quaternion.hpp

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            template<typename X>
            quaternion<T> &        operator += (quaternion<X> const & rhs)
            {
                T    at = a + static_cast<T>(rhs.R_component_1());    // exception guard
                T    bt = b + static_cast<T>(rhs.R_component_2());    // exception guard
                T    ct = c + static_cast<T>(rhs.R_component_3());    // exception guard
                T    dt = d + static_cast<T>(rhs.R_component_4());    // exception guard
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            
            quaternion<T> &        operator -= (T const & rhs)
            {
                T    at = a - rhs;    // exception guard
                
                a = at;
                
                return(*this);
            }
            
            
            quaternion<T> &        operator -= (::std::complex<T> const & rhs)
            {
                T    at = a - rhs.real();    // exception guard
                T    bt = b - rhs.imag();    // exception guard
                
                a = at;
                b = bt;
                
                return(*this);
            }
            
            
            template<typename X>
            quaternion<T> &        operator -= (quaternion<X> const & rhs)
            {
                T    at = a - static_cast<T>(rhs.R_component_1());    // exception guard
                T    bt = b - static_cast<T>(rhs.R_component_2());    // exception guard
                T    ct = c - static_cast<T>(rhs.R_component_3());    // exception guard
                T    dt = d - static_cast<T>(rhs.R_component_4());    // exception guard
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            quaternion<T> &        operator *= (T const & rhs)
            {
                T    at = a * rhs;    // exception guard
                T    bt = b * rhs;    // exception guard
                T    ct = c * rhs;    // exception guard
                T    dt = d * rhs;    // exception guard
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            quaternion<T> &        operator *= (::std::complex<T> const & rhs)
            {
                T    ar = rhs.real();
                T    br = rhs.imag();
                
                T    at = +a*ar-b*br;
                T    bt = +a*br+b*ar;
                T    ct = +c*ar+d*br;
                T    dt = -c*br+d*ar;
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            template<typename X>
            quaternion<T> &        operator *= (quaternion<X> const & rhs)
            {
                T    ar = static_cast<T>(rhs.R_component_1());
                T    br = static_cast<T>(rhs.R_component_2());
                T    cr = static_cast<T>(rhs.R_component_3());
                T    dr = static_cast<T>(rhs.R_component_4());
                
                T    at = +a*ar-b*br-c*cr-d*dr;
                T    bt = +a*br+b*ar+c*dr-d*cr;    //(a*br+ar*b)+(c*dr-cr*d);
                T    ct = +a*cr-b*dr+c*ar+d*br;    //(a*cr+ar*c)+(d*br-dr*b);
                T    dt = +a*dr+b*cr-c*br+d*ar;    //(a*dr+ar*d)+(b*cr-br*c);
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            
            quaternion<T> &        operator /= (T const & rhs)
            {
                T    at = a / rhs;    // exception guard
                T    bt = b / rhs;    // exception guard
                T    ct = c / rhs;    // exception guard
                T    dt = d / rhs;    // exception guard
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            quaternion<T> &        operator /= (::std::complex<T> const & rhs)
            {
                T    ar = rhs.real();
                T    br = rhs.imag();
                
                T    denominator = ar*ar+br*br;
                
                T    at = (+a*ar+b*br)/denominator;    //(a*ar+b*br)/denominator;
                T    bt = (-a*br+b*ar)/denominator;    //(ar*b-a*br)/denominator;
                T    ct = (+c*ar-d*br)/denominator;    //(ar*c-d*br)/denominator;
                T    dt = (+c*br+d*ar)/denominator;    //(ar*d+br*c)/denominator;
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            template<typename X>
            quaternion<T> &        operator /= (quaternion<X> const & rhs)
            {
                T    ar = static_cast<T>(rhs.R_component_1());
                T    br = static_cast<T>(rhs.R_component_2());
                T    cr = static_cast<T>(rhs.R_component_3());
                T    dr = static_cast<T>(rhs.R_component_4());
                
                T    denominator = ar*ar+br*br+cr*cr+dr*dr;
                
                T    at = (+a*ar+b*br+c*cr+d*dr)/denominator;    //(a*ar+b*br+c*cr+d*dr)/denominator;
                T    bt = (-a*br+b*ar-c*dr+d*cr)/denominator;    //((ar*b-a*br)+(cr*d-c*dr))/denominator;
                T    ct = (-a*cr+b*dr+c*ar-d*br)/denominator;    //((ar*c-a*cr)+(dr*b-d*br))/denominator;
                T    dt = (-a*dr-b*cr+c*br+d*ar)/denominator;    //((ar*d-a*dr)+(br*c-b*cr))/denominator;
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
        protected:
            
            BOOST_QUATERNION_MEMBER_DATA_GENERATOR(T)
            
            
        private:
            
        };
        
        
        // declaration of quaternion specialization
        
        template<>    class quaternion<float>;
        template<>    class quaternion<double>;
        template<>    class quaternion<long double>;
        
        
        // helper templates for converting copy constructors (declaration)
        
        namespace detail
        {
            
            template<   typename T,
                        typename U
                    >
            quaternion<T>    quaternion_type_converter(quaternion<U> const & rhs);
        }
        
        
        // implementation of quaternion specialization
        
        
#define    BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(type)                                                 \
            explicit            quaternion( type const & requested_a = static_cast<type>(0),            \
                                            type const & requested_b = static_cast<type>(0),            \
                                            type const & requested_c = static_cast<type>(0),            \
                                            type const & requested_d = static_cast<type>(0))            \
            :   a(requested_a),                                                                         \
                b(requested_b),                                                                         \
                c(requested_c),                                                                         \
                d(requested_d)                                                                          \
            {                                                                                           \
            }                                                                                           \
                                                                                                        \
            explicit            quaternion( ::std::complex<type> const & z0,                            \
                                            ::std::complex<type> const & z1 = ::std::complex<type>())   \
            :   a(z0.real()),                                                                           \
                b(z0.imag()),                                                                           \
                c(z1.real()),                                                                           \
                d(z1.imag())                                                                            \
            {                                                                                           \
            }
        
        
#define    BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type)             \
            quaternion<type> &        operator += (type const & rhs) \
            {                                                        \
                a += rhs;                                            \
                                                                     \
                return(*this);                                       \
            }
    
#define    BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type)                             \
            quaternion<type> &        operator += (::std::complex<type> const & rhs) \
            {                                                                        \
                a += rhs.real();                                                     \
                b += rhs.imag();                                                     \
                                                                                     \