/******************************************
 * C++ Complex Numbers
 * Version: 1.0.9
 * Author:  Douglas Wilhelm Harder
 * Date:    2008/03/03
 *
 * Copyright (c) 2006-2008 by Douglas Wilhelm Harder.
 * All rights reserved.
 ******************************************/

#ifndef CA_UWATERLOO_ALUMNI_DWHARDER_COMPLEX
#define CA_UWATERLOO_ALUMNI_DWHARDER_COMPLEX

#include <iostream>
#include <cmath>
#include <string>

template <typename T> class Complex;

template <typename T> std::ostream & operator << ( std::ostream &, const Complex<T> & );

template <typename T> Complex<T> operator + ( T, const Complex<T> & );
template <typename T> Complex<T> operator + ( long, const Complex<T> & );
template <typename T> Complex<T> operator - ( T, const Complex<T> & );
template <typename T> Complex<T> operator - ( long, const Complex<T> & );
template <typename T> Complex<T> operator * ( T, const Complex<T> & );
template <typename T> Complex<T> operator * ( long, const Complex<T> & );
template <typename T> Complex<T> operator / ( T, const Complex<T> & );
template <typename T> Complex<T> operator / ( long, const Complex<T> & );

template <typename T> bool operator == ( T, const Complex<T> & );
template <typename T> bool operator == ( long, const Complex<T> & );
template <typename T> bool operator != ( T, const Complex<T> & );
template <typename T> bool operator != ( long, const Complex<T> & );

template <typename T> T real( const Complex<T> & );
template <typename T> T imag_i( const Complex<T> & );
template <typename T> T csgn( const Complex<T> & );
template <typename T> T abs( const Complex<T> & );
template <typename T> T norm( const Complex<T> & );
template <typename T> T abs_imag( const Complex<T> & );
template <typename T> T norm_imag( const Complex<T> & );
template <typename T> T arg( const Complex<T> & );
template <typename T> Complex<T> imag( const Complex<T> & );
template <typename T> Complex<T> conj( const Complex<T> & );
template <typename T> Complex<T> signum( const Complex<T> & );
template <typename T> Complex<T> sqr( const Complex<T> & );
template <typename T> Complex<T> sqrt( const Complex<T> & );
template <typename T> Complex<T> exp( const Complex<T> & );
template <typename T> Complex<T> log( const Complex<T> & );
template <typename T> Complex<T> log10( const Complex<T> & );
template <typename T> Complex<T> pow( const Complex<T> &, const Complex<T> & );
template <typename T> Complex<T> pow( const Complex<T> &, T );
template <typename T> Complex<T> inverse( const Complex<T> & );
template <typename T> Complex<T> sin( const Complex<T> & );
template <typename T> Complex<T> cos( const Complex<T> & );
template <typename T> Complex<T> tan( const Complex<T> & );
template <typename T> Complex<T> sec( const Complex<T> & );
template <typename T> Complex<T> csc( const Complex<T> & );
template <typename T> Complex<T> cot( const Complex<T> & );
template <typename T> Complex<T> sinh( const Complex<T> & );
template <typename T> Complex<T> cosh( const Complex<T> & );
template <typename T> Complex<T> tanh( const Complex<T> & );
template <typename T> Complex<T> sech( const Complex<T> & );
template <typename T> Complex<T> csch( const Complex<T> & );
template <typename T> Complex<T> coth( const Complex<T> & );
template <typename T> Complex<T> asin( const Complex<T> & );
template <typename T> Complex<T> acos( const Complex<T> & );
template <typename T> Complex<T> atan( const Complex<T> & );
template <typename T> Complex<T> asec( const Complex<T> & );
template <typename T> Complex<T> acsc( const Complex<T> & );
template <typename T> Complex<T> acot( const Complex<T> & );
template <typename T> Complex<T> asinh( const Complex<T> & );
template <typename T> Complex<T> acosh( const Complex<T> & );
template <typename T> Complex<T> atanh( const Complex<T> & );
template <typename T> Complex<T> asech( const Complex<T> & );
template <typename T> Complex<T> acsch( const Complex<T> & );
template <typename T> Complex<T> acoth( const Complex<T> & );
template <typename T> Complex<T> bessel_J( int, const Complex<T> & );
template <typename T> Complex<T> floor( const Complex<T> & );
template <typename T> Complex<T> ceil( const Complex<T> & );
template <typename T> Complex<T> horner( const Complex<T> &, T *, unsigned int );
template <typename T> Complex<T> horner( const Complex<T> &, T *, T *, unsigned int );
template <typename T> Complex<T> horner( const Complex<T> &, Complex<T> *, unsigned int );
template <typename T> Complex<T> horner( const Complex<T> &, Complex<T> *, T *, unsigned int );
template <typename T> Complex<T> horner( const Complex<T> &, T *, Complex<T> *, unsigned int );
template <typename T> Complex<T> horner( const Complex<T> &, Complex<T> *, Complex<T> *, unsigned int );

template <typename T = double> class Complex {
	private:
		T r, i;
		static char imaginary_symbol;

	public:
		static char use_symbol( char sym );
		static char get_symbol();

		const static Complex ZERO;
		const static Complex ONE;
		const static Complex I;

		const static Complex UNITS[2];

