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 "fpmath.h"
32 #include "math.h"
33 #include "math_private.h"
34
35 /*
36 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
37 */
38 static const long double
39 pi_hi = 3.14159265358979322702026593105983920e+00L,
40 pi_lo = 1.14423774522196636802434264184180742e-17L;
41
42 #include "k_cospil.h"
43 #include "k_sinpil.h"
44
45 volatile static const double vzero = 0;
46
47 long double
sinpil(long double x)48 sinpil(long double x)
49 {
50 long double ai, ar, ax, hi, lo, s, xhi, xlo;
51
52 ax = fabsl(x);
53
54 if (ax < 1) {
55 if (ax < 0.25) {
56 if (ax < 0x1p-60) {
57 if (x == 0)
58 return (x);
59 hi = (double)x;
60 hi *= 0x1p113L;
61 lo = x * 0x1p113L - hi;
62 s = (pi_lo + pi_hi) * lo + pi_lo * lo +
63 pi_hi * hi;
64 return (s * 0x1p-113L);
65 }
66
67 s = __kernel_sinpil(ax);
68 return (x < 0 ? -s : s);
69 }
70
71 if (ax < 0.5)
72 s = __kernel_cospil(0.5 - ax);
73 else if (ax < 0.75)
74 s = __kernel_cospil(ax - 0.5);
75 else
76 s = __kernel_sinpil(1 - ax);
77 return (x < 0 ? -s : s);
78 }
79
80 if (ax < 0x1p112) {
81 /* Split ax = ai + ar with 0 <= ar < 1. */
82 FFLOORL128(ax, ai, ar);
83
84 if (ar == 0) {
85 s = 0;
86 } else {
87 if (ar < 0.5) {
88 if (ar <= 0.25)
89 s = __kernel_sinpil(ar);
90 else
91 s = __kernel_cospil(0.5 - ar);
92 } else {
93 if (ar < 0.75)
94 s = __kernel_cospil(ar - 0.5);
95 else
96 s = __kernel_sinpil(1 - ar);
97 }
98
99 s = fmodl(ai, 2.L) == 0 ? s : -s;
100 }
101 return (x < 0 ? -s : s);
102 }
103
104 if (isinf(x) || isnan(x))
105 return (vzero / vzero);
106
107 /*
108 * |x| >= 0x1p112 is always an integer, so return +-0.
109 */
110 return (copysignl(0, x));
111 }
112