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
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
/* Split a double into fraction and mantissa.
Copyright (C) 2007-2022 Free Software Foundation, Inc.
This file is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.
This file is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>. */
/* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and
Bruno Haible <bruno@clisp.org>, 2007. */
#if ! defined USE_LONG_DOUBLE
# include <config.h>
#endif
/* Specification. */
#include <math.h>
#include <float.h>
#ifdef USE_LONG_DOUBLE
# include "isnanl-nolibm.h"
# include "fpucw.h"
#else
# include "isnand-nolibm.h"
#endif
/* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater
than 2, or not even a power of 2, some rounding errors can occur, so that
then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0. */
#ifdef USE_LONG_DOUBLE
# define FUNC frexpl
# define DOUBLE long double
# define ISNAN isnanl
# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
# define L_(literal) literal##L
#else
# define FUNC frexp
# define DOUBLE double
# define ISNAN isnand
# define DECL_ROUNDING
# define BEGIN_ROUNDING()
# define END_ROUNDING()
# define L_(literal) literal
#endif
DOUBLE
FUNC (DOUBLE x, int *expptr)
{
int sign;
int exponent;
DECL_ROUNDING
/* Test for NaN, infinity, and zero. */
if (ISNAN (x) || x + x == x)
{
*expptr = 0;
return x;
}
sign = 0;
if (x < 0)
{
x = - x;
sign = -1;
}
BEGIN_ROUNDING ();
{
/* Since the exponent is an 'int', it fits in 64 bits. Therefore the
loops are executed no more than 64 times. */
DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
DOUBLE powh[64]; /* powh[i] = 2^-2^i */
int i;
exponent = 0;
if (x >= L_(1.0))
{
/* A positive exponent. */
DOUBLE pow2_i; /* = pow2[i] */
DOUBLE powh_i; /* = powh[i] */
/* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
x * 2^exponent = argument, x >= 1.0. */
for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
;
i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
{
if (x >= pow2_i)
{
exponent += (1 << i);
x *= powh_i;
}
else
break;
pow2[i] = pow2_i;
powh[i] = powh_i;
}
/* Avoid making x too small, as it could become a denormalized
number and thus lose precision. */
while (i > 0 && x < pow2[i - 1])
{
i--;
powh_i = powh[i];
}
exponent += (1 << i);
x *= powh_i;
/* Here 2^-2^i <= x < 1.0. */
}
else
{
/* A negative or zero exponent. */
DOUBLE pow2_i; /* = pow2[i] */
DOUBLE powh_i; /* = powh[i] */
/* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
x * 2^exponent = argument, x < 1.0. */
for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
;
i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
{
if (x < powh_i)
{
exponent -= (1 << i);
x *= pow2_i;
}
else
break;
pow2[i] = pow2_i;
powh[i] = powh_i;
}
/* Here 2^-2^i <= x < 1.0. */
}
/* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */
while (i > 0)
{
i--;
if (x < powh[i])
{
exponent -= (1 << i);
x *= pow2[i];
}
}
/* Here 0.5 <= x < 1.0. */
}
if (sign < 0)
x = - x;
END_ROUNDING ();
*expptr = exponent;
return x;
}
|
