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Octonion Specializations 

namespace boost{ namespace math{

template<>
class octonion<float>
{
public:
   typedef float value_type;

   explicit  octonion(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f, float const & requested_e = 0.0f, float const & requested_f = 0.0f, float const & requested_g = 0.0f, float const & requested_h = 0.0f);
   explicit  octonion(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>(), ::std::complex<float> const & z2 = ::std::complex<float>(), ::std::complex<float> const & z3 = ::std::complex<float>());
   explicit  octonion(::boost::math::quaternion<float> const & q0, ::boost::math::quaternion<float> const & q1 = ::boost::math::quaternion<float>());
   explicit  octonion(octonion<double> const & a_recopier);
   explicit  octonion(octonion<long double> const & a_recopier);

   float                             real() const;
   octonion<float>                   unreal() const;

   float                             R_component_1() const;
   float                             R_component_2() const;
   float                             R_component_3() const;
   float                             R_component_4() const;
   float                             R_component_5() const;
   float                             R_component_6() const;
   float                             R_component_7() const;
   float                             R_component_8() const;

   ::std::complex<float>             C_component_1() const;
   ::std::complex<float>             C_component_2() const;
   ::std::complex<float>             C_component_3() const;
   ::std::complex<float>             C_component_4() const;

   ::boost::math::quaternion<float>  H_component_1() const;
   ::boost::math::quaternion<float>  H_component_2() const;

   octonion<float> & operator = (octonion<float> const  & a_affecter);
   template<typename X>
   octonion<float> & operator = (octonion<X> const  & a_affecter);
   octonion<float> & operator = (float const  & a_affecter);
   octonion<float> & operator = (::std::complex<float> const & a_affecter);
   octonion<float> & operator = (::boost::math::quaternion<float> const & a_affecter);

   octonion<float> & operator += (float const & rhs);
   octonion<float> & operator += (::std::complex<float> const & rhs);
   octonion<float> & operator += (::boost::math::quaternion<float> const & rhs);
   template<typename X>
   octonion<float> & operator += (octonion<X> const & rhs);

   octonion<float> & operator -= (float const & rhs);
   octonion<float> & operator -= (::std::complex<float> const & rhs);
   octonion<float> & operator -= (::boost::math::quaternion<float> const & rhs);
   template<typename X>
   octonion<float> & operator -= (octonion<X> const & rhs);

   octonion<float> & operator *= (float const & rhs);
   octonion<float> & operator *= (::std::complex<float> const & rhs);
   octonion<float> & operator *= (::boost::math::quaternion<float> const & rhs);
   template<typename X>
   octonion<float> & operator *= (octonion<X> const & rhs);

   octonion<float> & operator /= (float const & rhs);
   octonion<float> & operator /= (::std::complex<float> const & rhs);
   octonion<float> & operator /= (::boost::math::quaternion<float> const & rhs);
   template<typename X>
   octonion<float> & operator /= (octonion<X> const & rhs);
};

template<>
class octonion<double>
{
public:
   typedef double value_type;

   explicit  octonion(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0, double const & requested_e = 0.0, double const & requested_f = 0.0, double const & requested_g = 0.0, double const & requested_h = 0.0);
   explicit  octonion(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>(), ::std::complex<double> const & z2 = ::std::complex<double>(), ::std::complex<double> const & z3 = ::std::complex<double>());
   explicit  octonion(::boost::math::quaternion<double> const & q0, ::boost::math::quaternion<double> const & q1 = ::boost::math::quaternion<double>());
   explicit  octonion(octonion<float> const & a_recopier);
   explicit  octonion(octonion<long double> const & a_recopier);

   double                             real() const;
   octonion<double>                   unreal() const;

   double                             R_component_1() const;
   double                             R_component_2() const;
   double                             R_component_3() const;
   double                             R_component_4() const;
   double                             R_component_5() const;
   double                             R_component_6() const;
   double                             R_component_7() const;
   double                             R_component_8() const;

   ::std::complex<double>             C_component_1() const;
   ::std::complex<double>             C_component_2() const;
   ::std::complex<double>             C_component_3() const;
   ::std::complex<double>             C_component_4() const;

