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## Re: [Qemu-devel] [PATCH] int128: optimize

 From: Paolo Bonzini Subject: Re: [Qemu-devel] [PATCH] int128: optimize Date: Thu, 20 Jun 2013 23:20:48 +0200 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:17.0) Gecko/20130514 Thunderbird/17.0.6

Il 20/06/2013 18:46, Richard Henderson ha scritto:
> On 06/20/2013 08:00 AM, Paolo Bonzini wrote:
>>  static inline Int128 int128_sub(Int128 a, Int128 b)
>>  {
>> -    return int128_add(a, int128_neg(b));
>> +    uint64_t lo = a.lo - b.lo;
>> +    return (Int128) { lo, (lo < a.lo) + a.hi - b.hi };
>
> This one isn't right.  Consider { 2, 0 } - { 2, 0 }
>
>   lo = 2 - 2 = 0;
>   = { 0, (0 < 2) + 0 - 0 }
>   = { 0, 1 }
>
> I'd be happier with a more traditional
>
>   (Int128){ a.lo - b.lo, a.hi - b.hi - (a.lo < b.lo) };

Yeah, I wasn't quite sure of this and I was waiting for testcases to
prove me wrong...  To fix it in the style I used you need

(Int128){ lo, a.hi - b.hi - (lo > a.lo) }

(We have to sum a + ~b + 1.  We have lo = a.lo + ~b.lo + 1, from which
the carry-out is either lo <= a.lo or lo <= ~b.lo, using <= because of
the carry-in.  Then the high part is

a.hi + ~b.hi       + (lo <= a.lo)
= a.hi + (-1 - b.hi) + 1 - (lo > a.lo)
= a.hi - b.hi        - (lo > a.lo)

).  But I'll go with your version, it probably generates better code
too.

Paolo

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