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Date: Tue, 4 Mar 2014 07:45:53 -0600 (CST)
From: Steve Thomas <steve@...tu.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] wider integer multiply on 32-bit x86

> On March 3, 2014 at 10:04 PM Samuel Neves <sneves@....uc.pt> wrote:
>
> static const uint16_t ctrl = 0x1f7f; // 64-bit mantissa, round to 0

Nice with that you can do umul64_hi with one fmul and one fscale:

#define __STDC_CONSTANT_MACROS
#include <inttypes.h>

uint64_t umul64_hi(uint64_t a, uint64_t b)
{
    uint64_t r;
    float    bit63 = 9223372036854775808.0; // 2^63
    int32_t  shift = -64;
    uint16_t ctrl  = 0x1f7f;

    a -= UINT64_C(0x8000000000000000);
    b -= UINT64_C(0x8000000000000000);
    asm(
        "fldcw   %4  \n\t"
        "fildl   %3  \n\t"
        "fildll  %1  \n\t"
        "fadd    %5  \n\t"
        "fildll  %2  \n\t"
        "fadd    %5  \n\t"
        "fmulp       \n\t"
        "fscale      \n\t"
        "fsub    %5  \n\t"
        "fistpll %0  \n\t"
        "ffree   %%st\n\t"
        : "=m"(r)
        : "m"(a), "m"(b), "m"(shift), "m"(ctrl), "m"(bit63));
    return r + UINT64_C(0x8000000000000000);
}

A few notes on the code fildll loads a signed 64 bit int so you need to
subtract 2^63 and load then add 2.0^63 to make it an unsigned load and the
reverse on the store. ffree is needed because after 6 calls the stack is full
or something and gives bad data. Lastly I have never done x87 before today.
So there's probably a better way to do it. Also this stack thing I don't get
it besides: there are 8 registers, it's a cyclical stack, you push and pop,
it breaks if you push to much instead of overwriting oldest, there's a notion
of free that isn't a pop but works like it?, and you can change the stack
pointer by +-1 and somehow doesn't make it implode.
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