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
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
|
/* GSL - Generic Sound Layer
* Copyright (C) 1999, 2001 Tim Janik
*
* This library 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 of the License, or (at your option) any later version.
*
* This library 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 library; if not, write to the
* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301, USA.
*/
#ifndef __GSL_IEEE754_H__
#define __GSL_IEEE754_H__
#include <gsl/gsldefs.h>
#ifdef __cplusplus
extern "C" {
#endif /* __cplusplus */
/* IEEE 754 single precision floating point layout:
* 31 30 23 22 0
* +--------+---------------+---------------+
* | s 1bit | e[30:23] 8bit | f[22:0] 23bit |
* +--------+---------------+---------------+
* B0------------------->B1------->B2-->B3-->
*
* IEEE 754 double precision floating point layout:
* 63 62 52 51 32 31 0
* +--------+----------------+----------------+ +---------------+
* | s 1bit | e[62:52] 11bit | f[51:32] 20bit | | f[31:0] 32bit |
* +--------+----------------+----------------+ +---------------+
* B0--------------->B1---------->B2--->B3----> B4->B5->B6->B7->
*/
/* floating point type related constants */
#define GSL_FLOAT_BIAS (127)
#define GSL_FLOAT_MAX_NORMAL (3.40282347e+38) /* 7f7fffff */
#define GSL_FLOAT_MIN_NORMAL (1.17549435e-38) /* 00800000 */
#define GSL_FLOAT_MAX_SUBNORMAL (1.17549421e-38) /* 007fffff */
#define GSL_FLOAT_MIN_SUBNORMAL (1.40129846e-45) /* 00000001 */
#define GSL_DOUBLE_BIAS (1023)
#define GSL_DOUBLE_MAX_NORMAL (1.7976931348623157e+308) /* 7fefffff ffffffff */
#define GSL_DOUBLE_MIN_NORMAL (2.2250738585072014e-308) /* 00100000 00000000 */
#define GSL_DOUBLE_MAX_SUBNORMAL (2.2250738585072009e-308) /* 000fffff ffffffff */
#define GSL_DOUBLE_MIN_SUBNORMAL (4.9406564584124654e-324) /* 00000000 00000001 */
#define GSL_DOUBLE_INF (_gsl_dinf_union.d)
#define GSL_DOUBLE_NAN (_gsl_dnan_union.d)
#define GSL_FLOAT_INF (_gsl_finf_union.f)
#define GSL_FLOAT_NAN (_gsl_fnan_union.f)
/* multiply with base2 exponent to get base10 exponent (for nomal numbers) */
#define GSL_LOG_2_BASE_10 (0.30102999566398119521)
/* the following macros work only on variables
* and evaluate arguments multiple times
*/
/* single precision value checks */
#define GSL_FLOAT_IS_ZERO(f) ((f) == 0.0) /* compiler knows this one */
#define GSL_FLOAT_IS_NORMAL(f) (GSL_FLOAT_PARTS (f).mpn.biased_exponent > 0 && \
GSL_FLOAT_PARTS (f).mpn.biased_exponent < 255)
#define GSL_FLOAT_IS_SUBNORMAL(f) (GSL_FLOAT_PARTS (f).mpn.biased_exponent == 0 && \
GSL_FLOAT_PARTS (f).mpn.mantissa != 0)
#define GSL_FLOAT_IS_NANINF(f) (GSL_FLOAT_PARTS (f).mpn.biased_exponent == 255)
#define GSL_FLOAT_IS_NAN(f) (GSL_FLOAT_IS_NANINF (f) && GSL_FLOAT_PARTS (f).mpn.mantissa != 0)
#define GSL_FLOAT_IS_INF(f) (GSL_FLOAT_IS_NANINF (f) && GSL_FLOAT_PARTS (f).mpn.mantissa == 0)
#define GSL_FLOAT_IS_INF_POSITIVE(f) (GSL_FLOAT_IS_INF (f) && GSL_FLOAT_PARTS (f).mpn.sign == 0)
#define GSL_FLOAT_IS_INF_NEGATIVE(f) (GSL_FLOAT_IS_INF (f) && GSL_FLOAT_PARTS (f).mpn.sign == 1)
#define GSL_FLOAT_SIGN(f) (GSL_FLOAT_PARTS (f).mpn.sign)
/* double precision value checks */
#define GSL_DOUBLE_IS_ZERO(d) ((d) == 0.0) /* compiler knows this one */
#define GSL_DOUBLE_IS_NORMAL(d) (GSL_DOUBLE_PARTS (d).mpn.biased_exponent > 0 && \
GSL_DOUBLE_PARTS (d).mpn.biased_exponent < 2047)
#define GSL_DOUBLE_IS_SUBNORMAL(d) (GSL_DOUBLE_PARTS (d).mpn.biased_exponent == 0 && \
(GSL_DOUBLE_PARTS (d).mpn.mantissa_low != 0 || \
GSL_DOUBLE_PARTS (d).mpn.mantissa_high != 0))
#define GSL_DOUBLE_IS_NANINF(d) (GSL_DOUBLE_PARTS (d).mpn.biased_exponent == 2047)
#define GSL_DOUBLE_IS_NAN(d) (GSL_DOUBLE_IS_NANINF (d) && \
(GSL_DOUBLE_PARTS (d).mpn.mantissa_low != 0 || \
GSL_DOUBLE_PARTS (d).mpn.mantissa_high != 0))
#define GSL_DOUBLE_IS_INF(d) (GSL_DOUBLE_IS_NANINF (d) && \
GSL_DOUBLE_PARTS (d).mpn.mantissa_low == 0 && \
GSL_DOUBLE_PARTS (d).mpn.mantissa_high == 0)
#define GSL_DOUBLE_IS_INF_POSITIVE(d) (GSL_DOUBLE_IS_INF (d) && GSL_DOUBLE_PARTS (d).mpn.sign == 0)
#define GSL_DOUBLE_IS_INF_NEGATIVE(d) (GSL_DOUBLE_IS_INF (d) && GSL_DOUBLE_PARTS (d).mpn.sign == 1)
#define GSL_DOUBLE_SIGN(d) (GSL_DOUBLE_PARTS (d).mpn.sign)
/* get structured parts of floating point numbers */
#define GSL_FLOAT_PARTS(f) (*((GslFloatIEEE754*) &(f)))
#define GSL_DOUBLE_PARTS(d) (*((GslDoubleIEEE754*) &(d)))
/* --- rounding --- */
typedef unsigned short int GslFpuState;
#if defined (__i386__) && defined (__GNUC__)
/* setting/restoring rounding mode shouldn't actually
* be necessary as round-to-nearest is the hardware
* default (can be checked with gsl_fpu_okround()).
