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_cospi.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
cospil(long double x)47 cospil(long double x)
48 {
49 long double ai, ar, ax, c;
50
51 ax = fabsl(x);
52
53 if (ax <= 1) {
54 if (ax < 0.25) {
55 if (ax < 0x1p-60) {
56 if ((int)x == 0)
57 return (1);
58 }
59 return (__kernel_cospil(ax));
60 }
61
62 if (ax < 0.5)
63 c = __kernel_sinpil(0.5 - ax);
64 else if (ax < 0.75) {
65 if (ax == 0.5)
66 return (0);
67 c = -__kernel_sinpil(ax - 0.5);
68 } else
69 c = -__kernel_cospil(1 - ax);
70 return (c);
71 }
72
73 if (ax < 0x1p112) {
74 /* Split ax = ai + ar with 0 <= ar < 1. */
75 FFLOORL128(ax, ai, ar);
76
77 if (ar < 0.5) {
78 if (ar < 0.25)
79 c = ar == 0 ? 1 : __kernel_cospil(ar);
80 else
81 c = __kernel_sinpil(0.5 - ar);
82 } else {
83 if (ar < 0.75) {
84 if (ar == 0.5)
85 return (0);
86 c = -__kernel_sinpil(ar - 0.5);
87 } else
88 c = -__kernel_cospil(1 - ar);
89 }
90 return (fmodl(ai, 2.L) == 0 ? c : -c);
91 }
92
93 if (isinf(x) || isnan(x))
94 return (vzero / vzero);
95
96 /*
97 * For |x| >= 0x1p113, it is always an even integer, so return 1.
98 */
99 if (ax >= 0x1p113)
100 return (1);
101 /*
102 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
103 * or odd integer to return 1 or -1.
104 */
105
106 return (fmodl(ax, 2.L) == 0 ? 1 : -1);
107 }
108