1 /*-
2 * Copyright (c) 2007 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 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD$");
29
30 /*
31 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows
32 * an accuracy of <= 0.7412 ULP.
33 */
34
35 #include <float.h>
36 #ifdef __i386__
37 #include <ieeefp.h>
38 #endif
39
40 #include "math.h"
41 #include "math_private.h"
42 #if LDBL_MANT_DIG == 64
43 #include "../ld80/e_rem_pio2l.h"
44 #elif LDBL_MANT_DIG == 113
45 #include "../ld128/e_rem_pio2l.h"
46 #else
47 #error "Unsupported long double format"
48 #endif
49
50 long double
cosl(long double x)51 cosl(long double x)
52 {
53 union IEEEl2bits z;
54 int e0;
55 long double y[2];
56 long double hi, lo;
57
58 z.e = x;
59 z.bits.sign = 0;
60
61 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */
62 if (z.bits.exp == 0)
63 return (1.0);
64
65 /* If x = NaN or Inf, then cos(x) = NaN. */
66 if (z.bits.exp == 32767)
67 return ((x - x) / (x - x));
68
69 ENTERI();
70
71 /* Optimize the case where x is already within range. */
72 if (z.e < M_PI_4)
73 RETURNI(__kernel_cosl(z.e, 0));
74
75 e0 = __ieee754_rem_pio2l(x, y);
76 hi = y[0];
77 lo = y[1];
78
79 switch (e0 & 3) {
80 case 0:
81 hi = __kernel_cosl(hi, lo);
82 break;
83 case 1:
84 hi = - __kernel_sinl(hi, lo, 1);
85 break;
86 case 2:
87 hi = - __kernel_cosl(hi, lo);
88 break;
89 case 3:
90 hi = __kernel_sinl(hi, lo, 1);
91 break;
92 }
93
94 RETURNI(hi);
95 }
96