1 /*
2 * Single-precision SVE sin(x) 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 "sv_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 static const struct data
13 {
14 float poly[4];
15 /* Pi-related values to be loaded as one quad-word and used with
16 svmla_lane. */
17 float negpi1, negpi2, negpi3, invpi;
18 float shift;
19 } data = {
20 .poly = {
21 /* Non-zero coefficients from the degree 9 Taylor series expansion of
22 sin. */
23 -0x1.555548p-3f, 0x1.110df4p-7f, -0x1.9f42eap-13f, 0x1.5b2e76p-19f
24 },
25 .negpi1 = -0x1.921fb6p+1f,
26 .negpi2 = 0x1.777a5cp-24f,
27 .negpi3 = 0x1.ee59dap-49f,
28 .invpi = 0x1.45f306p-2f,
29 .shift = 0x1.8p+23f
30 };
31
32 #define RangeVal 0x49800000 /* asuint32 (0x1p20f). */
33 #define C(i) sv_f32 (d->poly[i])
34
35 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t cmp)36 special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
37 {
38 return sv_call_f32 (sinf, x, y, cmp);
39 }
40
41 /* A fast SVE implementation of sinf.
42 Maximum error: 1.89 ULPs.
43 This maximum error is achieved at multiple values in [-2^18, 2^18]
44 but one example is:
45 SV_NAME_F1 (sin)(0x1.9247a4p+0) got 0x1.fffff6p-1 want 0x1.fffffap-1. */
SV_NAME_F1(sin)46 svfloat32_t SV_NAME_F1 (sin) (svfloat32_t x, const svbool_t pg)
47 {
48 const struct data *d = ptr_barrier (&data);
49
50 svfloat32_t ax = svabs_x (pg, x);
51 svuint32_t sign
52 = sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax));
53 svbool_t cmp = svcmpge (pg, svreinterpret_u32 (ax), RangeVal);
54
55 /* pi_vals are a quad-word of helper values - the first 3 elements contain
56 -pi in extended precision, the last contains 1 / pi. */
57 svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->negpi1);
58
59 /* n = rint(|x|/pi). */
60 svfloat32_t n = svmla_lane (sv_f32 (d->shift), ax, pi_vals, 3);
61 svuint32_t odd = svlsl_x (pg, svreinterpret_u32 (n), 31);
62 n = svsub_x (pg, n, d->shift);
63
64 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
65 svfloat32_t r;
66 r = svmla_lane (ax, n, pi_vals, 0);
67 r = svmla_lane (r, n, pi_vals, 1);
68 r = svmla_lane (r, n, pi_vals, 2);
69
70 /* sin(r) approx using a degree 9 polynomial from the Taylor series
71 expansion. Note that only the odd terms of this are non-zero. */
72 svfloat32_t r2 = svmul_x (pg, r, r);
73 svfloat32_t y;
74 y = svmla_x (pg, C (2), r2, C (3));
75 y = svmla_x (pg, C (1), r2, y);
76 y = svmla_x (pg, C (0), r2, y);
77 y = svmla_x (pg, r, r, svmul_x (pg, y, r2));
78
79 /* sign = y^sign^odd. */
80 sign = sveor_x (pg, sign, odd);
81
82 if (unlikely (svptest_any (pg, cmp)))
83 return special_case (x,
84 svreinterpret_f32 (sveor_x (
85 svnot_z (pg, cmp), svreinterpret_u32 (y), sign)),
86 cmp);
87 return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
88 }
89
90 PL_SIG (SV, F, 1, sin, -3.1, 3.1)
91 PL_TEST_ULP (SV_NAME_F1 (sin), 1.40)
92 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (sin), 0, 0x1p23, 1000000)
93 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (sin), 0x1p23, inf, 10000)
94