the math isn't automatically module 2^128Quite 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
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
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