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 "fpmath.h"
43 #include "math.h"
44 #include "math_private.h"
45 #if LDBL_MANT_DIG == 64
46 #include "../ld80/e_rem_pio2l.h"
47 static const union IEEEl2bits
48 pio4u = LD80C(0xc90fdaa22168c235, -00001, 7.85398163397448309628e-01L);
49 #define pio4 (pio4u.e)
50 #elif LDBL_MANT_DIG == 113
51 #include "../ld128/e_rem_pio2l.h"
52 long double pio4 = 7.85398163397448309615660845819875721e-1L;
53 #else
54 #error "Unsupported long double format"
55 #endif
56
57 long double
cosl(long double x)58 cosl(long double x)
59 {
60 union IEEEl2bits z;
61 int e0;
62 long double y[2];
63 long double hi, lo;
64
65 z.e = x;
66 z.bits.sign = 0;
67
68 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */
69 if (z.bits.exp == 0)
70 return (1.0);
71
72 /* If x = NaN or Inf, then cos(x) = NaN. */
73 if (z.bits.exp == 32767)
74 return ((x - x) / (x - x));
75
76 ENTERI();
77
78 /* Optimize the case where x is already within range. */
79 if (z.e < pio4)
80 RETURNI(__kernel_cosl(z.e, 0));
81
82 e0 = __ieee754_rem_pio2l(x, y);
83 hi = y[0];
84 lo = y[1];
85
86 switch (e0 & 3) {
87 case 0:
88 hi = __kernel_cosl(hi, lo);
89 break;
90 case 1:
91 hi = - __kernel_sinl(hi, lo, 1);
92 break;
93 case 2:
94 hi = - __kernel_cosl(hi, lo);
95 break;
96 case 3:
97 hi = __kernel_sinl(hi, lo, 1);
98 break;
99 }
100
101 RETURNI(hi);
102 }
103