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vtn: Improve accuracy of acos approximation. 

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.
This commit is contained in:
Francisco Jerez 2016-01-27 18:39:48 -08:00 committed by Kristian Høgsberg Kristensen
parent 7fb35a8228
commit 4604b2871a
1 changed files with 3 additions and 3 deletions
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6
src/glsl/nir/spirv/vtn_glsl450.c
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@ -228,7 +228,7 @@ static nir_ssa_def *
build_acos(nir_builder *b, nir_ssa_def *x)
{
/*
* acos(x) = sign(x) * sqrt(1 - |x|) * (pi / 4 - 1 + |x| * (0.086566724 + |x| * -0.03102955))
* poly(x) = sign(x) * sqrt(1 - |x|) * (pi / 2 + |x| * (pi / 4 - 1 + |x| * (0.08132463 + |x| * -0.02363318)))
*/
nir_ssa_def *abs_x = nir_fabs(b, x);
nir_ssa_def *poly = nir_fmul(b, nir_fsqrt(b, nir_fsub(b, nir_imm_float(b, 1.0f), abs_x)),
@ -236,9 +236,9 @@ build_acos(nir_builder *b, nir_ssa_def *x)
nir_fmul(b, abs_x,
nir_fadd(b, nir_imm_float(b, M_PI_4f - 1.0f),
nir_fmul(b, abs_x,
nir_fadd(b, nir_imm_float(b, 0.086566724f),
nir_fadd(b, nir_imm_float(b, 0.08132463f),
nir_fmul(b, abs_x,
nir_imm_float(b, -0.03102955f))))))));
nir_imm_float(b, -0.02363318f))))))));
return nir_bcsel(b, nir_flt(b, x, nir_imm_float(b, 0)),
nir_fsub(b, nir_imm_float(b, M_PI), poly),
poly);