1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision vector cospi function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2023, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "mathlib.h"
9*412f47f9SXin Li #include "v_math.h"
10*412f47f9SXin Li #include "poly_advsimd_f32.h"
11*412f47f9SXin Li #include "pl_sig.h"
12*412f47f9SXin Li #include "pl_test.h"
13*412f47f9SXin Li
14*412f47f9SXin Li static const struct data
15*412f47f9SXin Li {
16*412f47f9SXin Li float32x4_t poly[6];
17*412f47f9SXin Li float32x4_t range_val;
18*412f47f9SXin Li } data = {
19*412f47f9SXin Li /* Taylor series coefficents for sin(pi * x). */
20*412f47f9SXin Li .poly = { V4 (0x1.921fb6p1f), V4 (-0x1.4abbcep2f), V4 (0x1.466bc6p1f),
21*412f47f9SXin Li V4 (-0x1.32d2ccp-1f), V4 (0x1.50783p-4f), V4 (-0x1.e30750p-8f) },
22*412f47f9SXin Li .range_val = V4 (0x1p31f),
23*412f47f9SXin Li };
24*412f47f9SXin Li
25*412f47f9SXin Li static float32x4_t VPCS_ATTR NOINLINE
special_case(float32x4_t x,float32x4_t y,uint32x4_t odd,uint32x4_t cmp)26*412f47f9SXin Li special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
27*412f47f9SXin Li {
28*412f47f9SXin Li y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
29*412f47f9SXin Li return v_call_f32 (cospif, x, y, cmp);
30*412f47f9SXin Li }
31*412f47f9SXin Li
32*412f47f9SXin Li /* Approximation for vector single-precision cospi(x)
33*412f47f9SXin Li Maximum Error: 3.17 ULP:
34*412f47f9SXin Li _ZGVnN4v_cospif(0x1.d341a8p-5) got 0x1.f7cd56p-1
35*412f47f9SXin Li want 0x1.f7cd5p-1. */
V_NAME_F1(cospi)36*412f47f9SXin Li float32x4_t VPCS_ATTR V_NAME_F1 (cospi) (float32x4_t x)
37*412f47f9SXin Li {
38*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
39*412f47f9SXin Li
40*412f47f9SXin Li #if WANT_SIMD_EXCEPT
41*412f47f9SXin Li float32x4_t r = vabsq_f32 (x);
42*412f47f9SXin Li uint32x4_t cmp = vcaleq_f32 (v_f32 (0x1p32f), x);
43*412f47f9SXin Li
44*412f47f9SXin Li /* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd
45*412f47f9SXin Li to avoid them overflowing and throwing exceptions. */
46*412f47f9SXin Li r = v_zerofy_f32 (r, cmp);
47*412f47f9SXin Li uint32x4_t odd = vshlq_n_u32 (vcvtnq_u32_f32 (r), 31);
48*412f47f9SXin Li
49*412f47f9SXin Li #else
50*412f47f9SXin Li float32x4_t r = x;
51*412f47f9SXin Li uint32x4_t cmp = vcageq_f32 (r, d->range_val);
52*412f47f9SXin Li
53*412f47f9SXin Li uint32x4_t odd
54*412f47f9SXin Li = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (r)), 31);
55*412f47f9SXin Li
56*412f47f9SXin Li #endif
57*412f47f9SXin Li
58*412f47f9SXin Li /* r = x - rint(x). */
59*412f47f9SXin Li r = vsubq_f32 (r, vrndaq_f32 (r));
60*412f47f9SXin Li
61*412f47f9SXin Li /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */
62*412f47f9SXin Li r = vsubq_f32 (v_f32 (0.5f), vabsq_f32 (r));
63*412f47f9SXin Li
64*412f47f9SXin Li /* Pairwise Horner approximation for y = sin(r * pi). */
65*412f47f9SXin Li float32x4_t r2 = vmulq_f32 (r, r);
66*412f47f9SXin Li float32x4_t r4 = vmulq_f32 (r2, r2);
67*412f47f9SXin Li float32x4_t y = vmulq_f32 (v_pw_horner_5_f32 (r2, r4, d->poly), r);
68*412f47f9SXin Li
69*412f47f9SXin Li /* Fallback to scalar. */
70*412f47f9SXin Li if (unlikely (v_any_u32 (cmp)))
71*412f47f9SXin Li return special_case (x, y, odd, cmp);
72*412f47f9SXin Li
73*412f47f9SXin Li /* Reintroduce the sign bit for inputs which round to odd. */
74*412f47f9SXin Li return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
75*412f47f9SXin Li }
76*412f47f9SXin Li
77*412f47f9SXin Li PL_SIG (V, F, 1, cospi, -0.9, 0.9)
78*412f47f9SXin Li PL_TEST_ULP (V_NAME_F1 (cospi), 2.67)
79*412f47f9SXin Li PL_TEST_EXPECT_FENV (V_NAME_F1 (cospi), WANT_SIMD_EXCEPT)
80*412f47f9SXin Li PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0, 0x1p-31, 5000)
81*412f47f9SXin Li PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0x1p-31, 0.5, 10000)
82*412f47f9SXin Li PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0.5, 0x1p32f, 10000)
83*412f47f9SXin Li PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0x1p32f, inf, 10000)
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