Chris@16: // boost octonion.hpp header file Chris@16: Chris@16: // (C) Copyright Hubert Holin 2001. Chris@16: // Distributed under the Boost Software License, Version 1.0. (See Chris@16: // accompanying file LICENSE_1_0.txt or copy at Chris@16: // http://www.boost.org/LICENSE_1_0.txt) Chris@16: Chris@16: // See http://www.boost.org for updates, documentation, and revision history. Chris@16: Chris@16: Chris@16: #ifndef BOOST_OCTONION_HPP Chris@16: #define BOOST_OCTONION_HPP Chris@16: Chris@16: #include Chris@16: Chris@16: Chris@16: namespace boost Chris@16: { Chris@16: namespace math Chris@16: { Chris@16: Chris@16: #define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \ Chris@16: type real() const \ Chris@16: { \ Chris@16: return(a); \ Chris@16: } \ Chris@16: \ Chris@16: octonion unreal() const \ Chris@16: { \ Chris@16: return( octonion(static_cast(0),b,c,d,e,f,g,h)); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_1() const \ Chris@16: { \ Chris@16: return(a); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_2() const \ Chris@16: { \ Chris@16: return(b); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_3() const \ Chris@16: { \ Chris@16: return(c); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_4() const \ Chris@16: { \ Chris@16: return(d); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_5() const \ Chris@16: { \ Chris@16: return(e); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_6() const \ Chris@16: { \ Chris@16: return(f); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_7() const \ Chris@16: { \ Chris@16: return(g); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_8() const \ Chris@16: { \ Chris@16: return(h); \ Chris@16: } \ Chris@16: \ Chris@16: ::std::complex C_component_1() const \ Chris@16: { \ Chris@16: return(::std::complex(a,b)); \ Chris@16: } \ Chris@16: \ Chris@16: ::std::complex C_component_2() const \ Chris@16: { \ Chris@16: return(::std::complex(c,d)); \ Chris@16: } \ Chris@16: \ Chris@16: ::std::complex C_component_3() const \ Chris@16: { \ Chris@16: return(::std::complex(e,f)); \ Chris@16: } \ Chris@16: \ Chris@16: ::std::complex C_component_4() const \ Chris@16: { \ Chris@16: return(::std::complex(g,h)); \ Chris@16: } \ Chris@16: \ Chris@16: ::boost::math::quaternion H_component_1() const \ Chris@16: { \ Chris@16: return(::boost::math::quaternion(a,b,c,d)); \ Chris@16: } \ Chris@16: \ Chris@16: ::boost::math::quaternion H_component_2() const \ Chris@16: { \ Chris@16: return(::boost::math::quaternion(e,f,g,h)); \ Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \ Chris@16: template \ Chris@16: octonion & operator = (octonion const & a_affecter) \ Chris@16: { \ Chris@16: a = static_cast(a_affecter.R_component_1()); \ Chris@16: b = static_cast(a_affecter.R_component_2()); \ Chris@16: c = static_cast(a_affecter.R_component_3()); \ Chris@16: d = static_cast(a_affecter.R_component_4()); \ Chris@16: e = static_cast(a_affecter.R_component_5()); \ Chris@16: f = static_cast(a_affecter.R_component_6()); \ Chris@16: g = static_cast(a_affecter.R_component_7()); \ Chris@16: h = static_cast(a_affecter.R_component_8()); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: octonion & operator = (octonion const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter.a; \ Chris@16: b = a_affecter.b; \ Chris@16: c = a_affecter.c; \ Chris@16: d = a_affecter.d; \ Chris@16: e = a_affecter.e; \ Chris@16: f = a_affecter.f; \ Chris@16: g = a_affecter.g; \ Chris@16: h = a_affecter.h; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: octonion & operator = (type const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter; \ Chris@16: \ Chris@16: b = c = d = e = f= g = h = static_cast(0); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: octonion & operator = (::std::complex const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter.real(); \ Chris@16: b = a_affecter.imag(); \ Chris@16: \ Chris@16: c = d = e = f = g = h = static_cast(0); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: octonion & operator = (::boost::math::quaternion const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter.R_component_1(); \ Chris@16: b = a_affecter.R_component_2(); \ Chris@16: c = a_affecter.R_component_3(); \ Chris@16: d = a_affecter.R_component_4(); \ Chris@16: \ Chris@16: e = f = g = h = static_cast(0); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \ Chris@16: type a; \ Chris@16: type b; \ Chris@16: type c; \ Chris@16: type d; \ Chris@16: type e; \ Chris@16: type f; \ Chris@16: type g; \ Chris@16: type h; \ Chris@16: Chris@16: Chris@16: template Chris@16: class octonion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef T value_type; Chris@16: Chris@16: // constructor for O seen as R^8 Chris@16: // (also default constructor) Chris@16: Chris@16: explicit octonion( T const & requested_a = T(), Chris@16: T const & requested_b = T(), Chris@16: T const & requested_c = T(), Chris@16: T const & requested_d = T(), Chris@16: T const & requested_e = T(), Chris@16: T const & requested_f = T(), Chris@16: T const & requested_g = T(), Chris@16: T const & requested_h = T()) Chris@16: : a(requested_a), Chris@16: b(requested_b), Chris@16: c(requested_c), Chris@16: d(requested_d), Chris@16: e(requested_e), Chris@16: f(requested_f), Chris@16: g(requested_g), Chris@16: h(requested_h) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // constructor for H seen as C^4 Chris@16: Chris@16: explicit octonion( ::std::complex const & z0, Chris@16: ::std::complex const & z1 = ::std::complex(), Chris@16: ::std::complex