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/*
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 * Copyright (c) 2005 Michael Niedermayer <michaelni@gmx.at>
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 *
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 * This library is free software; you can redistribute it and/or
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 * modify it under the terms of the GNU Lesser General Public
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 * License as published by the Free Software Foundation; either
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 * version 2 of the License, or (at your option) any later version.
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 *
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 * This library is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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 * Lesser General Public License for more details.
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 *
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 * You should have received a copy of the GNU Lesser General Public
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 * License along with this library; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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 */
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/**
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 * @file mathematics.c
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 * Miscellaneous math routines and tables.
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 */
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#include "common.h"
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#include "mathematics.h"
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const uint8_t ff_sqrt_tab[128]={
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        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,
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        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,
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        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,
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        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
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};
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const uint8_t ff_log2_tab[256]={
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        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,
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        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,
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        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,
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        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,
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        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,
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        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,
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        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,
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        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
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};
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int64_t ff_gcd(int64_t a, int64_t b){
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    if(b) return ff_gcd(b, a%b);
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    else  return a;
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}
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int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
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    int64_t r=0;
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    assert(c > 0);
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    assert(b >=0);
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    assert(rnd >=0 && rnd<=5 && rnd!=4);
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    if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
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    if(rnd==AV_ROUND_NEAR_INF) r= c/2;
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    else if(rnd&1)             r= c-1;
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    if(b<=INT_MAX && c<=INT_MAX){
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        if(a<=INT_MAX)
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            return (a * b + r)/c;
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        else
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            return a/c*b + (a%c*b + r)/c;
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    }else{
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#if 1
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        uint64_t a0= a&0xFFFFFFFF;
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        uint64_t a1= a>>32;
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        uint64_t b0= b&0xFFFFFFFF;
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        uint64_t b1= b>>32;
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        uint64_t t1= a0*b1 + a1*b0;
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        uint64_t t1a= t1<<32;
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        int i;
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        a0 = a0*b0 + t1a;
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        a1 = a1*b1 + (t1>>32) + (a0<t1a);
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        a0 += r;
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        a1 += a0<r;
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        for(i=63; i>=0; i--){
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//            int o= a1 & 0x8000000000000000ULL;
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            a1+= a1 + ((a0>>i)&1);
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            t1+=t1;
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            if(/*o || */c <= a1){
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                a1 -= c;
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                t1++;
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            }
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        }
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        return t1;
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    }
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#else
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        AVInteger ai;
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        ai= av_mul_i(av_int2i(a), av_int2i(b));
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        ai= av_add_i(ai, av_int2i(r));
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        return av_i2int(av_div_i(ai, av_int2i(c)));
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    }
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#endif
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}
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int64_t av_rescale(int64_t a, int64_t b, int64_t c){
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    return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
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}
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int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
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    int64_t b= bq.num * (int64_t)cq.den;
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    int64_t c= cq.num * (int64_t)bq.den;
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    return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
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}
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#if 0
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#include "integer.h"
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#undef printf
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main(){
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    int64_t a,b,c,d,e;
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    for(a=7; a<(1LL<<62); a+=a/3+1){
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        for(b=3; b<(1LL<<62); b+=b/4+1){
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            for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
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                int64_t r= c/2;
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                AVInteger ai;
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                ai= av_mul_i(av_int2i(a), av_int2i(b));
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                ai= av_add_i(ai, av_int2i(r));
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                d= av_i2int(av_div_i(ai, av_int2i(c)));
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                e= av_rescale(a,b,c);
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                if((double)a * (double)b / (double)c > (1LL<<63))
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                    continue;
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                if(d!=e) printf("%Ld*%Ld/%Ld= %Ld=%Ld\n", a, b, c, d, e);
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            }
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        }
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    }
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}
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#endif