/******************************************
 * C++ Trigintaduonions
 * 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_TRIGINTADUONION
#define CA_UWATERLOO_ALUMNI_DWHARDER_TRIGINTADUONION

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

template <typename T> class Trigintaduonion;

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

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

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

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

template <typename T = double> class Trigintaduonion {
	private:
		T r, i, j, k, u1, i1, j1, k1, u2, i2, j2, k2, u3, i3, j3, k3, u4, i4, j4, k4, u5, i5, j5, k5, u6, i6, j6, k6, u7, i7, j7, k7;

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

	public:
		const static Trigintaduonion ZERO;
		const static Trigintaduonion ONE;
		const static Trigintaduonion I;
		const static Trigintaduonion J;
		const static Trigintaduonion K;
		const static Trigintaduonion U1;
		const static Trigintaduonion I1;
		const static Trigintaduonion J1;
		const static Trigintaduonion K1;
		const static Trigintaduonion U2;
		const static Trigintaduonion I2;
		const static Trigintaduonion J2;
		const static Trigintaduonion K2;
		const static Trigintaduonion U3;
		const static Trigintaduonion I3;
		const static Trigintaduonion J3;
		const static Trigintaduonion K3;
		const static Trigintaduonion U4;
		const static Trigintaduonion I4;
		const static Trigintaduonion J4;
		const static Trigintaduonion K4;
		const static Trigintaduonion U5;
		const static Trigintaduonion I5;
		const static Trigintaduonion J5;
		const static Trigintaduonion K5;
		const static Trigintaduonion U6;
		const static Trigintaduonion I6;
		const static Trigintaduonion J6;
		const static Trigintaduonion K6;
		const static Trigintaduonion U7;
		const static Trigintaduonion I7;
		const static Trigintaduonion J7;
		const static Trigintaduonion K7;

		const static Trigintaduonion UNITS[32];

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

		Trigintaduonion( T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T );
		Trigintaduonion( T = 0.0 );

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

		const Trigintaduonion & operator = ( T );

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

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

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

		Trigintaduonion & operator ++();
		Trigintaduonion operator ++( int );
		Trigintaduonion & operator --();
		Trigintaduonion 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 imag_u4() const;
		T imag_i4() const;
		T imag_j4() const;
		T imag_k4() const;
		T imag_u5() const;
		T imag_i5() const;
		T imag_j5() const;
		T imag_k5() const;
		T imag_u6() const;
		T imag_i6() const;
		T imag_j6() const;
		T imag_k6() const;
		T imag_u7() const;
		T imag_i7() const;
		T imag_j7() const;
		T imag_k7() const;
		T csgn() const;
		T abs() const;
		T norm() const;
		T abs_imag() const;
		T norm_imag() const;
		T arg() const;

		/******************************************
		 * Trigintaduonion-valued Functions
		 ******************************************/

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

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

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

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

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

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

		Trigintaduonion bessel_J( int ) const;

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

		Trigintaduonion ceil() const;
		Trigintaduonion floor() const;

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

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

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

		static Trigintaduonion random();
		static Trigintaduonion random_imag();
		static Trigintaduonion random_real();

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

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

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

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

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

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

		Trigintaduonion operator - () const;

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

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

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

#endif