chebyshev.cpp

#include <stdio.h>
#include <stdlib.h>

template<size_t N>
struct Chebyshev_CB
{
	double operator()(double x)
	{
		return 2.0 * x * Chebyshev_CB<N-1>()(x) - Chebyshev_CB<N-2>()(x);
	}
};

template<>
struct Chebyshev_CB<1>
{
	double operator()(double x)
	{
		return x;
	}
};

template<>
struct Chebyshev_CB<0>
{
	double operator()(double x)
	{
		return 1.0;
	}
};

template<size_t N, int F=1>
struct Chebyshev_Per
{
	double operator()(double x)
	{
		return x * Chebyshev_Per<N-1, 2*F>()(x) - Chebyshev_Per<N-2, F>()(x);
	}
};

template<int F>
struct Chebyshev_Per<1, F>
{
	double operator()(double x)
	{
		return double(F) * x;
	}
};

template<int F>
struct Chebyshev_Per<0, F>
{
	double operator()(double x)
	{
		return double(F);
	}
};

inline double chebyshev_ryg(int n, double x)
{
	double a = 1.0, b = x;
	while (n--) {
		const double t = b;
		b = 2.0 * x * b - a;
		a = t;
	}
	return a;
}

void test_per(double x)
{
	double per = Chebyshev_Per<10>()(x);
	printf("Per: %g\n", per);
}

void test_cb(double x)
{
	double cb = Chebyshev_CB<10>()(x);
	printf("Per: %g\n", cb);
}

void test_ryg(double x)
{
	double cb = chebyshev_ryg(10, x);
	printf("Ryg: %g\n", cb);
}

int main()
{
	char line[1024];
	while (true) {
		gets(line);
		double x = atof(line);
		test_per(x);
		test_cb(x);
		test_ryg(x);
	}
	return 0;
}