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/**
22 * @file libavutil/mathematics.c
23 * miscellaneous math routines and tables
24 */
25
26#include <assert.h>
27#include "avutil.h"
28#include "common.h"
29#include "mathematics.h"
30
31const uint8_t ff_sqrt_tab[256]={
32  0, 16, 23, 28, 32, 36, 40, 43, 46, 48, 51, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90,
33 91, 92, 94, 95, 96, 98, 99,100,102,103,104,105,107,108,109,110,111,112,114,115,116,117,118,119,120,121,122,123,124,125,126,127,
34128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,144,145,146,147,148,149,150,151,151,152,153,154,155,156,156,
35157,158,159,160,160,161,162,163,164,164,165,166,167,168,168,169,170,171,171,172,173,174,174,175,176,176,177,178,179,179,180,181,
36182,182,183,184,184,185,186,186,187,188,188,189,190,190,191,192,192,193,194,194,195,196,196,197,198,198,199,200,200,201,202,202,
37203,204,204,205,205,206,207,207,208,208,209,210,210,211,212,212,213,213,214,215,215,216,216,217,218,218,219,219,220,220,221,222,
38222,223,223,224,224,225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,235,236,236,237,237,238,238,239,239,
39240,240,241,242,242,243,243,244,244,245,245,246,246,247,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,255
40};
41
42const uint8_t ff_log2_tab[256]={
43        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,
44        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,
45        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,
46        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,
47        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,
48        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,
49        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,
50        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
51};
52
53int64_t av_gcd(int64_t a, int64_t b){
54    if(b) return av_gcd(b, a%b);
55    else  return a;
56}
57
58#if LIBAVUTIL_VERSION_MAJOR < 50
59int64_t ff_gcd(int64_t a, int64_t b){
60    return av_gcd(a, b);
61}
62#endif
63
64int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
65    int64_t r=0;
66    assert(c > 0);
67    assert(b >=0);
68    assert(rnd >=0 && rnd<=5 && rnd!=4);
69
70    if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
71
72    if(rnd==AV_ROUND_NEAR_INF) r= c/2;
73    else if(rnd&1)             r= c-1;
74
75    if(b<=INT_MAX && c<=INT_MAX){
76        if(a<=INT_MAX)
77            return (a * b + r)/c;
78        else
79            return a/c*b + (a%c*b + r)/c;
80    }else{
81#if 1
82        uint64_t a0= a&0xFFFFFFFF;
83        uint64_t a1= a>>32;
84        uint64_t b0= b&0xFFFFFFFF;
85        uint64_t b1= b>>32;
86        uint64_t t1= a0*b1 + a1*b0;
87        uint64_t t1a= t1<<32;
88        int i;
89
90        a0 = a0*b0 + t1a;
91        a1 = a1*b1 + (t1>>32) + (a0<t1a);
92        a0 += r;
93        a1 += a0<r;
94
95        for(i=63; i>=0; i--){
96//            int o= a1 & 0x8000000000000000ULL;
97            a1+= a1 + ((a0>>i)&1);
98            t1+=t1;
99            if(/*o || */c <= a1){
100                a1 -= c;
101                t1++;
102            }
103        }
104        return t1;
105    }
106#else
107        AVInteger ai;
108        ai= av_mul_i(av_int2i(a), av_int2i(b));
109        ai= av_add_i(ai, av_int2i(r));
110
111        return av_i2int(av_div_i(ai, av_int2i(c)));
112    }
113#endif
114}
115
116int64_t av_rescale(int64_t a, int64_t b, int64_t c){
117    return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
118}
119
120int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
121    int64_t b= bq.num * (int64_t)cq.den;
122    int64_t c= cq.num * (int64_t)bq.den;
123    return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
124}
125
126#ifdef TEST
127#include "integer.h"
128#undef printf
129int main(void){
130    int64_t a,b,c,d,e;
131
132    for(a=7; a<(1LL<<62); a+=a/3+1){
133        for(b=3; b<(1LL<<62); b+=b/4+1){
134            for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
135                int64_t r= c/2;
136                AVInteger ai;
137                ai= av_mul_i(av_int2i(a), av_int2i(b));
138                ai= av_add_i(ai, av_int2i(r));
139
140                d= av_i2int(av_div_i(ai, av_int2i(c)));
141
142                e= av_rescale(a,b,c);
143
144                if((double)a * (double)b / (double)c > (1LL<<63))
145                    continue;
146
147                if(d!=e) printf("%"PRId64"*%"PRId64"/%"PRId64"= %"PRId64"=%"PRId64"\n", a, b, c, d, e);
148            }
149        }
150    }
151    return 0;
152}
153#endif
154