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4251 lines
241 KiB
C++
4251 lines
241 KiB
C++
// boost octonion.hpp header file
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_OCTONION_HPP
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#define BOOST_OCTONION_HPP
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#include <boost/math/quaternion.hpp>
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namespace boost
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{
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namespace math
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{
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#define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
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type real() const \
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{ \
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return(a); \
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} \
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\
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octonion<type> unreal() const \
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{ \
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return( octonion<type>(static_cast<type>(0),b,c,d,e,f,g,h)); \
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} \
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\
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type R_component_1() const \
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{ \
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return(a); \
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} \
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\
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type R_component_2() const \
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{ \
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return(b); \
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} \
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\
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type R_component_3() const \
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{ \
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return(c); \
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} \
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\
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type R_component_4() const \
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{ \
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return(d); \
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} \
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\
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type R_component_5() const \
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{ \
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return(e); \
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} \
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\
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type R_component_6() const \
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{ \
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return(f); \
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} \
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\
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type R_component_7() const \
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{ \
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return(g); \
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} \
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\
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type R_component_8() const \
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{ \
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return(h); \
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} \
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\
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::std::complex<type> C_component_1() const \
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{ \
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return(::std::complex<type>(a,b)); \
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} \
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\
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::std::complex<type> C_component_2() const \
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{ \
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return(::std::complex<type>(c,d)); \
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} \
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\
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::std::complex<type> C_component_3() const \
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{ \
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return(::std::complex<type>(e,f)); \
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} \
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\
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::std::complex<type> C_component_4() const \
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{ \
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return(::std::complex<type>(g,h)); \
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} \
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\
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::boost::math::quaternion<type> H_component_1() const \
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{ \
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return(::boost::math::quaternion<type>(a,b,c,d)); \
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} \
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\
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::boost::math::quaternion<type> H_component_2() const \
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{ \
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return(::boost::math::quaternion<type>(e,f,g,h)); \
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}
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#define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
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template<typename X> \
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octonion<type> & operator = (octonion<X> const & a_affecter) \
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{ \
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a = static_cast<type>(a_affecter.R_component_1()); \
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b = static_cast<type>(a_affecter.R_component_2()); \
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c = static_cast<type>(a_affecter.R_component_3()); \
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d = static_cast<type>(a_affecter.R_component_4()); \
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e = static_cast<type>(a_affecter.R_component_5()); \
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f = static_cast<type>(a_affecter.R_component_6()); \
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g = static_cast<type>(a_affecter.R_component_7()); \
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h = static_cast<type>(a_affecter.R_component_8()); \
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\
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return(*this); \
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} \
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\
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octonion<type> & operator = (octonion<type> const & a_affecter) \
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{ \
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a = a_affecter.a; \
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b = a_affecter.b; \
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c = a_affecter.c; \
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d = a_affecter.d; \
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e = a_affecter.e; \
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f = a_affecter.f; \
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g = a_affecter.g; \
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h = a_affecter.h; \
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\
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return(*this); \
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} \
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\
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octonion<type> & operator = (type const & a_affecter) \
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{ \
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a = a_affecter; \
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\
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b = c = d = e = f= g = h = static_cast<type>(0); \
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\
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return(*this); \
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} \
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\
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octonion<type> & operator = (::std::complex<type> const & a_affecter) \
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{ \
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a = a_affecter.real(); \
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b = a_affecter.imag(); \
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\
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c = d = e = f = g = h = static_cast<type>(0); \
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\
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return(*this); \
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} \
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\
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octonion<type> & operator = (::boost::math::quaternion<type> const & a_affecter) \
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{ \
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a = a_affecter.R_component_1(); \
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b = a_affecter.R_component_2(); \
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c = a_affecter.R_component_3(); \
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d = a_affecter.R_component_4(); \
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\
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e = f = g = h = static_cast<type>(0); \
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\
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return(*this); \
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}
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#define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \
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type a; \
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type b; \
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type c; \
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type d; \
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type e; \
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type f; \
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type g; \
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type h; \
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template<typename T>
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class octonion
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{
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public:
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typedef T value_type;
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// constructor for O seen as R^8
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// (also default constructor)
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explicit octonion( T const & requested_a = T(),
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T const & requested_b = T(),
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T const & requested_c = T(),
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T const & requested_d = T(),
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T const & requested_e = T(),
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T const & requested_f = T(),
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T const & requested_g = T(),
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T const & requested_h = T())
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: a(requested_a),
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b(requested_b),
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c(requested_c),
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d(requested_d),
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e(requested_e),
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f(requested_f),
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g(requested_g),
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h(requested_h)
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{
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// nothing to do!
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}
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// constructor for H seen as C^4
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explicit octonion( ::std::complex<T> const & z0,
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::std::complex<T> const & z1 = ::std::complex<T>(),
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::std::complex<T> const & z2 = ::std::complex<T>(),
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::std::complex<T> const & z3 = ::std::complex<T>())
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: a(z0.real()),
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b(z0.imag()),
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c(z1.real()),
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d(z1.imag()),
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e(z2.real()),
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f(z2.imag()),
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g(z3.real()),
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h(z3.imag())
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{
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// nothing to do!
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}
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// constructor for O seen as H^2
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explicit octonion( ::boost::math::quaternion<T> const & q0,
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::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
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: a(q0.R_component_1()),
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b(q0.R_component_2()),
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c(q0.R_component_3()),
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d(q0.R_component_4()),
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e(q1.R_component_1()),
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f(q1.R_component_2()),
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g(q1.R_component_3()),
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h(q1.R_component_4())
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{
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// nothing to do!
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}
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// UNtemplated copy constructor
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// (this is taken care of by the compiler itself)
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// templated copy constructor
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template<typename X>
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explicit octonion(octonion<X> const & a_recopier)
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: a(static_cast<T>(a_recopier.R_component_1())),
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b(static_cast<T>(a_recopier.R_component_2())),
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c(static_cast<T>(a_recopier.R_component_3())),
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d(static_cast<T>(a_recopier.R_component_4())),
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e(static_cast<T>(a_recopier.R_component_5())),
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f(static_cast<T>(a_recopier.R_component_6())),
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g(static_cast<T>(a_recopier.R_component_7())),
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h(static_cast<T>(a_recopier.R_component_8()))
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{
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// nothing to do!
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}
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// destructor
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// (this is taken care of by the compiler itself)
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// accessors
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//
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// Note: Like complex number, octonions do have a meaningful notion of "real part",
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// but unlike them there is no meaningful notion of "imaginary part".
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// Instead there is an "unreal part" which itself is an octonion, and usually
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// nothing simpler (as opposed to the complex number case).
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// However, for practicallity, there are accessors for the other components
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// (these are necessary for the templated copy constructor, for instance).
