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

[Patrick Baggett]

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)",
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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>