1 /*-
2 * Copyright (c) 2017-2023 Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice unmodified, this list of conditions, and the following
10 * disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27 /*
28 * See ../src/s_sinpi.c for implementation details.
29 */
30
31 #include "math.h"
32 #include "math_private.h"
33
34 /*
35 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
36 */
37 static const long double
38 pi_hi = 3.14159265358979322702026593105983920e+00L,
39 pi_lo = 1.14423774522196636802434264184180742e-17L;
40
41 #include "k_cospil.h"
42 #include "k_sinpil.h"
43
44 static volatile const double vzero = 0;
45
46 long double
sinpil(long double x)47 sinpil(long double x)
48 {
49 long double ai, ar, ax, hi, lo, s;
50
51 ax = fabsl(x);
52
53 if (ax < 1) {
54 if (ax < 0.25) {
55 if (ax < 0x1p-60) {
56 if (x == 0)
57 return (x);
58 hi = (double)x;
59 hi *= 0x1p113L;
60 lo = x * 0x1p113L - hi;
61 s = (pi_lo + pi_hi) * lo + pi_lo * lo +
62 pi_hi * hi;
63 return (s * 0x1p-113L);
64 }
65
66 s = __kernel_sinpil(ax);
67 return (x < 0 ? -s : s);
68 }
69
70 if (ax < 0.5)
71 s = __kernel_cospil(0.5 - ax);
72 else if (ax < 0.75)
73 s = __kernel_cospil(ax - 0.5);
74 else
75 s = __kernel_sinpil(1 - ax);
76 return (x < 0 ? -s : s);
77 }
78
79 if (ax < 0x1p112) {
80 /* Split ax = ai + ar with 0 <= ar < 1. */
81 FFLOORL128(ax, ai, ar);
82
83 if (ar == 0) {
84 s = 0;
85 } else {
86 if (ar < 0.5) {
87 if (ar <= 0.25)
88 s = __kernel_sinpil(ar);
89 else
90 s = __kernel_cospil(0.5 - ar);
91 } else {
92 if (ar < 0.75)
93 s = __kernel_cospil(ar - 0.5);
94 else
95 s = __kernel_sinpil(1 - ar);
96 }
97
98 s = fmodl(ai, 2.L) == 0 ? s : -s;
99 }
100 return (x < 0 ? -s : s);
101 }
102
103 if (isinf(x) || isnan(x))
104 return (vzero / vzero);
105
106 /*
107 * |x| >= 0x1p112 is always an integer, so return +-0.
108 */
109 return (copysignl(0, x));
110 }
111