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BOOST_OCTONION_ACCESSOR_GENERATOR(T)
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// assignment operators
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BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
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// other assignment-related operators
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//
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// NOTE: Octonion multiplication is *NOT* commutative;
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// symbolically, "q *= rhs;" means "q = q * rhs;"
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// and "q /= rhs;" means "q = q * inverse_of(rhs);";
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// octonion multiplication is also *NOT* associative
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octonion<T> & operator += (T const & rhs)
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{
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T at = a + rhs; // exception guard
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a = at;
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return(*this);
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}
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octonion<T> & operator += (::std::complex<T> const & rhs)
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{
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T at = a + rhs.real(); // exception guard
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T bt = b + rhs.imag(); // exception guard
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a = at;
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b = bt;
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return(*this);
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}
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octonion<T> & operator += (::boost::math::quaternion<T> const & rhs)
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{
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T at = a + rhs.R_component_1(); // exception guard
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T bt = b + rhs.R_component_2(); // exception guard
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T ct = c + rhs.R_component_3(); // exception guard
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T dt = d + rhs.R_component_4(); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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template<typename X>
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octonion<T> & operator += (octonion<X> const & rhs)
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{
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T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
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T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
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T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
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T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
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T et = e + static_cast<T>(rhs.R_component_5()); // exception guard
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T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard
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T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard
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T ht = h + static_cast<T>(rhs.R_component_8()); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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e = et;
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f = ft;
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g = gt;
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h = ht;
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return(*this);
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}
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octonion<T> & operator -= (T const & rhs)
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{
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T at = a - rhs; // exception guard
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a = at;
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return(*this);
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}
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octonion<T> & operator -= (::std::complex<T> const & rhs)
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{
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T at = a - rhs.real(); // exception guard
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T bt = b - rhs.imag(); // exception guard
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a = at;
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b = bt;
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return(*this);
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}
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octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs)
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{
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T at = a - rhs.R_component_1(); // exception guard
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T bt = b - rhs.R_component_2(); // exception guard
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T ct = c - rhs.R_component_3(); // exception guard
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T dt = d - rhs.R_component_4(); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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template<typename X>
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octonion<T> & operator -= (octonion<X> const & rhs)
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{
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T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
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T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
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T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
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T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
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T et = e - static_cast<T>(rhs.R_component_5()); // exception guard
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T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard
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T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard
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T ht = h - static_cast<T>(rhs.R_component_8()); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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e = et;
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f = ft;
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g = gt;
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h = ht;
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return(*this);
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}
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octonion<T> & operator *= (T const & rhs)
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{
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T at = a * rhs; // exception guard
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T bt = b * rhs; // exception guard
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T ct = c * rhs; // exception guard
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T dt = d * rhs; // exception guard
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T et = e * rhs; // exception guard
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T ft = f * rhs; // exception guard
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T gt = g * rhs; // exception guard
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T ht = h * rhs; // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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e = et;
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f = ft;
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g = gt;
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h = ht;
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return(*this);
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}
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octonion<T> & operator *= (::std::complex<T> const & rhs)
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{
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T ar = rhs.real();
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T br = rhs.imag();
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T at = +a*ar-b*br;
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T bt = +a*br+b*ar;
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T ct = +c*ar+d*br;
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T dt = -c*br+d*ar;
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T et = +e*ar+f*br;
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T ft = -e*br+f*ar;
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T gt = +g*ar-h*br;
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T ht = +g*br+h*ar;
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a = at;
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b = bt;
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c = ct;
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d = dt;
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e = et;
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f = ft;
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g = gt;
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h = ht;
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return(*this);
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}
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octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs)
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{
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T ar = rhs.R_component_1();
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T br = rhs.R_component_2();
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T cr = rhs.R_component_2();
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T dr = rhs.R_component_2();
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T at = +a*ar-b*br-c*cr-d*dr;
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T bt = +a*br+b*ar+c*dr-d*cr;
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T ct = +a*cr-b*dr+c*ar+d*br;
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T dt = +a*dr+b*cr-c*br+d*ar;
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T et = +e*ar+f*br+g*cr+h*dr;
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T ft = -e*br+f*ar-g*dr+h*cr;
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T gt = -e*cr+f*dr+g*ar-h*br;
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T ht = -e*dr-f*cr+g*br+h*ar;
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a = at;
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b = bt;
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c = ct;
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d = dt;
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e = et;
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f = ft;
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g = gt;
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h = ht;
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return(*this);
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}
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template<typename X>
