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4349 | Serge | 1 | /* |
2 | * rational numbers |
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3 | * Copyright (c) 2003 Michael Niedermayer |
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4 | * |
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5 | * This file is part of FFmpeg. |
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6 | * |
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7 | * FFmpeg is free software; you can redistribute it and/or |
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8 | * modify it under the terms of the GNU Lesser General Public |
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9 | * License as published by the Free Software Foundation; either |
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10 | * version 2.1 of the License, or (at your option) any later version. |
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11 | * |
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12 | * FFmpeg is distributed in the hope that it will be useful, |
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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15 | * Lesser General Public License for more details. |
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16 | * |
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17 | * You should have received a copy of the GNU Lesser General Public |
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18 | * License along with FFmpeg; if not, write to the Free Software |
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19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
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20 | */ |
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21 | |||
22 | /** |
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23 | * @file |
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24 | * rational numbers |
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25 | * @author Michael Niedermayer |
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26 | */ |
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27 | |||
28 | #include "avassert.h" |
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29 | #include |
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30 | |||
31 | #include "common.h" |
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32 | #include "mathematics.h" |
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33 | #include "rational.h" |
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34 | |||
35 | int av_reduce(int *dst_num, int *dst_den, |
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36 | int64_t num, int64_t den, int64_t max) |
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37 | { |
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38 | AVRational a0 = { 0, 1 }, a1 = { 1, 0 }; |
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39 | int sign = (num < 0) ^ (den < 0); |
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40 | int64_t gcd = av_gcd(FFABS(num), FFABS(den)); |
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41 | |||
42 | if (gcd) { |
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43 | num = FFABS(num) / gcd; |
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44 | den = FFABS(den) / gcd; |
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45 | } |
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46 | if (num <= max && den <= max) { |
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47 | a1 = (AVRational) { num, den }; |
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48 | den = 0; |
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49 | } |
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50 | |||
51 | while (den) { |
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52 | uint64_t x = num / den; |
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53 | int64_t next_den = num - den * x; |
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54 | int64_t a2n = x * a1.num + a0.num; |
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55 | int64_t a2d = x * a1.den + a0.den; |
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56 | |||
57 | if (a2n > max || a2d > max) { |
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58 | if (a1.num) x = (max - a0.num) / a1.num; |
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59 | if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den); |
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60 | |||
61 | if (den * (2 * x * a1.den + a0.den) > num * a1.den) |
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62 | a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den }; |
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63 | break; |
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64 | } |
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65 | |||
66 | a0 = a1; |
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67 | a1 = (AVRational) { a2n, a2d }; |
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68 | num = den; |
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69 | den = next_den; |
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70 | } |
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71 | av_assert2(av_gcd(a1.num, a1.den) <= 1U); |
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72 | |||
73 | *dst_num = sign ? -a1.num : a1.num; |
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74 | *dst_den = a1.den; |
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75 | |||
76 | return den == 0; |
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77 | } |
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78 | |||
79 | AVRational av_mul_q(AVRational b, AVRational c) |
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80 | { |
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81 | av_reduce(&b.num, &b.den, |
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82 | b.num * (int64_t) c.num, |
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83 | b.den * (int64_t) c.den, INT_MAX); |
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84 | return b; |
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85 | } |
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86 | |||
87 | AVRational av_div_q(AVRational b, AVRational c) |
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88 | { |
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89 | return av_mul_q(b, (AVRational) { c.den, c.num }); |
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90 | } |
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91 | |||
92 | AVRational av_add_q(AVRational b, AVRational c) { |
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93 | av_reduce(&b.num, &b.den, |
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94 | b.num * (int64_t) c.den + |
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95 | c.num * (int64_t) b.den, |
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96 | b.den * (int64_t) c.den, INT_MAX); |
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97 | return b; |
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98 | } |
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99 | |||
100 | AVRational av_sub_q(AVRational b, AVRational c) |
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101 | { |
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102 | return av_add_q(b, (AVRational) { -c.num, c.den }); |
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103 | } |
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104 | |||
105 | AVRational av_d2q(double d, int max) |
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106 | { |
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107 | AVRational a; |
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108 | #define LOG2 0.69314718055994530941723212145817656807550013436025 |
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109 | int exponent; |
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110 | int64_t den; |
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111 | if (isnan(d)) |
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112 | return (AVRational) { 0,0 }; |
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113 | if (fabs(d) > INT_MAX + 3LL) |
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114 | return (AVRational) { d < 0 ? -1 : 1, 0 }; |
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115 | exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0); |
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116 | den = 1LL << (61 - exponent); |
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117 | // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64 |
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118 | av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max); |
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119 | if ((!a.num || !a.den) && d && max>0 && max |
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120 | av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX); |
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121 | |||
122 | return a; |
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123 | } |
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124 | |||
125 | int av_nearer_q(AVRational q, AVRational q1, AVRational q2) |
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126 | { |
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127 | /* n/d is q, a/b is the median between q1 and q2 */ |
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128 | int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den; |
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129 | int64_t b = 2 * (int64_t)q1.den * q2.den; |
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130 | |||
131 | /* rnd_up(a*d/b) > n => a*d/b > n */ |
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132 | int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP); |
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133 | |||
134 | /* rnd_down(a*d/b) < n => a*d/b < n */ |
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135 | int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN); |
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136 | |||
137 | return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1); |
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138 | } |
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139 | |||
140 | int av_find_nearest_q_idx(AVRational q, const AVRational* q_list) |
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141 | { |
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142 | int i, nearest_q_idx = 0; |
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143 | for (i = 0; q_list[i].den; i++) |
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144 | if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0) |
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145 | nearest_q_idx = i; |
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146 | |||
147 | return nearest_q_idx; |
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148 | } |
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149 | |||
150 | #ifdef TEST |
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151 | int main(void) |
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152 | { |
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153 | AVRational a,b,r; |
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154 | for (a.num = -2; a.num <= 2; a.num++) { |
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155 | for (a.den = -2; a.den <= 2; a.den++) { |
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156 | for (b.num = -2; b.num <= 2; b.num++) { |
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157 | for (b.den = -2; b.den <= 2; b.den++) { |
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158 | int c = av_cmp_q(a,b); |
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159 | double d = av_q2d(a) == av_q2d(b) ? |
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160 | |||
161 | if (d > 0) d = 1; |
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162 | else if (d < 0) d = -1; |
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163 | else if (d != d) d = INT_MIN; |
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164 | if (c != d) |
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165 | av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, |
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166 | a.den, b.num, b.den, c,d); |
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167 | r = av_sub_q(av_add_q(b,a), b); |
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168 | if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den)) |
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169 | av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den); |
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170 | } |
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171 | } |
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172 | } |
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173 | } |
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174 | return 0; |
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175 | } |
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176 | #endif>=>=>=>=>>>> |