| 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 | /** |
| 22 | * @file |
| 23 | * miscellaneous math routines and tables |
| 24 | */ |
| 25 | |
| 26 | #include <stdint.h> |
| 27 | #include <limits.h> |
| 28 | |
| 29 | #include "mathematics.h" |
| 30 | #include "libavutil/common.h" |
| 31 | #include "avassert.h" |
| 32 | #include "version.h" |
| 33 | |
| 34 | #if FF_API_AV_REVERSE |
| 35 | const uint8_t av_reverse[256] = { |
| 36 | 0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0, |
| 37 | 0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8, |
| 38 | 0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4, |
| 39 | 0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC, |
| 40 | 0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2, |
| 41 | 0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA, |
| 42 | 0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6, |
| 43 | 0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE, |
| 44 | 0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1, |
| 45 | 0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9, |
| 46 | 0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5, |
| 47 | 0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD, |
| 48 | 0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3, |
| 49 | 0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB, |
| 50 | 0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7, |
| 51 | 0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF, |
| 52 | }; |
| 53 | #endif |
| 54 | |
| 55 | int64_t av_gcd(int64_t a, int64_t b) |
| 56 | { |
| 57 | if (b) |
| 58 | return av_gcd(b, a % b); |
| 59 | else |
| 60 | return a; |
| 61 | } |
| 62 | |
| 63 | int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) |
| 64 | { |
| 65 | int64_t r = 0; |
| 66 | av_assert2(c > 0); |
| 67 | av_assert2(b >=0); |
| 68 | av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4); |
| 69 | |
| 70 | if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4)) |
| 71 | return INT64_MIN; |
| 72 | |
| 73 | if (rnd & AV_ROUND_PASS_MINMAX) { |
| 74 | if (a == INT64_MIN || a == INT64_MAX) |
| 75 | return a; |
| 76 | rnd -= AV_ROUND_PASS_MINMAX; |
| 77 | } |
| 78 | |
| 79 | if (a < 0 && a != INT64_MIN) |
| 80 | return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd >> 1) & 1)); |
| 81 | |
| 82 | if (rnd == AV_ROUND_NEAR_INF) |
| 83 | r = c / 2; |
| 84 | else if (rnd & 1) |
| 85 | r = c - 1; |
| 86 | |
| 87 | if (b <= INT_MAX && c <= INT_MAX) { |
| 88 | if (a <= INT_MAX) |
| 89 | return (a * b + r) / c; |
| 90 | else |
| 91 | return a / c * b + (a % c * b + r) / c; |
| 92 | } else { |
| 93 | #if 1 |
| 94 | uint64_t a0 = a & 0xFFFFFFFF; |
| 95 | uint64_t a1 = a >> 32; |
| 96 | uint64_t b0 = b & 0xFFFFFFFF; |
| 97 | uint64_t b1 = b >> 32; |
| 98 | uint64_t t1 = a0 * b1 + a1 * b0; |
| 99 | uint64_t t1a = t1 << 32; |
| 100 | int i; |
| 101 | |
| 102 | a0 = a0 * b0 + t1a; |
| 103 | a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a); |
| 104 | a0 += r; |
| 105 | a1 += a0 < r; |
| 106 | |
| 107 | for (i = 63; i >= 0; i--) { |
| 108 | a1 += a1 + ((a0 >> i) & 1); |
| 109 | t1 += t1; |
| 110 | if (c <= a1) { |
| 111 | a1 -= c; |
| 112 | t1++; |
| 113 | } |
| 114 | } |
| 115 | return t1; |
| 116 | } |
| 117 | #else |
| 118 | AVInteger ai; |
| 119 | ai = av_mul_i(av_int2i(a), av_int2i(b)); |
| 120 | ai = av_add_i(ai, av_int2i(r)); |
| 121 | |
| 122 | return av_i2int(av_div_i(ai, av_int2i(c))); |
| 123 | } |
| 124 | #endif |
| 125 | } |
| 126 | |
| 127 | int64_t av_rescale(int64_t a, int64_t b, int64_t c) |
| 128 | { |
| 129 | return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF); |
| 130 | } |
| 131 | |
| 132 | int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, |
| 133 | enum AVRounding rnd) |
| 134 | { |
| 135 | int64_t b = bq.num * (int64_t)cq.den; |
| 136 | int64_t c = cq.num * (int64_t)bq.den; |
| 137 | return av_rescale_rnd(a, b, c, rnd); |
| 138 | } |
| 139 | |
| 140 | int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) |
| 141 | { |
| 142 | return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF); |
| 143 | } |
| 144 | |
| 145 | int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b) |
| 146 | { |
| 147 | int64_t a = tb_a.num * (int64_t)tb_b.den; |
| 148 | int64_t b = tb_b.num * (int64_t)tb_a.den; |
| 149 | if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX) |
| 150 | return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b); |
| 151 | if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b) |
| 152 | return -1; |
| 153 | if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a) |
| 154 | return 1; |
| 155 | return 0; |
| 156 | } |
| 157 | |
| 158 | int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod) |
| 159 | { |
| 160 | int64_t c = (a - b) & (mod - 1); |
| 161 | if (c > (mod >> 1)) |
| 162 | c -= mod; |
| 163 | return c; |
| 164 | } |
| 165 | |
| 166 | int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){ |
| 167 | int64_t a, b, this; |
| 168 | |
| 169 | av_assert0(in_ts != AV_NOPTS_VALUE); |
| 170 | av_assert0(duration >= 0); |
| 171 | |
| 172 | if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) { |
| 173 | simple_round: |
| 174 | *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration; |
| 175 | return av_rescale_q(in_ts, in_tb, out_tb); |
| 176 | } |
| 177 | |
| 178 | a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1; |
| 179 | b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1; |
| 180 | if (*last < 2*a - b || *last > 2*b - a) |
| 181 | goto simple_round; |
| 182 | |
| 183 | this = av_clip64(*last, a, b); |
| 184 | *last = this + duration; |
| 185 | |
| 186 | return av_rescale_q(this, fs_tb, out_tb); |
| 187 | } |
| 188 | |
| 189 | int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc) |
| 190 | { |
| 191 | int64_t m, d; |
| 192 | |
| 193 | if (inc != 1) |
| 194 | inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1}); |
| 195 | |
| 196 | m = inc_tb.num * (int64_t)ts_tb.den; |
| 197 | d = inc_tb.den * (int64_t)ts_tb.num; |
| 198 | |
| 199 | if (m % d == 0) |
| 200 | return ts + m / d; |
| 201 | if (m < d) |
| 202 | return ts; |
| 203 | |
| 204 | { |
| 205 | int64_t old = av_rescale_q(ts, ts_tb, inc_tb); |
| 206 | int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb); |
| 207 | return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts); |
| 208 | } |
| 209 | } |