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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 static const SoftFloat FLOAT_MIN = { 0x20000000, MIN_EXP};
47 
48 
49 /**
50  * Convert a SoftFloat to a double precision float.
51  */
52 static inline av_const double av_sf2double(SoftFloat v) {
53  v.exp -= ONE_BITS +1;
54  return ldexp(v.mant, 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  int64_t temp = (int64_t)a.mant * (1<<(ONE_BITS+1));
118  temp /= b.mant;
119  a.exp -= b.exp;
120  a.mant = temp;
121  while (a.mant != temp) {
122  temp /= 2;
123  a.exp--;
124  a.mant = temp;
125  }
126  a = av_normalize1_sf(a);
127  if (!a.mant || a.exp < MIN_EXP)
128  return FLOAT_0;
129  return a;
130 }
131 
132 /**
133  * Compares two SoftFloats.
134  * @returns < 0 if the first is less
135  * > 0 if the first is greater
136  * 0 if they are equal
137  */
138 static inline av_const int av_cmp_sf(SoftFloat a, SoftFloat b){
139  int t= a.exp - b.exp;
140  if (t <-31) return - b.mant ;
141  else if (t < 0) return (a.mant >> (-t)) - b.mant ;
142  else if (t < 32) return a.mant - (b.mant >> t);
143  else return a.mant ;
144 }
145 
146 /**
147  * Compares two SoftFloats.
148  * @returns 1 if a is greater than b, 0 otherwise
149  */
150 static inline av_const int av_gt_sf(SoftFloat a, SoftFloat b)
151 {
152  int t= a.exp - b.exp;
153  if (t <-31) return 0 > b.mant ;
154  else if (t < 0) return (a.mant >> (-t)) > b.mant ;
155  else if (t < 32) return a.mant > (b.mant >> t);
156  else return a.mant > 0 ;
157 }
158 
159 /**
160  * @returns the sum of 2 SoftFloats.
161  */
163  int t= a.exp - b.exp;
164  if (t <-31) return b;
165  else if (t < 0) return av_normalize_sf(av_normalize1_sf((SoftFloat){ b.mant + (a.mant >> (-t)), b.exp}));
166  else if (t < 32) return av_normalize_sf(av_normalize1_sf((SoftFloat){ a.mant + (b.mant >> t ), a.exp}));
167  else return a;
168 }
169 
170 /**
171  * @returns the difference of 2 SoftFloats.
172  */
174  return av_add_sf(a, (SoftFloat){ -b.mant, b.exp});
175 }
176 
177 //FIXME log, exp, pow
178 
179 /**
180  * Converts a mantisse and exponent to a SoftFloat.
181  * This converts a fixed point value v with frac_bits fractional bits to a
182  * SoftFloat.
183  * @returns a SoftFloat with value v * 2^-frac_bits
184  */
185 static inline av_const SoftFloat av_int2sf(int v, int frac_bits){
186  int exp_offset = 0;
187  if(v <= INT_MIN + 1){
188  exp_offset = 1;
189  v>>=1;
190  }
191  return av_normalize_sf(av_normalize1_sf((SoftFloat){v, ONE_BITS + 1 - frac_bits + exp_offset}));
192 }
193 
194 /**
195  * Converts a SoftFloat to an integer.
196  * Rounding is to -inf.
197  */
198 static inline av_const int av_sf2int(SoftFloat v, int frac_bits){
199  v.exp += frac_bits - (ONE_BITS + 1);
200  if(v.exp >= 0) return v.mant << v.exp ;
201  else return v.mant >>(-v.exp);
202 }
203 
204 /**
205  * Rounding-to-nearest used.
206  */
208 {
209  int tabIndex, rem;
210 
211  if (val.mant == 0)
212  val.exp = MIN_EXP;
213  else if (val.mant < 0)
214  abort();
215  else
216  {
217  tabIndex = (val.mant - 0x20000000) >> 20;
218 
219  rem = val.mant & 0xFFFFF;
220  val.mant = (int)(((int64_t)av_sqrttbl_sf[tabIndex] * (0x100000 - rem) +
221  (int64_t)av_sqrttbl_sf[tabIndex + 1] * rem +
222  0x80000) >> 20);
223  val.mant = (int)(((int64_t)av_sqr_exp_multbl_sf[val.exp & 1] * val.mant +
224  0x10000000) >> 29);
225 
226  if (val.mant < 0x40000000)
227  val.exp -= 2;
228  else
229  val.mant >>= 1;
230 
231  val.exp = (val.exp >> 1) + 1;
232  }
233 
234  return val;
235 }
236 
237 /**
238  * Rounding-to-nearest used.
239  */
240 static av_unused void av_sincos_sf(int a, int *s, int *c)
241 {
242  int idx, sign;
243  int sv, cv;
244  int st, ct;
245 
246  idx = a >> 26;
247  sign = (int32_t)((unsigned)idx << 27) >> 31;
248  cv = av_costbl_1_sf[idx & 0xf];
249  cv = (cv ^ sign) - sign;
250 
251  idx -= 8;
252  sign = (int32_t)((unsigned)idx << 27) >> 31;
253  sv = av_costbl_1_sf[idx & 0xf];
254  sv = (sv ^ sign) - sign;
255 
256  idx = a >> 21;
257  ct = av_costbl_2_sf[idx & 0x1f];
258  st = av_sintbl_2_sf[idx & 0x1f];
259 
260  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
261 
262  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
263 
264  cv = idx;
265 
266  idx = a >> 16;
267  ct = av_costbl_3_sf[idx & 0x1f];
268  st = av_sintbl_3_sf[idx & 0x1f];
269 
270  idx = (int)(((int64_t)cv * ct - (int64_t)sv * st + 0x20000000) >> 30);
271 
272  sv = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
273  cv = idx;
274 
275  idx = a >> 11;
276 
277  ct = (int)(((int64_t)av_costbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
278  (int64_t)av_costbl_4_sf[(idx & 0x1f)+1]*(a & 0x7ff) +
279  0x400) >> 11);
280  st = (int)(((int64_t)av_sintbl_4_sf[idx & 0x1f] * (0x800 - (a & 0x7ff)) +
281  (int64_t)av_sintbl_4_sf[(idx & 0x1f) + 1] * (a & 0x7ff) +
282  0x400) >> 11);
283 
284  *c = (int)(((int64_t)cv * ct + (int64_t)sv * st + 0x20000000) >> 30);
285 
286  *s = (int)(((int64_t)cv * st + (int64_t)sv * ct + 0x20000000) >> 30);
287 }
288 
289 #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:207
const char const char void * val
Definition: avisynth_c.h:771
#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: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:52
#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:240
int32_t
static av_const int av_cmp_sf(SoftFloat a, SoftFloat b)
Compares two SoftFloats.
Definition: softfloat.h:138
#define FFABS(a)
Absolute value, Note, INT_MIN / INT64_MIN result in undefined behavior as they are not representable ...
Definition: common.h:72
#define s(width, name)
Definition: cbs_vp9.c:257
static av_const int av_gt_sf(SoftFloat a, SoftFloat b)
Compares two SoftFloats.
Definition: softfloat.h:150
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:198
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:173
static av_const SoftFloat av_add_sf(SoftFloat a, SoftFloat b)
Definition: softfloat.h:162
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
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]
static const SoftFloat FLOAT_MIN
Definition: softfloat.h:46
#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:185
#define av_always_inline
Definition: attributes.h:39
#define av_unused
Definition: attributes.h:125