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 "avutil.h"
30#include "mathematics.h"
31#include "libavutil/intmath.h"
32#include "libavutil/common.h"
33#include "avassert.h"
34
35/* Stein's binary GCD algorithm:
36 * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
37int64_t av_gcd(int64_t a, int64_t b) {
38    int za, zb, k;
39    int64_t u, v;
40    if (a == 0)
41        return b;
42    if (b == 0)
43        return a;
44    za = ff_ctzll(a);
45    zb = ff_ctzll(b);
46    k  = FFMIN(za, zb);
47    u = llabs(a >> za);
48    v = llabs(b >> zb);
49    while (u != v) {
50        if (u > v)
51            FFSWAP(int64_t, v, u);
52        v -= u;
53        v >>= ff_ctzll(v);
54    }
55    return (uint64_t)u << k;
56}
57
58int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59{
60    int64_t r = 0;
61    av_assert2(c > 0);
62    av_assert2(b >=0);
63    av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
64
65    if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
66        return INT64_MIN;
67
68    if (rnd & AV_ROUND_PASS_MINMAX) {
69        if (a == INT64_MIN || a == INT64_MAX)
70            return a;
71        rnd -= AV_ROUND_PASS_MINMAX;
72    }
73
74    if (a < 0)
75        return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77    if (rnd == AV_ROUND_NEAR_INF)
78        r = c / 2;
79    else if (rnd & 1)
80        r = c - 1;
81
82    if (b <= INT_MAX && c <= INT_MAX) {
83        if (a <= INT_MAX)
84            return (a * b + r) / c;
85        else {
86            int64_t ad = a / c;
87            int64_t a2 = (a % c * b + r) / c;
88            if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89                return INT64_MIN;
90            return ad * b + a2;
91        }
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        if (t1 > INT64_MAX)
116            return INT64_MIN;
117        return t1;
118#else
119        /* reference code doing (a*b + r) / c, requires libavutil/integer.h */
120        AVInteger ai;
121        ai = av_mul_i(av_int2i(a), av_int2i(b));
122        ai = av_add_i(ai, av_int2i(r));
123
124        return av_i2int(av_div_i(ai, av_int2i(c)));
125#endif
126    }
127}
128
129int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130{
131    return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132}
133
134int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135                         enum AVRounding rnd)
136{
137    int64_t b = bq.num * (int64_t)cq.den;
138    int64_t c = cq.num * (int64_t)bq.den;
139    return av_rescale_rnd(a, b, c, rnd);
140}
141
142int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143{
144    return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145}
146
147int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148{
149    int64_t a = tb_a.num * (int64_t)tb_b.den;
150    int64_t b = tb_b.num * (int64_t)tb_a.den;
151    if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152        return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153    if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154        return -1;
155    if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
156        return 1;
157    return 0;
158}
159
160int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
161{
162    int64_t c = (a - b) & (mod - 1);
163    if (c > (mod >> 1))
164        c -= mod;
165    return c;
166}
167
168int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
169    int64_t a, b, this;
170
171    av_assert0(in_ts != AV_NOPTS_VALUE);
172    av_assert0(duration >= 0);
173
174    if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175simple_round:
176        *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177        return av_rescale_q(in_ts, in_tb, out_tb);
178    }
179
180    a =  av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN)   >>1;
181    b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP  )+1)>>1;
182    if (*last < 2*a - b || *last > 2*b - a)
183        goto simple_round;
184
185    this = av_clip64(*last, a, b);
186    *last = this + duration;
187
188    return av_rescale_q(this, fs_tb, out_tb);
189}
190
191int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
192{
193    int64_t m, d;
194
195    if (inc != 1)
196        inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198    m = inc_tb.num * (int64_t)ts_tb.den;
199    d = inc_tb.den * (int64_t)ts_tb.num;
200
201    if (m % d == 0 && ts <= INT64_MAX - m / d)
202        return ts + m / d;
203    if (m < d)
204        return ts;
205
206    {
207        int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208        int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210        if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211            return ts;
212
213        return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214    }
215}
216