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
247
|
/*
* Copyright (c) 2013, Andreas Sandberg
* 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 COPYRIGHT HOLDERS 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
* COPYRIGHT OWNER 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 <fputils/fp80.h>
#include "fpbits.h"
#include <assert.h>
#include <stdint.h>
#include <stdio.h>
typedef union {
union {
uint64_t bits;
double value;
};
} fp64_t;
const fp80_t fp80_pinf = BUILD_FP80(0, 0, FP80_EXP_SPECIAL);
const fp80_t fp80_ninf = BUILD_FP80(1, 0, FP80_EXP_SPECIAL);
const fp80_t fp80_qnan = BUILD_FP80(0, FP80_FRAC_QNAN, FP80_EXP_SPECIAL);
const fp80_t fp80_qnani = BUILD_FP80(1, FP80_FRAC_QNANI, FP80_EXP_SPECIAL);
const fp80_t fp80_snan = BUILD_FP80(0, FP80_FRAC_SNAN, FP80_EXP_SPECIAL);
const fp80_t fp80_nan = BUILD_FP80(0, FP80_FRAC_QNAN, FP80_EXP_SPECIAL);
static const fp64_t fp64_pinf = BUILD_FP64(0, 0, FP64_EXP_SPECIAL);
static const fp64_t fp64_ninf = BUILD_FP64(1, 0, FP64_EXP_SPECIAL);
static const fp64_t fp64_qnan = BUILD_FP64(0, FP64_FRAC_QNAN,
FP64_EXP_SPECIAL);
static const fp64_t fp64_nqnan = BUILD_FP64(1, FP64_FRAC_QNAN,
FP64_EXP_SPECIAL);
static const fp64_t fp64_qnani = BUILD_FP64(1, FP64_FRAC_QNANI,
FP64_EXP_SPECIAL);
static const fp64_t fp64_snan = BUILD_FP64(0, FP64_FRAC_SNAN,
FP64_EXP_SPECIAL);
static const fp64_t fp64_nsnan = BUILD_FP64(1, FP64_FRAC_SNAN,
FP64_EXP_SPECIAL);
static double
build_fp64(int sign, uint64_t frac, int exp)
{
const fp64_t f = BUILD_FP64(sign, frac, exp);
return f.value;
}
int
fp80_sgn(fp80_t fp80)
{
return (fp80.u.repr.se & FP80_SIGN_BIT) ? -1 : 1;
}
int
fp80_isspecial(fp80_t fp80)
{
const int exp = FP80_EXP(fp80);
return exp == FP80_EXP_SPECIAL;
}
int
fp80_isinf(fp80_t fp80)
{
const uint64_t frac = FP80_FRAC(fp80);
return fp80_isspecial(fp80) && frac == 0 ? fp80_sgn(fp80) : 0;
}
int
fp80_isqnan(fp80_t fp80)
{
const uint64_t frac = FP80_FRAC(fp80);
return fp80_isspecial(fp80) && (frac & FP80_QNAN_BIT);
}
int
fp80_isqnani(fp80_t fp80)
{
const uint64_t frac_low = fp80.u.repr.fi & (FP80_FRAC_MASK >> 1);
return fp80_isqnan(fp80) && (fp80.u.repr.se & FP80_SIGN_BIT) && !frac_low;
}
int
fp80_issnan(fp80_t fp80)
{
const uint64_t frac = FP80_FRAC(fp80);
return fp80_isspecial(fp80) && !(frac & FP80_QNAN_BIT) && frac;
}
int
fp80_isfinite(fp80_t fp80)
{
return !fp80_isnan(fp80) && !fp80_isinf(fp80);
}
int
fp80_isnan(fp80_t fp80)
{
return fp80_issnan(fp80) || fp80_isqnan(fp80) ? fp80_sgn(fp80) : 0;
}
int
fp80_iszero(fp80_t fp80)
{
return fp80.u.repr.fi == 0 && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0;
}
int
fp80_isnormal(fp80_t fp80)
{
return FP80_EXP(fp80) != 0 && !fp80_isspecial(fp80) ?
