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/* Single-precision SVE inverse sin
Copyright (C) 2023 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
#include "poly_sve_f32.h"
static const struct data
{
float32_t poly[5];
float32_t pi_over_2f;
} data = {
/* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
[ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
.poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6,
0x1.3af7d8p-5, },
.pi_over_2f = 0x1.921fb6p+0f,
};
/* Single-precision SVE implementation of vector asin(x).
For |x| in [0, 0.5], use order 4 polynomial P such that the final
approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
The largest observed error in this region is 0.83 ulps,
_ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2
want 0x1.fef15cp-2.
For |x| in [0.5, 1.0], use same approximation with a change of variable
asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
The largest observed error in this region is 2.41 ulps,
_ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1
want -0x1.0c3a6p-1. */
svfloat32_t SV_NAME_F1 (asin) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000);
svfloat32_t ax = svabs_x (pg, x);
svbool_t a_ge_half = svacge (pg, x, 0.5);
/* Evaluate polynomial Q(x) = y + y * z * P(z) with
z = x ^ 2 and y = |x| , if |x| < 0.5
z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */
svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5),
svmul_x (pg, x, x));
svfloat32_t z = svsqrt_m (ax, a_ge_half, z2);
/* Use a single polynomial approximation P for both intervals. */
svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly);
/* Finalize polynomial: z + z * z2 * P(z2). */
p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
/* asin(|x|) = Q(|x|) , for |x| < 0.5
= pi/2 - 2 Q(|x|), for |x| >= 0.5. */
svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f);
/* Copy sign. */
return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign));
}
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