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