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octonion<T> & operator *= (octonion<X> const & rhs)
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{
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T ar = static_cast<T>(rhs.R_component_1());
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T br = static_cast<T>(rhs.R_component_2());
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T cr = static_cast<T>(rhs.R_component_3());
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T dr = static_cast<T>(rhs.R_component_4());
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T er = static_cast<T>(rhs.R_component_5());
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T fr = static_cast<T>(rhs.R_component_6());
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T gr = static_cast<T>(rhs.R_component_7());
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T hr = static_cast<T>(rhs.R_component_8());
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T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr;
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T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr;
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T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr;
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T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er;
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T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr;
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T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr;
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T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br;
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T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar;
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a = at;
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b = bt;
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c = ct;
|
|
d = dt;
|
|
e = et;
|
|
f = ft;
|
|
g = gt;
|
|
h = ht;
|
|
|
|
return(*this);
|
|
}
|
|
|
|
|
|
octonion<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
|
|
T et = e / rhs; // exception guard
|
|
T ft = f / rhs; // exception guard
|
|
T gt = g / rhs; // exception guard
|
|
T ht = h / rhs; // exception guard
|
|
|
|
a = at;
|
|
b = bt;
|
|
c = ct;
|
|
d = dt;
|
|
e = et;
|
|
f = ft;
|
|
g = gt;
|
|
h = ht;
|
|
|
|
return(*this);
|
|
}
|
|
|
|
|
|
octonion<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;
|
|
T bt = (-a*br+b*ar)/denominator;
|
|
T ct = (+c*ar-d*br)/denominator;
|
|
T dt = (+c*br+d*ar)/denominator;
|
|
T et = (+e*ar-f*br)/denominator;
|
|
T ft = (+e*br+f*ar)/denominator;
|
|
T gt = (+g*ar+h*br)/denominator;
|
|
T ht = (+g*br+h*ar)/denominator;
|
|
|
|
a = at;
|
|
b = bt;
|
|
c = ct;
|
|
d = dt;
|
|
e = et;
|
|
f = ft;
|
|
g = gt;
|
|
h = ht;
|
|
|
|
return(*this);
|
|
}
|
|
|
|
|
|
octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs)
|
|
{
|
|
T ar = rhs.R_component_1();
|
|
T br = rhs.R_component_2();
|
|
T cr = rhs.R_component_2();
|
|
T dr = rhs.R_component_2();
|
|
|
|
T denominator = ar*ar+br*br+cr*cr+dr*dr;
|
|
|
|
T at = (+a*ar+b*br+c*cr+d*dr)/denominator;
|
|
T bt = (-a*br+b*ar-c*dr+d*cr)/denominator;
|
|
T ct = (-a*cr+b*dr+c*ar-d*br)/denominator;
|
|
T dt = (-a*dr-b*cr+c*br+d*ar)/denominator;
|
|
T et = (+e*ar-f*br-g*cr-h*dr)/denominator;
|
|
T ft = (+e*br+f*ar+g*dr-h*cr)/denominator;
|
|
T gt = (+e*cr-f*dr+g*ar+h*br)/denominator;
|
|
T ht = (+e*dr+f*cr-g*br+h*ar)/denominator;
|
|
|
|
a = at;
|
|
b = bt;
|
|
c = ct;
|
|
d = dt;
|
|
e = et;
|
|
f = ft;
|
|
g = gt;
|
|
h = ht;
|
|
|
|
return(*this);
|
|
}
|
|
|
|
|
|
template<typename X>
|
|
octonion<T> & operator /= (octonion<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 er = static_cast<T>(rhs.R_component_5());
|
|
T fr = static_cast<T>(rhs.R_component_6());
|
|
T gr = static_cast<T>(rhs.R_component_7());
|
|
T hr = static_cast<T>(rhs.R_component_8());
|
|
|
|
T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr;
|
|
|
|
T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator;
|
|
T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator;
|
|
T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator;
|
|
T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator;
|
|
T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator;
|
|
T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator;
|
|
T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator;
|
|
T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator;
|
|
|
|
a = at;
|
|
b = bt;
|
|
c = ct;
|
|
d = dt;
|
|
e = et;
|
|
f = ft;
|
|
g = gt;
|
|
h = ht;
|
|
|
|
return(*this);
|
|
}
|
|
|
|
|
|
protected:
|
|
|
|
BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
|
|
|
|
|
|
private:
|
|
|
|
};
|
|
|
|
|
|
// declaration of octonion specialization
|
|
|
|
template<> class octonion<float>;
|
|
template<> class octonion<double>;
|
|
template<> class octonion<long double>;
|
|
|
|
|
|
// helper templates for converting copy constructors (declaration)
|
|
|
|
namespace detail
|
|
{
|
|
|
|
template< typename T,
|
|
typename U
|
|
>
|
|
octonion<T> octonion_type_converter(octonion<U> const & rhs);
|
|
}
|
|
|
|
|
|
// implementation of octonion specialization
|
|
|
|
|
|
#define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
|
|
explicit octonion( 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), \
|
|
type const & requested_e = static_cast<type>(0), \
|
|
type const & requested_f = static_cast<type>(0), \
|
|
type const & requested_g = static_cast<type>(0), \
|
|
type const & requested_h = static_cast<type>(0)) \
|
|
: a(requested_a), \
|
|
b(requested_b), \
|
|
c(requested_c), \
|
|
d(requested_d), \
|
|
e(requested_e), \
|
|
f(requested_f), \
|
|
g(requested_g), \
|
|
h(requested_h) \
|
|
{ \
|
|
} \
|
|
\
|
|
explicit octonion( ::std::complex<type> const & z0, \
|
|
::std::complex<type> const & z1 = ::std::complex<type>(), \
|
|
::std::complex<type> const & z2 = ::std::complex<type>(), \
|
|
::std::complex<type> const & z3 = ::std::complex<type>()) \
|
|
: a(z0.real()), \
|
|
b(z0.imag()), \
|
|
c(z1.real()), \
|
|
d(z1.imag()), \
|
|
e(z2.real()), \
|
|
f(z2.imag()), \
|
|
g(z3.real()), \
|
|
h(z3.imag()) \
|
|
{ \
|
|
} \
|
|
\
|
|
explicit octonion( ::boost::math::quaternion<type> const & q0, \
|
|
::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \
|
|
: a(q0.R_component_1()), \
|
|
b(q0.R_component_2()), \
|
|
c(q0.R_component_3()), \
|
|
d(q0.R_component_4()), \
|
|
e(q1.R_component_1()), \
|
|
f(q1.R_component_2()), \
|
|
g(q1.R_component_3()), \
|
|
h(q1.R_component_4()) \
|
|
{ \
|
|
}
|
|
|
|
|
|
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
|
|
octonion<type> & operator += (type const & rhs) \
|
|
{ \
|
|
a += rhs; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
|
|
octonion<type> & operator += (::std::complex<type> const & rhs) \
|
|
{ \
|
|
a += rhs.real(); \
|
|
b += rhs.imag(); \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
|
|
octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \
|
|
{ \
|
|
a += rhs.R_component_1(); \
|
|
b += rhs.R_component_2(); \
|
|
c += rhs.R_component_3(); \
|
|
d += rhs.R_component_4(); \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
|
|
template<typename X> \
|
|
octonion<type> & operator += (octonion<X> const & rhs) \
|
|
{ \
|
|
a += static_cast<type>(rhs.R_component_1()); \
|
|
b += static_cast<type>(rhs.R_component_2()); \
|
|
c += static_cast<type>(rhs.R_component_3()); \
|
|
d += static_cast<type>(rhs.R_component_4()); \
|
|
e += static_cast<type>(rhs.R_component_5()); \
|
|
f += static_cast<type>(rhs.R_component_6()); \
|
|
g += static_cast<type>(rhs.R_component_7()); \
|
|
h += static_cast<type>(rhs.R_component_8()); \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
|
|
octonion<type> & operator -= (type const & rhs) \
|
|
{ \
|
|
a -= rhs; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
|
|
octonion<type> & operator -= (::std::complex<type> const & rhs) \
|
|
{ \
|
|
a -= rhs.real(); \
|
|
b -= rhs.imag(); \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
|
|
octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \
|
|
{ \
|
|
a -= rhs.R_component_1(); \
|
|
b -= rhs.R_component_2(); \
|
|
c -= rhs.R_component_3(); \
|
|
d -= rhs.R_component_4(); \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
|
|
template<typename X> \
|
|
octonion<type> & operator -= (octonion<X> const & rhs) \
|
|
{ \
|
|
a -= static_cast<type>(rhs.R_component_1()); \
|
|
b -= static_cast<type>(rhs.R_component_2()); \
|
|
c -= static_cast<type>(rhs.R_component_3()); \
|
|
d -= static_cast<type>(rhs.R_component_4()); \
|
|
e -= static_cast<type>(rhs.R_component_5()); \
|
|
f -= static_cast<type>(rhs.R_component_6()); \
|
|
g -= static_cast<type>(rhs.R_component_7()); \
|
|
h -= static_cast<type>(rhs.R_component_8()); \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
|
|
octonion<type> & operator *= (type const & rhs) \
|
|
{ \
|
|
a *= rhs; \
|
|
b *= rhs; \
|
|
c *= rhs; \
|
|
d *= rhs; \
|
|
e *= rhs; \
|
|
f *= rhs; \
|
|
g *= rhs; \
|
|
h *= rhs; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
|
|
octonion<type> & operator *= (::std::complex<type> const & rhs) \
|
|
{ \
|
|
type ar = rhs.real(); \
|
|
type br = rhs.imag(); \
|
|
\
|
|
type at = +a*ar-b*br; \
|
|
type bt = +a*br+b*ar; \
|
|
type ct = +c*ar+d*br; \
|
|
type dt = -c*br+d*ar; \
|
|
type et = +e*ar+f*br; \
|
|
type ft = -e*br+f*ar; \
|
|
type gt = +g*ar-h*br; \
|
|
type ht = +g*br+h*ar; \
|
|
\
|
|
a = at; \
|
|
b = bt; \
|
|
c = ct; \
|
|
d = dt; \
|
|
e = et; \
|
|
f = ft; \
|
|
g = gt; \
|
|
h = ht; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
|
|
octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \
|
|
{ \
|
|
type ar = rhs.R_component_1(); \
|
|
type br = rhs.R_component_2(); \
|
|
type cr = rhs.R_component_2(); \
|
|
type dr = rhs.R_component_2(); \
|
|
\
|
|
type at = +a*ar-b*br-c*cr-d*dr; \
|
|
type bt = +a*br+b*ar+c*dr-d*cr; \
|
|
type ct = +a*cr-b*dr+c*ar+d*br; \
|
|
type dt = +a*dr+b*cr-c*br+d*ar; \
|
|
type et = +e*ar+f*br+g*cr+h*dr; \
|
|
type ft = -e*br+f*ar-g*dr+h*cr; \
|
|
type gt = -e*cr+f*dr+g*ar-h*br; \
|
|
type ht = -e*dr-f*cr+g*br+h*ar; \
|
|
\
|
|
a = at; \
|
|
b = bt; \
|
|
c = ct; \
|
|
d = dt; \
|
|
e = et; \
|
|
f = ft; \
|
|
g = gt; \
|
|
h = ht; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
|
|
template<typename X> \
|
|
octonion<type> & operator *= (octonion<X> const & rhs) \
|
|
{ \
|
|
type ar = static_cast<type>(rhs.R_component_1()); \
|
|
type br = static_cast<type>(rhs.R_component_2()); \
|
|
type cr = static_cast<type>(rhs.R_component_3()); \
|
|
type dr = static_cast<type>(rhs.R_component_4()); \
|
|
type er = static_cast<type>(rhs.R_component_5()); \
|
|
type fr = static_cast<type>(rhs.R_component_6()); \
|
|
type gr = static_cast<type>(rhs.R_component_7()); \
|
|
type hr = static_cast<type>(rhs.R_component_8()); \
|
|
\
|
|
type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \
|
|
type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \
|
|
type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \
|
|
type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \
|
|
type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \
|
|
type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \
|
|
type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \
|
|
type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \
|
|
\
|
|
a = at; \
|
|
b = bt; \
|
|
c = ct; \
|
|
d = dt; \
|
|
e = et; \
|
|
f = ft; \
|
|
g = gt; \
|
|
h = ht; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
// There is quite a lot of repetition in the code below. This is intentional.
