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

[Kenneth Graunke]

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}
---
 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;
 }
-- 
2.7.2