the math isn't automatically module 2^128

Quite so ... I don't think the gmp library provides a way of enforcing fixed precision. Therefore "the overflow" doesn't get automatically discarded, and you would have to remove it yourself by doing a mod(2 ** 128): 
#! perl -slw
use strict;
use Math::GMPz qw(:mpz);

my $ZERO = Math::GMPz->new( 0 );
my $ONE  = Math::GMPz->new( 1 );
my $MOD128  = Math::GMPz->new(1) << 128;
my $ALLONES = $MOD128 - 1;
my $MASK1 = $ALLONES / 3;
my $MASK2 = $ALLONES / 15 * 3;
my $MASK3 = $ALLONES / 255;
my $MASK4 = $MASK3 * 15;

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( ~$bits );
print bcount($ALLONES ^ $bits);

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 ) ) % $MOD128) >> 120;
    return $c;
}

__END__
C:\_64\pscrpt>perl buk1.pl
194447066811964836264785489961010406546
43
85

[download]
Not sure what to do with the ~ operator in Math::GMPz. Currently it just does a one's complement - which is not the right thing for your purposes.
I notice that Math::GMP doesn't overload the ~ operator ... perhaps Math::GMPz should do the same ?

Cheers,
Rob

In reply to Re^16: Module for 128-bit integer math? (updated) by syphilis
in thread Module for 128-bit integer math? by BrowserUk

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