   ::boost::math::quaternion<double>  H_component_1() const;
   ::boost::math::quaternion<double>  H_component_2() const;

   octonion<double> & operator = (octonion<double> const  & a_affecter);
   template<typename X>
   octonion<double> & operator = (octonion<X> const  & a_affecter);
   octonion<double> & operator = (double const  & a_affecter);
   octonion<double> & operator = (::std::complex<double> const & a_affecter);
   octonion<double> & operator = (::boost::math::quaternion<double> const & a_affecter);

   octonion<double> & operator += (double const & rhs);
   octonion<double> & operator += (::std::complex<double> const & rhs);
   octonion<double> & operator += (::boost::math::quaternion<double> const & rhs);
   template<typename X>
   octonion<double> & operator += (octonion<X> const & rhs);

   octonion<double> & operator -= (double const & rhs);
   octonion<double> & operator -= (::std::complex<double> const & rhs);
   octonion<double> & operator -= (::boost::math::quaternion<double> const & rhs);
   template<typename X>
   octonion<double> & operator -= (octonion<X> const & rhs);

   octonion<double> & operator *= (double const & rhs);
   octonion<double> & operator *= (::std::complex<double> const & rhs);
   octonion<double> & operator *= (::boost::math::quaternion<double> const & rhs);
   template<typename X>
   octonion<double> & operator *= (octonion<X> const & rhs);

   octonion<double> & operator /= (double const & rhs);
   octonion<double> & operator /= (::std::complex<double> const & rhs);
   octonion<double> & operator /= (::boost::math::quaternion<double> const & rhs);
   template<typename X>
   octonion<double> & operator /= (octonion<X> const & rhs);
};

template<>
class octonion<long double>
{
public:
   typedef long double value_type;

   explicit   octonion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L, long double const & requested_e = 0.0L, long double const & requested_f = 0.0L, long double const & requested_g = 0.0L, long double const & requested_h = 0.0L);
   explicit   octonion( ::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>(), ::std::complex<long double> const & z2 = ::std::complex<long double>(), ::std::complex<long double> const & z3 = ::std::complex<long double>());
   explicit   octonion( ::boost::math::quaternion<long double> const & q0, ::boost::math::quaternion<long double> const & z1 = ::boost::math::quaternion<long double>());
   explicit   octonion(octonion<float> const & a_recopier);
   explicit   octonion(octonion<double> const & a_recopier);

   long double                             real() const;
   octonion<long double>                   unreal() const;

   long double                             R_component_1() const;
   long double                             R_component_2() const;
   long double                             R_component_3() const;
   long double                             R_component_4() const;
   long double                             R_component_5() const;
   long double                             R_component_6() const;
   long double                             R_component_7() const;
   long double                             R_component_8() const;

   ::std::complex<long double>             C_component_1() const;
   ::std::complex<long double>             C_component_2() const;
   ::std::complex<long double>             C_component_3() const;
   ::std::complex<long double>             C_component_4() const;

   ::boost::math::quaternion<long double>  H_component_1() const;
   ::boost::math::quaternion<long double>  H_component_2() const;

   octonion<long double> & operator = (octonion<long double> const  & a_affecter);
   template<typename X>
   octonion<long double> & operator = (octonion<X> const  & a_affecter);
   octonion<long double> & operator = (long double const  & a_affecter);
   octonion<long double> & operator = (::std::complex<long double> const & a_affecter);
   octonion<long double> & operator = (::boost::math::quaternion<long double> const & a_affecter);

   octonion<long double> & operator += (long double const & rhs);
   octonion<long double> & operator += (::std::complex<long double> const & rhs);
   octonion<long double> & operator += (::boost::math::quaternion<long double> const & rhs);
   template<typename X>
   octonion<long double> & operator += (octonion<X> const & rhs);

   octonion<long double> & operator -= (long double const & rhs);
   octonion<long double> & operator -= (::std::complex<long double> const & rhs);
   octonion<long double> & operator -= (::boost::math::quaternion<long double> const & rhs);
   template<typename X>
   octonion<long double> & operator -= (octonion<X> const & rhs);

   octonion<long double> & operator *= (long double const & rhs);
   octonion<long double> & operator *= (::std::complex<long double> const & rhs);
   octonion<long double> & operator *= (::boost::math::quaternion<long double> const & rhs);
   template<typename X>
   octonion<long double> & operator *= (octonion<X> const & rhs);

   octonion<long double> & operator /= (long double const & rhs);
   octonion<long double> & operator /= (::std::complex<long double> const & rhs);
   octonion<long double> & operator /= (::boost::math::quaternion<long double> const & rhs);
   template<typename X>
   octonion<long double> & operator /= (octonion<X> const & rhs);
};

} } // namespaces
Copyright © 2006-2010, 2012-2014, 2017 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang

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)

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