FFmpeg
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Groups Pages
rational.c
Go to the documentation of this file.
1 /*
2  * rational numbers
3  * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
4  *
5  * This file is part of FFmpeg.
6  *
7  * FFmpeg is free software; you can redistribute it and/or
8  * modify it under the terms of the GNU Lesser General Public
9  * License as published by the Free Software Foundation; either
10  * version 2.1 of the License, or (at your option) any later version.
11  *
12  * FFmpeg is distributed in the hope that it will be useful,
13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15  * Lesser General Public License for more details.
16  *
17  * You should have received a copy of the GNU Lesser General Public
18  * License along with FFmpeg; if not, write to the Free Software
19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20  */
21 
22 /**
23  * @file
24  * rational numbers
25  * @author Michael Niedermayer <michaelni@gmx.at>
26  */
27 
28 #include "avassert.h"
29 #include <limits.h>
30 
31 #include "common.h"
32 #include "mathematics.h"
33 #include "rational.h"
34 
35 int av_reduce(int *dst_num, int *dst_den,
36  int64_t num, int64_t den, int64_t max)
37 {
38  AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
39  int sign = (num < 0) ^ (den < 0);
40  int64_t gcd = av_gcd(FFABS(num), FFABS(den));
41 
42  if (gcd) {
43  num = FFABS(num) / gcd;
44  den = FFABS(den) / gcd;
45  }
46  if (num <= max && den <= max) {
47  a1 = (AVRational) { num, den };
48  den = 0;
49  }
50 
51  while (den) {
52  uint64_t x = num / den;
53  int64_t next_den = num - den * x;
54  int64_t a2n = x * a1.num + a0.num;
55  int64_t a2d = x * a1.den + a0.den;
56 
57  if (a2n > max || a2d > max) {
58  if (a1.num) x = (max - a0.num) / a1.num;
59  if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
60 
61  if (den * (2 * x * a1.den + a0.den) > num * a1.den)
62  a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
63  break;
64  }
65 
66  a0 = a1;
67  a1 = (AVRational) { a2n, a2d };
68  num = den;
69  den = next_den;
70  }
71  av_assert2(av_gcd(a1.num, a1.den) <= 1U);
72  av_assert2(a1.num <= max && a1.den <= max);
73 
74  *dst_num = sign ? -a1.num : a1.num;
75  *dst_den = a1.den;
76 
77  return den == 0;
78 }
79 
81 {
82  av_reduce(&b.num, &b.den,
83  b.num * (int64_t) c.num,
84  b.den * (int64_t) c.den, INT_MAX);
85  return b;
86 }
87 
89 {
90  return av_mul_q(b, (AVRational) { c.den, c.num });
91 }
92 
94  av_reduce(&b.num, &b.den,
95  b.num * (int64_t) c.den +
96  c.num * (int64_t) b.den,
97  b.den * (int64_t) c.den, INT_MAX);
98  return b;
99 }
100 
102 {
103  return av_add_q(b, (AVRational) { -c.num, c.den });
104 }
105 
106 AVRational av_d2q(double d, int max)
107 {
108  AVRational a;
109  int exponent;
110  int64_t den;
111  if (isnan(d))
112  return (AVRational) { 0,0 };
113  if (fabs(d) > INT_MAX + 3LL)
114  return (AVRational) { d < 0 ? -1 : 1, 0 };
115  frexp(d, &exponent);
116  exponent = FFMAX(exponent-1, 0);
117  den = 1LL << (61 - exponent);
118  // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
119  av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
120  if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
121  av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
122 
123  return a;
124 }
125 
127 {
128  /* n/d is q, a/b is the median between q1 and q2 */
129  int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
130  int64_t b = 2 * (int64_t)q1.den * q2.den;
131 
132  /* rnd_up(a*d/b) > n => a*d/b > n */
133  int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
134 
135  /* rnd_down(a*d/b) < n => a*d/b < n */
136  int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
137 
138  return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
139 }
140 
142 {
143  int i, nearest_q_idx = 0;
144  for (i = 0; q_list[i].den; i++)
145  if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
146  nearest_q_idx = i;
147 
148  return nearest_q_idx;
149 }
150 
152  int64_t n;
153  int shift;
154  int sign = 0;
155 
156  if (q.den < 0) {
157  q.den *= -1;
158  q.num *= -1;
159  }
160  if (q.num < 0) {
161  q.num *= -1;
162  sign = 1;
163  }
164 
165  if (!q.num && !q.den) return 0xFFC00000;
166  if (!q.num) return 0;
167  if (!q.den) return 0x7F800000 | (q.num & 0x80000000);
168 
169  shift = 23 + av_log2(q.den) - av_log2(q.num);
170  if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
171  else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
172 
173  shift -= n >= (1<<24);
174  shift += n < (1<<23);
175 
176  if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
177  else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
178 
179  av_assert1(n < (1<<24));
180  av_assert1(n >= (1<<23));
181 
182  return sign<<31 | (150-shift)<<23 | (n - (1<<23));
183 }
184 
185 #ifdef TEST
186 
187 #include "integer.h"
188 
189 int main(void)
190 {
191  AVRational a,b,r;
192  int i,j,k;
193  static const int64_t numlist[] = {
194  INT64_MIN, INT64_MIN+1, INT64_MAX, INT32_MIN, INT32_MAX, 1,0,-1,
195  123456789, INT32_MAX-1, INT32_MAX+1LL, UINT32_MAX-1, UINT32_MAX, UINT32_MAX+1LL
196  };
197 
198  for (a.num = -2; a.num <= 2; a.num++) {
199  for (a.den = -2; a.den <= 2; a.den++) {
200  for (b.num = -2; b.num <= 2; b.num++) {
201  for (b.den = -2; b.den <= 2; b.den++) {
202  int c = av_cmp_q(a,b);
203  double d = av_q2d(a) == av_q2d(b) ?
