1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
|
/*-
* Copyright (c) 2007 Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* Compute cos(x) for x where x is reduced to y = x - k * pi / 2.
* Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows
* an accuracy of <= 0.7412 ULP.
*/
#include <float.h>
#include "math.h"
#include "math_private.h"
#include "fpmath.h"
#if LDBL_MANT_DIG == 64
#define NX 3
#define PREC 2
#elif LDBL_MANT_DIG == 113
#define NX 5
#define PREC 3
#else
#error "Unsupported long double format"
#endif
static const long double two24 = 1.67772160000000000000e+07L;
long double
cosl(long double x)
{
union IEEEl2bits z;
int i, e0;
double xd[NX], yd[PREC];
long double hi, lo;
z.e = x;
z.bits.sign = 0;
/* If x = +-0 or x is a subnormal number, then cos(x) = 1 */
if (z.bits.exp == 0)
return (1.0);
/* If x = NaN or Inf, then cos(x) = NaN. */
if (z.bits.exp == 32767)
return ((x - x) / (x - x));
/* Optimize the case where x is already within range. */
if (z.e < M_PI_4)
return (__kernel_cosl(z.e, 0));
/* Split z.e into a 24-bit representation. */
e0 = ilogbl(z.e) - 23;
z.e = scalbnl(z.e, -e0);
for (i = 0; i < NX; i++) {
xd[i] = (double)((int32_t)z.e);
z.e = (z.e - xd[i]) * two24;
}
/* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);
#if PREC == 2
hi = (long double)yd[0] + yd[1];
lo = yd[1] - (hi - yd[0]);
#else /* PREC == 3 */
long double t;
t = (long double)yd[2] + yd[1];
hi = t + yd[0];
lo = yd[0] - (hi - t);
#endif
switch (e0 & 3) {
case 0:
hi = __kernel_cosl(hi, lo);
break;
case 1:
hi = - __kernel_sinl(hi, lo, 1);
break;
case 2:
hi = - __kernel_cosl(hi, lo);
break;
case 3:
hi = __kernel_sinl(hi, lo, 1);
break;
}
return (hi);
}
|
