1000 ! Factorial.

Large factorial is a problem for a single variable but for an array, the problem is solved easily :D

#include <iostream>
#include <cmath>
#include <vector>

struct factorial {
    factorial( unsigned x ):x( x ), digits( static_cast< int >( cal_digs( x ) ) + 1, 0 ) {
        find_fact();
    }

    double cal_digs( unsigned N ) {
        double appr = 0.0;
        for( unsigned di = 2; di <= N; ++di )
            appr += std::log10( di );
        return appr;
    }

    void find_fact() {
       unsigned rem, tmp, val;
        digits.at( 0 ) = 1;
        double   appr  = 0.0;
        for( unsigned o = 2; o <= x; ++o ) {
            rem   = 0;
            appr += std::log10( o );
            tmp   = static_cast< unsigned >( appr );
            for( unsigned o1 = 0; o1 <= tmp; ++o1 ) {
                   val = ( digits.at( o1 ) * o ) + rem;
                   rem = val / 10;
                digits.at( o1 ) = val % 10;
            }
        }
    }

    std::ostream& out( std::ostream& o ) const {
        for( std::vector< unsigned >::const_reverse_iterator cib = digits.rbegin(), cie = digits.rend(); cib != cie; ++cib )
            o << *cib;
        return o << std::endl;
    }

private :
    unsigned x;
    std::vector< unsigned > digits;
};

std::ostream& operator <<( std::ostream& o, const factorial& fa ) {
    return fa.out( o );
}

int main()
{
    factorial f( 10000 );
    std::cout << f << "\n";
}