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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  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 
163 /**
164  * @returns the difference of 2 SoftFloats.
165  */
167  return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
168 }
169 
170 //FIXME log, exp, pow
171 
172 /**
173  * Converts a mantisse and exponent to a SoftFloat
174  * @returns a SoftFloat with value v * 2^frac_bits
175  */
176 static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
177  int exp_offset = 0;
178  if(v <= INT_MIN + 1){
179  exp_offset = 1;
180  v>>=1;
181  }
182  return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
183 }
184 
185 /**
186  * Converts a SoftFloat to an integer.
187  * Rounding is to -inf.
188  */
189 static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
190  v.exp += frac_bits - (ONE_BITS + 1);
191  if(v.exp >= 0) return v.mant << v.exp ;
192  else return v.mant >>(-v.exp);
193 }
194 
195 /**
196  * Rounding-to-nearest used.
197  */
199 {
200  int tabIndex, rem;
201 
202  if (val.mant == 0)
203  val.exp = MIN_EXP;
204  else if (val.mant < 0)
205  abort();
206  else
207  {
208  tabIndex = (val.mant - 0x20000000) >> 20;
209 
210  rem = val.mant & 0xFFFFF;
211  val.mant = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
212  (int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
213  0x80000) >> 20);
214  val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
215  0x10000000) >> 29);
216 
217  if (val.mant < 0x40000000)
218  val.exp -= 2;
219  else
220  val.mant >>= 1;
221 
222  val.exp = (val.exp >> 1) + 1;
223  }
224 
225  return val;
226 }
227 
228 /**
229  * Rounding-to-nearest used.
230  */
231 static av_unused void av_sincos_sf(int a, int *s, int *c)
232 {
233  int idx, sign;
234  int sv, cv;
235  int st, ct;
236 
237  idx = a >> 26;
238  sign = (idx << 27) >> 31;
239  cv = av_costbl_1_sf[idx & 0xf];
240  cv = (cv ^ sign) - sign;
241 
242  idx -= 8;
243  sign = (idx << 27) >> 31;
244  sv = av_costbl_1_sf[idx & 0xf];
245  sv = (sv ^ sign) - sign;
246 
247  idx = a >> 21;
248  ct = av_costbl_2_sf[idx & 0x1f];
249  st = av_sintbl_2_sf[idx & 0x1f];
250 
251  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
252 
253  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
254 
255  cv = idx;
256 
257  idx = a >> 16;
258  ct = av_costbl_3_sf[idx & 0x1f];
259  st = av_sintbl_3_sf[idx & 0x1f];
260 
261  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
262 
263  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
264  cv = idx;
265 
266  idx = a >> 11;
267 
268  ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
269  (int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
270  0x400) >> 11);
271  st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
272  (int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
273  0x400) >> 11);
274 
275  *c = (int)(((int64_t)cv * ct + (int64_t)sv * st + 0x20000000) >> 30);
276 
277  *s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
278 }
279 
280 #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:198
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
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: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: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:231
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)
Converts a SoftFloat to an integer.
Definition: softfloat.h:189
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:166
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]
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:102
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]
static AVCodec * c
#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:176
#define av_always_inline
Definition: attributes.h:39
#define av_unused
Definition: attributes.h:126