|
|
// The last conditional block is the normal form, and the others merely
|
|
// consist of workarounds for various compiler deficiencies. Hopefuly, when
|
|
// more compilers are conformant and we can retire support for those that are
|
|
// not, we will be able to remove the clutter. This is makes the situation
|
|
// (painfully) explicit.
|
|
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
|
|
octonion<type> & operator /= (type const & rhs) \
|
|
{ \
|
|
a /= rhs; \
|
|
b /= rhs; \
|
|
c /= rhs; \
|
|
d /= rhs; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
|
|
octonion<type> & operator /= (::std::complex<type> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
using ::std::abs; \
|
|
\
|
|
valarray<type> tr(2); \
|
|
\
|
|
tr[0] = rhs.real(); \
|
|
tr[1] = rhs.imag(); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(8); \
|
|
\
|
|
tt[0] = +a*tr[0]-b*tr[1]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]; \
|
|
tt[2] = +c*tr[0]-d*tr[1]; \
|
|
tt[3] = +c*tr[1]+d*tr[0]; \
|
|
tt[4] = +e*tr[0]-f*tr[1]; \
|
|
tt[5] = +e*tr[1]+f*tr[0]; \
|
|
tt[6] = +g*tr[0]+h*tr[1]; \
|
|
tt[7] = +g*tr[1]+h*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
e = tt[4]; \
|
|
f = tt[5]; \
|
|
g = tt[6]; \
|
|
h = tt[7]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#else
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
|
|
octonion<type> & operator /= (::std::complex<type> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<type> tr(2); \
|
|
\
|
|
tr[0] = rhs.real(); \
|
|
tr[1] = rhs.imag(); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(8); \
|
|
\
|
|
tt[0] = +a*tr[0]-b*tr[1]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]; \
|
|
tt[2] = +c*tr[0]-d*tr[1]; \
|
|
tt[3] = +c*tr[1]+d*tr[0]; \
|
|
tt[4] = +e*tr[0]-f*tr[1]; \
|
|
tt[5] = +e*tr[1]+f*tr[0]; \
|
|
tt[6] = +g*tr[0]+h*tr[1]; \
|
|
tt[7] = +g*tr[1]+h*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
e = tt[4]; \
|
|
f = tt[5]; \
|
|
g = tt[6]; \
|
|
h = tt[7]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
|
|
octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
using ::std::abs; \
|
|
\
|
|
valarray<type> tr(4); \
|
|
\
|
|
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
|
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
|
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
|
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(8); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
|
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
|
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
|
tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
|
|
tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
|
|
tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
|
|
tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
e = tt[4]; \
|
|
f = tt[5]; \
|
|
g = tt[6]; \
|
|
h = tt[7]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#else
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
|
|
octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<type> tr(4); \
|
|
\
|
|
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
|
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
|
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
|
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(8); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
|
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
|
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
|
tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
|
|
tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
|
|
tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
|
|
tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
e = tt[4]; \
|
|
f = tt[5]; \
|
|
g = tt[6]; \
|
|
h = tt[7]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
|
|
template<typename X> \
|
|
octonion<type> & operator /= (octonion<X> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
using ::std::abs; \
|
|
\
|
|
valarray<type> tr(8); \
|
|
\
|
|
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
|
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
|
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
|
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
|
tr[4] = static_cast<type>(rhs.R_component_5()); \
|
|
tr[5] = static_cast<type>(rhs.R_component_6()); \
|
|
tr[6] = static_cast<type>(rhs.R_component_7()); \
|
|
tr[7] = static_cast<type>(rhs.R_component_8()); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(8); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
|
|
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
|
|
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
|
|
tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
|
|
tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
|
|
tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
|
|
tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
e = tt[4]; \
|
|
f = tt[5]; \
|
|
g = tt[6]; \
|
|
h = tt[7]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#else
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
|
|
template<typename X> \
|
|
octonion<type> & operator /= (octonion<X> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<type> tr(8); \
|
|
\
|
|
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
|
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
|
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
|
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
|
tr[4] = static_cast<type>(rhs.R_component_5()); \
|
|
tr[5] = static_cast<type>(rhs.R_component_6()); \
|
|
tr[6] = static_cast<type>(rhs.R_component_7()); \
|
|
tr[7] = static_cast<type>(rhs.R_component_8()); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(8); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
|
|
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
|
|
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
|
|
tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
|
|
tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
|
|
tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
|
|
tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
e = tt[4]; \
|
|
f = tt[5]; \
|
|
g = tt[6]; \
|
|
h = tt[7]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
|
|
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
|
|
BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
|
|
BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
|
|
BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
|
|
|
|
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
|
|
BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
|
|
BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
|
|
BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
|
|
|
|
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
|
|
BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
|
|
BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
|
|
BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
|
|
|
|
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
|
|
BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
|
|
BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
|
|
BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
|
|
|
|
#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
|
|
BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
|
|
|
|
|
|
template<>
|
|
class octonion<float>
|
|
{
|
|
public:
|
|
|
|
typedef float value_type;
|
|
|
|
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
|
|
|
|
// UNtemplated copy constructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// explicit copy constructors (precision-loosing converters)
|
|
|
|
explicit octonion(octonion<double> const & a_recopier)
|
|
{
|
|
*this = detail::octonion_type_converter<float, double>(a_recopier);
|
|
}
|
|
|
|
explicit octonion(octonion<long double> const & a_recopier)
|
|
{
|
|
*this = detail::octonion_type_converter<float, long double>(a_recopier);
|
|
}
|
|
|
|
// destructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// accessors
|
|
//
|
|
// Note: Like complex number, octonions 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 an octonion, 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_OCTONION_ACCESSOR_GENERATOR(float)
|
|
|
|
// assignment operators
|
|
|
|
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
|
|
|
|
// other assignment-related operators
|
|
//
|
|
// NOTE: Octonion multiplication is *NOT* commutative;
|
|
// symbolically, "q *= rhs;" means "q = q * rhs;"
|
|
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
|
|
// octonion multiplication is also *NOT* associative
|
|
|
|
BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
|
|
|
|
|
|
protected:
|
|
|
|
BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
|
|
|
|
|
|
private:
|
|
|
|
};
|
|
|
|
|
|
template<>
|
|
class octonion<double>
|
|
{
|
|
public:
|
|
|
|
typedef double value_type;
|
|
|
|
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
|
|
|
|
// UNtemplated copy constructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// converting copy constructor
|
|
|
|
explicit octonion(octonion<float> const & a_recopier)
|
|
{
|
|
*this = detail::octonion_type_converter<double, float>(a_recopier);
|
|
}
|
|
|
|
