[Mesa-dev] [PATCH 08/10] nir: Simplify 0 < fabs(a)

[Ian Romanick]

On 03/11/2016 08:51 AM, Patrick Baggett wrote:
> On Fri, Mar 11, 2016 at 10:21 AM, Ian Romanick <idr at freedesktop.org> wrote:
>> On 03/10/2016 01:24 PM, Patrick Baggett wrote:
>>> On Thu, Mar 10, 2016 at 3:08 PM, Patrick Baggett
>>> <baggett.patrick at gmail.com> wrote:
>>>> On Thu, Mar 10, 2016 at 12:25 PM, Ian Romanick <idr at freedesktop.org> wrote:
>>>>> From: Ian Romanick <ian.d.romanick at intel.com>
>>>>>
>>>>> Sandy Bridge / Ivy Bridge / Haswell
>>>>> total instructions in shared programs: 8462180 -> 8462174 (-0.00%)
>>>>> instructions in affected programs: 564 -> 558 (-1.06%)
>>>>> helped: 6
>>>>> HURT: 0
>>>>>
>>>>> total cycles in shared programs: 117542462 -> 117542276 (-0.00%)
>>>>> cycles in affected programs: 9768 -> 9582 (-1.90%)
>>>>> helped: 12
>>>>> HURT: 0
>>>>>
>>>>> Broadwell / Skylake
>>>>> total instructions in shared programs: 8980833 -> 8980826 (-0.00%)
>>>>> instructions in affected programs: 626 -> 619 (-1.12%)
>>>>> helped: 7
>>>>> HURT: 0
>>>>>
>>>>> total cycles in shared programs: 70077900 -> 70077714 (-0.00%)
>>>>> cycles in affected programs: 9378 -> 9192 (-1.98%)
>>>>> helped: 12
>>>>> HURT: 0
>>>>>
>>>>> G45 and Ironlake showed no change.
>>>>>
>>>>> Signed-off-by: Ian Romanick <ian.d.romanick at intel.com>
>>>>> ---
>>>>>  src/compiler/nir/nir_opt_algebraic.py | 5 +++++
>>>>>  1 file changed, 5 insertions(+)
>>>>>
>>>>> diff --git a/src/compiler/nir/nir_opt_algebraic.py b/src/compiler/nir/nir_opt_algebraic.py
>>>>> index 4db8f84..1442ce8 100644
>>>>> --- a/src/compiler/nir/nir_opt_algebraic.py
>>>>> +++ b/src/compiler/nir/nir_opt_algebraic.py
>>>>> @@ -108,6 +108,11 @@ optimizations = [
>>>>>     # inot(a)
>>>>>     (('fge', 0.0, ('b2f', a)), ('inot', a)),
>>>>>
>>>>> +   # 0.0 < fabs(a)
>>>>> +   # 0.0 != fabs(a)  because fabs(a) must be >= 0
>>>> I think this is wrong. Because >= 0.0 can mean that fabs(a) == 0.0 for
>>>> some a, you can't say then fabs(a) != 0.0.
>>>>
>>>> Then, the counter-example is when a = 0.0
>>>>
>>>> 1) 0.0 != fabs(0.0)
>>>> 2) 0.0 != 0.0
>>>>
>>> Rather, I mean the comment is wrong, but the conclusion that:
>>> 0 < fabs(a) <-> a != 0.0
>>> is correct. You can just build a truth table or just observe that when
>>> a == 0, 0 < 0 is false, and
>>> when a != 0.0, fabs(a) will be > 0, so 0 < fabs(a) will be always true.
>>
>> How about if I change it to
>>
>>    # 0.0 != fabs(a)  Since fabs(a) >= 0, 0 <= fabs(a) must be true
>>
>> I think it's trivial to see how to get from "0 < fabs(a)" to "0 !=
>> fabs(a)" based on that.
> Yeah, I think what gave me a pause when I read was "0.0 != fabs(a)",

Right... I was forming this like a proof.  At each line I was just
trying to provide justification for the change from the previous line.
"0.0 != fabs(a)" is equivalent to "0.0 < fabs(a)" for the reason
provided.  I did the same thing in the previous patch.

I want to get consensus on the right way to do this because I have a
bunch more patches to nir_opt_algebraic.py that use the same technique
to show that a simplification is correct.

That's also part of the reason I sent this short series out ahead of the
rest. :)

> because that's not a general mathematical truth unless qualified by "a
> != 0.0". I don't have any particularly strong feelings about the
> wording. I personally didn't reason about it using (in)equalities at
> all. My logic was mostly based on domain analysis of the expression:
> let p(a) := 0 < fabs(a)
> p(0) <-> false
> p(a) <-> true, for any other value of a
> therefore p(a) <-> true when a != 0.0
> therefore p(a) <-> a != 0
> 
> It's up to you.
> 
>>>>> +   # 0.0 != a
>>>>> +   (('flt', 0.0, ('fabs', a)), ('fne', a, 0.0)),
>>>>> +
>>>>>     (('fge', ('fneg', ('fabs', a)), 0.0), ('feq', a, 0.0)),
>>>>>     (('bcsel', ('flt', a, b), a, b), ('fmin', a, b)),
>>>>>     (('bcsel', ('flt', a, b), b, a), ('fmax', a, b)),
>>>>> --
>>>>> 2.5.0
>>>>>
>>>>> _______________________________________________
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>>>>> mesa-dev at lists.freedesktop.org
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