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softfloat.h
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1 /*
2  * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
3  *
4  * This file is part of FFmpeg.
5  *
6  * FFmpeg is free software; you can redistribute it and/or
7  * modify it under the terms of the GNU Lesser General Public
8  * License as published by the Free Software Foundation; either
9  * version 2.1 of the License, or (at your option) any later version.
10  *
11  * FFmpeg is distributed in the hope that it will be useful,
12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14  * Lesser General Public License for more details.
15  *
16  * You should have received a copy of the GNU Lesser General Public
17  * License along with FFmpeg; if not, write to the Free Software
18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
19  */
20 
21 #ifndef AVUTIL_SOFTFLOAT_H
22 #define AVUTIL_SOFTFLOAT_H
23 
24 #include <stdint.h>
25 #include "common.h"
26 
27 #include "avassert.h"
28 #include "softfloat_tables.h"
29 
30 #define MIN_EXP -126
31 #define MAX_EXP 126
32 #define ONE_BITS 29
33 
34 typedef struct SoftFloat{
37 }SoftFloat;
38 
39 static const SoftFloat FLOAT_0 = { 0, MIN_EXP}; ///< 0.0
40 static const SoftFloat FLOAT_05 = { 0x20000000, 0}; ///< 0.5
41 static const SoftFloat FLOAT_1 = { 0x20000000, 1}; ///< 1.0
42 static const SoftFloat FLOAT_EPSILON = { 0x29F16B12, -16}; ///< A small value
43 static const SoftFloat FLOAT_1584893192 = { 0x32B771ED, 1}; ///< 1.584893192 (10^.2)
44 static const SoftFloat FLOAT_100000 = { 0x30D40000, 17}; ///< 100000
45 static const SoftFloat FLOAT_0999999 = { 0x3FFFFBCE, 0}; ///< 0.999999
46 
47 
48 /**
49  * Convert a SoftFloat to a double precision float.
50  */
51 static inline av_const double av_sf2double(SoftFloat v) {
52  v.exp -= ONE_BITS +1;
53  if(v.exp > 0) return (double)v.mant * (double)(1 << v.exp);
54  else return (double)v.mant / (double)(1 << (-v.exp));
55 }
56 
58  if(a.mant){
59 #if 1
60  while((a.mant + 0x1FFFFFFFU)<0x3FFFFFFFU){
61  a.mant += a.mant;
62  a.exp -= 1;
63  }
64 #else
65  int s=ONE_BITS - av_log2(FFABS(a.mant));
66  a.exp -= s;
67  a.mant <<= s;
68 #endif
69  if(a.exp < MIN_EXP){
70  a.exp = MIN_EXP;
71  a.mant= 0;
72  }
73  }else{
74  a.exp= MIN_EXP;
75  }
76  return a;
77 }
78 
80 #if 1
81  if((int32_t)(a.mant + 0x40000000U) <= 0){
82  a.exp++;
83  a.mant>>=1;
84  }
85  av_assert2(a.mant < 0x40000000 && a.mant > -0x40000000);
86  av_assert2(a.exp <= MAX_EXP);
87  return a;
88 #elif 1
89  int t= a.mant + 0x40000000 < 0;
90  return (SoftFloat){ a.mant>>t, a.exp+t};
91 #else
92  int t= (a.mant + 0x3FFFFFFFU)>>31;
93  return (SoftFloat){a.mant>>t, a.exp+t};
94 #endif
95 }
96 
97 /**
98  * @return Will not be more denormalized than a*b. So if either input is
99  * normalized, then the output will not be worse then the other input.
100  * If both are normalized, then the output will be normalized.
101  */
103  a.exp += b.exp;
104  av_assert2((int32_t)((a.mant * (int64_t)b.mant) >> ONE_BITS) == (a.mant * (int64_t)b.mant) >> ONE_BITS);
105  a.mant = (a.mant * (int64_t)b.mant) >> ONE_BITS;
106  a = av_normalize1_sf((SoftFloat){a.mant, a.exp - 1});
107  if (!a.mant || a.exp < MIN_EXP)
108  return FLOAT_0;
109  return a;
110 }
111 
112 /**
113  * b has to be normalized and not zero.
114  * @return Will not be more denormalized than a.
115  */
117  a.exp -= b.exp;
118  a.mant = ((int64_t)a.mant<<(ONE_BITS+1)) / b.mant;
119  a = av_normalize1_sf(a);
120  if (!a.mant || a.exp < MIN_EXP)
121  return FLOAT_0;
122  return a;
123 }
124 
125 /**
126  * Compares two SoftFloats.
127  * @returns < 0 if the first is less
128  * > 0 if the first is greater
129  * 0 if they are equal
130  */
131 static inline av_const int av_cmp_sf(SoftFloat a, SoftFloat b){
132  int t= a.exp - b.exp;
133  if (t <-31) return - b.mant ;
134  else if (t < 0) return (a.mant >> (-t)) - b.mant ;
135  else if (t < 32) return a.mant - (b.mant >> t);
136  else return a.mant ;
137 }
138 
139 /**
140  * Compares two SoftFloats.
141  * @returns 1 if a is greater than b, 0 otherwise
142  */
143 static inline av_const int av_gt_sf(SoftFloat a, SoftFloat b)
144 {
145  int t= a.exp - b.exp;
146  if (t <-31) return 0 > b.mant ;
147  else if (t < 0) return (a.mant >> (-t)) > b.mant ;
148  else if (t < 32) return a.mant > (b.mant >> t);
149  else return a.mant > 0 ;
150 }
151 
152 /**
153  * @returns the sum of 2 SoftFloats.
154  */
156  int t= a.exp - b.exp;
157  if (t <-31) return b;
158  else if (t < 0) return av_normalize_sf(av_normalize1_sf((SoftFloat){ b.mant + (a.mant >> (-t)), b.exp}));
159  else if (t < 32) return av_normalize_sf(av_normalize1_sf((SoftFloat){ a.mant + (b.mant >> t ), a.exp}));
160  else return a;
161 }
162 
164  return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
165 }
166 
167 //FIXME log, exp, pow
168 
169 /**
170  * Converts a mantisse and exponent to a SoftFloat
171  * @returns a SoftFloat with value v * 2^frac_bits
172  */
173 static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
174  int exp_offset = 0;
175  if(v == INT_MIN){
176  exp_offset = 1;
177  v>>=1;
178  }
179  return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
180 }
181 
182 /**
183  * Rounding is to -inf.
184  */
185 static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
186  v.exp += frac_bits - (ONE_BITS + 1);
187  if(v.exp >= 0) return v.mant << v.exp ;
188  else return v.mant >>(-v.exp);
189 }
190 
191 /**
192  * Rounding-to-nearest used.
193  */
195 {
196  int tabIndex, rem;
197 
198  if (val.mant == 0)
199  val.exp = MIN_EXP;
200  else if (val.mant < 0)
201  abort();
202  else
203  {
204  tabIndex = (val.mant - 0x20000000) >> 20;
205 
206  rem = val.mant & 0xFFFFF;
207  val.mant = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
208  (int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
209  0x80000) >> 20);
210  val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
211  0x10000000) >> 29);
212 
213  if (val.mant < 0x40000000)
214  val.exp -= 2;
215  else
216  val.mant >>= 1;
217 
218  val.exp = (val.exp >> 1) + 1;
219  }
220 
221  return val;
222 }
223 
224 /**
225  * Rounding-to-nearest used.
226  */
227 static av_unused void av_sincos_sf(int a, int *s, int *c)
228 {
229  int idx, sign;
230  int sv, cv;
231  int st, ct;
232 
233  idx = a >> 26;
234  sign = (idx << 27) >> 31;
235  cv = av_costbl_1_sf[idx & 0xf];
236  cv = (cv ^ sign) - sign;
237 
238  idx -= 8;
239  sign = (idx << 27) >> 31;
240  sv = av_costbl_1_sf[idx & 0xf];
241  sv = (sv ^ sign) - sign;
242 
243  idx = a >> 21;
244  ct = av_costbl_2_sf[idx & 0x1f];
245  st = av_sintbl_2_sf[idx & 0x1f];
246 
247  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
248 
249  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
250 
251  cv = idx;
252 
253  idx = a >> 16;
254  ct = av_costbl_3_sf[idx & 0x1f];
255  st = av_sintbl_3_sf[idx & 0x1f];
256 
257  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
258 
259  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
260  cv = idx;
261 
262  idx = a >> 11;
263 
264  ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
265  (int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
266  0x400) >> 11);
267  st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
268  (int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
269  0x400) >> 11);
270 
271  *c = (int)(((int64_t)cv * ct + (int64_t)sv * st + 0x20000000) >> 30);
272 
273  *s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
274 }
275 
276 #endif /* AVUTIL_SOFTFLOAT_H */
#define av_const
Definition: attributes.h:76
static av_always_inline SoftFloat av_sqrt_sf(SoftFloat val)
Rounding-to-nearest used.
Definition: softfloat.h:194
const char const char void * val
Definition: avisynth_c.h:634
const char * s
Definition: avisynth_c.h:631
#define ONE_BITS
Definition: softfloat.h:32
static const int32_t av_costbl_4_sf[33]
static const SoftFloat FLOAT_05
0.5
Definition: softfloat.h:40
static av_const SoftFloat av_div_sf(SoftFloat a, SoftFloat b)
b has to be normalized and not zero.
Definition: softfloat.h:116
const char * b
Definition: vf_curves.c:109
int av_log2(unsigned v)
Definition: intmath.c:26
static const int32_t av_sintbl_3_sf[32]
static const SoftFloat FLOAT_0
0.0
Definition: softfloat.h:39
static av_const double av_sf2double(SoftFloat v)
Convert a SoftFloat to a double precision float.
Definition: softfloat.h:51
#define av_assert2(cond)
assert() equivalent, that does lie in speed critical code.
Definition: avassert.h:63
int32_t mant
Definition: softfloat.h:35
static const SoftFloat FLOAT_100000
100000
Definition: softfloat.h:44
#define U(x)
Definition: vp56_arith.h:37
static av_const SoftFloat av_normalize_sf(SoftFloat a)
Definition: softfloat.h:57
static const SoftFloat FLOAT_1
1.0
Definition: softfloat.h:41
static const SoftFloat FLOAT_0999999
0.999999
Definition: softfloat.h:45
simple assert() macros that are a bit more flexible than ISO C assert().
static av_unused void av_sincos_sf(int a, int *s, int *c)
Rounding-to-nearest used.
Definition: softfloat.h:227
int32_t
static av_const int av_cmp_sf(SoftFloat a, SoftFloat b)
Compares two SoftFloats.
Definition: softfloat.h:131
#define FFABS(a)
Absolute value, Note, INT_MIN / INT64_MIN result in undefined behavior as they are not representable ...
Definition: common.h:72
static av_const int av_gt_sf(SoftFloat a, SoftFloat b)
Compares two SoftFloats.
Definition: softfloat.h:143
static av_const SoftFloat av_normalize1_sf(SoftFloat a)
Definition: softfloat.h:79
static const int32_t av_sqrttbl_sf[512+1]
static av_const int av_sf2int(SoftFloat v, int frac_bits)
Rounding is to -inf.
Definition: softfloat.h:185
static const int32_t av_costbl_2_sf[32]
static const int32_t av_costbl_1_sf[16]
#define MIN_EXP
Definition: softfloat.h:30
static const int32_t av_sintbl_2_sf[32]
static av_const SoftFloat av_sub_sf(SoftFloat a, SoftFloat b)
Definition: softfloat.h:163
static av_const SoftFloat av_add_sf(SoftFloat a, SoftFloat b)
Definition: softfloat.h:155
static const int32_t av_sqr_exp_multbl_sf[2]
common internal and external API header
static const SoftFloat FLOAT_1584893192
1.584893192 (10^.2)
Definition: softfloat.h:43
static av_const SoftFloat av_mul_sf(SoftFloat a, SoftFloat b)
Definition: softfloat.h:102
static double c[64]
int32_t exp
Definition: softfloat.h:36
static const SoftFloat FLOAT_EPSILON
A small value.
Definition: softfloat.h:42
static const int32_t av_sintbl_4_sf[33]
#define MAX_EXP
Definition: softfloat.h:31
static const int32_t av_costbl_3_sf[32]
static av_const SoftFloat av_int2sf(int v, int frac_bits)
Converts a mantisse and exponent to a SoftFloat.
Definition: softfloat.h:173
#define av_always_inline
Definition: attributes.h:39
#define av_unused
Definition: attributes.h:126