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b0e0a07018
This includes a fix for big-endian in AdvSIMD log, some cosmetic
changes, and numerous small optimisations mainly around inlining and
using indexed variants of MLA intrinsics.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
(cherry picked from commit e302e10213)
114 lines
4.1 KiB
C
114 lines
4.1 KiB
C
/* Double-precision AdvSIMD inverse sin
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Copyright (C) 2023-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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#include "poly_advsimd_f64.h"
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static const struct data
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{
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float64x2_t poly[12];
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float64x2_t pi_over_2;
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uint64x2_t abs_mask;
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} data = {
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/* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x))
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on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */
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.poly = { V2 (0x1.555555555554ep-3), V2 (0x1.3333333337233p-4),
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V2 (0x1.6db6db67f6d9fp-5), V2 (0x1.f1c71fbd29fbbp-6),
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V2 (0x1.6e8b264d467d6p-6), V2 (0x1.1c5997c357e9dp-6),
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V2 (0x1.c86a22cd9389dp-7), V2 (0x1.856073c22ebbep-7),
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V2 (0x1.fd1151acb6bedp-8), V2 (0x1.087182f799c1dp-6),
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V2 (-0x1.6602748120927p-7), V2 (0x1.cfa0dd1f9478p-6), },
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.pi_over_2 = V2 (0x1.921fb54442d18p+0),
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.abs_mask = V2 (0x7fffffffffffffff),
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};
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#define AllMask v_u64 (0xffffffffffffffff)
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#define One 0x3ff0000000000000
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#define Small 0x3e50000000000000 /* 2^-12. */
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#if WANT_SIMD_EXCEPT
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
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{
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return v_call_f64 (asin, x, y, special);
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}
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#endif
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/* Double-precision implementation of vector asin(x).
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For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct
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rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the
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following approximation.
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For |x| in [Small, 0.5], use an order 11 polynomial P such that the final
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approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
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The largest observed error in this region is 1.01 ulps,
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_ZGVnN2v_asin (0x1.da9735b5a9277p-2) got 0x1.ed78525a927efp-2
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want 0x1.ed78525a927eep-2.
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For |x| in [0.5, 1.0], use same approximation with a change of variable
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asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
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The largest observed error in this region is 2.69 ulps,
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_ZGVnN2v_asin (0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1
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want 0x1.110d7e85fdd53p-1. */
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float64x2_t VPCS_ATTR V_NAME_D1 (asin) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float64x2_t ax = vabsq_f64 (x);
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#if WANT_SIMD_EXCEPT
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/* Special values need to be computed with scalar fallbacks so
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that appropriate exceptions are raised. */
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uint64x2_t special
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= vcgtq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (ax), v_u64 (Small)),
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v_u64 (One - Small));
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (x, x, AllMask);
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#endif
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uint64x2_t a_lt_half = vcltq_f64 (ax, v_f64 (0.5));
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/* Evaluate polynomial Q(x) = y + y * z * P(z) with
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z = x ^ 2 and y = |x| , if |x| < 0.5
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z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */
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float64x2_t z2 = vbslq_f64 (a_lt_half, vmulq_f64 (x, x),
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vfmsq_n_f64 (v_f64 (0.5), ax, 0.5));
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float64x2_t z = vbslq_f64 (a_lt_half, ax, vsqrtq_f64 (z2));
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/* Use a single polynomial approximation P for both intervals. */
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float64x2_t z4 = vmulq_f64 (z2, z2);
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float64x2_t z8 = vmulq_f64 (z4, z4);
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float64x2_t z16 = vmulq_f64 (z8, z8);
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float64x2_t p = v_estrin_11_f64 (z2, z4, z8, z16, d->poly);
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/* Finalize polynomial: z + z * z2 * P(z2). */
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p = vfmaq_f64 (z, vmulq_f64 (z, z2), p);
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/* asin(|x|) = Q(|x|) , for |x| < 0.5
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= pi/2 - 2 Q(|x|), for |x| >= 0.5. */
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float64x2_t y = vbslq_f64 (a_lt_half, p, vfmsq_n_f64 (d->pi_over_2, p, 2.0));
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/* Copy sign. */
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return vbslq_f64 (d->abs_mask, y, x);
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}
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