slw
use strict;
use Math::GMPz;

my $ZERO = Math::GMPz->new( 0 );
my $ONE  = Math::GMPz->new( 1 );
my $ALLONES = ~ $ZERO;
my $MASK1 = $ALLONES / 3;
my $MASK2 = $ALLONES / 15 * 3;
my $MASK3 = $ALLONES / 255;
my $MASK4 = $MASK3 * 15;

sub bcount {
    my $v = shift;
    $v = $v - ( ( $v >> 1 ) & $MASK1 );
    $v = ( $v & $MASK2 ) + ( ( $v >> 2 ) & $MASK2 );
    $v = ( $v + ( $v >> 4 ) ) &  $MASK4;
    my $c = ( $v * ( $MASK3 ) ) >> 120;
    return $c;
}

my $bits = Math::GMPz->new( 0 );

## set every 3rd bit
$bits |= $ONE << $_ for map $_*3+1, 0 .. 42;
print $bits;

## count the bits (43)
print bcount( $bits );

## now invert them and count again. (85)
print bcount( ~$bits );

__END__
c:\test>gmpz-t.pl
194447066811964836264785489961010406546
0
0
[download]