// explicit copy constructors (precision-loosing converters)
|
|
|
|
explicit octonion(octonion<long double> const & a_recopier)
|
|
{
|
|
*this = detail::octonion_type_converter<double, long double>(a_recopier);
|
|
}
|
|
|
|
// destructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// accessors
|
|
//
|
|
// Note: Like complex number, octonions 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 an octonion, 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_OCTONION_ACCESSOR_GENERATOR(double)
|
|
|
|
// assignment operators
|
|
|
|
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
|
|
|
|
// other assignment-related operators
|
|
//
|
|
// NOTE: Octonion multiplication is *NOT* commutative;
|
|
// symbolically, "q *= rhs;" means "q = q * rhs;"
|
|
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
|
|
// octonion multiplication is also *NOT* associative
|
|
|
|
BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
|
|
|
|
|
|
protected:
|
|
|
|
BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
|
|
|
|
|
|
private:
|
|
|
|
};
|
|
|
|
|
|
template<>
|
|
class octonion<long double>
|
|
{
|
|
public:
|
|
|
|
typedef long double value_type;
|
|
|
|
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
|
|
|
|
// UNtemplated copy constructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// converting copy constructor
|
|
|
|
explicit octonion(octonion<float> const & a_recopier)
|
|
{
|
|
*this = detail::octonion_type_converter<long double, float>(a_recopier);
|
|
}
|
|
|
|
|
|
explicit octonion(octonion<double> const & a_recopier)
|
|
{
|
|
*this = detail::octonion_type_converter<long double, double>(a_recopier);
|
|
}
|
|
|
|
|
|
// destructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// accessors
|
|
//
|
|
// Note: Like complex number, octonions 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 an octonion, 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_OCTONION_ACCESSOR_GENERATOR(long double)
|
|
|
|
// assignment operators
|
|
|
|
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
|
|
|
|
// other assignment-related operators
|
|
//
|
|
// NOTE: Octonion multiplication is *NOT* commutative;
|
|
// symbolically, "q *= rhs;" means "q = q * rhs;"
|
|
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
|
|
// octonion multiplication is also *NOT* associative
|
|
|
|
BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
|
|
|
|
|
|
protected:
|
|
|
|
BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
|
|
|
|
|
|
private:
|
|
|
|
};
|
|
|
|
|
|
#undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
|
|
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
|
|
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
|
|
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
|
|
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
|
|
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
|
|
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
|
|
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
|
|
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
|
|
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
|
|
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
|
|
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
|
|
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
|
|
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
|
|
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
|
|
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
|
|
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
|
|
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
|
|
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
|
|
|
|
|
|
#undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_ACCESSOR_GENERATOR
|
|
|
|
|
|
// operators
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
|
|
{ \
|
|
octonion<T> res(lhs); \
|
|
res op##= rhs; \
|
|
return(res); \
|
|
}
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
|
|
template<typename T> \
|
|
inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
|
|
|
|
#define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
|
|
BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
|
|
|
|
|
|
BOOST_OCTONION_OPERATOR_GENERATOR(+)
|
|
BOOST_OCTONION_OPERATOR_GENERATOR(-)
|
|
BOOST_OCTONION_OPERATOR_GENERATOR(*)
|
|
BOOST_OCTONION_OPERATOR_GENERATOR(/)
|
|
|
|
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_4
|
|
|
|
#undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> operator + (octonion<T> const & o)
|
|
{
|
|
return(o);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> operator - (octonion<T> const & o)
|
|
{
|
|
return(octonion<T>(-o.R_component_1(),-o.R_component_2(),-o.R_component_3(),-o.R_component_4(),-o.R_component_5(),-o.R_component_6(),-o.R_component_7(),-o.R_component_8()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (T const & lhs, octonion<T> const & rhs)
|
|
{
|
|
return(
|
|
(rhs.R_component_1() == lhs)&&
|
|
(rhs.R_component_2() == static_cast<T>(0))&&
|
|
(rhs.R_component_3() == static_cast<T>(0))&&
|
|
(rhs.R_component_4() == static_cast<T>(0))&&
|
|
(rhs.R_component_5() == static_cast<T>(0))&&
|
|
(rhs.R_component_6() == static_cast<T>(0))&&
|
|
(rhs.R_component_7() == static_cast<T>(0))&&
|
|
(rhs.R_component_8() == static_cast<T>(0))
|
|
);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (octonion<T> const & lhs, T const & rhs)
|
|
{
|
|
return(
|
|
(lhs.R_component_1() == rhs)&&
|
|
(lhs.R_component_2() == static_cast<T>(0))&&
|
|
(lhs.R_component_3() == static_cast<T>(0))&&
|
|
(lhs.R_component_4() == static_cast<T>(0))&&
|
|
(lhs.R_component_5() == static_cast<T>(0))&&
|
|
(lhs.R_component_6() == static_cast<T>(0))&&
|
|
(lhs.R_component_7() == static_cast<T>(0))&&
|
|
(lhs.R_component_8() == static_cast<T>(0))
|
|
);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
|
|
{
|
|
return(
|
|
(rhs.R_component_1() == lhs.real())&&
|
|
(rhs.R_component_2() == lhs.imag())&&
|
|
(rhs.R_component_3() == static_cast<T>(0))&&
|
|
(rhs.R_component_4() == static_cast<T>(0))&&
|
|
(rhs.R_component_5() == static_cast<T>(0))&&
|
|
(rhs.R_component_6() == static_cast<T>(0))&&
|
|
(rhs.R_component_7() == static_cast<T>(0))&&
|
|
(rhs.R_component_8() == static_cast<T>(0))
|
|
);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
|
|
{
|
|
return(
|
|
(lhs.R_component_1() == rhs.real())&&
|
|
(lhs.R_component_2() == rhs.imag())&&
|
|
(lhs.R_component_3() == static_cast<T>(0))&&
|
|
(lhs.R_component_4() == static_cast<T>(0))&&
|
|
(lhs.R_component_5() == static_cast<T>(0))&&
|
|
(lhs.R_component_6() == static_cast<T>(0))&&
|
|
(lhs.R_component_7() == static_cast<T>(0))&&
|
|
(lhs.R_component_8() == static_cast<T>(0))
|
|
);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
|
|
{
|
|
return(
|
|
(rhs.R_component_1() == lhs.R_component_1())&&
|
|
(rhs.R_component_2() == lhs.R_component_2())&&
|
|
(rhs.R_component_3() == lhs.R_component_3())&&
|
|
(rhs.R_component_4() == lhs.R_component_4())&&
|
|
(rhs.R_component_5() == static_cast<T>(0))&&
|
|
(rhs.R_component_6() == static_cast<T>(0))&&
|
|
(rhs.R_component_7() == static_cast<T>(0))&&
|
|
(rhs.R_component_8() == static_cast<T>(0))
|
|
);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
|
|
{
|
|
return(
|
|
(lhs.R_component_1() == rhs.R_component_1())&&
|
|
(lhs.R_component_2() == rhs.R_component_2())&&
|
|
(lhs.R_component_3() == rhs.R_component_3())&&
|
|
(lhs.R_component_4() == rhs.R_component_4())&&
|
|
(lhs.R_component_5() == static_cast<T>(0))&&
|
|
(lhs.R_component_6() == static_cast<T>(0))&&
|
|
(lhs.R_component_7() == static_cast<T>(0))&&
|
|
(lhs.R_component_8() == static_cast<T>(0))
|
|
);
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
|
|
{
|
|
return(
|
|
(rhs.R_component_1() == lhs.R_component_1())&&
|
|
(rhs.R_component_2() == lhs.R_component_2())&&
|
|
(rhs.R_component_3() == lhs.R_component_3())&&
|
|
(rhs.R_component_4() == lhs.R_component_4())&&
|
|
(rhs.R_component_5() == lhs.R_component_5())&&
|
|
(rhs.R_component_6() == lhs.R_component_6())&&
|
|
(rhs.R_component_7() == lhs.R_component_7())&&
|
|
(rhs.R_component_8() == lhs.R_component_8())
|
|
);
|
|
}
|
|
|
|
|
|
#define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
|
|
{ \
|
|
return(!(lhs == rhs)); \
|
|
}
|
|
|
|
template<typename T>
|
|
inline bool operator != (T const & lhs, octonion<T> const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
template<typename T>
|
|
inline bool operator != (octonion<T> const & lhs, T const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
template<typename T>
|
|
inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
template<typename T>
|
|
inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
template<typename T>
|
|
inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
template<typename T>
|
|
inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
template<typename T>
|
|
inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
|
|
BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
#undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
|
|
|
|
|
|
// Note: the default values in the constructors of the complex and quaternions make for
|
|
// a very complex and ambiguous situation; we have made choices to disambiguate.
