1/*
2 * Double-precision vector sin function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9#include "mathlib.h"
10#include "v_math.h"
11#if V_SUPPORTED
12
13static const double Poly[] = {
14/* worst-case error is 3.5 ulp.
15 abs error: 0x1.be222a58p-53 in [-pi/2, pi/2]. */
16-0x1.9f4a9c8b21dc9p-41,
17 0x1.60e88a10163f2p-33,
18-0x1.ae6361b7254e7p-26,
19 0x1.71de382e8d62bp-19,
20-0x1.a01a019aeb4ffp-13,
21 0x1.111111110b25ep-7,
22-0x1.55555555554c3p-3,
23};
24
25#define C7 v_f64 (Poly[0])
26#define C6 v_f64 (Poly[1])
27#define C5 v_f64 (Poly[2])
28#define C4 v_f64 (Poly[3])
29#define C3 v_f64 (Poly[4])
30#define C2 v_f64 (Poly[5])
31#define C1 v_f64 (Poly[6])
32
33#define InvPi v_f64 (0x1.45f306dc9c883p-2)
34#define Pi1 v_f64 (0x1.921fb54442d18p+1)
35#define Pi2 v_f64 (0x1.1a62633145c06p-53)
36#define Pi3 v_f64 (0x1.c1cd129024e09p-106)
37#define Shift v_f64 (0x1.8p52)
38#define RangeVal v_f64 (0x1p23)
39#define AbsMask v_u64 (0x7fffffffffffffff)
40
41VPCS_ATTR
42__attribute__ ((noinline)) static v_f64_t
43specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
44{
45 return v_call_f64 (f: sin, x, y, p: cmp);
46}
47
48VPCS_ATTR
49v_f64_t
50V_NAME(sin) (v_f64_t x)
51{
52 v_f64_t n, r, r2, y;
53 v_u64_t sign, odd, cmp;
54
55 r = v_as_f64_u64 (x: v_as_u64_f64 (x) & AbsMask);
56 sign = v_as_u64_f64 (x) & ~AbsMask;
57 cmp = v_cond_u64 (x: v_as_u64_f64 (x: r) >= v_as_u64_f64 (RangeVal));
58
59 /* n = rint(|x|/pi). */
60 n = v_fma_f64 (InvPi, y: r, Shift);
61 odd = v_as_u64_f64 (x: n) << 63;
62 n -= Shift;
63
64 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
65 r = v_fma_f64 (x: -Pi1, y: n, z: r);
66 r = v_fma_f64 (x: -Pi2, y: n, z: r);
67 r = v_fma_f64 (x: -Pi3, y: n, z: r);
68
69 /* sin(r) poly approx. */
70 r2 = r * r;
71 y = v_fma_f64 (C7, y: r2, C6);
72 y = v_fma_f64 (x: y, y: r2, C5);
73 y = v_fma_f64 (x: y, y: r2, C4);
74 y = v_fma_f64 (x: y, y: r2, C3);
75 y = v_fma_f64 (x: y, y: r2, C2);
76 y = v_fma_f64 (x: y, y: r2, C1);
77 y = v_fma_f64 (x: y * r2, y: r, z: r);
78
79 /* sign. */
80 y = v_as_f64_u64 (x: v_as_u64_f64 (x: y) ^ sign ^ odd);
81
82 if (unlikely (v_any_u64 (cmp)))
83 return specialcase (x, y, cmp);
84 return y;
85}
86VPCS_ALIAS
87#endif
88

source code of libc/AOR_v20.02/math/v_sin.c