farey_seq.cpp

#include <iostream>
#include <iomanip>
#include <cmath>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <cstdlib>

using namespace std;

pair<long int,long int > farey(const __float80 &x, const long int &N){
    pair < long int , long int >  p;
    __float80 media;
    long int a = 0 ,b = 1,c = 1,d = 1;
    while ( b <= N && d <= N ){
        media = (__float80(a+c)/(b+d));
        //cout << media << endl;
        if ( x == media ){
            if ((b+d) <= N){
            return make_pair(a+c,b+d);
        }
            else if( d > b ){
                return make_pair(c,d);
            }
            else{
                return make_pair(a,b);
            }
        }
        else if( x > media ){
            a = a+c;
            b = b+d;
        }
        else {
            c = c+a;
            d = b+d;
        }
    }
    if ( b >  N ){
        return make_pair(c,d);
    }else{
        return make_pair(a,b);
    }
}

int main(int argc , char *argv[]){

    if (argc <= 1 ) {
        cout << "Necesita un argumento decimal entre 0 y 1" << endl;
        exit (1);
    }
    __float80 pp = atof(argv[1]);
    pair<long int,long int> p1 ,p2;
    __float80 rate = 1;
    __float80 prec = 1;
    __float80 decimal = pp;
    __float80 real_precision = 1E-12;
    long int j = 10000;

    while( prec > real_precision ){
        j   += 10000;
        p1   = farey(decimal,j);
        rate = __float80(double(p1.first))/(p1.second);
        prec = abs(decimal-rate);
    }

    cout << "la fracion es : ";
    cout << setw(6) << setprecision(15) << p1.first <<  "/" << p1.second ;
    cout <<"   "    << setw(9) << rate <<" "<< setw(12) << prec << endl;
    return 0;
}