rational.c 4.8 KB

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  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. * @file
  23. * rational numbers
  24. * @author Michael Niedermayer <michaelni@gmx.at>
  25. */
  26. #include "avassert.h"
  27. //#include <math.h>
  28. #include <limits.h>
  29. #include "common.h"
  30. #include "mathematics.h"
  31. #include "rational.h"
  32. int av_reduce(int *dst_num, int *dst_den,
  33. int64_t num, int64_t den, int64_t max)
  34. {
  35. AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
  36. int sign = (num < 0) ^ (den < 0);
  37. int64_t gcd = av_gcd(FFABS(num), FFABS(den));
  38. if (gcd) {
  39. num = FFABS(num) / gcd;
  40. den = FFABS(den) / gcd;
  41. }
  42. if (num <= max && den <= max) {
  43. a1 = (AVRational) { num, den };
  44. den = 0;
  45. }
  46. while (den) {
  47. uint64_t x = num / den;
  48. int64_t next_den = num - den * x;
  49. int64_t a2n = x * a1.num + a0.num;
  50. int64_t a2d = x * a1.den + a0.den;
  51. if (a2n > max || a2d > max) {
  52. if (a1.num) x = (max - a0.num) / a1.num;
  53. if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
  54. if (den * (2 * x * a1.den + a0.den) > num * a1.den)
  55. a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
  56. break;
  57. }
  58. a0 = a1;
  59. a1 = (AVRational) { a2n, a2d };
  60. num = den;
  61. den = next_den;
  62. }
  63. av_assert2(av_gcd(a1.num, a1.den) <= 1U);
  64. *dst_num = sign ? -a1.num : a1.num;
  65. *dst_den = a1.den;
  66. return den == 0;
  67. }
  68. AVRational av_mul_q(AVRational b, AVRational c)
  69. {
  70. av_reduce(&b.num, &b.den,
  71. b.num * (int64_t) c.num,
  72. b.den * (int64_t) c.den, INT_MAX);
  73. return b;
  74. }
  75. AVRational av_div_q(AVRational b, AVRational c)
  76. {
  77. return av_mul_q(b, (AVRational) { c.den, c.num });
  78. }
  79. AVRational av_add_q(AVRational b, AVRational c) {
  80. av_reduce(&b.num, &b.den,
  81. b.num * (int64_t) c.den +
  82. c.num * (int64_t) b.den,
  83. b.den * (int64_t) c.den, INT_MAX);
  84. return b;
  85. }
  86. AVRational av_sub_q(AVRational b, AVRational c)
  87. {
  88. return av_add_q(b, (AVRational) { -c.num, c.den });
  89. }
  90. AVRational av_d2q(double d, int max)
  91. {
  92. AVRational a;
  93. #define LOG2 0.69314718055994530941723212145817656807550013436025
  94. int exponent;
  95. int64_t den;
  96. if (isnan(d))
  97. return (AVRational) { 0,0 };
  98. if (isinf(d))
  99. return (AVRational) { d < 0 ? -1 : 1, 0 };
  100. exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
  101. den = 1LL << (61 - exponent);
  102. av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
  103. return a;
  104. }
  105. int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
  106. {
  107. /* n/d is q, a/b is the median between q1 and q2 */
  108. int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
  109. int64_t b = 2 * (int64_t)q1.den * q2.den;
  110. /* rnd_up(a*d/b) > n => a*d/b > n */
  111. int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
  112. /* rnd_down(a*d/b) < n => a*d/b < n */
  113. int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
  114. return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
  115. }
  116. int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
  117. {
  118. int i, nearest_q_idx = 0;
  119. for (i = 0; q_list[i].den; i++)
  120. if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
  121. nearest_q_idx = i;
  122. return nearest_q_idx;
  123. }
  124. #ifdef TEST
  125. int main(void)
  126. {
  127. AVRational a,b;
  128. for (a.num = -2; a.num <= 2; a.num++) {
  129. for (a.den = -2; a.den <= 2; a.den++) {
  130. for (b.num = -2; b.num <= 2; b.num++) {
  131. for (b.den = -2; b.den <= 2; b.den++) {
  132. int c = av_cmp_q(a,b);
  133. double d = av_q2d(a) == av_q2d(b) ?
  134. 0 : (av_q2d(a) - av_q2d(b));
  135. if (d > 0) d = 1;
  136. else if (d < 0) d = -1;
  137. else if (d != d) d = INT_MIN;
  138. if (c != d)
  139. av_log(0, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
  140. a.den, b.num, b.den, c,d);
  141. }
  142. }
  143. }
  144. }
  145. return 0;
  146. }
  147. #endif