1/* Double-precision vector (SVE) 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 "sv_math.h"
21
22static const struct data
23{
24 double inv_pio2, pio2_1, pio2_2, pio2_3, shift;
25} data = {
26 /* Polynomial coefficients are hardwired in FTMAD instructions. */
27 .inv_pio2 = 0x1.45f306dc9c882p-1,
28 .pio2_1 = 0x1.921fb50000000p+0,
29 .pio2_2 = 0x1.110b460000000p-26,
30 .pio2_3 = 0x1.1a62633145c07p-54,
31 /* Original shift used in AdvSIMD cos,
32 plus a contribution to set the bit #0 of q
33 as expected by trigonometric instructions. */
34 .shift = 0x1.8000000000001p52
35};
36
37#define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */
38
39static svfloat64_t NOINLINE
40special_case (svfloat64_t x, svfloat64_t y, svbool_t oob)
41{
42 return sv_call_f64 (f: cos, x, y, cmp: oob);
43}
44
45/* A fast SVE implementation of cos based on trigonometric
46 instructions (FTMAD, FTSSEL, FTSMUL).
47 Maximum measured error: 2.108 ULPs.
48 SV_NAME_D1 (cos)(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3
49 want -0x1.fddd4c65c7f05p-3. */
50svfloat64_t SV_NAME_D1 (cos) (svfloat64_t x, const svbool_t pg)
51{
52 const struct data *d = ptr_barrier (&data);
53
54 svfloat64_t r = svabs_x (pg, x);
55 svbool_t oob = svcmpge (pg, svreinterpret_u64 (r), RangeVal);
56
57 /* Load some constants in quad-word chunks to minimise memory access. */
58 svbool_t ptrue = svptrue_b64 ();
59 svfloat64_t invpio2_and_pio2_1 = svld1rq (ptrue, &d->inv_pio2);
60 svfloat64_t pio2_23 = svld1rq (ptrue, &d->pio2_2);
61
62 /* n = rint(|x|/(pi/2)). */
63 svfloat64_t q = svmla_lane (sv_f64 (x: d->shift), r, invpio2_and_pio2_1, 0);
64 svfloat64_t n = svsub_x (pg, q, d->shift);
65
66 /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
67 r = svmls_lane (r, n, invpio2_and_pio2_1, 1);
68 r = svmls_lane (r, n, pio2_23, 0);
69 r = svmls_lane (r, n, pio2_23, 1);
70
71 /* cos(r) poly approx. */
72 svfloat64_t r2 = svtsmul (r, svreinterpret_u64 (q));
73 svfloat64_t y = sv_f64 (x: 0.0);
74 y = svtmad (y, r2, 7);
75 y = svtmad (y, r2, 6);
76 y = svtmad (y, r2, 5);
77 y = svtmad (y, r2, 4);
78 y = svtmad (y, r2, 3);
79 y = svtmad (y, r2, 2);
80 y = svtmad (y, r2, 1);
81 y = svtmad (y, r2, 0);
82
83 /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
84 svfloat64_t f = svtssel (r, svreinterpret_u64 (q));
85
86 if (__glibc_unlikely (svptest_any (pg, oob)))
87 return special_case (x, y: svmul_x (svnot_z (pg, oob), y, f), oob);
88
89 /* Apply factor. */
90 return svmul_x (pg, f, y);
91}
92

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