}
/**
- * 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))))
+ * Approximate asin(x) by the piecewise formula:
+ * for |x| < 0.5, asin~(x) = x * (1 + x²(pS0 + x²(pS1 + x²*pS2)) / (1 + x²*qS1))
+ * for |x| ≥ 0.5, asin~(x) = sign(x) * (π/2 - sqrt(1 - |x|) * (π/2 + |x|(π/4 - 1 + |x|(p0 + |x|p1))))
*
- * which is correct to first order at x=0 and x=±1 regardless of the p
+ * The latter 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, float p0, float p1)
+build_asin(nir_builder *b, nir_ssa_def *x, float p0, float p1, bool piecewise)
{
if (x->bit_size == 16) {
/* The polynomial approximation isn't precise enough to meet half-float
* approximation in 32-bit math and then we convert the result back to
* 16-bit.
*/
- return nir_f2f16(b, build_asin(b, nir_f2f32(b, x), p0, p1));
+ return nir_f2f16(b, build_asin(b, nir_f2f32(b, x), p0, p1, piecewise));
}
-
nir_ssa_def *one = nir_imm_floatN_t(b, 1.0f, x->bit_size);
+ nir_ssa_def *half = nir_imm_floatN_t(b, 0.5f, x->bit_size);
nir_ssa_def *abs_x = nir_fabs(b, x);
nir_ssa_def *p0_plus_xp1 = nir_fadd_imm(b, nir_fmul_imm(b, abs_x, p1), p0);
M_PI_4f - 1.0f)),
M_PI_2f);
- return nir_fmul(b, nir_fsign(b, x),
+ nir_ssa_def *result0 = nir_fmul(b, nir_fsign(b, x),
nir_fsub(b, nir_imm_floatN_t(b, M_PI_2f, x->bit_size),
nir_fmul(b, nir_fsqrt(b, nir_fsub(b, one, abs_x)),
expr_tail)));
+ if (piecewise) {
+ /* approximation for |x| < 0.5 */
+ const float pS0 = 1.6666586697e-01f;
+ const float pS1 = -4.2743422091e-02f;
+ const float pS2 = -8.6563630030e-03f;
+ const float qS1 = -7.0662963390e-01f;
+
+ nir_ssa_def *x2 = nir_fmul(b, x, x);
+ nir_ssa_def *p = nir_fmul(b,
+ x2,
+ nir_fadd_imm(b,
+ nir_fmul(b,
+ x2,
+ nir_fadd_imm(b, nir_fmul_imm(b, x2, pS2),
+ pS1)),
+ pS0));
+
+ nir_ssa_def *q = nir_fadd(b, one, nir_fmul_imm(b, x2, qS1));
+ nir_ssa_def *result1 = nir_fadd(b, x, nir_fmul(b, x, nir_fdiv(b, p, q)));
+ return nir_bcsel(b, nir_flt(b, abs_x, half), result1, result0);
+ } else {
+ return result0;
+ }
}
static nir_op
}
case GLSLstd450Asin:
- val->ssa->def = build_asin(nb, src[0], 0.086566724, -0.03102955);
+ val->ssa->def = build_asin(nb, src[0], 0.086566724, -0.03102955, true);
return;
case GLSLstd450Acos:
val->ssa->def =
nir_fsub(nb, nir_imm_floatN_t(nb, M_PI_2f, src[0]->bit_size),
- build_asin(nb, src[0], 0.08132463, -0.02363318));
+ build_asin(nb, src[0], 0.08132463, -0.02363318, false));
return;
case GLSLstd450Atan:
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