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vtn: Clean up acos implementation.

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Parameterize build_asin() on the fit coefficients so the
implementation can be shared while still using different polynomials
for asin and acos.  Also switch back to implementing acos in terms of
asin -- The improvement obtained from cancelling out the pi/2 terms
was negligible compared to the approximation error.
This commit is contained in:
Francisco Jerez
2016-01-28 18:59:00 -08:00
parent f50a651726
commit cec6fe2ad8
1 changed files with 16 additions and 28 deletions
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44
src/compiler/nir/spirv/vtn_glsl450.c
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@@ -208,12 +208,19 @@ build_log(nir_builder *b, nir_ssa_def *x)
return nir_fmul(b, nir_flog2(b, x), nir_imm_float(b, 1.0 / M_LOG2E));
}
/**
* Approximate asin(x) by the formula:
* asin~(x) = sign(x) * (pi/2 - sqrt(1 - |x|) * (pi/2 + |x|(pi/4 - 1 + |x|(p0 + |x|p1))))
*
* which is correct to first order at x=0 and x=±1 regardless of the p
* coefficients but can be made second-order correct at both ends by selecting
* the fit coefficients appropriately. Different p coefficients can be used
* in the asin and acos implementation to minimize some relative error metric
* in each case.
*/
static nir_ssa_def *
build_asin(nir_builder *b, nir_ssa_def *x)
build_asin(nir_builder *b, nir_ssa_def *x, float p0, float p1)
{
/*
* asin(x) = sign(x) * (pi/2 - sqrt(1 - |x|) * (pi / 4 - 1 + |x| * (0.086566724 + |x| * -0.03102955)))
*/
nir_ssa_def *abs_x = nir_fabs(b, x);
return nir_fmul(b, nir_fsign(b, x),
nir_fsub(b, nir_imm_float(b, M_PI_2f),
@@ -222,29 +229,9 @@ build_asin(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, p0),
nir_fmul(b, abs_x,
nir_imm_float(b, -0.03102955f))))))))));
}
static nir_ssa_def *
build_acos(nir_builder *b, nir_ssa_def *x)
{
/*
* 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)),
nir_fadd(b, nir_imm_float(b, M_PI_2f),
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, 0.08132463f),
nir_fmul(b, abs_x,
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);
nir_imm_float(b, p1))))))))));
}
/**
@@ -605,11 +592,12 @@ handle_glsl450_alu(struct vtn_builder *b, enum GLSLstd450 entrypoint,
case GLSLstd450FindUMsb: op = nir_op_ufind_msb; break;
case GLSLstd450Asin:
val->ssa->def = build_asin(nb, src[0]);
val->ssa->def = build_asin(nb, src[0], 0.086566724, -0.03102955);
return;
case GLSLstd450Acos:
val->ssa->def = build_acos(nb, src[0]);
val->ssa->def = nir_fsub(nb, nir_imm_float(nb, M_PI_2f),
build_asin(nb, src[0], 0.08132463, -0.02363318));
return;
case GLSLstd450Atan: