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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 -149
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  return ldexp(v.mant, v.exp);
54 }
55 
57  if(a.mant){
58 #if 1
59  while((a.mant + 0x1FFFFFFFU)<0x3FFFFFFFU){
60  a.mant += a.mant;
61  a.exp -= 1;
62  }
63 #else
64  int s=ONE_BITS - av_log2(FFABS(a.mant));
65  a.exp -= s;
66  a.mant <<= s;
67 #endif
68  if(a.exp < MIN_EXP){
69  a.exp = MIN_EXP;
70  a.mant= 0;
71  }
72  }else{
73  a.exp= MIN_EXP;
74  }
75  return a;
76 }
77 
79 #if 1
80  if((int32_t)(a.mant + 0x40000000U) <= 0){
81  a.exp++;
82  a.mant>>=1;
83  }
84  av_assert2(a.mant < 0x40000000 && a.mant > -0x40000000);
85  av_assert2(a.exp <= MAX_EXP);
86  return a;
87 #elif 1
88  int t= a.mant + 0x40000000 < 0;
89  return (SoftFloat){ a.mant>>t, a.exp+t};
90 #else
91  int t= (a.mant + 0x3FFFFFFFU)>>31;
92  return (SoftFloat){a.mant>>t, a.exp+t};
93 #endif
94 }
95 
96 /**
97  * @return Will not be more denormalized than a*b. So if either input is
98  * normalized, then the output will not be worse then the other input.
99  * If both are normalized, then the output will be normalized.
100  */
102  a.exp += b.exp;
103  av_assert2((int32_t)((a.mant * (int64_t)b.mant) >> ONE_BITS) == (a.mant * (int64_t)b.mant) >> ONE_BITS);
104  a.mant = (a.mant * (int64_t)b.mant) >> ONE_BITS;
105  a = av_normalize1_sf((SoftFloat){a.mant, a.exp - 1});
106  if (!a.mant || a.exp < MIN_EXP)
107  return FLOAT_0;
108  return a;
109 }
110 
111 /**
112  * b has to be normalized and not zero.
113  * @return Will not be more denormalized than a.
114  */
116  int64_t temp = (int64_t)a.mant * (1<<(ONE_BITS+1));
117  temp /= b.mant;
118  a.exp -= b.exp;
119  a.mant = temp;
120  while (a.mant != temp) {
121  temp /= 2;
122  a.exp--;
123  a.mant = temp;
124  }
125  a = av_normalize1_sf(a);
126  if (!a.mant || a.exp < MIN_EXP)
127  return FLOAT_0;
128  return a;
129 }
130 
131 /**
132  * Compares two SoftFloats.
133  * @returns < 0 if the first is less
134  * > 0 if the first is greater
135  * 0 if they are equal
136  */
137 static inline av_const int av_cmp_sf(SoftFloat a, SoftFloat b){
138  int t= a.exp - b.exp;
139  if (t <-31) return - b.mant ;
140  else if (t < 0) return (a.mant >> (-t)) - b.mant ;
141  else if (t < 32) return a.mant - (b.mant >> t);
142  else return a.mant ;
143 }
144 
145 /**
146  * Compares two SoftFloats.
147  * @returns 1 if a is greater than b, 0 otherwise
148  */
149 static inline av_const int av_gt_sf(SoftFloat a, SoftFloat b)
150 {
151  int t= a.exp - b.exp;
152  if (t <-31) return 0 > b.mant ;
153  else if (t < 0) return (a.mant >> (-t)) > b.mant ;
154  else if (t < 32) return a.mant > (b.mant >> t);
155  else return a.mant > 0 ;
156 }
157 
158 /**
159  * @returns the sum of 2 SoftFloats.
160  */
162  int t= a.exp - b.exp;
163  if (t <-31) return b;
164  else if (t < 0) return av_normalize_sf(av_normalize1_sf((SoftFloat){ b.mant + (a.mant >> (-t)), b.exp}));
165  else if (t < 32) return av_normalize_sf(av_normalize1_sf((SoftFloat){ a.mant + (b.mant >> t ), a.exp}));
166  else return a;
167 }
168 
169 /**
170  * @returns the difference of 2 SoftFloats.
