1 /*
2 * Double-precision scalar sinpi function.
3 *
4 * Copyright (c) 2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #define _GNU_SOURCE
9 #include <math.h>
10 #include "mathlib.h"
11 #include "math_config.h"
12 #include "pl_sig.h"
13 #include "pl_test.h"
14 #include "poly_scalar_f64.h"
15
16 /* Taylor series coefficents for sin(pi * x).
17 C2 coefficient (orginally ~=5.16771278) has been split into two parts:
18 C2_hi = 4, C2_lo = C2 - C2_hi (~=1.16771278)
19 This change in magnitude reduces floating point rounding errors.
20 C2_hi is then reintroduced after the polynomial approxmation. */
21 static const double poly[]
22 = { 0x1.921fb54442d184p1, -0x1.2aef39896f94bp0, 0x1.466bc6775ab16p1,
23 -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
24 0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16, 0x1.af86ae521260bp-21,
25 -0x1.012a9870eeb7dp-25 };
26
27 #define Shift 0x1.8p+52
28
29 /* Approximation for scalar double-precision sinpi(x).
30 Maximum error: 3.03 ULP:
31 sinpi(0x1.a90da2818f8b5p+7) got 0x1.fe358f255a4b3p-1
32 want 0x1.fe358f255a4b6p-1. */
33 double
sinpi(double x)34 sinpi (double x)
35 {
36 if (isinf (x))
37 return __math_invalid (x);
38
39 double r = asdouble (asuint64 (x) & ~0x8000000000000000);
40 uint64_t sign = asuint64 (x) & 0x8000000000000000;
41
42 /* Edge cases for when sinpif should be exactly 0. (Integers)
43 0x1p53 is the limit for single precision to store any decimal places. */
44 if (r >= 0x1p53)
45 return 0;
46
47 /* If x is an integer, return 0. */
48 uint64_t m = (uint64_t) r;
49 if (r == m)
50 return 0;
51
52 /* For very small inputs, squaring r causes underflow.
53 Values below this threshold can be approximated via sinpi(x) ≈ pi*x. */
54 if (r < 0x1p-63)
55 return M_PI * x;
56
57 /* Any non-integer values >= 0x1x51 will be int + 0.5.
58 These values should return exactly 1 or -1. */
59 if (r >= 0x1p51)
60 {
61 uint64_t iy = ((m & 1) << 63) ^ asuint64 (1.0);
62 return asdouble (sign ^ iy);
63 }
64
65 /* n = rint(|x|). */
66 double n = r + Shift;
67 sign ^= (asuint64 (n) << 63);
68 n = n - Shift;
69
70 /* r = |x| - n (range reduction into -1/2 .. 1/2). */
71 r = r - n;
72
73 /* y = sin(r). */
74 double r2 = r * r;
75 double y = horner_9_f64 (r2, poly);
76 y = y * r;
77
78 /* Reintroduce C2_hi. */
79 y = fma (-4 * r2, r, y);
80
81 /* Copy sign of x to sin(|x|). */
82 return asdouble (asuint64 (y) ^ sign);
83 }
84
85 PL_SIG (S, D, 1, sinpi, -0.9, 0.9)
86 PL_TEST_ULP (sinpi, 2.53)
87 PL_TEST_SYM_INTERVAL (sinpi, 0, 0x1p-63, 5000)
88 PL_TEST_SYM_INTERVAL (sinpi, 0x1p-63, 0.5, 10000)
89 PL_TEST_SYM_INTERVAL (sinpi, 0.5, 0x1p51, 10000)
90 PL_TEST_SYM_INTERVAL (sinpi, 0x1p51, inf, 10000)
91