		/******************************************
		 * Constructor and Copy Constructor
		 ******************************************/

		Complex( T, T );
		Complex( T = 0.0 );

		/******************************************
		 * Assignment Operator
		 ******************************************/

		const Complex & operator = ( T );

		/******************************************
		 * Mutating Arithmetic Operators
		 ******************************************/

		Complex & operator += ( const Complex & );
		Complex & operator -= ( const Complex & );
		Complex & operator *= ( const Complex & );
		Complex & operator /= ( const Complex & );

		Complex & operator += ( T );
		Complex & operator -= ( T );
		Complex & operator *= ( T );
		Complex & operator /= ( T );

		Complex & operator ++();
		Complex operator ++( int );
		Complex & operator --();
		Complex operator --( int );

		/******************************************
		 * Real-valued Functions
		 ******************************************/

		T real() const;
		T operator []( int ) const;
		T& operator []( int );
		T imag_i() const;
		T csgn() const;
		T abs() const;
		T norm() const;
		T abs_imag() const;
		T norm_imag() const;
		T arg() const;

		/******************************************
		 * Complex-valued Functions
		 ******************************************/

		Complex imag() const;
		Complex conj() const;
		Complex operator * () const;
		Complex signum() const;
		Complex sqr() const;
		Complex sqrt() const;

		/******************************************
		 * Boolean-valued Functions
		 ******************************************/

		bool is_imaginary() const;
		bool is_inf() const;
		bool is_nan() const;
		bool is_neg_inf() const;
		bool is_pos_inf() const;
		bool is_real() const;
		bool is_real_inf() const;
		bool is_zero() const;

		/******************************************
		 * Exponential and Logarithmic Functions
		 ******************************************/

		Complex exp() const;
		Complex log() const;
		Complex log10() const;
		Complex pow( const Complex & ) const;
		Complex pow( T ) const;
		Complex inverse() const;

		/******************************************
		 * Trigonometric and Hyperbolic Functions
		 ******************************************/

		Complex   sin() const;   Complex   cos() const;   Complex   tan() const;
		Complex   sec() const;   Complex   csc() const;   Complex   cot() const;
		Complex  sinh() const;   Complex  cosh() const;   Complex  tanh() const;
		Complex  sech() const;   Complex  csch() const;   Complex  coth() const;
		Complex  asin() const;   Complex  acos() const;   Complex  atan() const;
		Complex  asec() const;   Complex  acsc() const;   Complex  acot() const;
		Complex asinh() const;   Complex acosh() const;   Complex atanh() const;
		Complex asech() const;   Complex acsch() const;   Complex acoth() const;

		Complex bessel_J( int ) const;

		/******************************************
		 * Integer Functions
		 ******************************************/

		Complex ceil() const;
		Complex floor() const;

		/******************************************
		 * Horner's Rule
		 ******************************************/

		Complex horner( T *, unsigned int ) const;
		Complex horner( T *, T *, unsigned int ) const;
		Complex horner( Complex<T> *, unsigned int ) const;
		Complex horner( Complex<T> *, T *, unsigned int ) const;
		Complex horner( T *, Complex<T> *, unsigned int ) const;
		Complex horner( Complex<T> *, Complex<T> *, unsigned int ) const;

		/******************************************
		 * Random Factories
		 ******************************************/

		static Complex random();
		static Complex random_imag();
		static Complex random_real();

		/******************************************
		 * Binary Arithmetic Operators
		 ******************************************/

		Complex operator + ( const Complex & ) const;
		Complex operator + ( T ) const;

		Complex operator - ( const Complex & ) const;
		Complex operator - ( T ) const;

		Complex operator * ( const Complex & ) const;
		Complex operator * ( T ) const;

		Complex operator / ( const Complex & ) const;
		Complex operator / ( T ) const;

		/******************************************
		 * Unary Arithmetic Operators
		 ******************************************/

		Complex operator - () const;

		/******************************************
		 * Binary Boolean Operators
		 ******************************************/

		bool operator == ( const Complex & ) const;
		bool operator == ( T ) const;

		bool operator != ( const Complex & ) const;
		bool operator != ( T ) const;
};

#endif