mirror of git://sourceware.org/git/glibc.git
113 lines
4.4 KiB
C
113 lines
4.4 KiB
C
/* Double-Precision vector (SVE) inverse cospi function
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Copyright (C) 2025 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 "sv_math.h"
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static const struct data
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{
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float64_t c1, c3, c5, c7, c9, c11;
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float64_t c0, c2, c4, c6, c8, c10;
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float64_t inv_pi, half;
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} data = {
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/* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2)
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on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using
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iterative approach for minimisation of relative error in asinpif Sollya
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file. */
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.c0 = 0x1.b2995e7b7b5fbp-5, .c1 = 0x1.8723a1d58d83p-6,
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.c2 = 0x1.d1a452eacf2fep-7, .c3 = 0x1.3ce52c4d75582p-7,
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.c4 = 0x1.d2b2a0aea27d5p-8, .c5 = 0x1.6a0b9b92cad8bp-8,
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.c6 = 0x1.2290c84438caep-8, .c7 = 0x1.efba896580d02p-9,
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.c8 = 0x1.44446707af38p-9, .c9 = 0x1.5070b3e7aa03ep-8,
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.c10 = -0x1.c70015d0ebdafp-9, .c11 = 0x1.27029c383fed9p-7,
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.inv_pi = 0x1.45f306dc9c883p-2, .half = 0.5,
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};
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/* Double-precision SVE implementation of vector acospi(x).
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For |x| in [0, 0.5], use order 11 polynomial P to approximate asinpi
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such that the final approximation of acospi is:
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acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)).
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The largest observed error in this region is 1.35 ulp:
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_ZGVsMxv_acospi (0x1.fb014996aea18p-2) got 0x1.572a91755bbf6p-2
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want 0x1.572a91755bbf7p-2.
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For |x| in [0.5, 1.0], use same approximation with a change of variable
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acospi(x) = y/pi + 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 2.55 ulp:
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_ZGVsMxv_acospi(0x1.d90d50357410cp-1) got 0x1.ffd43d5dd3a9ep-4
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want 0x1.ffd43d5dd3a9bp-4. */
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svfloat64_t SV_NAME_D1 (acospi) (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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svbool_t ptrue = svptrue_b64 ();
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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_gt_half = svacgt (pg, x, 0.5f);
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/* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with
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z2 = x ^ 2 and z = |x| , if |x| < 0.5
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z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */
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svfloat64_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5),
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svmul_x (ptrue, x, x));
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svfloat64_t z = svsqrt_m (ax, a_gt_half, z2);
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/* Order-11 Estrin. */
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svfloat64_t z4 = svmul_x (ptrue, z2, z2);
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svfloat64_t z8 = svmul_x (ptrue, z4, z4);
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svfloat64_t c13 = svld1rq (ptrue, &d->c1);
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svfloat64_t c57 = svld1rq (ptrue, &d->c5);
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svfloat64_t c911 = svld1rq (ptrue, &d->c9);
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svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0);
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svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1);
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svfloat64_t p03 = svmla_x (pg, p01, z4, p23);
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svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0);
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svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1);
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svfloat64_t p47 = svmla_x (pg, p45, z4, p67);
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svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0);
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svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1);
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svfloat64_t p811 = svmla_x (pg, p89, z4, p1011);
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svfloat64_t p411 = svmla_x (pg, p47, z8, p811);
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svfloat64_t p = svmla_x (pg, p03, z8, p411);
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p = svmla_x (pg, sv_f64 (d->inv_pi), z2, p);
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p = svmul_x (ptrue, p, z);
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/* acospi(|x|) = 1/2 - sign(x) * Q(|x|), for |x| < 0.5
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= 2 Q(|x|) , for 0.5 < x < 1.0
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= 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */
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svfloat64_t mul = svreinterpret_f64 (
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svlsl_m (a_gt_half, svreinterpret_u64 (sv_f64 (1.0)), 10));
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mul = svreinterpret_f64 (sveor_x (ptrue, svreinterpret_u64 (mul), sign));
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svfloat64_t add = svreinterpret_f64 (
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svorr_x (ptrue, sign, svreinterpret_u64 (sv_f64 (d->half))));
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add = svsub_m (a_gt_half, sv_f64 (d->half), add);
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return svmsb_x (pg, p, mul, add);
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}
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