#ifndef DEF_AUTOMATIC_DIFFERENTIATION_MATH
#define DEF_AUTOMATIC_DIFFERENTIATION_MATH

#include <cmath>

// Basic mathematical functions for Scalar numbers

// Trigonometric functions
template<typename Scalar> Scalar sec(const Scalar & x) {
	return Scalar(1.)/cos(x);
}

template<typename Scalar> Scalar cot(const Scalar & x) {
	return cos(x)/sin(x);
}

template<typename Scalar> Scalar csc(const Scalar & x) {
	return Scalar(1.)/sin(x);
}

// Inverse trigonometric functions
template<typename Scalar> Scalar asec(const Scalar & x) {
	return acos(Scalar(1.)/x);
}

template<typename Scalar> Scalar acot(const Scalar & x) {
	return atan(Scalar(1.)/x);
}

template<typename Scalar> Scalar acsc(const Scalar & x) {
	return asin(Scalar(1.)/x);
}

// Hyperbolic trigonometric functions
template<typename Scalar> Scalar sech(const Scalar & x) {
	return Scalar(1.)/cosh(x);
}

template<typename Scalar> Scalar coth(const Scalar & x) {
	return cosh(x)/sinh(x);
}

template<typename Scalar> Scalar csch(const Scalar & x) {
	return Scalar(1.)/sinh(x);
}

// Inverse hyperbolic trigonometric functions
template<typename Scalar> Scalar asech(const Scalar & x) {
	return log((Scalar(1.) + sqrt(Scalar(1.) - x*x))/x);
}

template<typename Scalar> Scalar acoth(const Scalar & x) {
	return Scalar(0.5)*log((x + Scalar(1.))/(x - Scalar(1.)));
}

template<typename Scalar> Scalar acsch(const Scalar & x) {
	return (x >= Scalar(0.)) ? log((Scalar(1.) + sqrt(Scalar(1.) + x*x))/x) : log((Scalar(1.) - sqrt(Scalar(1.) + x*x))/x);
}

// Other functions
template<typename Scalar> Scalar exp10(const Scalar & x) {
	return exp(x*log(Scalar(10.)));
}

template<typename Scalar> Scalar sign(const Scalar & x) {
	return (x >= Scalar(0.)) ? ((x > Scalar(0.)) ? Scalar(1.) : Scalar(0.)) : Scalar(-1.);
}

template<typename Scalar> Scalar heaviside(const Scalar & x) {
	return Scalar(x >= Scalar(0.));
}

template<typename Scalar> Scalar abs(const Scalar & x) {
	return (x >= Scalar(0.)) ? x : -x;
}

#endif