1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
3 *
4 * Copyright (c) 2007 Steven G. Kargl
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice unmodified, this list of conditions, and the following
12 * disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 * notice, this list of conditions and the following disclaimer in the
15 * documentation and/or other materials provided with the distribution.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27 */
28
29 #include <sys/cdefs.h>
30 __FBSDID("$FreeBSD$");
31
32 /*
33 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows
34 * an accuracy of <= 0.7412 ULP.
35 */
36
37 #include <float.h>
38 #ifdef __i386__
39 #include <ieeefp.h>
40 #endif
41
42 #include "math.h"
43 #include "math_private.h"
44 #if LDBL_MANT_DIG == 64
45 #include "../ld80/e_rem_pio2l.h"
46 #elif LDBL_MANT_DIG == 113
47 #include "../ld128/e_rem_pio2l.h"
48 #else
49 #error "Unsupported long double format"
50 #endif
51
52 long double
cosl(long double x)53 cosl(long double x)
54 {
55 union IEEEl2bits z;
56 int e0;
57 long double y[2];
58 long double hi, lo;
59
60 z.e = x;
61 z.bits.sign = 0;
62
63 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */
64 if (z.bits.exp == 0)
65 return (1.0);
66
67 /* If x = NaN or Inf, then cos(x) = NaN. */
68 if (z.bits.exp == 32767)
69 return ((x - x) / (x - x));
70
71 ENTERI();
72
73 /* Optimize the case where x is already within range. */
74 if (z.e < M_PI_4)
75 RETURNI(__kernel_cosl(z.e, 0));
76
77 e0 = __ieee754_rem_pio2l(x, y);
78 hi = y[0];
79 lo = y[1];
80
81 switch (e0 & 3) {
82 case 0:
83 hi = __kernel_cosl(hi, lo);
84 break;
85 case 1:
86 hi = - __kernel_sinl(hi, lo, 1);
87 break;
88 case 2:
89 hi = - __kernel_cosl(hi, lo);
90 break;
91 case 3:
92 hi = __kernel_sinl(hi, lo, 1);
93 break;
94 }
95
96 RETURNI(hi);
97 }
98