2023-11-03 12:12:19 +00:00
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/* Double-precision SVE inverse sin
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2024-01-01 18:12:26 +00:00
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Copyright (C) 2023-2024 Free Software Foundation, Inc.
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2023-11-03 12:12:19 +00:00
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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 "sv_math.h"
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#include "poly_sve_f64.h"
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static const struct data
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{
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float64_t poly[12];
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float64_t pi_over_2f;
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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 = { 0x1.555555555554ep-3, 0x1.3333333337233p-4,
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0x1.6db6db67f6d9fp-5, 0x1.f1c71fbd29fbbp-6,
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0x1.6e8b264d467d6p-6, 0x1.1c5997c357e9dp-6,
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0x1.c86a22cd9389dp-7, 0x1.856073c22ebbep-7,
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0x1.fd1151acb6bedp-8, 0x1.087182f799c1dp-6,
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-0x1.6602748120927p-7, 0x1.cfa0dd1f9478p-6, },
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.pi_over_2f = 0x1.921fb54442d18p+0,
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};
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#define P(i) sv_f64 (d->poly[i])
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/* Double-precision SVE implementation of vector asin(x).
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For |x| in [0, 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 0.52 ulps,
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_ZGVsMxv_asin(0x1.d95ae04998b6cp-2) got 0x1.ec13757305f27p-2
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want 0x1.ec13757305f26p-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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_ZGVsMxv_asin(0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1
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want 0x1.110d7e85fdd53p-1. */
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svfloat64_t SV_NAME_D1 (asin) (svfloat64_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000);
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svfloat64_t ax = svabs_x (pg, x);
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svbool_t a_ge_half = svacge (pg, x, 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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svfloat64_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5),
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svmul_x (pg, x, x));
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svfloat64_t z = svsqrt_m (ax, a_ge_half, z2);
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/* Use a single polynomial approximation P for both intervals. */
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svfloat64_t z4 = svmul_x (pg, z2, z2);
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svfloat64_t z8 = svmul_x (pg, z4, z4);
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svfloat64_t z16 = svmul_x (pg, z8, z8);
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svfloat64_t p = sv_estrin_11_f64_x (pg, z2, z4, z8, z16, d->poly);
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/* Finalize polynomial: z + z * z2 * P(z2). */
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p = svmla_x (pg, z, svmul_x (pg, 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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svfloat64_t y = svmad_m (a_ge_half, p, sv_f64 (-2.0), d->pi_over_2f);
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/* Copy sign. */
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return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign));
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}
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