[Mesa-dev] [PATCH] glsl: improve the accuracy of the asin() builtin function.

[Paul Berry]

I forgot to mention:

Fixes piglit tests {vs,fs}-asin-float and {vs,fs}-atan-*

On 27 July 2011 15:15, Paul Berry <stereotype441 at gmail.com> wrote:
> The previous formula for asin(x) was algebraically equivalent to:
>
> sign(x)*(pi/2 - sqrt(1-|x|)*(A + B|x| + C|x|^2))
>
> where A, B, and C were arbitrary constants determined by a curve fit.
>
> This formula had a worst case absolute error of 0.00448, an unbounded
> worst case relative error, and a discontinuity near x=0.
>
> Changed the formula to:
>
> sign(x)*(pi/2 - sqrt(1-|x|)*(pi/2 + (pi/4-1)|x| + A|x|^2 + B|x|^3))
>
> where A and B are arbitrary constants determined by a curve fit.  This
> has a worst case absolute error of 0.00039, a worst case relative
> error of 0.000405, and no discontinuities.
>
> I don't expect a significant performance degradation, since the extra
> multiply-accumulate should be fast compared to the sqrt() computation.
> ---
>  src/glsl/builtins/ir/asin |   68 ++++++++++++++++++++++++++------------------
>  1 files changed, 40 insertions(+), 28 deletions(-)
>
> diff --git a/src/glsl/builtins/ir/asin b/src/glsl/builtins/ir/asin
> index e230ad6..45d9e67 100644
> --- a/src/glsl/builtins/ir/asin
> +++ b/src/glsl/builtins/ir/asin
> @@ -5,23 +5,26 @@
>      ((return (expression float *
>               (expression float sign (var_ref x))
>               (expression float -
> -               (expression float *
> -                (constant float (3.1415926))
> -                (constant float (0.5)))
> +               (constant float (1.5707964))
>                (expression float *
>                 (expression float sqrt
>                  (expression float -
>                   (constant float (1.0))
>                   (expression float abs (var_ref x))))
>                 (expression float +
> -                 (constant float (1.5707288))
> +                 (constant float (1.5707964))
>                  (expression float *
>                   (expression float abs (var_ref x))
>                   (expression float +
> -                   (constant float (-0.2121144))
> +                   (constant float (-0.21460183))
>                    (expression float *
> -                    (constant float (0.0742610))
> -                    (expression float abs (var_ref x))))))))))))
> +                    (expression float abs (var_ref x))
> +                     (expression float +
> +                      (constant float (0.086566724))
> +                      (expression float *
> +                       (expression float abs (var_ref x))
> +                       (constant float (-0.03102955))
> +                    ))))))))))))
>
>    (signature vec2
>      (parameters
> @@ -29,23 +32,26 @@
>      ((return (expression vec2 *
>               (expression vec2 sign (var_ref x))
>               (expression vec2 -
> -               (expression float *
> -                (constant float (3.1415926))
> -                (constant float (0.5)))
> +               (constant float (1.5707964))
>                (expression vec2 *
>                 (expression vec2 sqrt
>                  (expression vec2 -
>                   (constant float (1.0))
>                   (expression vec2 abs (var_ref x))))
>                 (expression vec2 +
> -                 (constant float (1.5707288))
> +                 (constant float (1.5707964))
>                  (expression vec2 *
>                   (expression vec2 abs (var_ref x))
>                   (expression vec2 +
> -                   (constant float (-0.2121144))
> +                   (constant float (-0.21460183))
>                    (expression vec2 *
> -                    (constant float (0.0742610))
> -                    (expression vec2 abs (var_ref x))))))))))))
> +                    (expression vec2 abs (var_ref x))
> +                     (expression vec2 +
> +                      (constant float (0.086566724))
> +                      (expression vec2 *
> +                       (expression vec2 abs (var_ref x))
> +                       (constant float (-0.03102955))
> +                    ))))))))))))
>
>    (signature vec3
>      (parameters
> @@ -53,23 +59,26 @@
>      ((return (expression vec3 *
>               (expression vec3 sign (var_ref x))
>               (expression vec3 -
> -               (expression float *
> -                (constant float (3.1415926))
> -                (constant float (0.5)))
> +               (constant float (1.5707964))
>                (expression vec3 *
>                 (expression vec3 sqrt
>                  (expression vec3 -
>                   (constant float (1.0))
>                   (expression vec3 abs (var_ref x))))
>                 (expression vec3 +
> -                 (constant float (1.5707288))
> +                 (constant float (1.5707964))
>                  (expression vec3 *
>                   (expression vec3 abs (var_ref x))
>                   (expression vec3 +
> -                   (constant float (-0.2121144))
> +                   (constant float (-0.21460183))
>                    (expression vec3 *
> -                    (constant float (0.0742610))
> -                    (expression vec3 abs (var_ref x))))))))))))
> +                    (expression vec3 abs (var_ref x))
> +                     (expression vec3 +
> +                      (constant float (0.086566724))
> +                      (expression vec3 *
> +                       (expression vec3 abs (var_ref x))
> +                       (constant float (-0.03102955))
> +                    ))))))))))))
>
>    (signature vec4
>      (parameters
> @@ -77,21 +86,24 @@
>      ((return (expression vec4 *
>               (expression vec4 sign (var_ref x))
>               (expression vec4 -
> -               (expression float *
> -                (constant float (3.1415926))
> -                (constant float (0.5)))
> +               (constant float (1.5707964))
>                (expression vec4 *
>                 (expression vec4 sqrt
>                  (expression vec4 -
>                   (constant float (1.0))
>                   (expression vec4 abs (var_ref x))))
>                 (expression vec4 +
> -                 (constant float (1.5707288))
> +                 (constant float (1.5707964))
>                  (expression vec4 *
>                   (expression vec4 abs (var_ref x))
>                   (expression vec4 +
> -                   (constant float (-0.2121144))
> +                   (constant float (-0.21460183))
>                    (expression vec4 *
> -                    (constant float (0.0742610))
> -                    (expression vec4 abs (var_ref x))))))))))))
> +                    (expression vec4 abs (var_ref x))
> +                     (expression vec4 +
> +                      (constant float (0.086566724))
> +                      (expression vec4 *
> +                       (expression vec4 abs (var_ref x))
> +                       (constant float (-0.03102955))
> +                    ))))))))))))
>  ))
> --
> 1.7.6
>
>