1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision scalar sinpi 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 #define _GNU_SOURCE
9*f3087befSAndrew Turner #include <math.h>
10*f3087befSAndrew Turner #include "mathlib.h"
11*f3087befSAndrew Turner #include "math_config.h"
12*f3087befSAndrew Turner #include "test_sig.h"
13*f3087befSAndrew Turner #include "test_defs.h"
14*f3087befSAndrew Turner #include "poly_scalar_f64.h"
15*f3087befSAndrew Turner
16*f3087befSAndrew Turner /* Taylor series coefficents for sin(pi * x).
17*f3087befSAndrew Turner C2 coefficient (orginally ~=5.16771278) has been split into two parts:
18*f3087befSAndrew Turner C2_hi = 4, C2_lo = C2 - C2_hi (~=1.16771278)
19*f3087befSAndrew Turner This change in magnitude reduces floating point rounding errors.
20*f3087befSAndrew Turner C2_hi is then reintroduced after the polynomial approxmation. */
21*f3087befSAndrew Turner static const double poly[]
22*f3087befSAndrew Turner = { 0x1.921fb54442d184p1, -0x1.2aef39896f94bp0, 0x1.466bc6775ab16p1,
23*f3087befSAndrew Turner -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
24*f3087befSAndrew Turner 0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16, 0x1.af86ae521260bp-21,
25*f3087befSAndrew Turner -0x1.012a9870eeb7dp-25 };
26*f3087befSAndrew Turner
27*f3087befSAndrew Turner #define Shift 0x1.8p+52
28*f3087befSAndrew Turner /* TODO Store constant in structure for more efficient load. */
29*f3087befSAndrew Turner #define Pi 0x1.921fb54442d18p+1
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner /* Approximation for scalar double-precision sinpi(x).
32*f3087befSAndrew Turner Maximum error: 3.03 ULP:
33*f3087befSAndrew Turner sinpi(0x1.a90da2818f8b5p+7) got 0x1.fe358f255a4b3p-1
34*f3087befSAndrew Turner want 0x1.fe358f255a4b6p-1. */
35*f3087befSAndrew Turner double
arm_math_sinpi(double x)36*f3087befSAndrew Turner arm_math_sinpi (double x)
37*f3087befSAndrew Turner {
38*f3087befSAndrew Turner if (isinf (x) || isnan (x))
39*f3087befSAndrew Turner return __math_invalid (x);
40*f3087befSAndrew Turner
41*f3087befSAndrew Turner double r = asdouble (asuint64 (x) & ~0x8000000000000000);
42*f3087befSAndrew Turner uint64_t sign = asuint64 (x) & 0x8000000000000000;
43*f3087befSAndrew Turner
44*f3087befSAndrew Turner /* Edge cases for when sinpif should be exactly 0. (Integers)
45*f3087befSAndrew Turner 0x1p53 is the limit for single precision to store any decimal places. */
46*f3087befSAndrew Turner if (r >= 0x1p53)
47*f3087befSAndrew Turner return asdouble (sign);
48*f3087befSAndrew Turner
49*f3087befSAndrew Turner /* If x is an integer, return 0. */
50*f3087befSAndrew Turner uint64_t m = (uint64_t) r;
51*f3087befSAndrew Turner if (r == m)
52*f3087befSAndrew Turner return asdouble (sign);
53*f3087befSAndrew Turner
54*f3087befSAndrew Turner /* For very small inputs, squaring r causes underflow.
55*f3087befSAndrew Turner Values below this threshold can be approximated via sinpi(x) ≈ pi*x. */
56*f3087befSAndrew Turner if (r < 0x1p-63)
57*f3087befSAndrew Turner return Pi * x;
58*f3087befSAndrew Turner
59*f3087befSAndrew Turner /* Any non-integer values >= 0x1x51 will be int + 0.5.
60*f3087befSAndrew Turner These values should return exactly 1 or -1. */
61*f3087befSAndrew Turner if (r >= 0x1p51)
62*f3087befSAndrew Turner {
63*f3087befSAndrew Turner uint64_t iy = ((m & 1) << 63) ^ asuint64 (1.0);
64*f3087befSAndrew Turner return asdouble (sign ^ iy);
65*f3087befSAndrew Turner }
66*f3087befSAndrew Turner
67*f3087befSAndrew Turner /* n = rint(|x|). */
68*f3087befSAndrew Turner double n = r + Shift;
69*f3087befSAndrew Turner sign ^= (asuint64 (n) << 63);
70*f3087befSAndrew Turner n = n - Shift;
71*f3087befSAndrew Turner
72*f3087befSAndrew Turner /* r = |x| - n (range reduction into -1/2 .. 1/2). */
73*f3087befSAndrew Turner r = r - n;
74*f3087befSAndrew Turner
75*f3087befSAndrew Turner /* y = sin(r). */
76*f3087befSAndrew Turner double r2 = r * r;
77*f3087befSAndrew Turner double y = horner_9_f64 (r2, poly);
78*f3087befSAndrew Turner y = y * r;
79*f3087befSAndrew Turner
80*f3087befSAndrew Turner /* Reintroduce C2_hi. */
81*f3087befSAndrew Turner y = fma (-4 * r2, r, y);
82*f3087befSAndrew Turner
83*f3087befSAndrew Turner /* Copy sign of x to sin(|x|). */
84*f3087befSAndrew Turner return asdouble (asuint64 (y) ^ sign);
85*f3087befSAndrew Turner }
86*f3087befSAndrew Turner
87*f3087befSAndrew Turner #if WANT_EXPERIMENTAL_MATH
88*f3087befSAndrew Turner double
sinpi(double x)89*f3087befSAndrew Turner sinpi (double x)
90*f3087befSAndrew Turner {
91*f3087befSAndrew Turner return arm_math_sinpi (x);
92*f3087befSAndrew Turner }
93*f3087befSAndrew Turner #endif
94*f3087befSAndrew Turner
95*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS
96*f3087befSAndrew Turner TEST_ULP (arm_math_sinpi, 2.53)
97*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_sinpi, 0, 0x1p-63, 5000)
98*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_sinpi, 0x1p-63, 0.5, 10000)
99*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_sinpi, 0.5, 0x1p51, 10000)
100*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_sinpi, 0x1p51, inf, 10000)
101*f3087befSAndrew Turner #endif
102