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
30
34
36 int64_t num, int64_t den, int64_t max)
37 {
39 int sign = (num < 0) ^ (den < 0);
41
42 if (gcd) {
43 num =
FFABS(num) / gcd;
44 den =
FFABS(den) / gcd;
45 }
46 if (num <= max && den <= max) {
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;
60
61 if (den * (2 * x *
a1.den + a0.
den) > num *
a1.den)
63 break;
64 }
65
68 num = den;
69 den = next_den;
70 }
73
74 *dst_num = sign ? -
a1.num :
a1.num;
76
77 return den == 0;
78 }
79
81 {
84 b.
den * (int64_t) c.
den, INT_MAX);
86 }
87
89 {
91 }
92
97 b.
den * (int64_t) c.
den, INT_MAX);
99 }
100
102 {
104 }
105
107 {
109 int exponent;
110 int64_t den;
113 if (fabs(d) > INT_MAX + 3LL)
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
120 if ((!a.
num || !a.
den) && d && max>0 && max<INT_MAX)
122
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 */
134
135 /* rnd_down(a*d/b) < n => a*d/b < n */
137
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
154 int sign = 0;
155
159 }
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
172
173 shift -= n >= (1<<24);
174 shift += n < (1<<23);
175
178
181
182 return sign<<31 | (150-
shift)<<23 | (n - (1<<23));
183 }
184
185 #ifdef TEST
186
188
190 {
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
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)
214 }
215 }
216 }
217 }
218
220 int64_t a = numlist[i];
221
223 int64_t b = numlist[j];
224 if (b<=0)
225 continue;
227 int64_t c = numlist[k];
228 int64_t res;
230
231 if (c<=0)
232 continue;
234
237
239 continue;
241 continue;
243 continue;
244
245 // Special exception for INT64_MIN, remove this in case INT64_MIN is handled without off by 1 error
247 continue;
248
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++) {
261 if (
av_gcd(b.num, b.den) > 1)
262 continue;
264 continue;
265 for (start = 0; start < 10 ; start++) {
267 int i;
268
269 for (i = 0; i<100; i++) {
272 if (
FFABS(acc - exact) > 2) {
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) {
288 if (fabs(f - f2) > fabs(f)/5000000) {
290 a.den, f, f2);
291 return 1;
292 }
293
294 }
295 }
296
297 return 0;
298 }
299 #endif
static int shift(int a, int b)
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.
static av_always_inline float av_int2float(uint32_t i)
Reinterpret a 32-bit integer as a float.
uint32_t av_q2intfloat(AVRational q)
Converts a AVRational to a IEEE 32bit float.
static int av_cmp_q(AVRational a, AVRational b)
Compare two rationals.
static const uint8_t q1[256]
#define av_assert2(cond)
assert() equivalent, that does lie in speed critical code.
static double av_q2d(AVRational a)
Convert rational to double.
AVRational av_mul_q(AVRational b, AVRational c)
Multiply two rationals.
int64_t av_i2int(AVInteger a)
Convert the given AVInteger to an int64_t.
AVRational av_add_q(AVRational b, AVRational c)
Add two rationals.
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
Rescale a 64-bit integer by 2 rational numbers.
AVInteger av_int2i(int64_t a)
Convert the given int64_t to an AVInteger.
#define AV_LOG_ERROR
Something went wrong and cannot losslessly be recovered.
int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
AVRational av_div_q(AVRational b, AVRational c)
Divide one rational by another.
AVInteger av_mul_i(AVInteger a, AVInteger b)
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.
int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max)
Reduce a fraction.
AVRational av_sub_q(AVRational b, AVRational c)
Subtract one rational from another.
AVRational av_d2q(double d, int max)
Convert a double precision floating point number to a rational.
#define av_assert1(cond)
assert() equivalent, that does not lie in speed critical code.
int64_t av_rescale(int64_t a, int64_t b, int64_t c)
Rescale a 64-bit integer with rounding to nearest.
int av_cmp_i(AVInteger a, AVInteger b)
Return 0 if a==b, 1 if a>b and -1 if a<b.
#define FFABS(a)
Absolute value, Note, INT_MIN / INT64_MIN result in undefined behavior as they are not representable ...
int av_find_nearest_q_idx(AVRational q, const AVRational *q_list)
Find the nearest value in q_list to q.
#define FF_ARRAY_ELEMS(a)
rational number numerator/denominator
arbitrary precision integers
common internal and external API header
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
Add a value to a timestamp.
AVInteger av_div_i(AVInteger a, AVInteger b)
Return a/b.
int main(int argc, char **argv)