*/
static inline void gsl_fpu_setround (GslFpuState *cw);
static inline int gsl_fpu_okround (void);
static inline void gsl_fpu_restore (GslFpuState cv);
static inline int gsl_ftoi /* nearest */ (float f) G_GNUC_CONST;
static inline int gsl_dtoi /* nearest */ (double f) G_GNUC_CONST;
/* fallbacks for the !386 case are below */
#endif
/* --- implementation bits --- */
#if G_BYTE_ORDER == G_LITTLE_ENDIAN
typedef union
{
float v_float;
struct {
unsigned int mantissa : 23;
unsigned int biased_exponent : 8;
unsigned int sign : 1;
} mpn;
} GslFloatIEEE754;
typedef union
{
double v_double;
struct {
unsigned int mantissa_low : 32;
unsigned int mantissa_high : 20;
unsigned int biased_exponent : 11;
unsigned int sign : 1;
} mpn;
} GslDoubleIEEE754;
#define _GSL_DOUBLE_INF_BYTES { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf0, 0x7f }
#define _GSL_DOUBLE_NAN_BYTES { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x7f }
#define _GSL_FLOAT_INF_BYTES { 0x00, 0x00, 0x80, 0x7f }
#define _GSL_FLOAT_NAN_BYTES { 0x00, 0x00, 0xc0, 0x7f }
#elif G_BYTE_ORDER == G_BIG_ENDIAN
typedef union
{
float v_float;
struct {
unsigned int sign : 1;
unsigned int biased_exponent : 8;
unsigned int mantissa : 23;
} mpn;
} GslFloatIEEE754;
typedef union
{
double v_double;
struct {
unsigned int sign : 1;
unsigned int biased_exponent : 11;
unsigned int mantissa_high : 20;
unsigned int mantissa_low : 32;
} mpn;
} GslDoubleIEEE754;
#define _GSL_DOUBLE_INF_BYTES { 0x7f, 0xf0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }
#define _GSL_DOUBLE_NAN_BYTES { 0x7f, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }
#define _GSL_FLOAT_INF_BYTES { 0x7f, 0x80, 0x00, 0x00 }
#define _GSL_FLOAT_NAN_BYTES { 0x7f, 0xc0, 0x00, 0x00 }
#else /* !G_LITTLE_ENDIAN && !G_BIG_ENDIAN */
#error unknown ENDIAN type
#endif /* !G_LITTLE_ENDIAN && !G_BIG_ENDIAN */
static const union { unsigned char c[8]; double d; } _gsl_dnan_union = { _GSL_DOUBLE_NAN_BYTES };
static const union { unsigned char c[8]; double d; } _gsl_dinf_union = { _GSL_DOUBLE_INF_BYTES };
static const union { unsigned char c[4]; float f; } _gsl_fnan_union = { _GSL_FLOAT_NAN_BYTES };
static const union { unsigned char c[4]; float f; } _gsl_finf_union = { _GSL_FLOAT_INF_BYTES };
#if defined (__i386__) && defined (__GNUC__)
static inline void
gsl_fpu_setround (GslFpuState *cw)
{
GslFpuState cv;
__asm__ ("fnstcw %0"
: "=m" (*&cv));
*cw = cv;
cv &= ~0x0c00;
__asm__ ("fldcw %0"
:
: "m" (*&cv));
}
static inline int
gsl_fpu_okround (void)
{
GslFpuState cv;
__asm__ ("fnstcw %0"
: "=m" (*&cv));
return !(cv & 0x0c00);
}
static inline void
gsl_fpu_restore (GslFpuState cv)
{
__asm__ ("fldcw %0"
:
: "m" (*&cv));
}
static inline int G_GNUC_CONST
gsl_ftoi (float f)
{
int r;
__asm__ ("fistl %0"
: "=m" (r)
: "t" (f));
return r;
}
static inline int G_GNUC_CONST
gsl_dtoi (double f)
{
int r;
__asm__ ("fistl %0"
: "=m" (r)
: "t" (f));
return r;
}
#else /* !386 */
# define gsl_fpu_setround(p) ((void) (p));
# define gsl_fpu_okround() (1)
# define gsl_fpu_restore(x) /* nop */
static inline int G_GNUC_CONST
gsl_ftoi (float v)
{
return v < -0.0 ? v - 0.5 : v + 0.5;
}
static inline int G_GNUC_CONST
gsl_dtoi (double v)
{
return v < -0.0 ? v - 0.5 : v + 0.5;
}
#endif
#ifdef __cplusplus
}
#endif /* __cplusplus */
#endif /* __GSL_IEEE754_H__ */ /* vim: set ts=8 sw=2 sts=2: */
|
