1/* Double-precision vector (Advanced SIMD) cos 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 "v_math.h"
21
22static const struct data
23{
24 float64x2_t poly[7];
25 float64x2_t range_val, shift, inv_pi, half_pi, pi_1, pi_2, pi_3;
26} data = {
27 /* Worst-case error is 3.3 ulp in [-pi/2, pi/2]. */
28 .poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7),
29 V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19),
30 V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33),
31 V2 (-0x1.9e9540300a1p-41) },
32 .inv_pi = V2 (0x1.45f306dc9c883p-2),
33 .half_pi = V2 (0x1.921fb54442d18p+0),
34 .pi_1 = V2 (0x1.921fb54442d18p+1),
35 .pi_2 = V2 (0x1.1a62633145c06p-53),
36 .pi_3 = V2 (0x1.c1cd129024e09p-106),
37 .shift = V2 (0x1.8p52),
38 .range_val = V2 (0x1p23)
39};
40
41#define C(i) d->poly[i]
42
43static float64x2_t VPCS_ATTR NOINLINE
44special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
45{
46 y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
47 return v_call_f64 (cos, x, y, cmp);
48}
49
50float64x2_t VPCS_ATTR V_NAME_D1 (cos) (float64x2_t x)
51{
52 const struct data *d = ptr_barrier (&data);
53 float64x2_t n, r, r2, r3, r4, t1, t2, t3, y;
54 uint64x2_t odd, cmp;
55
56#if WANT_SIMD_EXCEPT
57 r = vabsq_f64 (x);
58 cmp = vcgeq_u64 (vreinterpretq_u64_f64 (r),
59 vreinterpretq_u64_f64 (d->range_val));
60 if (__glibc_unlikely (v_any_u64 (cmp)))
61 /* If fenv exceptions are to be triggered correctly, set any special lanes
62 to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by
63 special-case handler later. */
64 r = vbslq_f64 (cmp, v_f64 (1.0), r);
65#else
66 cmp = vcageq_f64 (x, d->range_val);
67 r = x;
68#endif
69
70 /* n = rint((|x|+pi/2)/pi) - 0.5. */
71 n = vfmaq_f64 (d->shift, d->inv_pi, vaddq_f64 (r, d->half_pi));
72 odd = vshlq_n_u64 (vreinterpretq_u64_f64 (n), 63);
73 n = vsubq_f64 (n, d->shift);
74 n = vsubq_f64 (n, v_f64 (0.5));
75
76 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
77 r = vfmsq_f64 (r, d->pi_1, n);
78 r = vfmsq_f64 (r, d->pi_2, n);
79 r = vfmsq_f64 (r, d->pi_3, n);
80
81 /* sin(r) poly approx. */
82 r2 = vmulq_f64 (r, r);
83 r3 = vmulq_f64 (r2, r);
84 r4 = vmulq_f64 (r2, r2);
85
86 t1 = vfmaq_f64 (C (4), C (5), r2);
87 t2 = vfmaq_f64 (C (2), C (3), r2);
88 t3 = vfmaq_f64 (C (0), C (1), r2);
89
90 y = vfmaq_f64 (t1, C (6), r4);
91 y = vfmaq_f64 (t2, y, r4);
92 y = vfmaq_f64 (t3, y, r4);
93 y = vfmaq_f64 (r, y, r3);
94
95 if (__glibc_unlikely (v_any_u64 (cmp)))
96 return special_case (x, y, odd, cmp);
97 return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
98}
99

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