quaternion.hpp

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//  boost quaternion.hpp header file

//  (C) Copyright Hubert Holin 2001.
//  Distributed under the Boost Software License, Version 1.0. (See
//  accompanying file LICENSE_1_0.txt or copy at
//  http://www.boost.org/LICENSE_1_0.txt)

// See http://www.boost.org for updates, documentation, and revision history.

#ifndef BOOST_QUATERNION_HPP
#define BOOST_QUATERNION_HPP


#include <complex>
#include <iosfwd>                                    // for the "<<" and ">>" operators
#include <sstream>                                    // for the "<<" operator

#include <boost/config.hpp> // for BOOST_NO_STD_LOCALE
#ifndef    BOOST_NO_STD_LOCALE
    #include <locale>                                    // for the "<<" operator
#endif /* BOOST_NO_STD_LOCALE */

#include <valarray>



#include <boost/math/special_functions/sinc.hpp>    // for the Sinus cardinal
#include <boost/math/special_functions/sinhc.hpp>    // for the Hyperbolic Sinus cardinal


namespace boost
{
    namespace math
    {
#if defined(__GNUC__) && (__GNUC__ < 3)
        // gcc 2.95.x uses expression templates for valarray calculations, but
        // the result is not conforming. We need BOOST_GET_VALARRAY to get an
        // actual valarray result when we need to call a member function
    #define    BOOST_GET_VALARRAY(T,x)    ::std::valarray<T>(x)
        // gcc 2.95.x has an "std::ios" class that is similar to 
        // "std::ios_base", so we just use a #define
    #define    BOOST_IOS_BASE    ::std::ios
        // gcc 2.x ignores function scope using declarations,
        // put them in the scope of the enclosing namespace instead:
        using    ::std::valarray;
        using    ::std::sqrt;
        using    ::std::cos;
        using    ::std::sin;
        using    ::std::exp;
        using    ::std::cosh;
#endif /* defined(__GNUC__) && (__GNUC__ < 3) */

#define    BOOST_QUATERNION_ACCESSOR_GENERATOR(type)                    \
            type                    real() const                        \
            {                                                           \
                return(a);                                              \
            }                                                           \
                                                                        \
            quaternion<type>        unreal() const                      \
            {                                                           \
                return(quaternion<type>(static_cast<type>(0),b,c,d));   \
            }                                                           \
                                                                        \
            type                    R_component_1() const               \
            {                                                           \
                return(a);                                              \
            }                                                           \
                                                                        \
            type                    R_component_2() const               \
            {                                                           \
                return(b);                                              \
            }                                                           \
                                                                        \
            type                    R_component_3() const               \
            {                                                           \
                return(c);                                              \
            }                                                           \
                                                                        \
            type                    R_component_4() const               \
            {                                                           \
                return(d);                                              \
            }                                                           \
                                                                        \
            ::std::complex<type>    C_component_1() const               \
            {                                                           \
                return(::std::complex<type>(a,b));                      \
            }                                                           \
                                                                        \
            ::std::complex<type>    C_component_2() const               \
            {                                                           \
                return(::std::complex<type>(c,d));                      \
            }
        
        
#define    BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type)                               \
            template<typename X>                                                            \
            quaternion<type> &        operator = (quaternion<X> const  & a_affecter)        \
            {                                                                               \
                a = static_cast<type>(a_affecter.R_component_1());                          \
                b = static_cast<type>(a_affecter.R_component_2());                          \
                c = static_cast<type>(a_affecter.R_component_3());                          \
                d = static_cast<type>(a_affecter.R_component_4());                          \
                                                                                            \
                return(*this);                                                              \
            }                                                                               \
                                                                                            \
            quaternion<type> &        operator = (quaternion<type> const & a_affecter)      \
            {                                                                               \
                a = a_affecter.a;                                                           \
                b = a_affecter.b;                                                           \
                c = a_affecter.c;                                                           \
                d = a_affecter.d;                                                           \
                                                                                            \
                return(*this);                                                              \
            }                                                                               \
                                                                                            \
            quaternion<type> &        operator = (type const & a_affecter)                  \
            {                                                                               \
                a = a_affecter;                                                             \
                                                                                            \
                b = c = d = static_cast<type>(0);                                           \
                                                                                            \
                return(*this);                                                              \
            }                                                                               \
                                                                                            \
            quaternion<type> &        operator = (::std::complex<type> const & a_affecter)  \
            {                                                                               \
                a = a_affecter.real();                                                      \
                b = a_affecter.imag();                                                      \
                                                                                            \
                c = d = static_cast<type>(0);                                               \
                                                                                            \
                return(*this);                                                              \
            }
        
        
#define    BOOST_QUATERNION_MEMBER_DATA_GENERATOR(type)       \
            type    a;                                        \
            type    b;                                        \
            type    c;                                        \
            type    d;
        
        
        template<typename T>
        class quaternion
        {
        public:
            
            typedef T value_type;
            
            
            // constructor for H seen as R^4
            // (also default constructor)
            
            explicit            quaternion( T const & requested_a = T(),
                                            T const & requested_b = T(),
                                            T const & requested_c = T(),
                                            T const & requested_d = T())
            :   a(requested_a),
                b(requested_b),
                c(requested_c),
                d(requested_d)
            {
                // nothing to do!
            }
            
            
            // constructor for H seen as C^2
                
            explicit            quaternion( ::std::complex<T> const & z0,
                                            ::std::complex<T> const & z1 = ::std::complex<T>())
            :   a(z0.real()),
                b(z0.imag()),
                c(z1.real()),
                d(z1.imag())
            {
                // nothing to do!
            }
            
            
            // UNtemplated copy constructor
            // (this is taken care of by the compiler itself)
            
            
            // templated copy constructor
            
            template<typename X>
            explicit            quaternion(quaternion<X> const & a_recopier)
            :   a(static_cast<T>(a_recopier.R_component_1())),
                b(static_cast<T>(a_recopier.R_component_2())),
                c(static_cast<T>(a_recopier.R_component_3())),
                d(static_cast<T>(a_recopier.R_component_4()))
            {
                // nothing to do!
            }
            
            
            // destructor
            // (this is taken care of by the compiler itself)
            
            
            // accessors
            //
            // Note:    Like complex number, quaternions do have a meaningful notion of "real part",
            //            but unlike them there is no meaningful notion of "imaginary part".
            //            Instead there is an "unreal part" which itself is a quaternion, and usually
            //            nothing simpler (as opposed to the complex number case).
            //            However, for practicallity, there are accessors for the other components
            //            (these are necessary for the templated copy constructor, for instance).
            
            BOOST_QUATERNION_ACCESSOR_GENERATOR(T)
            
            // assignment operators
            
            BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T)
            
            // other assignment-related operators
            //
            // NOTE:    Quaternion multiplication is *NOT* commutative;
            //            symbolically, "q *= rhs;" means "q = q * rhs;"
            //            and "q /= rhs;" means "q = q * inverse_of(rhs);"
            
            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);
            }