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
11 static 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
32 static float32x4_t VPCS_ATTR NOINLINE
special_case(float32x4_t x,float32x4_t y,uint32x4_t odd,uint32x4_t cmp)33 special_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
V_NAME_F1(cos)40 float32x4_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