2023-11-03 12:12:19 +00:00
|
|
|
/* Single-precision SVE inverse sin
|
|
|
|
|
|
2024-01-01 18:12:26 +00:00
|
|
|
Copyright (C) 2023-2024 Free Software Foundation, Inc.
|
2023-11-03 12:12:19 +00:00
|
|
|
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));
|
|
|
|
|
}
|
