1 /*
2 * Core approximation for single-precision vector sincos
3 *
4 * Copyright (c) 2023-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9
10 const static struct sv_sincosf_data
11 {
12 float poly_sin[3], poly_cos[3], pio2[3], inv_pio2, shift, range_val;
13 } sv_sincosf_data = {
14 .poly_sin = { /* Generated using Remez, odd coeffs only, in [-pi/4, pi/4]. */
15 -0x1.555546p-3, 0x1.11076p-7, -0x1.994eb4p-13 },
16 .poly_cos = { /* Generated using Remez, even coeffs only, in [-pi/4, pi/4]. */
17 0x1.55554ap-5, -0x1.6c0c1ap-10, 0x1.99e0eep-16 },
18 .pio2 = { 0x1.921fb6p+0f, -0x1.777a5cp-25f, -0x1.ee59dap-50f },
19 .inv_pio2 = 0x1.45f306p-1f,
20 .shift = 0x1.8p23,
21 .range_val = 0x1p20
22 };
23
24 static inline svbool_t
check_ge_rangeval(svbool_t pg,svfloat32_t x,const struct sv_sincosf_data * d)25 check_ge_rangeval (svbool_t pg, svfloat32_t x, const struct sv_sincosf_data *d)
26 {
27 svbool_t in_bounds = svaclt (pg, x, d->range_val);
28 return svnot_z (pg, in_bounds);
29 }
30
31 /* Single-precision vector function allowing calculation of both sin and cos in
32 one function call, using shared argument reduction and separate low-order
33 polynomials.
34 Worst-case error for sin is 1.67 ULP:
35 sv_sincosf_sin(0x1.c704c4p+19) got 0x1.fff698p-5 want 0x1.fff69cp-5
36 Worst-case error for cos is 1.81 ULP:
37 sv_sincosf_cos(0x1.e506fp+19) got -0x1.ffec6ep-6 want -0x1.ffec72p-6. */
38 static inline svfloat32x2_t
sv_sincosf_inline(svbool_t pg,svfloat32_t x,const struct sv_sincosf_data * d)39 sv_sincosf_inline (svbool_t pg, svfloat32_t x, const struct sv_sincosf_data *d)
40 {
41 /* n = rint ( x / (pi/2) ). */
42 svfloat32_t q = svmla_x (pg, sv_f32 (d->shift), x, d->inv_pio2);
43 q = svsub_x (pg, q, d->shift);
44 svint32_t n = svcvt_s32_x (pg, q);
45
46 /* Reduce x such that r is in [ -pi/4, pi/4 ]. */
47 svfloat32_t r = x;
48 r = svmls_x (pg, r, q, d->pio2[0]);
49 r = svmls_x (pg, r, q, d->pio2[1]);
50 r = svmls_x (pg, r, q, d->pio2[2]);
51
52 /* Approximate sin(r) ~= r + r^3 * poly_sin(r^2). */
53 svfloat32_t r2 = svmul_x (pg, r, r), r3 = svmul_x (pg, r, r2);
54 svfloat32_t s = svmla_x (pg, sv_f32 (d->poly_sin[1]), r2, d->poly_sin[2]);
55 s = svmad_x (pg, r2, s, d->poly_sin[0]);
56 s = svmla_x (pg, r, r3, s);
57
58 /* Approximate cos(r) ~= 1 - (r^2)/2 + r^4 * poly_cos(r^2). */
59 svfloat32_t r4 = svmul_x (pg, r2, r2);
60 svfloat32_t p = svmla_x (pg, sv_f32 (d->poly_cos[1]), r2, d->poly_cos[2]);
61 svfloat32_t c = svmad_x (pg, sv_f32 (d->poly_cos[0]), r2, -0.5);
62 c = svmla_x (pg, c, r4, p);
63 c = svmad_x (pg, r2, c, 1);
64
65 svuint32_t un = svreinterpret_u32 (n);
66 /* If odd quadrant, swap cos and sin. */
67 svbool_t swap = svcmpeq (pg, svlsl_x (pg, un, 31), 0);
68 svfloat32_t ss = svsel (swap, s, c);
69 svfloat32_t cc = svsel (swap, c, s);
70
71 /* Fix signs according to quadrant.
72 ss = asfloat(asuint(ss) ^ ((n & 2) << 30))
73 cc = asfloat(asuint(cc) & (((n + 1) & 2) << 30)). */
74 svuint32_t sin_sign = svlsl_x (pg, svand_x (pg, un, 2), 30);
75 svuint32_t cos_sign = svlsl_x (
76 pg, svand_x (pg, svreinterpret_u32 (svadd_x (pg, n, 1)), 2), 30);
77 ss = svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ss), sin_sign));
78 cc = svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (cc), cos_sign));
79
80 return svcreate2 (ss, cc);
81 }
82