2) It removes the need for sub bcount()

That does miss the point, which was not what the bcount() sub did, but the way it did it.

The result of using bitwise math using arbitrary precision doesn't follow the fix-width integer semantics. Ie. the math isn't automatically module 2^128.

That means you get quite different results:

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

my $ZERO = Math::GMPz->new( 0 );
my $ONE  = Math::GMPz->new( 1 );
#my $ALLONES = ~ $ZERO;
my $ALLONES = (Math::GMPz->new(1) << 128) - 1;
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
4019000903644796537894933644280473643
6698389137940470254461716813547458644
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