1*412f47f9SXin Li /*
2*412f47f9SXin Li * Double-precision SVE sin(x) function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2019-2023, 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 "sv_math.h"
9*412f47f9SXin Li #include "pl_sig.h"
10*412f47f9SXin Li #include "pl_test.h"
11*412f47f9SXin Li
12*412f47f9SXin Li static const struct data
13*412f47f9SXin Li {
14*412f47f9SXin Li double inv_pi, pi_1, pi_2, pi_3, shift, range_val;
15*412f47f9SXin Li double poly[7];
16*412f47f9SXin Li } data = {
17*412f47f9SXin Li .poly = { -0x1.555555555547bp-3, 0x1.1111111108a4dp-7, -0x1.a01a019936f27p-13,
18*412f47f9SXin Li 0x1.71de37a97d93ep-19, -0x1.ae633919987c6p-26,
19*412f47f9SXin Li 0x1.60e277ae07cecp-33, -0x1.9e9540300a1p-41, },
20*412f47f9SXin Li
21*412f47f9SXin Li .inv_pi = 0x1.45f306dc9c883p-2,
22*412f47f9SXin Li .pi_1 = 0x1.921fb54442d18p+1,
23*412f47f9SXin Li .pi_2 = 0x1.1a62633145c06p-53,
24*412f47f9SXin Li .pi_3 = 0x1.c1cd129024e09p-106,
25*412f47f9SXin Li .shift = 0x1.8p52,
26*412f47f9SXin Li .range_val = 0x1p23,
27*412f47f9SXin Li };
28*412f47f9SXin Li
29*412f47f9SXin Li #define C(i) sv_f64 (d->poly[i])
30*412f47f9SXin Li
31*412f47f9SXin Li static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t cmp)32*412f47f9SXin Li special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
33*412f47f9SXin Li {
34*412f47f9SXin Li return sv_call_f64 (sin, x, y, cmp);
35*412f47f9SXin Li }
36*412f47f9SXin Li
37*412f47f9SXin Li /* A fast SVE implementation of sin.
38*412f47f9SXin Li Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
39*412f47f9SXin Li is 2.87 ULP:
40*412f47f9SXin Li _ZGVsMxv_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
41*412f47f9SXin Li want 0x1.fffffffa7dc05p-1
42*412f47f9SXin Li Maximum observed error in the entire non-special domain ([-2^23, 2^23])
43*412f47f9SXin Li is 3.22 ULP:
44*412f47f9SXin Li _ZGVsMxv_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
45*412f47f9SXin Li want 0x1.ffdcd125c84f8p-3. */
SV_NAME_D1(sin)46*412f47f9SXin Li svfloat64_t SV_NAME_D1 (sin) (svfloat64_t x, const svbool_t pg)
47*412f47f9SXin Li {
48*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
49*412f47f9SXin Li
50*412f47f9SXin Li /* Load some values in quad-word chunks to minimise memory access. */
51*412f47f9SXin Li const svbool_t ptrue = svptrue_b64 ();
52*412f47f9SXin Li svfloat64_t shift = sv_f64 (d->shift);
53*412f47f9SXin Li svfloat64_t inv_pi_and_pi1 = svld1rq (ptrue, &d->inv_pi);
54*412f47f9SXin Li svfloat64_t pi2_and_pi3 = svld1rq (ptrue, &d->pi_2);
55*412f47f9SXin Li
56*412f47f9SXin Li /* n = rint(|x|/pi). */
57*412f47f9SXin Li svfloat64_t n = svmla_lane (shift, x, inv_pi_and_pi1, 0);
58*412f47f9SXin Li svuint64_t odd = svlsl_x (pg, svreinterpret_u64 (n), 63);
59*412f47f9SXin Li n = svsub_x (pg, n, shift);
60*412f47f9SXin Li
61*412f47f9SXin Li /* r = |x| - n*(pi/2) (range reduction into -pi/2 .. pi/2). */
62*412f47f9SXin Li svfloat64_t r = x;
63*412f47f9SXin Li r = svmls_lane (r, n, inv_pi_and_pi1, 1);
64*412f47f9SXin Li r = svmls_lane (r, n, pi2_and_pi3, 0);
65*412f47f9SXin Li r = svmls_lane (r, n, pi2_and_pi3, 1);
66*412f47f9SXin Li
67*412f47f9SXin Li /* sin(r) poly approx. */
68*412f47f9SXin Li svfloat64_t r2 = svmul_x (pg, r, r);
69*412f47f9SXin Li svfloat64_t r3 = svmul_x (pg, r2, r);
70*412f47f9SXin Li svfloat64_t r4 = svmul_x (pg, r2, r2);
71*412f47f9SXin Li
72*412f47f9SXin Li svfloat64_t t1 = svmla_x (pg, C (4), C (5), r2);
73*412f47f9SXin Li svfloat64_t t2 = svmla_x (pg, C (2), C (3), r2);
74*412f47f9SXin Li svfloat64_t t3 = svmla_x (pg, C (0), C (1), r2);
75*412f47f9SXin Li
76*412f47f9SXin Li svfloat64_t y = svmla_x (pg, t1, C (6), r4);
77*412f47f9SXin Li y = svmla_x (pg, t2, y, r4);
78*412f47f9SXin Li y = svmla_x (pg, t3, y, r4);
79*412f47f9SXin Li y = svmla_x (pg, r, y, r3);
80*412f47f9SXin Li
81*412f47f9SXin Li svbool_t cmp = svacle (pg, x, d->range_val);
82*412f47f9SXin Li cmp = svnot_z (pg, cmp);
83*412f47f9SXin Li if (unlikely (svptest_any (pg, cmp)))
84*412f47f9SXin Li return special_case (x,
85*412f47f9SXin Li svreinterpret_f64 (sveor_z (
86*412f47f9SXin Li svnot_z (pg, cmp), svreinterpret_u64 (y), odd)),
87*412f47f9SXin Li cmp);
88*412f47f9SXin Li
89*412f47f9SXin Li /* Copy sign. */
90*412f47f9SXin Li return svreinterpret_f64 (sveor_z (pg, svreinterpret_u64 (y), odd));
91*412f47f9SXin Li }
92*412f47f9SXin Li
93*412f47f9SXin Li PL_SIG (SV, D, 1, sin, -3.1, 3.1)
94*412f47f9SXin Li PL_TEST_ULP (SV_NAME_D1 (sin), 2.73)
95*412f47f9SXin Li PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sin), 0, 0x1p23, 1000000)
96*412f47f9SXin Li PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sin), 0x1p23, inf, 10000)
97