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 #ifdef __i386__
32 #include <ieeefp.h>
33 #endif
34 #include <stdint.h>
35
36 #include "fpmath.h"
37 #include "math.h"
38 #include "math_private.h"
39
40 static const double
41 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
42 pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
43
44 #include "k_cospil.h"
45 #include "k_sinpil.h"
46
47 volatile static const double vzero = 0;
48
49 long double
cospil(long double x)50 cospil(long double x)
51 {
52 long double ax, c;
53 uint64_t lx, m;
54 uint32_t j0;
55 uint16_t hx, ix;
56
57 EXTRACT_LDBL80_WORDS(hx, lx, x);
58 ix = hx & 0x7fff;
59 INSERT_LDBL80_WORDS(ax, ix, lx);
60
61 ENTERI();
62
63 if (ix < 0x3fff) { /* |x| < 1 */
64 if (ix < 0x3ffd) { /* |x| < 0.25 */
65 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
66 if ((int)x == 0)
67 RETURNI(1);
68 }
69 RETURNI(__kernel_cospil(ax));
70 }
71
72 if (ix < 0x3ffe) /* |x| < 0.5 */
73 c = __kernel_sinpil(0.5 - ax);
74 else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
75 if (ax == 0.5)
76 RETURNI(0);
77 c = -__kernel_sinpil(ax - 0.5);
78 } else
79 c = -__kernel_cospil(1 - ax);
80 RETURNI(c);
81 }
82
83 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
84 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
85 ax -= x;
86 EXTRACT_LDBL80_WORDS(ix, lx, ax);
87
88 if (ix < 0x3ffe) { /* |x| < 0.5 */
89 if (ix < 0x3ffd) /* |x| < 0.25 */
90 c = ix == 0 ? 1 : __kernel_cospil(ax);
91 else
92 c = __kernel_sinpil(0.5 - ax);
93
94 } else {
95 if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
96 if (ax == 0.5)
97 RETURNI(0);
98 c = -__kernel_sinpil(ax - 0.5);
99 } else
100 c = -__kernel_cospil(1 - ax);
101 }
102
103 if (j0 > 40)
104 x -= 0x1p40;
105 if (j0 > 30)
106 x -= 0x1p30;
107 j0 = (uint32_t)x;
108
109 RETURNI(j0 & 1 ? -c : c);
110 }
111
112 if (ix >= 0x7fff)
113 RETURNI(vzero / vzero);
114
115 /*
116 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
117 * or odd integer to return t = +1 or -1.
118 * For |x| >= 0x1p64, it is always an even integer, so t = 1.
119 */
120 RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1));
121 }
122