[Mesa-dev] [PATCH 2/2] glsl: Improve the accuracy of the acos() approximation.

[Francisco Jerez]

Iago Toral <itoral at igalia.com> writes:

> On Thu, 2016-03-03 at 01:30 -0800, Kenneth Graunke wrote:
>> From: Francisco Jerez <currojerez at riseup.net>
>> 
>> The adjusted polynomial coefficients come from the numerical
>> minimization of the L2 norm of the relative error.  The old
>> coefficients would give a maximum relative error of about 15000 ULP in
>> the neighborhood around acos(x) = 0, the new ones give a relative
>> error bounded by less than 2000 ULP in the same neighborhood.
>> 
>> Fixes four dEQP subtests:
>> dEQP-GLES31.functional.shaders.builtin_functions.precision.acos.
>> highp_compute.{scalar,vec2,vec3,vec4}
>
> Cool! I thought we would have to use higher order polynomials. Series
> is:
>
> Reviewed-by: Iago Toral Quiroga <itoral at igalia.com>
>
> What about asin? It looks like the new coefficients should be useful
> there as well.
>
That's likely to be more harmful than helpful, the new polynomial
coefficients are optimized to minimize the relative error of acos
*only*, which has a different magnitude profile from asin -- The
relative error of acos(x) used to explode around x=1, while the relative
error of asin(x) is likely to be highest around x=0, because that's
where its magnitude is lowest.  If you switch asin over to the acos
coefficients its overall relative error will likely increase, because it
will improve its accuracy around x=1 where it barely matters and worsen
it around x=0 where it's the most sensitive.  Feel free to put my R-b on
the series:

Reviewed-by: Francisco Jerez <currojerez at riseup.net>

>> ---
>>  src/compiler/glsl/builtin_functions.cpp | 2 +-
>>  1 file changed, 1 insertion(+), 1 deletion(-)
>> 
>> Curro originally wrote this code for the SPIR-V front-end when working
>> on Vulkan conformance.  I copy and pasted it over to GLSL, but all of
>> the actual work is Curro's.
>> 
>> diff --git a/src/compiler/glsl/builtin_functions.cpp b/src/compiler/glsl/builtin_functions.cpp
>> index 0d289c1..10fb21b 100644
>> --- a/src/compiler/glsl/builtin_functions.cpp
>> +++ b/src/compiler/glsl/builtin_functions.cpp
>> @@ -3262,7 +3262,7 @@ builtin_builder::_acos(const glsl_type *type)
>>     ir_variable *x = in_var(type, "x");
>>     MAKE_SIG(type, always_available, 1, x);
>>  
>> -   body.emit(ret(sub(imm(M_PI_2f), asin_expr(x, 0.086566724f, -0.03102955f))));
>> +   body.emit(ret(sub(imm(M_PI_2f), asin_expr(x, 0.08132463f, -0.02363318f))));
>>  
>>     return sig;
>>  }
>
>
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