// Functions can call other functions...
#include <iostream>
#include <cmath>
using namespace std;

double norm( double x, double y = 0.0, double z = 0.0 );
double abs_max( double x, double y, double z = 0.0 );

int main()
{
    cout << "norm(-5.25) = " << norm( -5.25 ) << endl;
    cout << "norm(3.0,-4.0) = " << norm( 3.0, -4.0 ) << endl;
    cout << "norm(-9,8.7,-0.95) = " << norm( -9.0, 8.7, -0.95 ) << endl;
    
    cout << "\n\n"; system( "PAUSE" );
    return( 0 );
}

// This function returns the magnitude of vector <x,y,z>
// Must be called with one, two, or three arguments.
double norm( double x, double y, double z )
{
    double result, max = abs_max( x, y, z );
    if ( max == 0.0 )
        result = 0.0;
    else {
        result = pow( x / max, 2 ) + pow( y / max, 2 ) + pow( z / max, 2 );
        result = max * sqrt( result );
    }
    return( result );
}

// This function returns the maximum value of { |x|, |y|, |z| }.
// Must be called with two or three arguments.
double abs_max( double x, double y, double z )
{
    double max = abs( x );
    if ( max < abs( y ) ) max = abs( y );
    if ( max < abs( z ) ) max = abs( z );
    return( max );
}