1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision SVE sin(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2019-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "sv_math.h"
9*f3087befSAndrew Turner #include "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner static const struct data
13*f3087befSAndrew Turner {
14*f3087befSAndrew Turner float poly[4];
15*f3087befSAndrew Turner /* Pi-related values to be loaded as one quad-word and used with
16*f3087befSAndrew Turner svmla_lane. */
17*f3087befSAndrew Turner float negpi1, negpi2, negpi3, invpi;
18*f3087befSAndrew Turner float shift;
19*f3087befSAndrew Turner } data = {
20*f3087befSAndrew Turner .poly = {
21*f3087befSAndrew Turner /* Non-zero coefficients from the degree 9 Taylor series expansion of
22*f3087befSAndrew Turner sin. */
23*f3087befSAndrew Turner -0x1.555548p-3f, 0x1.110df4p-7f, -0x1.9f42eap-13f, 0x1.5b2e76p-19f
24*f3087befSAndrew Turner },
25*f3087befSAndrew Turner .negpi1 = -0x1.921fb6p+1f,
26*f3087befSAndrew Turner .negpi2 = 0x1.777a5cp-24f,
27*f3087befSAndrew Turner .negpi3 = 0x1.ee59dap-49f,
28*f3087befSAndrew Turner .invpi = 0x1.45f306p-2f,
29*f3087befSAndrew Turner .shift = 0x1.8p+23f
30*f3087befSAndrew Turner };
31*f3087befSAndrew Turner
32*f3087befSAndrew Turner #define RangeVal 0x49800000 /* asuint32 (0x1p20f). */
33*f3087befSAndrew Turner #define C(i) sv_f32 (d->poly[i])
34*f3087befSAndrew Turner
35*f3087befSAndrew Turner static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t cmp)36*f3087befSAndrew Turner special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
37*f3087befSAndrew Turner {
38*f3087befSAndrew Turner return sv_call_f32 (sinf, x, y, cmp);
39*f3087befSAndrew Turner }
40*f3087befSAndrew Turner
41*f3087befSAndrew Turner /* A fast SVE implementation of sinf.
42*f3087befSAndrew Turner Maximum error: 1.89 ULPs.
43*f3087befSAndrew Turner This maximum error is achieved at multiple values in [-2^18, 2^18]
44*f3087befSAndrew Turner but one example is:
45*f3087befSAndrew Turner SV_NAME_F1 (sin)(0x1.9247a4p+0) got 0x1.fffff6p-1 want 0x1.fffffap-1. */
SV_NAME_F1(sin)46*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (sin) (svfloat32_t x, const svbool_t pg)
47*f3087befSAndrew Turner {
48*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
49*f3087befSAndrew Turner
50*f3087befSAndrew Turner svfloat32_t ax = svabs_x (pg, x);
51*f3087befSAndrew Turner svuint32_t sign
52*f3087befSAndrew Turner = sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax));
53*f3087befSAndrew Turner svbool_t cmp = svcmpge (pg, svreinterpret_u32 (ax), RangeVal);
54*f3087befSAndrew Turner
55*f3087befSAndrew Turner /* pi_vals are a quad-word of helper values - the first 3 elements contain
56*f3087befSAndrew Turner -pi in extended precision, the last contains 1 / pi. */
57*f3087befSAndrew Turner svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->negpi1);
58*f3087befSAndrew Turner
59*f3087befSAndrew Turner /* n = rint(|x|/pi). */
60*f3087befSAndrew Turner svfloat32_t n = svmla_lane (sv_f32 (d->shift), ax, pi_vals, 3);
61*f3087befSAndrew Turner svuint32_t odd = svlsl_x (pg, svreinterpret_u32 (n), 31);
62*f3087befSAndrew Turner n = svsub_x (pg, n, d->shift);
63*f3087befSAndrew Turner
64*f3087befSAndrew Turner /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
65*f3087befSAndrew Turner svfloat32_t r;
66*f3087befSAndrew Turner r = svmla_lane (ax, n, pi_vals, 0);
67*f3087befSAndrew Turner r = svmla_lane (r, n, pi_vals, 1);
68*f3087befSAndrew Turner r = svmla_lane (r, n, pi_vals, 2);
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner /* sin(r) approx using a degree 9 polynomial from the Taylor series
71*f3087befSAndrew Turner expansion. Note that only the odd terms of this are non-zero. */
72*f3087befSAndrew Turner svfloat32_t r2 = svmul_x (pg, r, r);
73*f3087befSAndrew Turner svfloat32_t y;
74*f3087befSAndrew Turner y = svmla_x (pg, C (2), r2, C (3));
75*f3087befSAndrew Turner y = svmla_x (pg, C (1), r2, y);
76*f3087befSAndrew Turner y = svmla_x (pg, C (0), r2, y);
77*f3087befSAndrew Turner y = svmla_x (pg, r, r, svmul_x (pg, y, r2));
78*f3087befSAndrew Turner
79*f3087befSAndrew Turner /* sign = y^sign^odd. */
80*f3087befSAndrew Turner sign = sveor_x (pg, sign, odd);
81*f3087befSAndrew Turner
82*f3087befSAndrew Turner if (unlikely (svptest_any (pg, cmp)))
83*f3087befSAndrew Turner return special_case (x,
84*f3087befSAndrew Turner svreinterpret_f32 (sveor_x (
85*f3087befSAndrew Turner svnot_z (pg, cmp), svreinterpret_u32 (y), sign)),
86*f3087befSAndrew Turner cmp);
87*f3087befSAndrew Turner return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
88*f3087befSAndrew Turner }
89*f3087befSAndrew Turner
90*f3087befSAndrew Turner TEST_SIG (SV, F, 1, sin, -3.1, 3.1)
91*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (sin), 1.40)
92*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (sin))
93*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (sin), 0, 0x1p23, 1000000)
94*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (sin), 0x1p23, inf, 10000)
95*f3087befSAndrew Turner CLOSE_SVE_ATTR
96