/******************************************
 * C++ Sedenions
 * 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_SEDENION
#define CA_UWATERLOO_ALUMNI_DWHARDER_SEDENION

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

template <typename T> class Sedenion;

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

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

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

template <typename T> T real( const Sedenion<T> & );
template <typename T> T imag_i( const Sedenion<T> & );
template <typename T> T imag_j( const Sedenion<T> & );
template <typename T> T imag_k( const Sedenion<T> & );
template <typename T> T imag_u1( const Sedenion<T> & );
template <typename T> T imag_i1( const Sedenion<T> & );
template <typename T> T imag_j1( const Sedenion<T> & );
template <typename T> T imag_k1( const Sedenion<T> & );
template <typename T> T imag_u2( const Sedenion<T> & );
template <typename T> T imag_i2( const Sedenion<T> & );
template <typename T> T imag_j2( const Sedenion<T> & );
template <typename T> T imag_k2( const Sedenion<T> & );
template <typename T> T imag_u3( const Sedenion<T> & );
template <typename T> T imag_i3( const Sedenion<T> & );
template <typename T> T imag_j3( const Sedenion<T> & );
template <typename T> T imag_k3( const Sedenion<T> & );
template <typename T> T csgn( const Sedenion<T> & );
template <typename T> T abs( const Sedenion<T> & );
template <typename T> T norm( const Sedenion<T> & );
template <typename T> T abs_imag( const Sedenion<T> & );
template <typename T> T norm_imag( const Sedenion<T> & );
template <typename T> T arg( const Sedenion<T> & );
template <typename T> Sedenion<T> imag( const Sedenion<T> & );
template <typename T> Sedenion<T> conj( const Sedenion<T> & );
template <typename T> Sedenion<T> signum( const Sedenion<T> & );
template <typename T> Sedenion<T> sqr( const Sedenion<T> & );
template <typename T> Sedenion<T> sqrt( const Sedenion<T> & );
template <typename T> Sedenion<T> rotate( const Sedenion<T> &, const Sedenion<T> & );
template <typename T> Sedenion<T> exp( const Sedenion<T> & );
template <typename T> Sedenion<T> log( const Sedenion<T> & );
template <typename T> Sedenion<T> log10( const Sedenion<T> & );
template <typename T> Sedenion<T> pow( const Sedenion<T> &, const Sedenion<T> & );
template <typename T> Sedenion<T> pow( const Sedenion<T> &, T );
template <typename T> Sedenion<T> inverse( const Sedenion<T> & );
template <typename T> Sedenion<T> sin( const Sedenion<T> & );
template <typename T> Sedenion<T> cos( const Sedenion<T> & );
template <typename T> Sedenion<T> tan( const Sedenion<T> & );
template <typename T> Sedenion<T> sec( const Sedenion<T> & );
template <typename T> Sedenion<T> csc( const Sedenion<T> & );
template <typename T> Sedenion<T> cot( const Sedenion<T> & );
template <typename T> Sedenion<T> sinh( const Sedenion<T> & );
template <typename T> Sedenion<T> cosh( const Sedenion<T> & );
template <typename T> Sedenion<T> tanh( const Sedenion<T> & );
template <typename T> Sedenion<T> sech( const Sedenion<T> & );
template <typename T> Sedenion<T> csch( const Sedenion<T> & );
template <typename T> Sedenion<T> coth( const Sedenion<T> & );
template <typename T> Sedenion<T> asin( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> acos( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> atan( const Sedenion<T> & );
template <typename T> Sedenion<T> asec( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> acsc( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> acot( const Sedenion<T> & );
template <typename T> Sedenion<T> asinh( const Sedenion<T> & );
template <typename T> Sedenion<T> acosh( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> atanh( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> asech( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> acsch( const Sedenion<T> & );
template <typename T> Sedenion<T> acoth( const Sedenion<T> &, const Sedenion<T> & = Sedenion<T>::I );
template <typename T> Sedenion<T> bessel_J( int, const Sedenion<T> & );
template <typename T> Sedenion<T> floor( const Sedenion<T> & );
template <typename T> Sedenion<T> ceil( const Sedenion<T> & );
template <typename T> Sedenion<T> horner( const Sedenion<T> &, T *, unsigned int );
template <typename T> Sedenion<T> horner( const Sedenion<T> &, T *, T*, unsigned int );

