1/*
2 * Double-precision vector cos function.
3 *
4 * Copyright (c) 2019, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8#include "mathlib.h"
9#include "v_math.h"
10#if V_SUPPORTED
11
12static const double Poly[] = {
13/* worst-case error is 3.5 ulp.
14   abs error: 0x1.be222a58p-53 in [-pi/2, pi/2].  */
15-0x1.9f4a9c8b21dc9p-41,
16 0x1.60e88a10163f2p-33,
17-0x1.ae6361b7254e7p-26,
18 0x1.71de382e8d62bp-19,
19-0x1.a01a019aeb4ffp-13,
20 0x1.111111110b25ep-7,
21-0x1.55555555554c3p-3,
22};
23
24#define C7 v_f64 (Poly[0])
25#define C6 v_f64 (Poly[1])
26#define C5 v_f64 (Poly[2])
27#define C4 v_f64 (Poly[3])
28#define C3 v_f64 (Poly[4])
29#define C2 v_f64 (Poly[5])
30#define C1 v_f64 (Poly[6])
31
32#define InvPi v_f64 (0x1.45f306dc9c883p-2)
33#define HalfPi v_f64 (0x1.921fb54442d18p+0)
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 (cos, x, y, cmp);
46}
47
48VPCS_ATTR
49v_f64_t
50V_NAME(cos) (v_f64_t x)
51{
52  v_f64_t n, r, r2, y;
53  v_u64_t odd, cmp;
54
55  r = v_as_f64_u64 (v_as_u64_f64 (x) & AbsMask);
56  cmp = v_cond_u64 (v_as_u64_f64 (r) >= v_as_u64_f64 (RangeVal));
57
58  /* n = rint((|x|+pi/2)/pi) - 0.5.  */
59  n = v_fma_f64 (InvPi, r + HalfPi, Shift);
60  odd = v_as_u64_f64 (n) << 63;
61  n -= Shift;
62  n -= v_f64 (0.5);
63
64  /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2).  */
65  r = v_fma_f64 (-Pi1, n, r);
66  r = v_fma_f64 (-Pi2, n, r);
67  r = v_fma_f64 (-Pi3, n, r);
68
69  /* sin(r) poly approx.  */
70  r2 = r * r;
71  y = v_fma_f64 (C7, r2, C6);
72  y = v_fma_f64 (y, r2, C5);
73  y = v_fma_f64 (y, r2, C4);
74  y = v_fma_f64 (y, r2, C3);
75  y = v_fma_f64 (y, r2, C2);
76  y = v_fma_f64 (y, r2, C1);
77  y = v_fma_f64 (y * r2, r, r);
78
79  /* sign.  */
80  y = v_as_f64_u64 (v_as_u64_f64 (y) ^ odd);
81
82  if (unlikely (v_any_u64 (cmp)))
83    return specialcase (x, y, cmp);
84  return y;
85}
86VPCS_ALIAS
87#endif
88