204  0 : (av_q2d(a) - av_q2d(b));
205  if (d > 0) d = 1;
206  else if (d < 0) d = -1;
207  else if (d != d) d = INT_MIN;
208  if (c != d)
209  av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
210  a.den, b.num, b.den, c,d);
211  r = av_sub_q(av_add_q(b,a), b);
212  if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
213  av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
214  }
215  }
216  }
217  }
218 
219  for (i = 0; i < FF_ARRAY_ELEMS(numlist); i++) {
220  int64_t a = numlist[i];
221 
222  for (j = 0; j < FF_ARRAY_ELEMS(numlist); j++) {
223  int64_t b = numlist[j];
224  if (b<=0)
225  continue;
226  for (k = 0; k < FF_ARRAY_ELEMS(numlist); k++) {
227  int64_t c = numlist[k];
228  int64_t res;
229  AVInteger ai;
230 
231  if (c<=0)
232  continue;
233  res = av_rescale_rnd(a,b,c, AV_ROUND_ZERO);
234 
235  ai = av_mul_i(av_int2i(a), av_int2i(b));
236  ai = av_div_i(ai, av_int2i(c));
237 
238  if (av_cmp_i(ai, av_int2i(INT64_MAX)) > 0 && res == INT64_MIN)
239  continue;
240  if (av_cmp_i(ai, av_int2i(INT64_MIN)) < 0 && res == INT64_MIN)
241  continue;
242  if (av_cmp_i(ai, av_int2i(res)) == 0)
243  continue;
244 
245  // Special exception for INT64_MIN, remove this in case INT64_MIN is handled without off by 1 error
246  if (av_cmp_i(ai, av_int2i(res-1)) == 0 && a == INT64_MIN)
247  continue;
248 
249  av_log(NULL, AV_LOG_ERROR, "%"PRId64" * %"PRId64" / %"PRId64" = %"PRId64" or %"PRId64"\n", a,b,c, res, av_i2int(ai));
250  }
251  }
252  }
253 
254  for (a.num = 1; a.num <= 10; a.num++) {
255  for (a.den = 1; a.den <= 10; a.den++) {
256  if (av_gcd(a.num, a.den) > 1)
257  continue;
258  for (b.num = 1; b.num <= 10; b.num++) {
259  for (b.den = 1; b.den <= 10; b.den++) {
260  int start;
261  if (av_gcd(b.num, b.den) > 1)
262  continue;
263  if (av_cmp_q(b, a) < 0)
264  continue;
265  for (start = 0; start < 10 ; start++) {
266  int acc= start;
267  int i;
268 
269  for (i = 0; i<100; i++) {
270  int exact = start + av_rescale_q(i+1, b, a);
271  acc = av_add_stable(a, acc, b, 1);
272  if (FFABS(acc - exact) > 2) {
273  av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
274  a.den, b.num, b.den, acc, exact);
275  return 1;
276  }
277  }
278  }
279  }
280  }
281  }
282  }
283 
284  for (a.den = 1; a.den < 0x100000000U/3; a.den*=3) {
285  for (a.num = -1; a.num < (1<<27); a.num += 1 + a.num/100) {
286  float f = av_int2float(av_q2intfloat(a));
287  float f2 = av_q2d(a);
288  if (fabs(f - f2) > fabs(f)/5000000) {
289  av_log(NULL, AV_LOG_ERROR, "%d/%d %f %f\n", a.num,
290  a.den, f, f2);
291  return 1;
292  }
293 
294  }
295  }
296 
297  return 0;
298 }
299 #endif
#define NULL
Definition: coverity.c:32
static int shift(int a, int b)
Definition: sonic.c:82
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
Rescale a 64-bit integer with specified rounding.