171  */
173  return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
174 }
175 
176 //FIXME log, exp, pow
177 
178 /**
179  * Converts a mantisse and exponent to a SoftFloat.
180  * This converts a fixed point value v with frac_bits fractional bits to a
181  * SoftFloat.
182  * @returns a SoftFloat with value v * 2^-frac_bits
183  */
184 static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
185  int exp_offset = 0;
186  if(v <= INT_MIN + 1){
187  exp_offset = 1;
188  v>>=1;
189  }
190  return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
191 }
192 
193 /**
194  * Converts a SoftFloat to an integer.
195  * Rounding is to -inf.
196  */
197 static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
198  v.exp += frac_bits - (ONE_BITS + 1);
199  if(v.exp >= 0) return v.mant << v.exp ;
200  else return v.mant >>(-v.exp);
201 }
202 
203 /**
204  * Rounding-to-nearest used.
205  */
207 {
208  int tabIndex, rem;
209 
210  if (val.mant == 0)
211  val.exp = MIN_EXP;
212  else if (val.mant < 0)
213  abort();
214  else
215  {
216  tabIndex = (val.mant - 0x20000000) >> 20;
217 
218  rem = val.mant & 0xFFFFF;
219  val.mant = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
220  (int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
221  0x80000) >> 20);
222  val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
223  0x10000000) >> 29);
224 
225  if (val.mant < 0x40000000)
226  val.exp -= 2;
227  else
228  val.mant >>= 1;
229 
230  val.exp = (val.exp >> 1) + 1;
231  }
232 
233  return val;
234 }
235 
236 /**
237  * Rounding-to-nearest used.
238  */
239 static av_unused void av_sincos_sf(int a, int *s, int *c)
240 {
241  int idx, sign;
242  int sv, cv;
243  int st, ct;
244 
245  idx = a >> 26;
246  sign = (int32_t)((unsigned)idx << 27) >> 31;
247  cv = av_costbl_1_sf[idx & 0xf];
248  cv = (cv ^ sign) - sign;
249 
250  idx -= 8;
251  sign = (int32_t)((unsigned)idx << 27) >> 31;
252  sv = av_costbl_1_sf[idx & 0xf];
253  sv = (sv ^ sign) - sign;
254 
255  idx = a >> 21;
256  ct = av_costbl_2_sf[idx & 0x1f];
257  st = av_sintbl_2_sf[idx & 0x1f];
258 
259  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
260 
261  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
262 
263  cv = idx;
264 
265  idx = a >> 16;
266  ct = av_costbl_3_sf[idx & 0x1f];
267  st = av_sintbl_3_sf[idx & 0x1f];
268 
269  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
270 
271  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
272  cv = idx;
273 
274  idx = a >> 11;
275 
276  ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
277  (int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
278  0x400) >> 11);
279  st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
280  (int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
281  0x400) >> 11);
282 
283  *c = (int)(((int64_t)cv * ct + (int64_t)sv * st + 0x20000000) >> 30);
284 
285  *s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
286 }
287 
288 #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:206
const char const char void * val
Definition: avisynth_c.h:771
const char * s
Definition: avisynth_c.h:768
#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
else temp
Definition: vf_mcdeint.c:256
static av_const SoftFloat av_div_sf(SoftFloat a, SoftFloat b)
b has to be normalized and not zero.
Definition: softfloat.h:115
const char * b
Definition: vf_curves.c:113
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:64
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:56
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:239
int32_t
static av_const int av_cmp_sf(SoftFloat a, SoftFloat b)
Compares two SoftFloats.
Definition: softfloat.h:137
#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:149
static av_const SoftFloat av_normalize1_sf(SoftFloat a)
Definition: softfloat.h:78
static const int32_t av_sqrttbl_sf[512+1]
static av_const int av_sf2int(SoftFloat v, int frac_bits)
Converts a SoftFloat to an integer.
Definition: softfloat.h:197
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:172
static av_const SoftFloat av_add_sf(SoftFloat a, SoftFloat b)
Definition: softfloat.h:161
static const int32_t av_sqr_exp_multbl_sf[2]
int
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:101
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:184
#define av_always_inline
Definition: attributes.h:39
#define av_unused
Definition: attributes.h:125