#include "solve.h"

#include <float.h>
#include <math.h>
#include <stdio.h>

// Newton's interpolation polynomial with derivative
double t4_solve (
		const double x_0, const int n, 
		const double * restrict X, 
		double * restrict Y,
		double * restrict D
		)
{
	double value, start_value;
	double x_j = X[n-1];
	double y_j = Y[n-1];

	for (int i = n-2; i >= 0; --i)
	{
		const double x_i = X[i];
		const double y_i = Y[i];
		
		if (fabs(x_j - x_i) < DBL_EPSILON)
			return DBL_MAX;
		
		Y[i+1] = (y_j - y_i) / (x_j - x_i);

		y_j = y_i;
		x_j = x_i;
	}

	for (int k = 1; k < n*2-1; ++k)
	{
		double f_j = D[n-1];

		for (int l = n*2-2; l >= k; --l)
		{
			const int i = l >> 1;
			double x_i, f_i, *f;
			
			if (l & 1)
			{
				x_i = X[i-(k>>1)];

				f_i = D[i];
				f = Y + i + 1;
			} else 
			{
				x_j = X[i];
				x_i = X[i-(k>>1)-(k&1)];

				f_i = Y[i];
				f = D + i;
			}

			if (fabs(x_j - x_i) < DBL_EPSILON)
				return DBL_MAX;
			
			*f = (f_j - f_i) / (x_j - x_i);
			f_j = f_i;	
		}
	}

	start_value = 1;
	value = 0;

	for (int i = 0; i < n; ++i)
	{
		const double diff = (x_0 - X[i]);

		value += Y[i] * start_value;
		start_value *= diff;

		value += D[i] * start_value;
		start_value *= diff;
	}

	return value;
}