const & z2 = ::std::complex(), Chris@16: ::std::complex const & z3 = ::std::complex()) Chris@16: : a(z0.real()), Chris@16: b(z0.imag()), Chris@16: c(z1.real()), Chris@16: d(z1.imag()), Chris@16: e(z2.real()), Chris@16: f(z2.imag()), Chris@16: g(z3.real()), Chris@16: h(z3.imag()) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // constructor for O seen as H^2 Chris@16: Chris@16: explicit octonion( ::boost::math::quaternion const & q0, Chris@16: ::boost::math::quaternion const & q1 = ::boost::math::quaternion()) Chris@16: : a(q0.R_component_1()), Chris@16: b(q0.R_component_2()), Chris@16: c(q0.R_component_3()), Chris@16: d(q0.R_component_4()), Chris@16: e(q1.R_component_1()), Chris@16: f(q1.R_component_2()), Chris@16: g(q1.R_component_3()), Chris@16: h(q1.R_component_4()) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: Chris@16: // templated copy constructor Chris@16: Chris@16: template Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: : a(static_cast(a_recopier.R_component_1())), Chris@16: b(static_cast(a_recopier.R_component_2())), Chris@16: c(static_cast(a_recopier.R_component_3())), Chris@16: d(static_cast(a_recopier.R_component_4())), Chris@16: e(static_cast(a_recopier.R_component_5())), Chris@16: f(static_cast(a_recopier.R_component_6())), Chris@16: g(static_cast(a_recopier.R_component_7())), Chris@16: h(static_cast(a_recopier.R_component_8())) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, octonions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is an octonion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_OCTONION_ACCESSOR_GENERATOR(T) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Octonion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);"; Chris@16: // octonion multiplication is also *NOT* associative Chris@16: Chris@16: octonion & operator += (T const & rhs) Chris@16: { Chris@16: T at = a + rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator += (::std::complex const & rhs) Chris@16: { Chris@16: T at = a + rhs.real(); // exception guard Chris@16: T bt = b + rhs.imag(); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator += (::boost::math::quaternion const & rhs) Chris@16: { Chris@16: T at = a + rhs.R_component_1(); // exception guard Chris@16: T bt = b + rhs.R_component_2(); // exception guard Chris@16: T ct = c + rhs.R_component_3(); // exception guard Chris@16: T dt = d + rhs.R_component_4(); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: octonion & operator += (octonion const & rhs) Chris@16: { Chris@16: T at = a + static_cast(rhs.R_component_1()); // exception guard Chris@16: T bt = b + static_cast(rhs.R_component_2()); // exception guard Chris@16: T ct = c + static_cast(rhs.R_component_3()); // exception guard Chris@16: T dt = d + static_cast(rhs.R_component_4()); // exception guard Chris@16: T et = e + static_cast(rhs.R_component_5()); // exception guard Chris@16: T ft = f + static_cast(rhs.R_component_6()); // exception guard Chris@16: T gt = g + static_cast(rhs.R_component_7()); // exception guard Chris@16: T ht = h + static_cast(rhs.R_component_8()); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: Chris@16: octonion & operator -= (T const & rhs) Chris@16: { Chris@16: T at = a - rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator -= (::std::complex const & rhs) Chris@16: { Chris@16: T at = a - rhs.real(); // exception guard Chris@16: T bt = b - rhs.imag(); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator -= (::boost::math::quaternion const & rhs) Chris@16: { Chris@16: T at = a - rhs.R_component_1(); // exception guard Chris@16: T bt = b - rhs.R_component_2(); // exception guard Chris@16: T ct = c - rhs.R_component_3(); // exception guard Chris@16: T dt = d - rhs.R_component_4(); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: octonion & operator -= (octonion const & rhs) Chris@16: { Chris@16: T at = a - static_cast(rhs.R_component_1()); // exception guard Chris@16: T bt = b - static_cast(rhs.R_component_2()); // exception guard Chris@16: T ct = c - static_cast(rhs.R_component_3()); // exception guard Chris@16: T dt = d - static_cast(rhs.R_component_4()); // exception guard Chris@16: T et = e - static_cast(rhs.R_component_5()); // exception guard Chris@16: T ft = f - static_cast(rhs.R_component_6()); // exception guard Chris@16: T gt = g - static_cast(rhs.R_component_7()); // exception guard Chris@16: T ht = h - static_cast(rhs.R_component_8()); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator *= (T const & rhs) Chris@16: { Chris@16: T at = a * rhs; // exception guard Chris@16: T bt = b * rhs; // exception guard Chris@16: T ct = c * rhs; // exception guard Chris@16: T dt = d * rhs; // exception guard Chris@16: T et = e * rhs; // exception guard Chris@16: T ft = f * rhs; // exception guard Chris@16: T gt = g * rhs; // exception guard Chris@16: T ht = h * rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator *= (::std::complex const & rhs) Chris@16: { Chris@16: T ar = rhs.real(); Chris@16: T br = rhs.imag(); Chris@16: Chris@16: T at = +a*ar-b*br; Chris@16: T bt = +a*br+b*ar; Chris@16: T ct = +c*ar+d*br; Chris@16: T dt = -c*br+d*ar; Chris@16: T et = +e*ar+f*br; Chris@16: T ft = -e*br+f*ar; Chris@16: T gt = +g*ar-h*br; Chris@16: T ht = +g*br+h*ar; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator *= (::boost::math::quaternion const & rhs) Chris@16: { Chris@16: T ar = rhs.R_component_1(); Chris@16: T br = rhs.R_component_2(); Chris@16: T cr = rhs.R_component_2(); Chris@16: T dr = rhs.R_component_2(); Chris@16: Chris@16: T at = +a*ar-b*br-c*cr-d*dr; Chris@16: T bt = +a*br+b*ar+c*dr-d*cr; Chris@16: T ct = +a*cr-b*dr+c*ar+d*br; Chris@16: T dt = +a*dr+b*cr-c*br+d*ar; Chris@16: T et = +e*ar+f*br+g*cr+h*dr; Chris@16: T ft = -e*br+f*ar-g*dr+h*cr; Chris@16: T gt = -e*cr+f*dr+g*ar-h*br; Chris@16: T ht = -e*dr-f*cr+g*br+h*ar; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: octonion & operator *= (octonion const & rhs) Chris@16: { Chris@16: T ar = static_cast(rhs.R_component_1()); Chris@16: T br = static_cast(rhs.R_component_2()); Chris@16: T cr = static_cast(rhs.R_component_3()); Chris@16: T dr = static_cast(rhs.R_component_4()); Chris@16: T er = static_cast(rhs.R_component_5()); Chris@16: T fr = static_cast(rhs.R_component_6()); Chris@16: T gr = static_cast(rhs.R_component_7()); Chris@16: T hr = static_cast(rhs.R_component_8()); Chris@16: Chris@16: T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; Chris@16: T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; Chris@16: T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; Chris@16: T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; Chris@16: T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; Chris@16: T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; Chris@16: T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; Chris@16: T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator /= (T const & rhs) Chris@16: { Chris@16: T at = a / rhs; // exception guard Chris@16: T bt = b / rhs; // exception guard Chris@16: T ct = c / rhs; // exception guard Chris@16: T dt = d / rhs; // exception guard Chris@16: T et = e / rhs; // exception guard Chris@16: T ft = f / rhs; // exception guard Chris@16: T gt = g / rhs; // exception guard Chris@16: T ht = h / rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator /= (::std::complex const & rhs) Chris@16: { Chris@16: T ar = rhs.real(); Chris@16: T br = rhs.imag(); Chris@16: Chris@16: T denominator = ar*ar+br*br; Chris@16: Chris@16: T at = (+a*ar-b*br)/denominator; Chris@16: T bt = (-a*br+b*ar)/denominator; Chris@16: T ct = (+c*ar-d*br)/denominator; Chris@16: T dt = (+c*br+d*ar)/denominator; Chris@16: T et = (+e*ar-f*br)/denominator; Chris@16: T ft = (+e*br+f*ar)/denominator; Chris@16: T gt = (+g*ar+h*br)/denominator; Chris@16: T ht = (+g*br+h*ar)/denominator; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: octonion & operator /= (::boost::math::quaternion const & rhs) Chris@16: { Chris@16: T ar = rhs.R_component_1(); Chris@16: T br = rhs.R_component_2(); Chris@16: T cr = rhs.R_component_2(); Chris@16: T dr = rhs.R_component_2(); Chris@16: Chris@16: T denominator = ar*ar+br*br+cr*cr+dr*dr; Chris@16: Chris@16: T at = (+a*ar+b*br+c*cr+d*dr)/denominator; Chris@16: T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; Chris@16: T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; Chris@16: T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; Chris@16: T et = (+e*ar-f*br-g*cr-h*dr)/denominator; Chris@16: T ft = (+e*br+f*ar+g*dr-h*cr)/denominator; Chris@16: T gt = (+e*cr-f*dr+g*ar+h*br)/denominator; Chris@16: T ht = (+e*dr+f*cr-g*br+h*ar)/denominator; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: octonion & operator /= (octonion const & rhs) Chris@16: { Chris@16: T ar = static_cast(rhs.R_component_1()); Chris@16: T br = static_cast(rhs.R_component_2()); Chris@16: T cr = static_cast(rhs.R_component_3()); Chris@16: T dr = static_cast(rhs.R_component_4()); Chris@16: T er = static_cast(rhs.R_component_5()); Chris@16: T fr = static_cast(rhs.R_component_6()); Chris@16: T gr = static_cast(rhs.R_component_7()); Chris@16: T hr = static_cast(rhs.R_component_8()); Chris@16: Chris@16: T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr; Chris@16: Chris@16: T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator; Chris@16: T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator; Chris@16: T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator; Chris@16: T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator; Chris@16: T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator; Chris@16: T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator; Chris@16: T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator; Chris@16: T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: e = et; Chris@16: f = ft; Chris@16: g = gt; Chris@16: h = ht; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_OCTONION_MEMBER_DATA_GENERATOR(T) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: // declaration of octonion specialization Chris@16: Chris@16: template<> class octonion; Chris@16: template<> class octonion; Chris@16: template<> class octonion; Chris@16: Chris@16: Chris@16: // helper templates for converting copy constructors (declaration) Chris@16: Chris@16: namespace detail Chris@16: { Chris@16: Chris@16: template< typename T, Chris@16: typename U Chris@16: > Chris@16: octonion octonion_type_converter(octonion const & rhs); Chris@16: } Chris@16: Chris@16: Chris@16: // implementation of octonion specialization Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \ Chris@16: explicit octonion( type const & requested_a = static_cast(0), \ Chris@16: type const & requested_b = static_cast(0), \ Chris@16: type const & requested_c = static_cast(0), \ Chris@16: type const & requested_d = static_cast(0), \ Chris@16: type const & requested_e = static_cast(0), \ Chris@16: type const & requested_f = static_cast(0), \ Chris@16: type const & requested_g = static_cast(0), \ Chris@16: type const & requested_h = static_cast(0)) \ Chris@16: : a(requested_a), \ Chris@16: