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

[Iago Toral]

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.

> ---
>  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;
>  }