mathematics.c 4.3 KB

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  1. /*
  2. * Copyright (c) 2005 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 mathematics.c
  22. * Miscellaneous math routines and tables.
  23. */
  24. #include "common.h"
  25. #include "mathematics.h"
  26. const uint8_t ff_sqrt_tab[128]={
  27. 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5,
  28. 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
  29. 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
  30. 9, 9, 9, 9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11
  31. };
  32. const uint8_t ff_log2_tab[256]={
  33. 0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
  34. 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
  35. 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
  36. 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
  37. 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  38. 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  39. 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  40. 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
  41. };
  42. int64_t ff_gcd(int64_t a, int64_t b){
  43. if(b) return ff_gcd(b, a%b);
  44. else return a;
  45. }
  46. int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
  47. int64_t r=0;
  48. assert(c > 0);
  49. assert(b >=0);
  50. assert(rnd >=0 && rnd<=5 && rnd!=4);
  51. if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
  52. if(rnd==AV_ROUND_NEAR_INF) r= c/2;
  53. else if(rnd&1) r= c-1;
  54. if(b<=INT_MAX && c<=INT_MAX){
  55. if(a<=INT_MAX)
  56. return (a * b + r)/c;
  57. else
  58. return a/c*b + (a%c*b + r)/c;
  59. }else{
  60. #if 1
  61. uint64_t a0= a&0xFFFFFFFF;
  62. uint64_t a1= a>>32;
  63. uint64_t b0= b&0xFFFFFFFF;
  64. uint64_t b1= b>>32;
  65. uint64_t t1= a0*b1 + a1*b0;
  66. uint64_t t1a= t1<<32;
  67. int i;
  68. a0 = a0*b0 + t1a;
  69. a1 = a1*b1 + (t1>>32) + (a0<t1a);
  70. a0 += r;
  71. a1 += a0<r;
  72. for(i=63; i>=0; i--){
  73. // int o= a1 & 0x8000000000000000ULL;
  74. a1+= a1 + ((a0>>i)&1);
  75. t1+=t1;
  76. if(/*o || */c <= a1){
  77. a1 -= c;
  78. t1++;
  79. }
  80. }
  81. return t1;
  82. }
  83. #else
  84. AVInteger ai;
  85. ai= av_mul_i(av_int2i(a), av_int2i(b));
  86. ai= av_add_i(ai, av_int2i(r));
  87. return av_i2int(av_div_i(ai, av_int2i(c)));
  88. }
  89. #endif
  90. }
  91. int64_t av_rescale(int64_t a, int64_t b, int64_t c){
  92. return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
  93. }
  94. int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
  95. int64_t b= bq.num * (int64_t)cq.den;
  96. int64_t c= cq.num * (int64_t)bq.den;
  97. return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
  98. }
  99. #if 0
  100. #include "integer.h"
  101. #undef printf
  102. main(){
  103. int64_t a,b,c,d,e;
  104. for(a=7; a<(1LL<<62); a+=a/3+1){
  105. for(b=3; b<(1LL<<62); b+=b/4+1){
  106. for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
  107. int64_t r= c/2;
  108. AVInteger ai;
  109. ai= av_mul_i(av_int2i(a), av_int2i(b));
  110. ai= av_add_i(ai, av_int2i(r));
  111. d= av_i2int(av_div_i(ai, av_int2i(c)));
  112. e= av_rescale(a,b,c);
  113. if((double)a * (double)b / (double)c > (1LL<<63))
  114. continue;
  115. if(d!=e) printf("%Ld*%Ld/%Ld= %Ld=%Ld\n", a, b, c, d, e);
  116. }
  117. }
  118. }
  119. }
  120. #endif