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
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
|
/* Correctly-rounded base-2 exponent function biased by 1 for binary32 value.
Copyright (c) 2022-2024 Alexei Sibidanov.
The original version of this file was copied from the CORE-MATH
project (file src/binary32/exp2m1/exp2m1f.c, revision baf5f6b).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#include <fenv.h>
#include <math.h>
#include "math_config.h"
#include <libm-alias-float.h>
#include <math-narrow-eval.h>
#include <float.h>
float
__exp2m1f (float x)
{
double z = x;
uint32_t ux = asuint (x);
uint32_t ax = ux & (~0u >> 1);
if (__glibc_unlikely (ux >= 0xc1c80000u))
{ /* x <= -25 */
if (ax > (0xffu << 23))
return x + x; /* nan */
return (ux == 0xff800000) ? -0x1p+0f : -0x1p+0f + 0x1p-26f;
}
else if (__glibc_unlikely (ax >= 0x43000000u))
{ /* x >= 128 */
if (ax >= asuint (INFINITY))
return x + x; /* +Inf or NaN */
/* exp2m1 (MAX_EXP) should not overflow when rounding towards zero
or towards -Inf. We round FLT_MAX + 2^103 which is in the middle
between FLT_MAX and 2^128 (the next number with unbounded range). */
float ret = math_narrow_eval (FLT_MAX + 0x1p103f);
if (x == FLT_MAX_EXP && ret == FLT_MAX)
return ret;
return __math_oflowf (0);
}
else if (__glibc_unlikely (ax < 0x3df95f1fu))
{ /* |x| < 8.44e-2/log(2) */
double z2 = z * z, r;
if (__glibc_unlikely (ax < 0x3d67a4ccu))
{ /* |x| < 3.92e-2/log(2) */
if (__glibc_unlikely (ax < 0x3caa2feeu))
{ /* |x| < 1.44e-2/log(2) */
if (__glibc_unlikely (ax < 0x3bac1405u))
{ /* |x| < 3.64e-3/log(2) */
if (__glibc_unlikely (ax < 0x3a358876u))
{ /* |x| < 4.8e-4/log(2) */
if (__glibc_unlikely (ax < 0x37d32ef6u))
{ /* |x| < 1.745e-5/log(2) */
if (__glibc_unlikely (ax < 0x331fdd82u))
{ /* |x| < 2.58e-8/log(2) */
if (__glibc_unlikely (ax < 0x2538aa3bu))
/* |x| < 1.60171e-16 */
r = 0x1.62e42fefa39efp-1;
else
r = 0x1.62e42fefa39fp-1
+ z * 0x1.ebfbdff82c58fp-3;
}
else
{
if (__glibc_unlikely (ux == 0xb3d85005u))
return -0x1.2bdf76p-24 - 0x1.8p-77;
if (__glibc_unlikely (ux == 0x3338428du))
return 0x1.fee08ap-26 + 0x1p-80;
static const double c[] =
{
0x1.62e42fefa39efp-1, 0x1.ebfbdff8548fdp-3,
0x1.c6b08d704a06dp-5
};
r = c[0] + z * (c[1] + z * c[2]);
}
}
else
{
if (__glibc_unlikely (ux == 0x388bca4fu))
return 0x1.839702p-15 - 0x1.8p-68;
static const double c[] =
{
0x1.62e42fefa39efp-1, 0x1.ebfbdff82c58fp-3,
0x1.c6b08dc82b347p-5, 0x1.3b2ab6fbad172p-7
};
r = (c[0] + z * c[1]) + z2 * (c[2] + z * c[3]);
}
}
else
{
static const double c[] =
{
0x1.62e42fefa39efp-1, 0x1.ebfbdff82c068p-3,
0x1.c6b08d704a6dcp-5, 0x1.3b2ac262c3eedp-7,
0x1.5d87fe7af779ap-10
};
r = (c[0] + z * c[1])
+ z2 * (c[2] + z * (c[3] + z * c[4]));
}
}
else
{
static const double c[] =
{
0x1.62e42fefa39fp-1, 0x1.ebfbdff82c58dp-3,
0x1.c6b08d7011d13p-5, 0x1.3b2ab6fbd267dp-7,
0x1.5d88a81cea49ep-10, 0x1.430912ea9b963p-13
};
r = (c[0] + z * c[1])
+ z2 * ((c[2] + z * c[3]) + z2 * (c[4] + z * c[5]));
}
}
else
{
static const double c[] =
{
0x1.62e42fefa39efp-1, 0x1.ebfbdff82c639p-3,
0x1.c6b08d7049f1cp-5, 0x1.3b2ab6f5243bdp-7,
0x1.5d87fe80a9e6cp-10, 0x1.430d0b9257fa8p-13,
0x1.ffcbfc4cf0952p-17
};
r = (c[0] + z * c[1])
+ z2 * ((c[2] + z * c[3])
+ z2 * (c[4] + z * (c[5] + z * c[6])));
}
}
else
{
static const double c[] =
{
0x1.62e42fefa39efp-1, 0x1.ebfbdff82c591p-3,
0x1.c6b08d704cf6bp-5, 0x1.3b2ab6fba00cep-7,
0x1.5d87fdfdaadb4p-10, 0x1.4309137333066p-13,
0x1.ffe5e90daf7ddp-17, 0x1.62c0220eed731p-20
};
r = ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]))
+ (z2 * z2) * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7]));
}
r *= z;
return r;
}
else
{
static const double c[] =
{
0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11,
0x1.c6b08d4ad86d3p-17, 0x1.3b2ad1b1716a2p-23,
0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
};
static const double tb[] =
{
0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
0x1.ea4afa2a490dap+0
};
double a = 16.0 * z;
double ia = floor (a);
double h = a - ia;
double h2 = h * h;
int64_t i = ia, j = i & 0xf, e = i - j;
e >>= 4;
double s = tb[j];
s *= asdouble ((e + 0x3ffull) << 52);
double c0 = c[0] + h * c[1];
double c2 = c[2] + h * c[3];
double c4 = c[4] + h * c[5];
c0 += h2 * (c2 + h2 * c4);
double w = s * h;
return (s - 1.0) + w * c0;
}
}
#ifndef __exp2m1f
libm_alias_float (__exp2m1, exp2m1)
#endif
|
