typedef unsigned int __uint128 __attribute__ ((__mode__ (TI)));
[download]

typedef unsigned __int128 uint128_t;
to
typedef __uint128 uint128_t;
[download]

ppm install http://www.sisyphusion.tk/ppm/Math-Int128.ppd
[download]

BrowserUk (or anyone else, of course), if you want a ppm package

Thanks syphilis. That works perfectly.

And especially thanks to salva.

I still intend to pursue an MSVC/SSE* solution to this, but this gives me a reference point.

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

And especially thanks to salva

I'll second that !!

There are of course, more things to consider than just *performance* when it comes to choosing which Math module to use - but I was curious to see how Math::Int128 compared for speed with Math::GMPz (which uses the gmp C library).

I found that, if using overloaded operators with Math::GMPz, then Math::GMPz was roughly twice as slow as Math::Int128 - but if using the arithmetic functions that Math::GMPz also provides, then Math::GMPz was roughly twice as fast as Math::Int128.

Without yet having taken the time to look closely at Math::Int128, I believe there would be a way of having it out-perform Math::GMPz. (And I'm about to embark upon a little excercise to satisfy myself that this is so.)
For any Windows users who want to check the comparisons for themselves, there are ppm packages for 64-bit perl (5.10 and 5.12) available:

ppm install http://www.sisyphusion.tk/ppm/Math-GMPz.ppd
ppm install http://www.sisyphusion.tk/ppm/Math-Int128.ppd
[download]

The benchmarks I ran are as follows:

use warnings;
use Math::Int128 qw(int128);
use Math::GMPz qw(:mpz);
use Benchmark qw(:all);

$count = 40000;

$mpz1  = Math::GMPz->new('676469752303423489');
$mpz2  = Math::GMPz->new('776469752999423489');
$i_1   = int128("$mpz1");
$i_2   = int128("$mpz2");

$mpz_sub = Math::GMPz->new('976469752313423489');
$i_sub   = int128("$mpz_sub");

$mpz_div = Math::GMPz->new('76469752313423489');
$i_div   = int128("$mpz_div");

$mpz_ret = Rmpz_init2(128);

print "
******************
**MULTIPLICATION**
******************\n\n";

cmpthese($count * 9, {
    'mul_M::I' => '$ri = Math::Int128::_mul($i_1, $i_2, 0)',
    'mul_M::G1' =>'$mpz_ret = $mpz1 * $mpz2',
    'mul_M::G2'=> 'Rmpz_mul($mpz_ret, $mpz1, $mpz2)',
});


die "Error 1:\n$ri\n$mpz_ret\n" if $ri != int128("$mpz_ret")
 || $ri != int128('525258301482620425304858018020933121');


$i_1 *= $i_1;
$i_2 *= $i_2;
$mpz1 *= $mpz1;
$mpz2 *= $mpz2;


print "
******************
*****DIVISION*****
******************\n\n";

cmpthese($count * 9, {
    'div_M::I' => '$ri = Math::Int128::_div($i_1, $i_div, 0)',
    'div_M::G1' =>'$mpz_ret = $mpz1 / $mpz_div',
    'div_M::G2'=> 'Rmpz_tdiv_q($mpz_ret, $mpz1, $mpz_div)',
});


die "Error 2:\n$ri\n$mpz_ret\n" if $ri != int128("$mpz_ret")
 || $ri != int128('5984213521522366751');

print"
******************
*****ADDITION*****
******************\n\n";

cmpthese($count * 10, {
    'add_M::I' => '$ri = Math::Int128::_add($i_1, $i_2, 0)',
    'add_M::G1' => '$mpz_ret = $mpz1  + $mpz2',
    'add_M::G2' => 'Rmpz_add($mpz_ret, $mpz1, $mpz2)',
});


die "Error 3:\n$ri\n$mpz_ret\n" if $ri != int128("$mpz_ret") 
 || $ri != int128('1060516603104440851094132036041866242');

print "
******************
****SUBTRACTION***
******************\n\n";

cmpthese($count * 10, {
    'add_M::I' => '$ri = Math::Int128::_sub($i_1, $i_sub, 0)',
    'add_M::G1' => '$mpz_ret = $mpz1 - $mpz_sub',
    'add_M::G2' => 'Rmpz_sub($mpz_ret, $mpz1, $mpz_sub)',
});


die "Error 4:\n$ri\n$mpz_ret\n" if $ri != int128("$mpz_ret") 
 || $ri != int128('457611325781455127825205517363509632');
[download]

The output I got was:

C:\_64\pscrpt>perl bench.pl
Name "main::i_div" used only once: possible typo at bench.pl line 17.
Name "main::i_sub" used only once: possible typo at bench.pl line 14.

******************
**MULTIPLICATION**
******************

              Rate mul_M::G1  mul_M::I mul_M::G2
mul_M::G1 156726/s        --      -58%      -82%
mul_M::I  371517/s      137%        --      -58%
mul_M::G2 886700/s      466%      139%        --

******************
*****DIVISION*****
******************

              Rate div_M::G1  div_M::I div_M::G2
div_M::G1 148637/s        --      -57%      -81%
div_M::I  344168/s      132%        --      -57%
div_M::G2 794702/s      435%      131%        --

******************
*****ADDITION*****
******************

              Rate add_M::G1  add_M::I add_M::G2
add_M::G1 148810/s        --      -60%      -83%
add_M::I  376648/s      153%        --      -56%
add_M::G2 852878/s      473%      126%        --

******************
****SUBTRACTION***
******************

              Rate add_M::G1  add_M::I add_M::G2
add_M::G1 147113/s        --      -60%      -83%
add_M::I  365631/s      149%        --      -59%
add_M::G2 883002/s      500%      142%        --

C:\_64\pscrpt>
[download]

Update: I've since written an Inline::C script where the __int128 multiplications beat Math::GMPz ... but not by much:

            Rate    gmpz mul_128
gmpz    900000/s      --     -3%
mul_128 927835/s      3%      --
[download]

The code I used is still a bit rough, but I don't see much scope for improvement at the moment.

Cheers,
Rob