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 <stdint.h>
32
33 #include "math.h"
34 #include "math_private.h"
35
36 static const double
37 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
38 pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
39
40 #include "k_cospil.h"
41 #include "k_sinpil.h"
42
43 static volatile const double vzero = 0;
44
45 long double
cospil(long double x)46 cospil(long double x)
47 {
48 long double ax, c;
49 uint64_t lx;
50 uint32_t j0;
51 uint16_t hx, ix;
52
53 EXTRACT_LDBL80_WORDS(hx, lx, x);
54 ix = hx & 0x7fff;
55 INSERT_LDBL80_WORDS(ax, ix, lx);
56
57 ENTERI();
58
59 if (ix < 0x3fff) { /* |x| < 1 */
60 if (ix < 0x3ffd) { /* |x| < 0.25 */
61 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
62 if ((int)x == 0)
63 RETURNI(1);
64 }
65 RETURNI(__kernel_cospil(ax));
66 }
67
68 if (ix < 0x3ffe) /* |x| < 0.5 */
69 c = __kernel_sinpil(0.5 - ax);
70 else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
71 if (ax == 0.5)
72 RETURNI(0);
73 c = -__kernel_sinpil(ax - 0.5);
74 } else
75 c = -__kernel_cospil(1 - ax);
76 RETURNI(c);
77 }
78
79 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
80 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
81 ax -= x;
82 EXTRACT_LDBL80_WORDS(ix, lx, ax);
83
84 if (ix < 0x3ffe) { /* |x| < 0.5 */
85 if (ix < 0x3ffd) /* |x| < 0.25 */
86 c = ix == 0 ? 1 : __kernel_cospil(ax);
87 else
88 c = __kernel_sinpil(0.5 - ax);
89
90 } else {
91 if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
92 if (ax == 0.5)
93 RETURNI(0);
94 c = -__kernel_sinpil(ax - 0.5);
95 } else
96 c = -__kernel_cospil(1 - ax);
97 }
98
99 if (j0 > 40)
100 x -= 0x1p40;
101 if (j0 > 30)
102 x -= 0x1p30;
103 j0 = (uint32_t)x;
104
105 RETURNI(j0 & 1 ? -c : c);
106 }
107
108 if (ix >= 0x7fff)
109 RETURNI(vzero / vzero);
110
111 /*
112 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
113 * or odd integer to return t = +1 or -1.
114 * For |x| >= 0x1p64, it is always an even integer, so t = 1.
115 */
116 RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1));
117 }
118