1 /*
2 * Single-precision vector sinpi function.
3 *
4 * Copyright (c) 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 #include "poly_advsimd_f32.h"
11 #include "pl_sig.h"
12 #include "pl_test.h"
13
14 static const struct data
15 {
16 float32x4_t poly[6];
17 } data = {
18 /* Taylor series coefficents for sin(pi * x). */
19 .poly = { V4 (0x1.921fb6p1f), V4 (-0x1.4abbcep2f), V4 (0x1.466bc6p1f),
20 V4 (-0x1.32d2ccp-1f), V4 (0x1.50783p-4f), V4 (-0x1.e30750p-8f) },
21 };
22
23 #if WANT_SIMD_EXCEPT
24 # define TinyBound v_u32 (0x30000000) /* asuint32(0x1p-31f). */
25 # define Thresh v_u32 (0x1f000000) /* asuint32(0x1p31f) - TinyBound. */
26
27 static float32x4_t VPCS_ATTR NOINLINE
special_case(float32x4_t x,float32x4_t y,uint32x4_t odd,uint32x4_t cmp)28 special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
29 {
30 /* Fall back to scalar code. */
31 y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
32 return v_call_f32 (sinpif, x, y, cmp);
33 }
34 #endif
35
36 /* Approximation for vector single-precision sinpi(x)
37 Maximum Error 3.03 ULP:
38 _ZGVnN4v_sinpif(0x1.c597ccp-2) got 0x1.f7cd56p-1
39 want 0x1.f7cd5p-1. */
V_NAME_F1(sinpi)40 float32x4_t VPCS_ATTR V_NAME_F1 (sinpi) (float32x4_t x)
41 {
42 const struct data *d = ptr_barrier (&data);
43
44 #if WANT_SIMD_EXCEPT
45 uint32x4_t ir = vreinterpretq_u32_f32 (vabsq_f32 (x));
46 uint32x4_t cmp = vcgeq_u32 (vsubq_u32 (ir, TinyBound), Thresh);
47
48 /* When WANT_SIMD_EXCEPT = 1, special lanes should be set to 0
49 to avoid them under/overflowing and throwing exceptions. */
50 float32x4_t r = v_zerofy_f32 (x, cmp);
51 #else
52 float32x4_t r = x;
53 #endif
54
55 /* If r is odd, the sign of the result should be inverted. */
56 uint32x4_t odd
57 = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (r)), 31);
58
59 /* r = x - rint(x). Range reduction to -1/2 .. 1/2. */
60 r = vsubq_f32 (r, vrndaq_f32 (r));
61
62 /* Pairwise Horner approximation for y = sin(r * pi). */
63 float32x4_t r2 = vmulq_f32 (r, r);
64 float32x4_t r4 = vmulq_f32 (r2, r2);
65 float32x4_t y = vmulq_f32 (v_pw_horner_5_f32 (r2, r4, d->poly), r);
66
67 #if WANT_SIMD_EXCEPT
68 if (unlikely (v_any_u32 (cmp)))
69 return special_case (x, y, odd, cmp);
70 #endif
71
72 return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
73 }
74
75 PL_SIG (V, F, 1, sinpi, -0.9, 0.9)
76 PL_TEST_ULP (V_NAME_F1 (sinpi), 2.54)
77 PL_TEST_EXPECT_FENV (V_NAME_F1 (sinpi), WANT_SIMD_EXCEPT)
78 PL_TEST_SYM_INTERVAL (V_NAME_F1 (sinpi), 0, 0x1p-31, 5000)
79 PL_TEST_SYM_INTERVAL (V_NAME_F1 (sinpi), 0x1p-31, 0.5, 10000)
80 PL_TEST_SYM_INTERVAL (V_NAME_F1 (sinpi), 0.5, 0x1p31f, 10000)
81 PL_TEST_SYM_INTERVAL (V_NAME_F1 (sinpi), 0x1p31f, inf, 10000)
82