template <typename T = double> class Sedenion {
	private:
		T r, i, j, k, u1, i1, j1, k1, u2, i2, j2, k2, u3, i3, j3, k3;

		inline static Sedenion multiplier( T, T, const Sedenion & );
		inline static Sedenion make_inf( T, T );
		inline static Sedenion make_i( T, T );

	public:
		const static Sedenion ZERO;
		const static Sedenion ONE;
		const static Sedenion I;
		const static Sedenion J;
		const static Sedenion K;
		const static Sedenion U1;
		const static Sedenion I1;
		const static Sedenion J1;
		const static Sedenion K1;
		const static Sedenion U2;
		const static Sedenion I2;
		const static Sedenion J2;
		const static Sedenion K2;
		const static Sedenion U3;
		const static Sedenion I3;
		const static Sedenion J3;
		const static Sedenion K3;

		const static Sedenion UNITS[16];

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

		Sedenion( T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T );
		Sedenion( T = 0.0 );

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

		const Sedenion & operator = ( const T & );

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

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

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

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

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

		T real() const;
		T operator []( int ) const;
		T& operator []( int );
		T imag_i() const;
		T imag_j() const;
		T imag_k() const;
		T imag_u1() const;
		T imag_i1() const;
		T imag_j1() const;
		T imag_k1() const;
		T imag_u2() const;
		T imag_i2() const;
		T imag_j2() const;
		T imag_k2() const;
		T imag_u3() const;
		T imag_i3() const;
		T imag_j3() const;
		T imag_k3() const;
		T csgn() const;
		T abs() const;
		T norm() const;
		T abs_imag() const;
		T norm_imag() const;
		T arg() const;

		/******************************************
		 * Sedenion-valued Functions
		 ******************************************/

		Sedenion imag() const;
		Sedenion conj() const;
		Sedenion operator * () const;
		Sedenion signum() const;
		Sedenion sqr() const;
		Sedenion sqrt() const;
		Sedenion rotate( const Sedenion & ) 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
		 ******************************************/

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

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

		Sedenion   sin() const;   Sedenion   cos() const;   Sedenion   tan() const;
		Sedenion   sec() const;   Sedenion   csc() const;   Sedenion   cot() const;
		Sedenion  sinh() const;   Sedenion  cosh() const;   Sedenion  tanh() const;
		Sedenion  sech() const;   Sedenion  csch() const;   Sedenion  coth() const;
		Sedenion  asin( const Sedenion & = I ) const;
		Sedenion  acos( const Sedenion & = I ) const;       Sedenion  atan() const;
		Sedenion  asec( const Sedenion & = I ) const;
		Sedenion  acsc( const Sedenion & = I ) const;       Sedenion  acot() const;

		Sedenion asinh() const;
		Sedenion acosh( const Sedenion & = I ) const;
		Sedenion atanh( const Sedenion & = I ) const;

		Sedenion asech( const Sedenion & = I ) const;
		Sedenion acsch() const;
		Sedenion acoth( const Sedenion & = I ) const;

		Sedenion bessel_J( int ) const;

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

		Sedenion ceil() const;
		Sedenion floor() const;

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

		Sedenion horner( T *, unsigned int ) const;
		Sedenion horner( T *, T *, unsigned int ) const;

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

		static Sedenion random();
		static Sedenion random_imag();
		static Sedenion random_real();

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

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

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

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

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

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

		Sedenion operator - () const;

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

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

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

#endif