mathematics.c 6.4 KB

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  1. /*
  2. * Copyright (c) 2005-2012 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. * @file
  22. * miscellaneous math routines and tables
  23. */
  24. #include <stdint.h>
  25. #include <limits.h>
  26. #include "mathematics.h"
  27. #include "libavutil/common.h"
  28. #include "avassert.h"
  29. #include "version.h"
  30. #if FF_API_AV_REVERSE
  31. const uint8_t av_reverse[256] = {
  32. 0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0,
  33. 0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8,
  34. 0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4,
  35. 0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC,
  36. 0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2,
  37. 0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA,
  38. 0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6,
  39. 0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE,
  40. 0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1,
  41. 0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9,
  42. 0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5,
  43. 0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD,
  44. 0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3,
  45. 0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB,
  46. 0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7,
  47. 0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF,
  48. };
  49. #endif
  50. int64_t av_gcd(int64_t a, int64_t b)
  51. {
  52. if (b)
  53. return av_gcd(b, a % b);
  54. else
  55. return a;
  56. }
  57. int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
  58. {
  59. int64_t r = 0;
  60. av_assert2(c > 0);
  61. av_assert2(b >=0);
  62. av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
  63. if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
  64. return INT64_MIN;
  65. if (rnd & AV_ROUND_PASS_MINMAX) {
  66. if (a == INT64_MIN || a == INT64_MAX)
  67. return a;
  68. rnd -= AV_ROUND_PASS_MINMAX;
  69. }
  70. if (a < 0 && a != INT64_MIN)
  71. return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd >> 1) & 1));
  72. if (rnd == AV_ROUND_NEAR_INF)
  73. r = c / 2;
  74. else if (rnd & 1)
  75. r = c - 1;
  76. if (b <= INT_MAX && c <= INT_MAX) {
  77. if (a <= INT_MAX)
  78. return (a * b + r) / c;
  79. else
  80. return a / c * b + (a % c * b + r) / c;
  81. } else {
  82. #if 1
  83. uint64_t a0 = a & 0xFFFFFFFF;
  84. uint64_t a1 = a >> 32;
  85. uint64_t b0 = b & 0xFFFFFFFF;
  86. uint64_t b1 = b >> 32;
  87. uint64_t t1 = a0 * b1 + a1 * b0;
  88. uint64_t t1a = t1 << 32;
  89. int i;
  90. a0 = a0 * b0 + t1a;
  91. a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
  92. a0 += r;
  93. a1 += a0 < r;
  94. for (i = 63; i >= 0; i--) {
  95. a1 += a1 + ((a0 >> i) & 1);
  96. t1 += t1;
  97. if (c <= a1) {
  98. a1 -= c;
  99. t1++;
  100. }
  101. }
  102. return t1;
  103. }
  104. #else
  105. AVInteger ai;
  106. ai = av_mul_i(av_int2i(a), av_int2i(b));
  107. ai = av_add_i(ai, av_int2i(r));
  108. return av_i2int(av_div_i(ai, av_int2i(c)));
  109. }
  110. #endif
  111. }
  112. int64_t av_rescale(int64_t a, int64_t b, int64_t c)
  113. {
  114. return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
  115. }
  116. int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
  117. enum AVRounding rnd)
  118. {
  119. int64_t b = bq.num * (int64_t)cq.den;
  120. int64_t c = cq.num * (int64_t)bq.den;
  121. return av_rescale_rnd(a, b, c, rnd);
  122. }
  123. int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
  124. {
  125. return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
  126. }
  127. int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
  128. {
  129. int64_t a = tb_a.num * (int64_t)tb_b.den;
  130. int64_t b = tb_b.num * (int64_t)tb_a.den;
  131. if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX)
  132. return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
  133. if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
  134. return -1;
  135. if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
  136. return 1;
  137. return 0;
  138. }
  139. int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
  140. {
  141. int64_t c = (a - b) & (mod - 1);
  142. if (c > (mod >> 1))
  143. c -= mod;
  144. return c;
  145. }
  146. int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
  147. int64_t a, b, this;
  148. av_assert0(in_ts != AV_NOPTS_VALUE);
  149. av_assert0(duration >= 0);
  150. if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
  151. simple_round:
  152. *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
  153. return av_rescale_q(in_ts, in_tb, out_tb);
  154. }
  155. a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
  156. b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
  157. if (*last < 2*a - b || *last > 2*b - a)
  158. goto simple_round;
  159. this = av_clip64(*last, a, b);
  160. *last = this + duration;
  161. return av_rescale_q(this, fs_tb, out_tb);
  162. }
  163. int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
  164. {
  165. int64_t m, d;
  166. if (inc != 1)
  167. inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
  168. m = inc_tb.num * (int64_t)ts_tb.den;
  169. d = inc_tb.den * (int64_t)ts_tb.num;
  170. if (m % d == 0)
  171. return ts + m / d;
  172. if (m < d)
  173. return ts;
  174. {
  175. int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
  176. int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
  177. return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts);
  178. }
  179. }