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 "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
cospil(long double x)48 cospil(long double x)
49 {
50 long double ai, ar, ax, c;
51
52 ax = fabsl(x);
53
54 if (ax <= 1) {
55 if (ax < 0.25) {
56 if (ax < 0x1p-60) {
57 if ((int)x == 0)
58 return (1);
59 }
60 return (__kernel_cospil(ax));
61 }
62
63 if (ax < 0.5)
64 c = __kernel_sinpil(0.5 - ax);
65 else if (ax < 0.75) {
66 if (ax == 0.5)
67 return (0);
68 c = -__kernel_sinpil(ax - 0.5);
69 } else
70 c = -__kernel_cospil(1 - ax);
71 return (c);
72 }
73
74 if (ax < 0x1p112) {
75 /* Split ax = ai + ar with 0 <= ar < 1. */
76 FFLOORL128(ax, ai, ar);
77
78 if (ar < 0.5) {
79 if (ar < 0.25)
80 c = ar == 0 ? 1 : __kernel_cospil(ar);
81 else
82 c = __kernel_sinpil(0.5 - ar);
83 } else {
84 if (ar < 0.75) {
85 if (ar == 0.5)
86 return (0);
87 c = -__kernel_sinpil(ar - 0.5);
88 } else
89 c = -__kernel_cospil(1 - ar);
90 }
91 return (fmodl(ai, 2.L) == 0 ? c : -c);
92 }
93
94 if (isinf(x) || isnan(x))
95 return (vzero / vzero);
96
97 /*
98 * For |x| >= 0x1p113, it is always an even integer, so return 1.
99 */
100 if (ax >= 0x1p113)
101 return (1);
102 /*
103 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
104 * or odd integer to return 1 or -1.
105 */
106
107 return (fmodl(ax, 2.L) == 0 ? 1 : -1);
108 }
109