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
248
249
250
251
252
253
254
255
256
257
258
259
|
/*
* Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
*
* This file is part of FFmpeg.
*
* FFmpeg 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.
*
* FFmpeg 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 FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifndef AVUTIL_SOFTFLOAT_H
#define AVUTIL_SOFTFLOAT_H
#include <stdint.h>
#include "common.h"
#include "avassert.h"
#include "softfloat_tables.h"
#define MIN_EXP -149
#define MAX_EXP 126
#define ONE_BITS 29
typedef struct SoftFloat{
int32_t mant;
int32_t exp;
}SoftFloat;
static const SoftFloat FLOAT_0 = { 0, MIN_EXP};
static const SoftFloat FLOAT_05 = { 0x20000000, 0};
static const SoftFloat FLOAT_1 = { 0x20000000, 1};
static const SoftFloat FLOAT_EPSILON = { 0x29F16B12, -16};
static const SoftFloat FLOAT_1584893192 = { 0x32B771ED, 1};
static const SoftFloat FLOAT_100000 = { 0x30D40000, 17};
static const SoftFloat FLOAT_0999999 = { 0x3FFFFBCE, 0};
static inline av_const double av_sf2double(SoftFloat v) {
v.exp -= ONE_BITS +1;
if(v.exp > 0) return (double)v.mant * (double)(1 << v.exp);
else return (double)v.mant / (double)(1 << (-v.exp));
}
static av_const SoftFloat av_normalize_sf(SoftFloat a){
if(a.mant){
#if 1
while((a.mant + 0x1FFFFFFFU)<0x3FFFFFFFU){
a.mant += a.mant;
a.exp -= 1;
}
#else
int s=ONE_BITS - av_log2(FFABS(a.mant));
a.exp -= s;
a.mant <<= s;
#endif
if(a.exp < MIN_EXP){
a.exp = MIN_EXP;
a.mant= 0;
}
}else{
a.exp= MIN_EXP;
}
return a;
}
static inline av_const SoftFloat av_normalize1_sf(SoftFloat a){
#if 1
if((int32_t)(a.mant + 0x40000000U) <= 0){
a.exp++;
a.mant>>=1;
}
av_assert2(a.mant < 0x40000000 && a.mant > -0x40000000);
av_assert2(a.exp <= MAX_EXP);
return a;
#elif 1
int t= a.mant + 0x40000000 < 0;
return (SoftFloat){ a.mant>>t, a.exp+t};
#else
int t= (a.mant + 0x3FFFFFFFU)>>31;
return (SoftFloat){a.mant>>t, a.exp+t};
#endif
}
/**
* @return Will not be more denormalized than a*b. So if either input is
* normalized, then the output will not be worse then the other input.
* If both are normalized, then the output will be normalized.
*/
static inline av_const SoftFloat av_mul_sf(SoftFloat a, SoftFloat b){
a.exp += b.exp;
av_assert2((int32_t)((a.mant * (int64_t)b.mant) >> ONE_BITS) == (a.mant * (int64_t)b.mant) >> ONE_BITS);
a.mant = (a.mant * (int64_t)b.mant) >> ONE_BITS;
a = av_normalize1_sf((SoftFloat){a.mant, a.exp - 1});
if (!a.mant || a.exp < MIN_EXP)
return FLOAT_0;
return a;
}
/**
* b has to be normalized and not zero.
* @return Will not be more denormalized than a.
*/
static inline av_const SoftFloat av_div_sf(SoftFloat a, SoftFloat b){
a.exp -= b.exp;
a.mant = ((int64_t)a.mant<<(ONE_BITS+1)) / b.mant;
a = av_normalize1_sf(a);
if (!a.mant || a.exp < MIN_EXP)
return FLOAT_0;
return a;
}
static inline av_const int av_cmp_sf(SoftFloat a, SoftFloat b){
int t= a.exp - b.exp;
if (t <-31) return - b.mant ;
else if (t < 0) return (a.mant >> (-t)) - b.mant ;
else if (t < 32) return a.mant - (b.mant >> t);
else return a.mant ;
}
static inline av_const int av_gt_sf(SoftFloat a, SoftFloat b)
{
int t= a.exp - b.exp;
if (t <-31) return 0 > b.mant ;
else if (t < 0) return (a.mant >> (-t)) > b.mant ;
else if (t < 32) return a.mant > (b.mant >> t);
else return a.mant > 0 ;
}
static inline av_const SoftFloat av_add_sf(SoftFloat a, SoftFloat b){
int t= a.exp - b.exp;
if (t <-31) return b;
else if (t < 0) return av_normalize_sf(av_normalize1_sf((SoftFloat){ b.mant + (a.mant >> (-t)), b.exp}));
else if (t < 32) return av_normalize_sf(av_normalize1_sf((SoftFloat){ a.mant + (b.mant >> t ), a.exp}));
else return a;
}
static inline av_const SoftFloat av_sub_sf(SoftFloat a, SoftFloat b){
return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
}
//FIXME log, exp, pow
/**
* Converts a mantisse and exponent to a SoftFloat
* @returns a SoftFloat with value v * 2^frac_bits
*/
static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
int exp_offset = 0;
if(v <= INT_MIN + 1){
exp_offset = 1;
v>>=1;
}
return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
}
/**
* Rounding is to -inf.
*/
static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
v.exp += frac_bits - (ONE_BITS + 1);
if(v.exp >= 0) return v.mant << v.exp ;
else return v.mant >>(-v.exp);
}
/**
* Rounding-to-nearest used.
*/
static av_always_inline SoftFloat av_sqrt_sf(SoftFloat val)
{
int tabIndex, rem;
if (val.mant == 0)
val.exp = MIN_EXP;
else if (val.mant < 0)
abort();
else
{
tabIndex = (val.mant - 0x20000000) >> 20;
rem = val.mant & 0xFFFFF;
val.mant = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
(int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
0x80000) >> 20);
val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
0x10000000) >> 29);
if (val.mant < 0x40000000)
val.exp -= 2;
else
val.mant >>= 1;
val.exp = (val.exp >> 1) + 1;
}
return val;
}
/**
* Rounding-to-nearest used.
*/
static av_unused void av_sincos_sf(int a, int *s, int *c)
{
int idx, sign;
int sv, cv;
int st, ct;
idx = a >> 26;
sign = (idx << 27) >> 31;
cv = av_costbl_1_sf[idx & 0xf];
cv = (cv ^ sign) - sign;
idx -= 8;
sign = (idx << 27) >> 31;
sv = av_costbl_1_sf[idx & 0xf];
sv = (sv ^ sign) - sign;
idx = a >> 21;
ct = av_costbl_2_sf[idx & 0x1f];
st = av_sintbl_2_sf[idx & 0x1f];
idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
cv = idx;
idx = a >> 16;
ct = av_costbl_3_sf[idx & 0x1f];
st = av_sintbl_3_sf[idx & 0x1f];
idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
cv = idx;
idx = a >> 11;
ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
(int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
0x400) >> 11);
st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
(int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
0x400) >> 11);
*c = (int)(((int64_t)cv * ct + (int64_t)sv * st + 0x20000000) >> 30);
*s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
}
#endif /* AVUTIL_SOFTFLOAT_H */
|
