1/* Single-precision SVE inverse sin
2
3 Copyright (C) 2023-2024 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20#include "sv_math.h"
21#include "poly_sve_f32.h"
22
23static const struct data
24{
25 float32_t poly[5];
26 float32_t pi_over_2f;
27} data = {
28 /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
29 [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
30 .poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6,
31 0x1.3af7d8p-5, },
32 .pi_over_2f = 0x1.921fb6p+0f,
33};
34
35/* Single-precision SVE implementation of vector asin(x).
36
37 For |x| in [0, 0.5], use order 4 polynomial P such that the final
38 approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
39
40 The largest observed error in this region is 0.83 ulps,
41 _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2
42 want 0x1.fef15cp-2.
43
44 For |x| in [0.5, 1.0], use same approximation with a change of variable
45
46 asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z).
47
48 The largest observed error in this region is 2.41 ulps,
49 _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1
50 want -0x1.0c3a6p-1. */
51svfloat32_t SV_NAME_F1 (asin) (svfloat32_t x, const svbool_t pg)
52{
53 const struct data *d = ptr_barrier (&data);
54
55 svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000);
56
57 svfloat32_t ax = svabs_x (pg, x);
58 svbool_t a_ge_half = svacge (pg, x, 0.5);
59
60 /* Evaluate polynomial Q(x) = y + y * z * P(z) with
61 z = x ^ 2 and y = |x| , if |x| < 0.5
62 z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */
63 svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (x: 0.5), ax, 0.5),
64 svmul_x (pg, x, x));
65 svfloat32_t z = svsqrt_m (ax, a_ge_half, z2);
66
67 /* Use a single polynomial approximation P for both intervals. */
68 svfloat32_t p = sv_horner_4_f32_x (pg, x: z2, poly: d->poly);
69 /* Finalize polynomial: z + z * z2 * P(z2). */
70 p = svmla_x (pg, z, svmul_x (pg, z, z2), p);
71
72 /* asin(|x|) = Q(|x|) , for |x| < 0.5
73 = pi/2 - 2 Q(|x|), for |x| >= 0.5. */
74 svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (x: -2.0), d->pi_over_2f);
75
76 /* Copy sign. */
77 return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign));
78}
79

source code of glibc/sysdeps/aarch64/fpu/asinf_sve.c