1/* Double-precision vector (SVE) sin function.
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
22static const struct data
23{
24 double inv_pi, pi_1, pi_2, pi_3, shift, range_val;
25 double poly[7];
26} data = {
27 .poly = { -0x1.555555555547bp-3, 0x1.1111111108a4dp-7, -0x1.a01a019936f27p-13,
28 0x1.71de37a97d93ep-19, -0x1.ae633919987c6p-26,
29 0x1.60e277ae07cecp-33, -0x1.9e9540300a1p-41, },
30
31 .inv_pi = 0x1.45f306dc9c883p-2,
32 .pi_1 = 0x1.921fb54442d18p+1,
33 .pi_2 = 0x1.1a62633145c06p-53,
34 .pi_3 = 0x1.c1cd129024e09p-106,
35 .shift = 0x1.8p52,
36 .range_val = 0x1p23,
37};
38
39#define C(i) sv_f64 (d->poly[i])
40
41static svfloat64_t NOINLINE
42special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
43{
44 return sv_call_f64 (f: sin, x, y, cmp);
45}
46
47/* A fast SVE implementation of sin.
48 Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
49 is 2.87 ULP:
50 _ZGVsMxv_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
51 want 0x1.fffffffa7dc05p-1
52 Maximum observed error in the entire non-special domain ([-2^23, 2^23])
53 is 3.22 ULP:
54 _ZGVsMxv_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
55 want 0x1.ffdcd125c84f8p-3. */
56svfloat64_t SV_NAME_D1 (sin) (svfloat64_t x, const svbool_t pg)
57{
58 const struct data *d = ptr_barrier (&data);
59
60 /* Load some values in quad-word chunks to minimise memory access. */
61 const svbool_t ptrue = svptrue_b64 ();
62 svfloat64_t shift = sv_f64 (x: d->shift);
63 svfloat64_t inv_pi_and_pi1 = svld1rq (ptrue, &d->inv_pi);
64 svfloat64_t pi2_and_pi3 = svld1rq (ptrue, &d->pi_2);
65
66 /* n = rint(|x|/pi). */
67 svfloat64_t n = svmla_lane (shift, x, inv_pi_and_pi1, 0);
68 svuint64_t odd = svlsl_x (pg, svreinterpret_u64 (n), 63);
69 n = svsub_x (pg, n, shift);
70
71 /* r = |x| - n*(pi/2) (range reduction into -pi/2 .. pi/2). */
72 svfloat64_t r = x;
73 r = svmls_lane (r, n, inv_pi_and_pi1, 1);
74 r = svmls_lane (r, n, pi2_and_pi3, 0);
75 r = svmls_lane (r, n, pi2_and_pi3, 1);
76
77 /* sin(r) poly approx. */
78 svfloat64_t r2 = svmul_x (pg, r, r);
79 svfloat64_t r3 = svmul_x (pg, r2, r);
80 svfloat64_t r4 = svmul_x (pg, r2, r2);
81
82 svfloat64_t t1 = svmla_x (pg, C (4), C (5), r2);
83 svfloat64_t t2 = svmla_x (pg, C (2), C (3), r2);
84 svfloat64_t t3 = svmla_x (pg, C (0), C (1), r2);
85
86 svfloat64_t y = svmla_x (pg, t1, C (6), r4);
87 y = svmla_x (pg, t2, y, r4);
88 y = svmla_x (pg, t3, y, r4);
89 y = svmla_x (pg, r, y, r3);
90
91 svbool_t cmp = svacle (pg, x, d->range_val);
92 cmp = svnot_z (pg, cmp);
93 if (__glibc_unlikely (svptest_any (pg, cmp)))
94 return special_case (x,
95 y: svreinterpret_f64 (sveor_z (
96 svnot_z (pg, cmp), svreinterpret_u64 (y), odd)),
97 cmp);
98
99 /* Copy sign. */
100 return svreinterpret_f64 (sveor_z (pg, svreinterpret_u64 (y), odd));
101}
102

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