b(requested_b), \ Chris@16: c(requested_c), \ Chris@16: d(requested_d), \ Chris@16: e(requested_e), \ Chris@16: f(requested_f), \ Chris@16: g(requested_g), \ Chris@16: h(requested_h) \ Chris@16: { \ Chris@16: } \ Chris@16: \ Chris@16: explicit octonion( ::std::complex const & z0, \ Chris@16: ::std::complex const & z1 = ::std::complex(), \ Chris@16: ::std::complex const & z2 = ::std::complex(), \ Chris@16: ::std::complex const & z3 = ::std::complex()) \ Chris@16: : a(z0.real()), \ Chris@16: b(z0.imag()), \ Chris@16: c(z1.real()), \ Chris@16: d(z1.imag()), \ Chris@16: e(z2.real()), \ Chris@16: f(z2.imag()), \ Chris@16: g(z3.real()), \ Chris@16: h(z3.imag()) \ Chris@16: { \ Chris@16: } \ Chris@16: \ Chris@16: explicit octonion( ::boost::math::quaternion const & q0, \ Chris@16: ::boost::math::quaternion const & q1 = ::boost::math::quaternion()) \ Chris@16: : a(q0.R_component_1()), \ Chris@16: b(q0.R_component_2()), \ Chris@16: c(q0.R_component_3()), \ Chris@16: d(q0.R_component_4()), \ Chris@16: e(q1.R_component_1()), \ Chris@16: f(q1.R_component_2()), \ Chris@16: g(q1.R_component_3()), \ Chris@16: h(q1.R_component_4()) \ Chris@16: { \ Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \ Chris@16: octonion & operator += (type const & rhs) \ Chris@16: { \ Chris@16: a += rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \ Chris@16: octonion & operator += (::std::complex const & rhs) \ Chris@16: { \ Chris@16: a += rhs.real(); \ Chris@16: b += rhs.imag(); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \ Chris@16: octonion & operator += (::boost::math::quaternion const & rhs) \ Chris@16: { \ Chris@16: a += rhs.R_component_1(); \ Chris@16: b += rhs.R_component_2(); \ Chris@16: c += rhs.R_component_3(); \ Chris@16: d += rhs.R_component_4(); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \ Chris@16: template \ Chris@16: octonion & operator += (octonion const & rhs) \ Chris@16: { \ Chris@16: a += static_cast(rhs.R_component_1()); \ Chris@16: b += static_cast(rhs.R_component_2()); \ Chris@16: c += static_cast(rhs.R_component_3()); \ Chris@16: d += static_cast(rhs.R_component_4()); \ Chris@16: e += static_cast(rhs.R_component_5()); \ Chris@16: f += static_cast(rhs.R_component_6()); \ Chris@16: g += static_cast(rhs.R_component_7()); \ Chris@16: h += static_cast(rhs.R_component_8()); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \ Chris@16: octonion & operator -= (type const & rhs) \ Chris@16: { \ Chris@16: a -= rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \ Chris@16: octonion & operator -= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: a -= rhs.real(); \ Chris@16: b -= rhs.imag(); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \ Chris@16: octonion & operator -= (::boost::math::quaternion const & rhs) \ Chris@16: { \ Chris@16: a -= rhs.R_component_1(); \ Chris@16: b -= rhs.R_component_2(); \ Chris@16: c -= rhs.R_component_3(); \ Chris@16: d -= rhs.R_component_4(); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \ Chris@16: template \ Chris@16: octonion & operator -= (octonion const & rhs) \ Chris@16: { \ Chris@16: a -= static_cast(rhs.R_component_1()); \ Chris@16: b -= static_cast(rhs.R_component_2()); \ Chris@16: c -= static_cast(rhs.R_component_3()); \ Chris@16: d -= static_cast(rhs.R_component_4()); \ Chris@16: e -= static_cast(rhs.R_component_5()); \ Chris@16: f -= static_cast(rhs.R_component_6()); \ Chris@16: g -= static_cast(rhs.R_component_7()); \ Chris@16: h -= static_cast(rhs.R_component_8()); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \ Chris@16: octonion & operator *= (type const & rhs) \ Chris@16: { \ Chris@16: a *= rhs; \ Chris@16: b *= rhs; \ Chris@16: c *= rhs; \ Chris@16: d *= rhs; \ Chris@16: e *= rhs; \ Chris@16: f *= rhs; \ Chris@16: g *= rhs; \ Chris@16: h *= rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \ Chris@16: octonion & operator *= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: type ar = rhs.real(); \ Chris@16: type br = rhs.imag(); \ Chris@16: \ Chris@16: type at = +a*ar-b*br; \ Chris@16: type bt = +a*br+b*ar; \ Chris@16: type ct = +c*ar+d*br; \ Chris@16: type dt = -c*br+d*ar; \ Chris@16: type et = +e*ar+f*br; \ Chris@16: type ft = -e*br+f*ar; \ Chris@16: type gt = +g*ar-h*br; \ Chris@16: type ht = +g*br+h*ar; \ Chris@16: \ Chris@16: a = at; \ Chris@16: b = bt; \ Chris@16: c = ct; \ Chris@16: d = dt; \ Chris@16: e = et; \ Chris@16: f = ft; \ Chris@16: g = gt; \ Chris@16: h = ht; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \ Chris@16: octonion & operator *= (::boost::math::quaternion const & rhs) \ Chris@16: { \ Chris@16: type ar = rhs.R_component_1(); \ Chris@16: type br = rhs.R_component_2(); \ Chris@16: type cr = rhs.R_component_2(); \ Chris@16: type dr = rhs.R_component_2(); \ Chris@16: \ Chris@16: type at = +a*ar-b*br-c*cr-d*dr; \ Chris@16: type bt = +a*br+b*ar+c*dr-d*cr; \ Chris@16: type ct = +a*cr-b*dr+c*ar+d*br; \ Chris@16: type dt = +a*dr+b*cr-c*br+d*ar; \ Chris@16: type et = +e*ar+f*br+g*cr+h*dr; \ Chris@16: type ft = -e*br+f*ar-g*dr+h*cr; \ Chris@16: type gt = -e*cr+f*dr+g*ar-h*br; \ Chris@16: type ht = -e*dr-f*cr+g*br+h*ar; \ Chris@16: \ Chris@16: a = at; \ Chris@16: b = bt; \ Chris@16: c = ct; \ Chris@16: d = dt; \ Chris@16: e = et; \ Chris@16: f = ft; \ Chris@16: g = gt; \ Chris@16: h = ht; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \ Chris@16: template \ Chris@16: octonion & operator *= (octonion const & rhs) \ Chris@16: { \ Chris@16: type ar = static_cast(rhs.R_component_1()); \ Chris@16: type br = static_cast(rhs.R_component_2()); \ Chris@16: type cr = static_cast(rhs.R_component_3()); \ Chris@16: type dr = static_cast(rhs.R_component_4()); \ Chris@16: type er = static_cast(rhs.R_component_5()); \ Chris@16: type fr = static_cast(rhs.R_component_6()); \ Chris@16: type gr = static_cast(rhs.R_component_7()); \ Chris@16: type hr = static_cast(rhs.R_component_8()); \ Chris@16: \ Chris@16: type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \ Chris@16: type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \ Chris@16: type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \ Chris@16: type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \ Chris@16: type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \ Chris@16: type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \ Chris@16: type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \ Chris@16: type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \ Chris@16: \ Chris@16: a = at; \ Chris@16: b = bt; \ Chris@16: c = ct; \ Chris@16: d = dt; \ Chris@16: e = et; \ Chris@16: f = ft; \ Chris@16: g = gt; \ Chris@16: h = ht; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: // There is quite a lot of repetition in the code below. This is intentional. Chris@16: // The last conditional block is the normal form, and the others merely Chris@16: // consist of workarounds for various compiler deficiencies. Hopefuly, when Chris@16: // more compilers are conformant and we can retire support for those that are Chris@16: // not, we will be able to remove the clutter. This is makes the situation Chris@16: // (painfully) explicit. Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \ Chris@16: octonion & operator /= (type const & rhs) \ Chris@16: { \ Chris@16: a /= rhs; \ Chris@16: b /= rhs; \ Chris@16: c /= rhs; \ Chris@16: d /= rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@101: #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ Chris@16: octonion & operator /= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: using ::std::abs; \ Chris@16: \ Chris@16: valarray tr(2); \ Chris@16: \ Chris@16: tr[0] = rhs.real(); \ Chris@16: tr[1] = rhs.imag(); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(8); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]-b*tr[1]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]; \ Chris@16: tt[2] = +c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = +c*tr[1]+d*tr[0]; \ Chris@16: tt[4] = +e*tr[0]-f*tr[1]; \ Chris@16: tt[5] = +e*tr[1]+f*tr[0]; \ Chris@16: tt[6] = +g*tr[0]+h*tr[1]; \ Chris@16: tt[7] = +g*tr[1]+h*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: e = tt[4]; \ Chris@16: f = tt[5]; \ Chris@16: g = tt[6]; \ Chris@16: h = tt[7]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: #else Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ Chris@16: octonion & operator /= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray tr(2); \ Chris@16: \ Chris@16: tr[0] = rhs.real(); \ Chris@16: tr[1] = rhs.imag(); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(8); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]-b*tr[1]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]; \ Chris@16: tt[2] = +c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = +c*tr[1]+d*tr[0]; \ Chris@16: tt[4] = +e*tr[0]-f*tr[1]; \ Chris@16: tt[5] = +e*tr[1]+f*tr[0]; \ Chris@16: tt[6] = +g*tr[0]+h*tr[1]; \ Chris@16: tt[7] = +g*tr[1]+h*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: e = tt[4]; \ Chris@16: f = tt[5]; \ Chris@16: g = tt[6]; \ Chris@16: h = tt[7]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@101: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@101: #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ Chris@16: octonion & operator /= (::boost::math::quaternion const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: using ::std::abs; \ Chris@16: \ Chris@16: valarray tr(4); \ Chris@16: \ Chris@16: tr[0] = static_cast(rhs.R_component_1()); \ Chris@16: tr[1] = static_cast(rhs.R_component_2()); \ Chris@16: tr[2] = static_cast(rhs.R_component_3()); \ Chris@16: tr[3] = static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(8); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ Chris@16: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ Chris@16: tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ Chris@16: tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ Chris@16: tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ Chris@16: tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: e = tt[4]; \ Chris@16: f = tt[5]; \ Chris@16: g = tt[6]; \ Chris@16: h = tt[7]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: #else Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ Chris@16: octonion & operator /= (::boost::math::quaternion const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray tr(4); \ Chris@16: \ Chris@16: tr[0] = static_cast(rhs.R_component_1()); \ Chris@16: tr[1] = static_cast(rhs.R_component_2()); \ Chris@16: tr[2] = static_cast(rhs.R_component_3()); \ Chris@16: tr[3] = static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(8); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ Chris@16: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ Chris@16: tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ Chris@16: tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ Chris@16: tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ Chris@16: tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: e = tt[4]; \ Chris@16: f = tt[5]; \ Chris@16: g = tt[6]; \ Chris@16: h = tt[7]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@101: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@101: #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ Chris@16: template \ Chris@16: octonion & operator /= (octonion const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: using ::std::abs; \ Chris@16: \ Chris@16: valarray tr(8); \ Chris@16: \ Chris@16: tr[0] = static_cast(rhs.R_component_1()); \ Chris@16: tr[1] = static_cast(rhs.R_component_2()); \ Chris@16: tr[2] = static_cast(rhs.R_component_3()); \ Chris@16: tr[3] = static_cast(rhs.R_component_4()); \ Chris@16: tr[4] = static_cast(rhs.R_component_5()); \ Chris@16: tr[5] = static_cast(rhs.R_component_6()); \ Chris@16: tr[6] = static_cast(rhs.R_component_7()); \ Chris@16: tr[7] = static_cast(rhs.R_component_8()); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(8); \ Chris@16: \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: e = tt[4]; \ Chris@16: f = tt[5]; \ Chris@16: g = tt[6]; \ Chris@16: h = tt[7]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: #else Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ Chris@16: template \ Chris@16: octonion & operator /= (octonion const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray tr(8); \ Chris@16: \ Chris@16: tr[0] = static_cast(rhs.R_component_1()); \ Chris@16: tr[1] = static_cast(rhs.R_component_2()); \ Chris@16: tr[2] = static_cast(rhs.R_component_3()); \ Chris@16: tr[3] = static_cast(rhs.R_component_4()); \ Chris@16: tr[4] = static_cast(rhs.R_component_5()); \ Chris@16: tr[5] = static_cast(rhs.R_component_6()); \ Chris@16: tr[6] = static_cast(rhs.R_component_7()); \ Chris@16: tr[7] = static_cast(rhs.R_component_8()); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(8); \ Chris@16: \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: 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]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: e = tt[4]; \ Chris@16: f = tt[5]; \ Chris@16: g = tt[6]; \ Chris@16: h = tt[7]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@101: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \ Chris@16: BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \ Chris@16: BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \ Chris@16: BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \ Chris@16: BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \ Chris@16: BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \ Chris@16: BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \ Chris@16: BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \ Chris@16: BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \ Chris@16: BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \ Chris@16: BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ Chris@16: BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ Chris@16: BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) Chris@16: Chris@16: #define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \ Chris@16: BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) Chris@16: Chris@16: Chris@16: template<> Chris@16: class octonion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef float value_type; Chris@16: Chris@16: BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float) Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // explicit copy constructors (precision-loosing converters) Chris@16: Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: { Chris@16: *this = detail::octonion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: { Chris@16: *this = detail::octonion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, octonions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is an octonion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_OCTONION_ACCESSOR_GENERATOR(float) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Octonion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);"; Chris@16: // octonion multiplication is also *NOT* associative Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float) Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_OCTONION_MEMBER_DATA_GENERATOR(float) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: template<> Chris@16: class octonion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef double value_type; Chris@16: Chris@16: BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double) Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // converting copy constructor Chris@16: Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: { Chris@16: *this = detail::octonion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // explicit copy constructors (precision-loosing converters) Chris@16: Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: { Chris@16: *this = detail::octonion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, octonions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is an octonion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_OCTONION_ACCESSOR_GENERATOR(double) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Octonion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);"; Chris@16: // octonion multiplication is also *NOT* associative Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double) Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_OCTONION_MEMBER_DATA_GENERATOR(double) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: template<> Chris@16: class octonion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef long double value_type; Chris@16: Chris@16: BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double) Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // converting