1/*
2 * Single-precision vector cos function.
3 *
4 * Copyright (c) 2019-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "mathlib.h"
9#include "v_math.h"
10
11static const struct data
12{
13  float32x4_t poly[4];
14  float32x4_t range_val, inv_pi, half_pi, shift, pi_1, pi_2, pi_3;
15} data = {
16  /* 1.886 ulp error.  */
17  .poly = { V4 (-0x1.555548p-3f), V4 (0x1.110df4p-7f), V4 (-0x1.9f42eap-13f),
18	    V4 (0x1.5b2e76p-19f) },
19
20  .pi_1 = V4 (0x1.921fb6p+1f),
21  .pi_2 = V4 (-0x1.777a5cp-24f),
22  .pi_3 = V4 (-0x1.ee59dap-49f),
23
24  .inv_pi = V4 (0x1.45f306p-2f),
25  .shift = V4 (0x1.8p+23f),
26  .half_pi = V4 (0x1.921fb6p0f),
27  .range_val = V4 (0x1p20f)
28};
29
30#define C(i) d->poly[i]
31
32static float32x4_t VPCS_ATTR NOINLINE
33special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
34{
35  /* Fall back to scalar code.  */
36  y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
37  return v_call_f32 (cosf, x, y, cmp);
38}
39
40float32x4_t VPCS_ATTR V_NAME_F1 (cos) (float32x4_t x)
41{
42  const struct data *d = ptr_barrier (&data);
43  float32x4_t n, r, r2, r3, y;
44  uint32x4_t odd, cmp;
45
46#if WANT_SIMD_EXCEPT
47  r = vabsq_f32 (x);
48  cmp = vcgeq_u32 (vreinterpretq_u32_f32 (r),
49		   vreinterpretq_u32_f32 (d->range_val));
50  if (unlikely (v_any_u32 (cmp)))
51    /* If fenv exceptions are to be triggered correctly, set any special lanes
52       to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by
53       special-case handler later.  */
54    r = vbslq_f32 (cmp, v_f32 (1.0f), r);
55#else
56  cmp = vcageq_f32 (x, d->range_val);
57  r = x;
58#endif
59
60  /* n = rint((|x|+pi/2)/pi) - 0.5.  */
61  n = vfmaq_f32 (d->shift, d->inv_pi, vaddq_f32 (r, d->half_pi));
62  odd = vshlq_n_u32 (vreinterpretq_u32_f32 (n), 31);
63  n = vsubq_f32 (n, d->shift);
64  n = vsubq_f32 (n, v_f32 (0.5f));
65
66  /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2).  */
67  r = vfmsq_f32 (r, d->pi_1, n);
68  r = vfmsq_f32 (r, d->pi_2, n);
69  r = vfmsq_f32 (r, d->pi_3, n);
70
71  /* y = sin(r).  */
72  r2 = vmulq_f32 (r, r);
73  r3 = vmulq_f32 (r2, r);
74  y = vfmaq_f32 (C (2), C (3), r2);
75  y = vfmaq_f32 (C (1), y, r2);
76  y = vfmaq_f32 (C (0), y, r2);
77  y = vfmaq_f32 (r, y, r3);
78
79  if (unlikely (v_any_u32 (cmp)))
80    return special_case (x, y, odd, cmp);
81  return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
82}
83