|
|
template<typename T, typename charT, class traits>
|
|
::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
|
|
octonion<T> & o)
|
|
{
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
#else
|
|
const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
T a = T();
|
|
T b = T();
|
|
T c = T();
|
|
T d = T();
|
|
T e = T();
|
|
T f = T();
|
|
T g = T();
|
|
T h = T();
|
|
|
|
::std::complex<T> u = ::std::complex<T>();
|
|
::std::complex<T> v = ::std::complex<T>();
|
|
::std::complex<T> x = ::std::complex<T>();
|
|
::std::complex<T> y = ::std::complex<T>();
|
|
|
|
::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
|
|
::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
|
|
|
|
charT ch = charT();
|
|
char cc;
|
|
|
|
is >> ch; // get the first lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "("
|
|
{
|
|
is >> ch; // get the second lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(("
|
|
{
|
|
is >> ch; // get the third lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((("
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> u; // read "((u"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((u)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (((a))), (((a,b)))
|
|
{
|
|
o = octonion<T>(u);
|
|
}
|
|
else if (cc == ',') // read "((u),"
|
|
{
|
|
p = ::boost::math::quaternion<T>(u);
|
|
|
|
is >> q; // read "((u),q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (((a)),q), (((a,b)),q)
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc ==',') // read "((u,"
|
|
{
|
|
is >> v; // read "((u,v"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((u,v)"
|
|
{
|
|
p = ::boost::math::quaternion<T>(u,v);
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (((a),v)), (((a,b),v))
|
|
{
|
|
o = octonion<T>(p);
|
|
}
|
|
else if (cc == ',') // read "((u,v),"
|
|
{
|
|
is >> q; // read "(p,q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "((a"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> a; // we extract the first component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a))"
|
|
{
|
|
o = octonion<T>(a);
|
|
}
|
|
else if (cc == ',') // read "((a),"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a),("
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a),(("
|
|
{
|
|
is.putback(ch);
|
|
|
|
is.putback(ch); // we backtrack twice, with the same value!
|
|
|
|
is >> q; // read "((a),q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),q)"
|
|
{
|
|
p = ::boost::math::quaternion<T>(a);
|
|
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "((a),(c" or "((a),(e"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> c;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c)" (ambiguity resolution)
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c))"
|
|
{
|
|
o = octonion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "((a),(c),"
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
v = ::std::complex<T>(c);
|
|
|
|
is >> x; // read "((a),(c),x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c),x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "((a),(c),x,"
|
|
{
|
|
is >> y; // read "((a),(c),x,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c),x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a),(c," or "((a),(e,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
|
|
{
|
|
p = ::boost::math::quaternion<T>(a);
|
|
|
|
x = ::std::complex<T>(c); // "c" was actually "e"
|
|
|
|
is.putback(ch); // we can only backtrace once
|
|
|
|
is >> y; // read "((a),(e,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(e,y)"
|
|
{
|
|
q = ::boost::math::quaternion<T>(x,y);
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(e,y))"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "((a),(c,d" or "((a),(e,f"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> d;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c,d))"
|
|
{
|
|
o = octonion<T>(a,b,c,d);
|
|
}
|
|
else if (cc == ',') // read "((a),(c,d),"
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
v = ::std::complex<T>(c,d);
|
|
|
|
is >> x; // read "((a),(c,d),x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c,d),x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "((a),(c,d),x,"
|
|
{
|
|
is >> y; // read "((a),(c,d),x,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(c,d),x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
|
|
{
|
|
p = ::boost::math::quaternion<T>(a);
|
|
|
|
is >> g; // read "((a),(e,f,g" (too late to backtrack)
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(e,f,g)"
|
|
{
|
|
q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(e,f,g))"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a),(e,f,g,"
|
|
{
|
|
is >> h; // read "((a),(e,f,g,h"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(e,f,g,h)"
|
|
{
|
|
q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),(e,f,g,h))"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // read "((a),c" (ambiguity resolution)
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> c; // we extract the third component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),c)"
|
|
{
|
|
o = octonion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "((a),c,"
|
|
{
|
|
is >> x; // read "((a),c,x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),c,x)"
|
|
{
|
|
o = octonion<T>(a,b,c,d,x.real(),x.imag());
|
|
}
|
|
else if (cc == ',') // read "((a),c,x,"
|
|
{
|
|
is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a),c,x,y)"
|
|
{
|
|
o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc ==',') // read "((a,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a,("
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
is.putback(ch); // can only backtrack so much
|
|
|
|
is >> v; // read "((a,v"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,v)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,v))"
|
|
{
|
|
o = octonion<T>(u,v);
|
|
}
|
|
else if (cc == ',') // read "((a,v),"
|
|
{
|
|
p = ::boost::math::quaternion<T>(u,v);
|
|
|
|
is >> q; // read "((a,v),q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,v),q)"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> b; // read "((a,b"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b))"
|
|
{
|
|
o = octonion<T>(a,b);
|
|
}
|
|
else if (cc == ',') // read "((a,b),"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a,b),("
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a,b),(("
|
|
{
|
|
p = ::boost::math::quaternion<T>(a,b);
|
|
|
|
is.putback(ch);
|
|
|
|
is.putback(ch); // we backtrack twice, with the same value
|
|
|
|
is >> q; // read "((a,b),q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),q)"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "((a,b),(c" or "((a,b),(e"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> c;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c))"
|
|
{
|
|
o = octonion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "((a,b),(c),"
|
|
{
|
|
u = ::std::complex<T>(a,b);
|
|
|
|
v = ::std::complex<T>(c);
|
|
|
|
is >> x; // read "((a,b),(c),x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c),x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "((a,b),(c),x,"
|
|
{
|
|
is >> y; // read "((a,b),(c),x,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c),x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
|
|
{
|
|
u = ::std::complex<T>(a,b);
|
|
|
|
x = ::std::complex<T>(c); // "c" is actually "e"
|
|
|
|
is.putback(ch);
|
|
|
|
is >> y; // read "((a,b),(e,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(e,y)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(e,y))"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "((a,b),(c,d" or "((a,b),(e,f"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> d;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
|
|
{
|
|
u = ::std::complex<T>(a,b);
|
|
|
|
v = ::std::complex<T>(c,d);
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c,d))"
|
|
{
|
|
o = octonion<T>(u,v);
|
|
}
|
|
else if (cc == ',') // read "((a,b),(c,d),"
|
|
{
|
|
is >> x; // read "((a,b),(c,d),x
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c,d),x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "((a,b),(c,d),x,"
|
|
{
|
|
is >> y; // read "((a,b),(c,d),x,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(c,d),x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
|
|
{
|
|
p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
|
|
|
|
is >> g; // read "((a,b),(e,f,g"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(e,f,g)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(e,f,g))"
|
|
{
|
|
q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
|
|
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a,b),(e,f,g,"
|
|
{
|
|
is >> h; // read "((a,b),(e,f,g,h"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b),(e,f,g,h)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read ((a,b),(e,f,g,h))"
|
|
{
|
|
q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
|
|
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a,b,"
|
|
{
|
|
is >> c; // read "((a,b,c"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b,c)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b,c))"
