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/* Single-Precision vector (SVE) inverse sinpi function
Copyright (C) 2025 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"
static const struct data
{
float32_t c1, c3, c5;
float32_t c0, c2, c4, inv_pi;
} data = {
/* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
[ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
.c0 = 0x1.b2995ep-5f, .c1 = 0x1.8724ep-6f, .c2 = 0x1.d1301ep-7f,
.c3 = 0x1.446d3cp-7f, .c4 = 0x1.654848p-8f, .c5 = 0x1.5fdaa8p-7f,
.inv_pi = 0x1.45f306p-2f,
};
/* Single-precision SVE implementation of vector asin(x).
For |x| in [0, 0.5], use order 5 polynomial P such that the final
approximation is an odd polynomial: asinpi(x) ~ x/pi + x^3 P(x^2).
The largest observed error in this region is 1.96 ulps:
_ZGVsMxv_asinpif (0x1.8e534ep-3) got 0x1.fe6ab4p-5
want 0x1.fe6ab8p-5.
For |x| in [0.5, 1.0], use same approximation with a change of variable
asinpi(x) = 1/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
The largest observed error in this region is 3.46 ulps:
_ZGVsMxv_asinpif (0x1.0df892p-1) got 0x1.6a114cp-3
want 0x1.6a1146p-3. */
svfloat32_t SV_NAME_F1 (asinpi) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svbool_t ptrue = svptrue_b32 ();
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);
svfloat32_t z4 = svmul_x (ptrue, z2, z2);
svfloat32_t c135_two = svld1rq (ptrue, &d->c1);
/* Order-5 Pairwise Horner evaluation scheme. */
svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), z2, c135_two, 0);
svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), z2, c135_two, 1);
svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), z2, c135_two, 2);
svfloat32_t p25 = svmla_x (pg, p23, z4, p45);
svfloat32_t p = svmla_x (pg, p01, z4, p25);
/* Add 1/pi as final coeff. */
p = svmla_x (pg, sv_f32 (d->inv_pi), z2, p);
p = svmul_x (pg, p, z);
/* asinpi(|x|) = Q(|x|), for |x| < 0.5
= 1/2 - 2 Q(|x|), for |x| >= 0.5. */
svfloat32_t y = svmsb_m (a_ge_half, p, sv_f32 (2.0), 0.5);
/* Reinsert sign from argument. */
return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
}
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