Definition: mathematics.c:58
int acc
Definition: yuv2rgb.c:543
static av_always_inline float av_int2float(uint32_t i)
Reinterpret a 32-bit integer as a float.
Definition: intfloat.h:40
#define a0
Definition: regdef.h:46
uint32_t av_q2intfloat(AVRational q)
Converts a AVRational to a IEEE 32bit float.
Definition: rational.c:151
int num
numerator
Definition: rational.h:44
const char * b
Definition: vf_curves.c:109
int av_log2(unsigned v)
Definition: intmath.c:26
static int av_cmp_q(AVRational a, AVRational b)
Compare two rationals.
Definition: rational.h:66
#define a1
Definition: regdef.h:47
static const uint8_t q1[256]
Definition: twofish.c:96
Round toward +infinity.
Definition: mathematics.h:74
#define av_assert2(cond)
assert() equivalent, that does lie in speed critical code.
Definition: avassert.h:63
static double av_q2d(AVRational a)
Convert rational to double.
Definition: rational.h:80
AVRational av_mul_q(AVRational b, AVRational c)
Multiply two rationals.
Definition: rational.c:80
#define av_log(a,...)
int64_t av_i2int(AVInteger a)
Convert the given AVInteger to an int64_t.
Definition: integer.c:158
AVRational av_add_q(AVRational b, AVRational c)
Add two rationals.
Definition: rational.c:93
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
Rescale a 64-bit integer by 2 rational numbers.
Definition: mathematics.c:142
#define U(x)
Definition: vp56_arith.h:37
AVInteger av_int2i(int64_t a)
Convert the given int64_t to an AVInteger.
Definition: integer.c:147
#define AV_LOG_ERROR
Something went wrong and cannot losslessly be recovered.
Definition: log.h:176
int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
Definition: rational.c:126
AVRational av_div_q(AVRational b, AVRational c)
Divide one rational by another.
Definition: rational.c:88
const char * r
Definition: vf_curves.c:107
AVInteger av_mul_i(AVInteger a, AVInteger b)
Definition: integer.c:64
simple assert() macros that are a bit more flexible than ISO C assert().
int64_t av_gcd(int64_t a, int64_t b)
Compute the greatest common divisor of a and b.
Definition: mathematics.c:37
#define FFMAX(a, b)
Definition: common.h:94
int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max)
Reduce a fraction.
Definition: rational.c:35
AVRational av_sub_q(AVRational b, AVRational c)
Subtract one rational from another.
Definition: rational.c:101
AVRational av_d2q(double d, int max)
Convert a double precision floating point number to a rational.
Definition: rational.c:106
#define av_assert1(cond)
assert() equivalent, that does not lie in speed critical code.
Definition: avassert.h:53
int64_t av_rescale(int64_t a, int64_t b, int64_t c)
Rescale a 64-bit integer with rounding to nearest.
Definition: mathematics.c:129
int av_cmp_i(AVInteger a, AVInteger b)
Return 0 if a==b, 1 if a>b and -1 if a<b.
Definition: integer.c:85
#define FFMIN(a, b)
Definition: common.h:96
Round toward zero.
Definition: mathematics.h:71
#define FFABS(a)
Absolute value, Note, INT_MIN / INT64_MIN result in undefined behavior as they are not representable ...
Definition: common.h:72
int n
Definition: avisynth_c.h:547
int av_find_nearest_q_idx(AVRational q, const AVRational *q_list)
Find the nearest value in q_list to q.
Definition: rational.c:141
#define FF_ARRAY_ELEMS(a)
rational number numerator/denominator
Definition: rational.h:43
#define isnan(x)
Definition: libm.h:340
Round toward -infinity.
Definition: mathematics.h:73
arbitrary precision integers
common internal and external API header
if(ret< 0)
Definition: vf_mcdeint.c:282
rational numbers
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
Add a value to a timestamp.
Definition: mathematics.c:191
static double c[64]
AVInteger av_div_i(AVInteger a, AVInteger b)
Return a/b.
Definition: integer.c:141
int den
denominator
Definition: rational.h:45
void INT64 start
Definition: avisynth_c.h:553
int main(int argc, char **argv)
Definition: main.c:22