|
|
{
|
|
o = octonion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "((a,b,c),"
|
|
{
|
|
p = ::boost::math::quaternion<T>(a,b,c);
|
|
|
|
is >> q; // read "((a,b,c),q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b,c),q)"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "((a,b,c,"
|
|
{
|
|
is >> d; // read "((a,b,c,d"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b,c,d)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b,c,d))"
|
|
{
|
|
o = octonion<T>(a,b,c,d);
|
|
}
|
|
else if (cc == ',') // read "((a,b,c,d),"
|
|
{
|
|
p = ::boost::math::quaternion<T>(a,b,c,d);
|
|
|
|
is >> q; // read "((a,b,c,d),q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "((a,b,c,d),q)"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // read "(a"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> a; // we extract the first component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a)"
|
|
{
|
|
o = octonion<T>(a);
|
|
}
|
|
else if (cc == ',') // read "(a,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(a,("
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(a,(("
|
|
{
|
|
p = ::boost::math::quaternion<T>(a);
|
|
|
|
is.putback(ch);
|
|
|
|
is.putback(ch); // we backtrack twice, with the same value
|
|
|
|
is >> q; // read "(a,q"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,q)"
|
|
{
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "(a,(c" or "(a,(e"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> c;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c)" (ambiguity resolution)
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c))"
|
|
{
|
|
o = octonion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "(a,(c),"
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
v = ::std::complex<T>(c);
|
|
|
|
is >> x; // read "(a,(c),x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c),x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "(a,(c),x,"
|
|
{
|
|
is >> y; // read "(a,(c),x,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c),x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "(a,(c," or "(a,(e,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
x = ::std::complex<T>(c); // "c" is actually "e"
|
|
|
|
is.putback(ch); // we backtrack
|
|
|
|
is >> y; // read "(a,(e,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(e,y)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(e,y))"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "(a,(c,d" or "(a,(e,f"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> d;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c,d))"
|
|
{
|
|
o = octonion<T>(a,b,c,d);
|
|
}
|
|
else if (cc == ',') // read "(a,(c,d),"
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
v = ::std::complex<T>(c,d);
|
|
|
|
is >> x; // read "(a,(c,d),x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c,d),x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "(a,(c,d),x,"
|
|
{
|
|
is >> y; // read "(a,(c,d),x,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(c,d),x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
|
|
{
|
|
p = ::boost::math::quaternion<T>(a);
|
|
|
|
is >> g; // read "(a,(e,f,g"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(e,f,g)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(e,f,g))"
|
|
{
|
|
q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
|
|
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else if (cc == ',') // read "(a,(e,f,g,"
|
|
{
|
|
is >> h; // read "(a,(e,f,g,h"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(e,f,g,h)"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,(e,f,g,h))"
|
|
{
|
|
q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
|
|
|
|
o = octonion<T>(p,q);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // read "(a,b" or "(a,c" (ambiguity resolution)
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> b;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b)" (ambiguity resolution)
|
|
{
|
|
o = octonion<T>(a,b);
|
|
}
|
|
else if (cc == ',') // read "(a,b," or "(a,c,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(a,c,(" (ambiguity resolution)
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
v = ::std::complex<T>(b); // "b" is actually "c"
|
|
|
|
is.putback(ch); // we backtrack
|
|
|
|
is >> x; // read "(a,c,x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,c,x)"
|
|
{
|
|
o = octonion<T>(u,v,x);
|
|
}
|
|
else if (cc == ',') // read "(a,c,x,"
|
|
{
|
|
is >> y; // read "(a,c,x,y" // read "(a,c,x"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,c,x,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "(a,b,c" or "(a,c,e"
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> c;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
|
|
{
|
|
o = octonion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
|
|
{
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
|
|
{
|
|
u = ::std::complex<T>(a);
|
|
|
|
v = ::std::complex<T>(b); // "b" is actually "c"
|
|
|
|
x = ::std::complex<T>(c); // "c" is actually "e"
|
|
|
|
is.putback(ch); // we backtrack
|
|
|
|
is >> y; // read "(a,c,e,y"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,c,e,y)"
|
|
{
|
|
o = octonion<T>(u,v,x,y);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "(a,b,c,d" (ambiguity resolution)
|
|
{
|
|
is.putback(ch); // we backtrack
|
|
|
|
is >> d;
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b,c,d)"
|
|
{
|
|
o = octonion<T>(a,b,c,d);
|
|
}
|
|
else if (cc == ',') // read "(a,b,c,d,"
|
|
{
|
|
is >> e; // read "(a,b,c,d,e"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b,c,d,e)"
|
|
{
|
|
o = octonion<T>(a,b,c,d,e);
|
|
}
|
|
else if (cc == ',') // read "(a,b,c,d,e,"
|
|
{
|
|
is >> f; // read "(a,b,c,d,e,f"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b,c,d,e,f)"
|
|
{
|
|
o = octonion<T>(a,b,c,d,e,f);
|
|
}
|
|
else if (cc == ',') // read "(a,b,c,d,e,f,"
|
|
{
|
|
is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b,c,d,e,f,g)"
|
|
{
|
|
o = octonion<T>(a,b,c,d,e,f,g);
|
|
}
|
|
else if (cc == ',') // read "(a,b,c,d,e,f,g,"
|
|
{
|
|
is >> h; // read "(a,b,c,d,e,f,g,h" // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
|
|
{
|
|
o = octonion<T>(a,b,c,d,e,f,g,h);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // format: a
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> a; // we extract the first component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
o = octonion<T>(a);
|
|
}
|
|
|
|
finish:
|
|
return(is);
|
|
}
|
|
|
|
|
|
template<typename T, typename charT, class traits>
|
|
::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
|
|
octonion<T> const & o)
|
|
{
|
|
::std::basic_ostringstream<charT,traits> s;
|
|
|
|
s.flags(os.flags());
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
#else
|
|
s.imbue(os.getloc());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
s.precision(os.precision());
|
|
|
|
s << '(' << o.R_component_1() << ','
|
|
<< o.R_component_2() << ','
|
|
<< o.R_component_3() << ','
|
|
<< o.R_component_4() << ','
|
|
<< o.R_component_5() << ','
|
|
<< o.R_component_6() << ','
|
|
<< o.R_component_7() << ','
|
|
<< o.R_component_8() << ')';
|
|
|
|
return os << s.str();
|
|
}
|
|
|
|
|
|
// values
|
|
|
|
template<typename T>
|
|
inline T real(octonion<T> const & o)
|
|
{
|
|
return(o.real());
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> unreal(octonion<T> const & o)
|
|
{
|
|
return(o.unreal());
|
|
}
|
|
|
|
|
|
#define BOOST_OCTONION_VALARRAY_LOADER \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<T> temp(8); \
|
|
\
|
|
temp[0] = o.R_component_1(); \
|
|
temp[1] = o.R_component_2(); \
|
|
temp[2] = o.R_component_3(); \
|
|
temp[3] = o.R_component_4(); \
|
|
temp[4] = o.R_component_5(); \
|
|
temp[5] = o.R_component_6(); \
|
|
temp[6] = o.R_component_7(); \
|
|
temp[7] = o.R_component_8();
|
|
|
|
|
|
template<typename T>
|
|
inline T sup(octonion<T> const & o)
|
|
{
|
|
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
|
using ::std::abs;
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
BOOST_OCTONION_VALARRAY_LOADER
|
|
|
|
return((abs(temp).max)());
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline T l1(octonion<T> const & o)
|
|
{
|
|
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
|
using ::std::abs;
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
BOOST_OCTONION_VALARRAY_LOADER
|
|
|
|
return(abs(temp).sum());
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline T abs(const octonion<T> & o)
|
|
{
|
|
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
|
using ::std::abs;
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
using ::std::sqrt;
|
|
|
|
BOOST_OCTONION_VALARRAY_LOADER
|
|
|
|
T maxim = (abs(temp).max)(); // overflow protection
|
|
|
|
if (maxim == static_cast<T>(0))
|
|
{
|
|
return(maxim);
|
|
}
|
|
else
|
|
{
|
|
T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
|
|
|
|
temp *= mixam;
|
|
|
|
temp *= temp;
|
|
|
|
return(maxim*sqrt(temp.sum()));
|
|
}
|
|
|
|
//return(::std::sqrt(norm(o)));
|
|
}
|
|
|
|
|
|
#undef BOOST_OCTONION_VALARRAY_LOADER
|
|
|
|
|
|
// Note: This is the Cayley norm, not the Euclidian norm...
