1*412f47f9SXin Li /*
2*412f47f9SXin Li * Core approximation for double-precision vector sincos
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 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 "poly_sve_f64.h"
10*412f47f9SXin Li
11*412f47f9SXin Li static const struct sv_sincos_data
12*412f47f9SXin Li {
13*412f47f9SXin Li double sin_poly[7], cos_poly[6], pio2[3];
14*412f47f9SXin Li double inv_pio2, shift, range_val;
15*412f47f9SXin Li } sv_sincos_data = {
16*412f47f9SXin Li .inv_pio2 = 0x1.45f306dc9c882p-1,
17*412f47f9SXin Li .pio2 = { 0x1.921fb50000000p+0, 0x1.110b460000000p-26,
18*412f47f9SXin Li 0x1.1a62633145c07p-54 },
19*412f47f9SXin Li .shift = 0x1.8p52,
20*412f47f9SXin Li .sin_poly = { /* Computed using Remez in [-pi/2, pi/2]. */
21*412f47f9SXin Li -0x1.555555555547bp-3, 0x1.1111111108a4dp-7,
22*412f47f9SXin Li -0x1.a01a019936f27p-13, 0x1.71de37a97d93ep-19,
23*412f47f9SXin Li -0x1.ae633919987c6p-26, 0x1.60e277ae07cecp-33,
24*412f47f9SXin Li -0x1.9e9540300a1p-41 },
25*412f47f9SXin Li .cos_poly = { /* Computed using Remez in [-pi/4, pi/4]. */
26*412f47f9SXin Li 0x1.555555555554cp-5, -0x1.6c16c16c1521fp-10,
27*412f47f9SXin Li 0x1.a01a019cbf62ap-16, -0x1.27e4f812b681ep-22,
28*412f47f9SXin Li 0x1.1ee9f152a57cdp-29, -0x1.8fb131098404bp-37 },
29*412f47f9SXin Li .range_val = 0x1p23, };
30*412f47f9SXin Li
31*412f47f9SXin Li static inline svbool_t
check_ge_rangeval(svbool_t pg,svfloat64_t x,const struct sv_sincos_data * d)32*412f47f9SXin Li check_ge_rangeval (svbool_t pg, svfloat64_t x, const struct sv_sincos_data *d)
33*412f47f9SXin Li {
34*412f47f9SXin Li svbool_t in_bounds = svaclt (pg, x, d->range_val);
35*412f47f9SXin Li return svnot_z (pg, in_bounds);
36*412f47f9SXin Li }
37*412f47f9SXin Li
38*412f47f9SXin Li /* Double-precision vector function allowing calculation of both sin and cos in
39*412f47f9SXin Li one function call, using shared argument reduction and separate polynomials.
40*412f47f9SXin Li Largest observed error is for sin, 3.22 ULP:
41*412f47f9SXin Li v_sincos_sin (0x1.d70eef40f39b1p+12) got -0x1.ffe9537d5dbb7p-3
42*412f47f9SXin Li want -0x1.ffe9537d5dbb4p-3. */
43*412f47f9SXin Li static inline svfloat64x2_t
sv_sincos_inline(svbool_t pg,svfloat64_t x,const struct sv_sincos_data * d)44*412f47f9SXin Li sv_sincos_inline (svbool_t pg, svfloat64_t x, const struct sv_sincos_data *d)
45*412f47f9SXin Li {
46*412f47f9SXin Li /* q = nearest integer to 2 * x / pi. */
47*412f47f9SXin Li svfloat64_t q = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_pio2),
48*412f47f9SXin Li d->shift);
49*412f47f9SXin Li svint64_t n = svcvt_s64_x (pg, q);
50*412f47f9SXin Li
51*412f47f9SXin Li /* Reduce x such that r is in [ -pi/4, pi/4 ]. */
52*412f47f9SXin Li svfloat64_t r = x;
53*412f47f9SXin Li r = svmls_x (pg, r, q, d->pio2[0]);
54*412f47f9SXin Li r = svmls_x (pg, r, q, d->pio2[1]);
55*412f47f9SXin Li r = svmls_x (pg, r, q, d->pio2[2]);
56*412f47f9SXin Li
57*412f47f9SXin Li svfloat64_t r2 = svmul_x (pg, r, r), r3 = svmul_x (pg, r2, r),
58*412f47f9SXin Li r4 = svmul_x (pg, r2, r2);
59*412f47f9SXin Li
60*412f47f9SXin Li /* Approximate sin(r) ~= r + r^3 * poly_sin(r^2). */
61*412f47f9SXin Li svfloat64_t s = sv_pw_horner_6_f64_x (pg, r2, r4, d->sin_poly);
62*412f47f9SXin Li s = svmla_x (pg, r, r3, s);
63*412f47f9SXin Li
64*412f47f9SXin Li /* Approximate cos(r) ~= 1 - (r^2)/2 + r^4 * poly_cos(r^2). */
65*412f47f9SXin Li svfloat64_t c = sv_pw_horner_5_f64_x (pg, r2, r4, d->cos_poly);
66*412f47f9SXin Li c = svmad_x (pg, c, r2, -0.5);
67*412f47f9SXin Li c = svmad_x (pg, c, r2, 1);
68*412f47f9SXin Li
69*412f47f9SXin Li svuint64_t un = svreinterpret_u64 (n);
70*412f47f9SXin Li /* If odd quadrant, swap cos and sin. */
71*412f47f9SXin Li svbool_t swap = svcmpeq (pg, svlsl_x (pg, un, 63), 0);
72*412f47f9SXin Li svfloat64_t ss = svsel (swap, s, c);
73*412f47f9SXin Li svfloat64_t cc = svsel (swap, c, s);
74*412f47f9SXin Li
75*412f47f9SXin Li /* Fix signs according to quadrant.
76*412f47f9SXin Li ss = asdouble(asuint64(ss) ^ ((n & 2) << 62))
77*412f47f9SXin Li cc = asdouble(asuint64(cc) & (((n + 1) & 2) << 62)). */
78*412f47f9SXin Li svuint64_t sin_sign = svlsl_x (pg, svand_x (pg, un, 2), 62);
79*412f47f9SXin Li svuint64_t cos_sign = svlsl_x (
80*412f47f9SXin Li pg, svand_x (pg, svreinterpret_u64 (svadd_x (pg, n, 1)), 2), 62);
81*412f47f9SXin Li ss = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ss), sin_sign));
82*412f47f9SXin Li cc = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (cc), cos_sign));
83*412f47f9SXin Li
84*412f47f9SXin Li return svcreate2 (ss, cc);
85*412f47f9SXin Li }
86