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
115
116
117
118
119
120
121
122
|
/*-
* Copyright (c) 2017-2023 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.
*/
/*
* See ../src/s_tanpi.c for implementation details.
*/
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
/*
* pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
*/
static const long double
pi_hi = 3.14159265358979322702026593105983920e+00L,
pi_lo = 1.14423774522196636802434264184180742e-17L;
static inline long double
__kernel_tanpil(long double x)
{
long double hi, lo, t;
if (x < 0.25) {
hi = (double)x;
lo = x - hi;
lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
hi *= pi_hi;
_2sumF(hi, lo);
t = __kernel_tanl(hi, lo, -1);
} else if (x > 0.25) {
x = 0.5 - x;
hi = (double)x;
lo = x - hi;
lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
hi *= pi_hi;
_2sumF(hi, lo);
t = - __kernel_tanl(hi, lo, 1);
} else
t = 1;
return (t);
}
volatile static const double vzero = 0;
long double
tanpil(long double x)
{
long double ai, ar, ax, hi, lo, t;
double odd;
ax = fabsl(x);
if (ax < 1) {
if (ax < 0.5) {
if (ax < 0x1p-60) {
if (x == 0)
return (x);
hi = (double)x;
hi *= 0x1p113L;
lo = x * 0x1p113L - hi;
t = (pi_lo + pi_hi) * lo + pi_lo * lo +
pi_hi * hi;
return (t * 0x1p-113L);
}
t = __kernel_tanpil(ax);
} else if (ax == 0.5)
t = 1 / vzero;
else
t = -__kernel_tanpil(1 - ax);
return (x < 0 ? -t : t);
}
if (ax < 0x1p112) {
/* Split ax = ai + ar with 0 <= ar < 1. */
FFLOORL128(ax, ai, ar);
odd = fmodl(ai, 2.L) == 0 ? 1 : -1;
if (ar < 0.5)
t = ar == 0 ? copysign(0., odd) : __kernel_tanpil(ar);
else if (ar == 0.5)
t = odd / vzero;
else
t = -__kernel_tanpil(1 - ar);
return (x < 0 ? -t : t);
}
/* x = +-inf or nan. */
if (isinf(x) || isnan(x))
return (vzero / vzero);
/*
* For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
* or odd integer to set t = +0 or -0.
* For |x| >= 0x1p113, it is always an even integer, so t = 0.
*/
t = fmodl(ax,2.L) == 0 ? 0 : copysign(0., -1.);
return (copysignl(t, x));
}
|
