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
|
/*-
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
* 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, 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 AND CONTRIBUTORS ``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 OR CONTRIBUTORS 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: head/lib/msun/src/k_exp.c 275819 2014-12-16 09:21:56Z ed $");
#include <complex.h>
#include "math.h"
#include "math_private.h"
static const uint32_t k = 1799; /* constant for reduction */
static const double kln2 = 1246.97177782734161156; /* k * ln2 */
/*
* Compute exp(x), scaled to avoid spurious overflow. An exponent is
* returned separately in 'expt'.
*
* Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
* Output: 2**1023 <= y < 2**1024
*/
static double
__frexp_exp(double x, int *expt)
{
double exp_x;
uint32_t hx;
/*
* We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
* minimize |exp(kln2) - 2**k|. We also scale the exponent of
* exp_x to MAX_EXP so that the result can be multiplied by
* a tiny number without losing accuracy due to denormalization.
*/
exp_x = exp(x - kln2);
GET_HIGH_WORD(hx, exp_x);
*expt = (hx >> 20) - (0x3ff + 1023) + k;
SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
return (exp_x);
}
/*
* __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
* They are intended for large arguments (real part >= ln(DBL_MAX))
* where care is needed to avoid overflow.
*
* The present implementation is narrowly tailored for our hyperbolic and
* exponential functions. We assume expt is small (0 or -1), and the caller
* has filtered out very large x, for which overflow would be inevitable.
*/
double
__ldexp_exp(double x, int expt)
{
double exp_x, scale;
int ex_expt;
exp_x = __frexp_exp(x, &ex_expt);
expt += ex_expt;
INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
return (exp_x * scale);
}
double complex
__ldexp_cexp(double complex z, int expt)
{
double x, y, exp_x, scale1, scale2;
int ex_expt, half_expt;
x = creal(z);
y = cimag(z);
exp_x = __frexp_exp(x, &ex_expt);
expt += ex_expt;
/*
* Arrange so that scale1 * scale2 == 2**expt. We use this to
* compensate for scalbn being horrendously slow.
*/
half_expt = expt / 2;
INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
half_expt = expt - half_expt;
INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
return (CMPLX(cos(y) * exp_x * scale1 * scale2,
sin(y) * exp_x * scale1 * scale2));
}
|