|
|
|
|
template<typename T>
|
|
inline T norm(octonion<T> const & o)
|
|
{
|
|
return(real(o*conj(o)));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> conj(octonion<T> const & o)
|
|
{
|
|
return(octonion<T>( +o.R_component_1(),
|
|
-o.R_component_2(),
|
|
-o.R_component_3(),
|
|
-o.R_component_4(),
|
|
-o.R_component_5(),
|
|
-o.R_component_6(),
|
|
-o.R_component_7(),
|
|
-o.R_component_8()));
|
|
}
|
|
|
|
|
|
// Note: There is little point, for the octonions, to introduce the equivalents
|
|
// to the complex "arg" and the quaternionic "cylindropolar".
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> spherical(T const & rho,
|
|
T const & theta,
|
|
T const & phi1,
|
|
T const & phi2,
|
|
T const & phi3,
|
|
T const & phi4,
|
|
T const & phi5,
|
|
T const & phi6)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
//T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
|
|
//T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
|
|
//T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
|
|
//T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
|
|
//T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
|
|
//T f = sin(phi4)*cos(phi5)*cos(phi6);
|
|
//T g = sin(phi5)*cos(phi6);
|
|
//T h = sin(phi6);
|
|
|
|
T courrant = static_cast<T>(1);
|
|
|
|
T h = sin(phi6);
|
|
|
|
courrant *= cos(phi6);
|
|
|
|
T g = sin(phi5)*courrant;
|
|
|
|
courrant *= cos(phi5);
|
|
|
|
T f = sin(phi4)*courrant;
|
|
|
|
courrant *= cos(phi4);
|
|
|
|
T e = sin(phi3)*courrant;
|
|
|
|
courrant *= cos(phi3);
|
|
|
|
T d = sin(phi2)*courrant;
|
|
|
|
courrant *= cos(phi2);
|
|
|
|
T c = sin(phi1)*courrant;
|
|
|
|
courrant *= cos(phi1);
|
|
|
|
T b = sin(theta)*courrant;
|
|
T a = cos(theta)*courrant;
|
|
|
|
return(rho*octonion<T>(a,b,c,d,e,f,g,h));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> multipolar(T const & rho1,
|
|
T const & theta1,
|
|
T const & rho2,
|
|
T const & theta2,
|
|
T const & rho3,
|
|
T const & theta3,
|
|
T const & rho4,
|
|
T const & theta4)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
T a = rho1*cos(theta1);
|
|
T b = rho1*sin(theta1);
|
|
T c = rho2*cos(theta2);
|
|
T d = rho2*sin(theta2);
|
|
T e = rho3*cos(theta3);
|
|
T f = rho3*sin(theta3);
|
|
T g = rho4*cos(theta4);
|
|
T h = rho4*sin(theta4);
|
|
|
|
return(octonion<T>(a,b,c,d,e,f,g,h));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> cylindrical(T const & r,
|
|
T const & angle,
|
|
T const & h1,
|
|
T const & h2,
|
|
T const & h3,
|
|
T const & h4,
|
|
T const & h5,
|
|
T const & h6)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
T a = r*cos(angle);
|
|
T b = r*sin(angle);
|
|
|
|
return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> exp(octonion<T> const & o)
|
|
{
|
|
using ::std::exp;
|
|
using ::std::cos;
|
|
|
|
using ::boost::math::sinc_pi;
|
|
|
|
T u = exp(real(o));
|
|
|
|
T z = abs(unreal(o));
|
|
|
|
T w = sinc_pi(z);
|
|
|
|
return(u*octonion<T>(cos(z),
|
|
w*o.R_component_2(), w*o.R_component_3(),
|
|
w*o.R_component_4(), w*o.R_component_5(),
|
|
w*o.R_component_6(), w*o.R_component_7(),
|
|
w*o.R_component_8()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> cos(octonion<T> const & o)
|
|
{
|
|
using ::std::sin;
|
|
using ::std::cos;
|
|
using ::std::cosh;
|
|
|
|
using ::boost::math::sinhc_pi;
|
|
|
|
T z = abs(unreal(o));
|
|
|
|
T w = -sin(o.real())*sinhc_pi(z);
|
|
|
|
return(octonion<T>(cos(o.real())*cosh(z),
|
|
w*o.R_component_2(), w*o.R_component_3(),
|
|
w*o.R_component_4(), w*o.R_component_5(),
|
|
w*o.R_component_6(), w*o.R_component_7(),
|
|
w*o.R_component_8()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> sin(octonion<T> const & o)
|
|
{
|
|
using ::std::sin;
|
|
using ::std::cos;
|
|
using ::std::cosh;
|
|
|
|
using ::boost::math::sinhc_pi;
|
|
|
|
T z = abs(unreal(o));
|
|
|
|
T w = +cos(o.real())*sinhc_pi(z);
|
|
|
|
return(octonion<T>(sin(o.real())*cosh(z),
|
|
w*o.R_component_2(), w*o.R_component_3(),
|
|
w*o.R_component_4(), w*o.R_component_5(),
|
|
w*o.R_component_6(), w*o.R_component_7(),
|
|
w*o.R_component_8()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> tan(octonion<T> const & o)
|
|
{
|
|
return(sin(o)/cos(o));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> cosh(octonion<T> const & o)
|
|
{
|
|
return((exp(+o)+exp(-o))/static_cast<T>(2));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> sinh(octonion<T> const & o)
|
|
{
|
|
return((exp(+o)-exp(-o))/static_cast<T>(2));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline octonion<T> tanh(octonion<T> const & o)
|
|
{
|
|
return(sinh(o)/cosh(o));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
octonion<T> pow(octonion<T> const & o,
|
|
int n)
|
|
{
|
|
if (n > 1)
|
|
{
|
|
int m = n>>1;
|
|
|
|
octonion<T> result = pow(o, m);
|
|
|
|
result *= result;
|
|
|
|
if (n != (m<<1))
|
|
{
|
|
result *= o; // n odd
|
|
}
|
|
|
|
return(result);
|
|
}
|
|
else if (n == 1)
|
|
{
|
|
return(o);
|
|
}
|
|
else if (n == 0)
|
|
{
|
|
return(octonion<T>(static_cast<T>(1)));
|
|
}
|
|
else /* n < 0 */
|
|
{
|
|
return(pow(octonion<T>(static_cast<T>(1))/o,-n));
|
|
}
|
|
}
|
|
|
|
|
|
// helper templates for converting copy constructors (definition)
|
|
|
|
namespace detail
|
|
{
|
|
|
|
template< typename T,
|
|
typename U
|
|
>
|
|
octonion<T> octonion_type_converter(octonion<U> const & rhs)
|
|
{
|
|
return(octonion<T>( static_cast<T>(rhs.R_component_1()),
|
|
static_cast<T>(rhs.R_component_2()),
|
|
static_cast<T>(rhs.R_component_3()),
|
|
static_cast<T>(rhs.R_component_4()),
|
|
static_cast<T>(rhs.R_component_5()),
|
|
static_cast<T>(rhs.R_component_6()),
|
|
static_cast<T>(rhs.R_component_7()),
|
|
static_cast<T>(rhs.R_component_8())));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* BOOST_OCTONION_HPP */
|