1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision vector cospi function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2023-2024, 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 "mathlib.h"
9*f3087befSAndrew Turner #include "v_math.h"
10*f3087befSAndrew Turner #include "v_poly_f64.h"
11*f3087befSAndrew Turner #include "test_sig.h"
12*f3087befSAndrew Turner #include "test_defs.h"
13*f3087befSAndrew Turner
14*f3087befSAndrew Turner static const struct data
15*f3087befSAndrew Turner {
16*f3087befSAndrew Turner float64x2_t poly[10];
17*f3087befSAndrew Turner float64x2_t range_val;
18*f3087befSAndrew Turner } data = {
19*f3087befSAndrew Turner /* Polynomial coefficients generated using Remez algorithm,
20*f3087befSAndrew Turner see sinpi.sollya for details. */
21*f3087befSAndrew Turner .poly = { V2 (0x1.921fb54442d184p1), V2 (-0x1.4abbce625be53p2),
22*f3087befSAndrew Turner V2 (0x1.466bc6775ab16p1), V2 (-0x1.32d2cce62dc33p-1),
23*f3087befSAndrew Turner V2 (0x1.507834891188ep-4), V2 (-0x1.e30750a28c88ep-8),
24*f3087befSAndrew Turner V2 (0x1.e8f48308acda4p-12), V2 (-0x1.6fc0032b3c29fp-16),
25*f3087befSAndrew Turner V2 (0x1.af86ae521260bp-21), V2 (-0x1.012a9870eeb7dp-25) },
26*f3087befSAndrew Turner .range_val = V2 (0x1p63),
27*f3087befSAndrew Turner };
28*f3087befSAndrew Turner
29*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE
special_case(float64x2_t x,float64x2_t y,uint64x2_t odd,uint64x2_t cmp)30*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
31*f3087befSAndrew Turner {
32*f3087befSAndrew Turner /* Fall back to scalar code. */
33*f3087befSAndrew Turner y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
34*f3087befSAndrew Turner return v_call_f64 (arm_math_cospi, x, y, cmp);
35*f3087befSAndrew Turner }
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner /* Approximation for vector double-precision cospi(x).
38*f3087befSAndrew Turner Maximum Error 3.06 ULP:
39*f3087befSAndrew Turner _ZGVnN2v_cospi(0x1.7dd4c0b03cc66p-5) got 0x1.fa854babfb6bep-1
40*f3087befSAndrew Turner want 0x1.fa854babfb6c1p-1. */
V_NAME_D1(cospi)41*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (cospi) (float64x2_t x)
42*f3087befSAndrew Turner {
43*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
44*f3087befSAndrew Turner
45*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT
46*f3087befSAndrew Turner float64x2_t r = vabsq_f64 (x);
47*f3087befSAndrew Turner uint64x2_t cmp = vcaleq_f64 (v_f64 (0x1p64), x);
48*f3087befSAndrew Turner
49*f3087befSAndrew Turner /* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd
50*f3087befSAndrew Turner to avoid them overflowing and throwing exceptions. */
51*f3087befSAndrew Turner r = v_zerofy_f64 (r, cmp);
52*f3087befSAndrew Turner uint64x2_t odd = vshlq_n_u64 (vcvtnq_u64_f64 (r), 63);
53*f3087befSAndrew Turner
54*f3087befSAndrew Turner #else
55*f3087befSAndrew Turner float64x2_t r = x;
56*f3087befSAndrew Turner uint64x2_t cmp = vcageq_f64 (r, d->range_val);
57*f3087befSAndrew Turner uint64x2_t odd
58*f3087befSAndrew Turner = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtaq_s64_f64 (r)), 63);
59*f3087befSAndrew Turner
60*f3087befSAndrew Turner #endif
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner r = vsubq_f64 (r, vrndaq_f64 (r));
63*f3087befSAndrew Turner
64*f3087befSAndrew Turner /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */
65*f3087befSAndrew Turner r = vsubq_f64 (v_f64 (0.5), vabsq_f64 (r));
66*f3087befSAndrew Turner
67*f3087befSAndrew Turner /* y = sin(r). */
68*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r);
69*f3087befSAndrew Turner float64x2_t r4 = vmulq_f64 (r2, r2);
70*f3087befSAndrew Turner float64x2_t y = vmulq_f64 (v_pw_horner_9_f64 (r2, r4, d->poly), r);
71*f3087befSAndrew Turner
72*f3087befSAndrew Turner /* Fallback to scalar. */
73*f3087befSAndrew Turner if (unlikely (v_any_u64 (cmp)))
74*f3087befSAndrew Turner return special_case (x, y, odd, cmp);
75*f3087befSAndrew Turner
76*f3087befSAndrew Turner /* Reintroduce the sign bit for inputs which round to odd. */
77*f3087befSAndrew Turner return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
78*f3087befSAndrew Turner }
79*f3087befSAndrew Turner
80*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS
81*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (cospi), 2.56)
82*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (cospi), WANT_SIMD_EXCEPT)
83*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0, 0x1p-63, 5000)
84*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p-63, 0.5, 10000)
85*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0.5, 0x1p51, 10000)
86*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p51, inf, 10000)
87*f3087befSAndrew Turner #endif
88