fp80_sgn(fp80) : 0;
}
int
fp80_issubnormal(fp80_t fp80)
{
return FP80_FRAC(fp80) && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0;
}
int
fp80_classify(fp80_t fp80)
{
if (fp80_issubnormal(fp80)) {
return FP_SUBNORMAL;
} else if (fp80_iszero(fp80)) {
return FP_ZERO;
} else if (fp80_isinf(fp80)) {
return FP_INFINITE;
} else if (fp80_isnan(fp80)) {
return FP_NAN;
} else {
assert(fp80_isfinite(fp80));
return FP_NORMAL;
}
}
double
fp80_cvtd(fp80_t fp80)
{
const int sign = fp80.u.repr.se & FP80_SIGN_BIT;
if (!fp80_isspecial(fp80)) {
const uint64_t frac = fp80.u.repr.fi;
const int unb_exp = FP80_EXP(fp80) - FP80_EXP_BIAS;
const int fp64_exp = unb_exp + FP64_EXP_BIAS;
const uint64_t fp64_frac = frac >> (FP80_FRAC_BITS - FP64_FRAC_BITS);
if (fp64_exp > 0 && fp64_exp < FP64_EXP_SPECIAL) {
/* These numbers fall in the range of what we can express
* as normals */
return build_fp64(sign, fp64_frac, fp64_exp);
} else if (fp64_exp <= 0) {
uint64_t fp64_denormal_frac = fp64_frac >> (-fp64_exp);
/* Generate a denormal or zero */
return build_fp64(sign, fp64_denormal_frac, 0);
} else {
/* Infinity */
return build_fp64(sign, 0, FP64_EXP_SPECIAL);
}
} else {
if (fp80_isinf(fp80)) {
return build_fp64(sign, 0, FP64_EXP_SPECIAL);
} else if (fp80_issnan(fp80)) {
return fp80_sgn(fp80) > 0 ? fp64_snan.value : fp64_nsnan.value;
} else if (fp80_isqnani(fp80)) {
return fp64_qnani.value;
} else {
assert(fp80_isqnan(fp80));
return fp80_sgn(fp80) > 0 ? fp64_qnan.value : fp64_nqnan.value;
}
}
}
fp80_t
fp80_cvfd(double value)
{
const fp64_t fp64 = { .value = value };
const uint64_t frac = FP64_FRAC(fp64);
const unsigned exp = FP64_EXP(fp64);
const int unb_exp = exp - FP64_EXP_BIAS;
const uint64_t fp80_frac = frac << (FP80_FRAC_BITS - FP64_FRAC_BITS);
if (exp != 0) {
// Normal, inf, nan
const unsigned fp80_exp = exp == FP64_EXP_SPECIAL ?
FP80_EXP_SPECIAL : (unb_exp + FP80_EXP_BIAS);
const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT,
fp80_frac, fp80_exp);
return fp80;
} else if (exp == 0 && frac == 0) {
// Zero
const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT, 0, 0);
return fp80;
} else {
// Denormal
uint64_t fp80_fi = fp80_frac;
int shift_amt = 0;
while (!(fp80_fi & FP80_INT_BIT)) {
fp80_fi <<= 1;
++shift_amt;
}
const unsigned fp80_exp = (unb_exp - shift_amt) + FP80_EXP_BIAS;
const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT,
fp80_fi, fp80_exp);
return fp80;
}
}
void
fp80_debug_dump(FILE *fout, fp80_t fp80)
{
fprintf(fout, "sgn: %i, int: %i, frac: 0x%llx, exp: 0x%x (%i)\n",
fp80_sgn(fp80), !!(fp80.u.repr.fi & FP80_INT_BIT), FP80_FRAC(fp80),
FP80_EXP(fp80), FP80_EXP(fp80) - FP80_EXP_BIAS);
}
|
