//-------------------------------------------------------------------
//	rootfind.cpp
//
//	This program illustrates the Newton-Raphson Method by using
//	it to calculate the twelfth-root of two (a number which has 
//	significance in music theory).
//
//	programmer: ALLAN CRUSE
//	written on: 07 NOV 2005
//-------------------------------------------------------------------

#include <stdio.h>	// for printf(), perror() 
#include <math.h>	// for fabs()

double f( double x )
{
	// returns  x**12 - 2
	double	power = 1.0;
	for (int i = 0; i < 12; i++) power *= x;
	power -= 2.0;
	return	power; 
}

double g( double x )
{
	// returns  12 * x**11
	double	power = 1.0;
	for (int i = 0; i < 11; i++) power *= x;
	power *= 12.0;
	return	power;
}


int main( int argc, char **argv )
{
	printf( "\nUsing Newton-Raphson Method " );
	printf( "to find the twelfth-root of two \n" );

	// compute the root of the equation:  f(r) = 0
	double	r0 = 1.0;	// initial value
	double	r_next = r0, r_curr = r0;
	for (int i = 0; i < 20; i++)
		{
		r_curr = r_next;
		printf( "\n\tr%d = %2.5f ", i, r_curr );
		r_next = r_curr - f( r_curr )/g( r_curr );
		if ( fabs( r_next - r_curr ) < 0.00000000001 ) break;
		}	
	
	// check the result
	double	r = 1.0;
	for (int i = 0; i < 12; i++) r *= r_curr;	
	printf( "\n\nCheck: %2.5f**12 = %2.5f \n\n", r_curr, r );
}