copy constructor Chris@16: Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: { Chris@16: *this = detail::octonion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: Chris@16: explicit octonion(octonion const & a_recopier) Chris@16: { Chris@16: *this = detail::octonion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, octonions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is an octonion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_OCTONION_ACCESSOR_GENERATOR(long double) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Octonion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);"; Chris@16: // octonion multiplication is also *NOT* associative Chris@16: Chris@16: BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double) Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: #undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR Chris@16: #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR Chris@16: #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR Chris@16: #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1 Chris@16: #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2 Chris@16: #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3 Chris@16: #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4 Chris@16: #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1 Chris@16: #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2 Chris@16: #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3 Chris@16: #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4 Chris@16: #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1 Chris@16: #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2 Chris@16: #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3 Chris@16: #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4 Chris@16: #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1 Chris@16: #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2 Chris@16: #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3 Chris@16: #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4 Chris@16: Chris@16: Chris@16: #undef BOOST_OCTONION_MEMBER_DATA_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_ACCESSOR_GENERATOR Chris@16: Chris@16: Chris@16: // operators Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \ Chris@16: { \ Chris@16: octonion res(lhs); \ Chris@16: res op##= rhs; \ Chris@16: return(res); \ Chris@16: } Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \ Chris@16: template \ Chris@16: inline octonion operator op (T const & lhs, octonion const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \ Chris@16: template \ Chris@16: inline octonion operator op (octonion const & lhs, T const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \ Chris@16: template \ Chris@16: inline octonion operator op (::std::complex const & lhs, octonion const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \ Chris@16: template \ Chris@16: inline octonion operator op (octonion const & lhs, ::std::complex const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \ Chris@16: template \ Chris@16: inline octonion operator op (::boost::math::quaternion const & lhs, octonion const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \ Chris@16: template \ Chris@16: inline octonion operator op (octonion const & lhs, ::boost::math::quaternion const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \ Chris@16: template \ Chris@16: inline octonion operator op (octonion const & lhs, octonion const & rhs) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_OCTONION_OPERATOR_GENERATOR(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \ Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR_4(op) Chris@16: Chris@16: Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR(+) Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR(-) Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR(*) Chris@16: BOOST_OCTONION_OPERATOR_GENERATOR(/) Chris@16: Chris@16: Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_4 Chris@16: Chris@16: #undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion operator + (octonion const & o) Chris@16: { Chris@16: return(o); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion operator - (octonion const & o) Chris@16: { Chris@16: return(octonion(-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())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (T const & lhs, octonion const & rhs) Chris@16: { Chris@16: return( Chris@16: (rhs.R_component_1() == lhs)&& Chris@16: (rhs.R_component_2() == static_cast(0))&& Chris@16: (rhs.R_component_3() == static_cast(0))&& Chris@16: (rhs.R_component_4() == static_cast(0))&& Chris@16: (rhs.R_component_5() == static_cast(0))&& Chris@16: (rhs.R_component_6() == static_cast(0))&& Chris@16: (rhs.R_component_7() == static_cast(0))&& Chris@16: (rhs.R_component_8() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (octonion const & lhs, T const & rhs) Chris@16: { Chris@16: return( Chris@16: (lhs.R_component_1() == rhs)&& Chris@16: (lhs.R_component_2() == static_cast(0))&& Chris@16: (lhs.R_component_3() == static_cast(0))&& Chris@16: (lhs.R_component_4() == static_cast(0))&& Chris@16: (lhs.R_component_5() == static_cast(0))&& Chris@16: (lhs.R_component_6() == static_cast(0))&& Chris@16: (lhs.R_component_7() == static_cast(0))&& Chris@16: (lhs.R_component_8() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (::std::complex const & lhs, octonion const & rhs) Chris@16: { Chris@16: return( Chris@16: (rhs.R_component_1() == lhs.real())&& Chris@16: (rhs.R_component_2() == lhs.imag())&& Chris@16: (rhs.R_component_3() == static_cast(0))&& Chris@16: (rhs.R_component_4() == static_cast(0))&& Chris@16: (rhs.R_component_5() == static_cast(0))&& Chris@16: (rhs.R_component_6() == static_cast(0))&& Chris@16: (rhs.R_component_7() == static_cast(0))&& Chris@16: (rhs.R_component_8() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (octonion const & lhs, ::std::complex const & rhs) Chris@16: { Chris@16: return( Chris@16: (lhs.R_component_1() == rhs.real())&& Chris@16: (lhs.R_component_2() == rhs.imag())&& Chris@16: (lhs.R_component_3() == static_cast(0))&& Chris@16: (lhs.R_component_4() == static_cast(0))&& Chris@16: (lhs.R_component_5() == static_cast(0))&& Chris@16: (lhs.R_component_6() == static_cast(0))&& Chris@16: (lhs.R_component_7() == static_cast(0))&& Chris@16: (lhs.R_component_8() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (::boost::math::quaternion const & lhs, octonion const & rhs) Chris@16: { Chris@16: return( Chris@16: (rhs.R_component_1() == lhs.R_component_1())&& Chris@16: (rhs.R_component_2() == lhs.R_component_2())&& Chris@16: (rhs.R_component_3() == lhs.R_component_3())&& Chris@16: (rhs.R_component_4() == lhs.R_component_4())&& Chris@16: (rhs.R_component_5() == static_cast(0))&& Chris@16: (rhs.R_component_6() == static_cast(0))&& Chris@16: (rhs.R_component_7() == static_cast(0))&& Chris@16: (rhs.R_component_8() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (octonion const & lhs, ::boost::math::quaternion const & rhs) Chris@16: { Chris@16: return( Chris@16: (lhs.R_component_1() == rhs.R_component_1())&& Chris@16: (lhs.R_component_2() == rhs.R_component_2())&& Chris@16: (lhs.R_component_3() == rhs.R_component_3())&& Chris@16: (lhs.R_component_4() == rhs.R_component_4())&& Chris@16: (lhs.R_component_5() == static_cast(0))&& Chris@16: (lhs.R_component_6() == static_cast(0))&& Chris@16: (lhs.R_component_7() == static_cast(0))&& Chris@16: (lhs.R_component_8() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (octonion const & lhs, octonion const & rhs) Chris@16: { Chris@16: return( Chris@16: (rhs.R_component_1() == lhs.R_component_1())&& Chris@16: (rhs.R_component_2() == lhs.R_component_2())&& Chris@16: (rhs.R_component_3() == lhs.R_component_3())&& Chris@16: (rhs.R_component_4() == lhs.R_component_4())&& Chris@16: (rhs.R_component_5() == lhs.R_component_5())&& Chris@16: (rhs.R_component_6() == lhs.R_component_6())&& Chris@16: (rhs.R_component_7() == lhs.R_component_7())&& Chris@16: (rhs.R_component_8() == lhs.R_component_8()) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_NOT_EQUAL_GENERATOR \ Chris@16: { \ Chris@16: return(!(lhs == rhs)); \ Chris@16: } Chris@16: Chris@16: template Chris@16: inline bool operator != (T const & lhs, octonion const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (octonion const & lhs, T const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (::std::complex const & lhs, octonion const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (octonion const & lhs, ::std::complex const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (::boost::math::quaternion const & lhs, octonion const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (octonion const & lhs, ::boost::math::quaternion const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (octonion const & lhs, octonion const & rhs) Chris@16: BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: Chris@16: // Note: the default values in the constructors of the complex and quaternions make for Chris@16: // a very complex and ambiguous situation; we have made choices to disambiguate. Chris@16: template Chris@16: ::std::basic_istream & operator >> ( ::std::basic_istream & is, Chris@16: octonion & o) Chris@16: { Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: #else Chris@16: const ::std::ctype & ct = ::std::use_facet< ::std::ctype >(is.getloc()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: T a = T(); Chris@16: T b = T(); Chris@16: T c = T(); Chris@16: T d = T(); Chris@16: T e = T(); Chris@16: T f = T(); Chris@16: T g = T(); Chris@16: T h = T(); Chris@16: Chris@16: ::std::complex u = ::std::complex(); Chris@16: ::std::complex v = ::std::complex(); Chris@16: ::std::complex x = ::std::complex(); Chris@16: ::std::complex y = ::std::complex(); Chris@16: Chris@16: ::boost::math::quaternion p = ::boost::math::quaternion(); Chris@16: ::boost::math::quaternion q = ::boost::math::quaternion(); Chris@16: Chris@16: charT ch = charT(); Chris@16: char cc; Chris@16: Chris@16: is >> ch; // get the first lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(" Chris@16: { Chris@16: is >> ch; // get the second lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((" Chris@16: { Chris@16: is >> ch; // get the third lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(((" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> u; // read "((u" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((u)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (((a))), (((a,b))) Chris@16: { Chris@16: o = octonion(u); Chris@16: } Chris@16: else if (cc == ',') // read "((u)," Chris@16: { Chris@16: p = ::boost::math::quaternion(u); Chris@16: Chris@16: is >> q; // read "((u),q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (((a)),q), (((a,b)),q) Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc ==',') // read "((u," Chris@16: { Chris@16: is >> v; // read "((u,v" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((u,v)" Chris@16: { Chris@16: p = ::boost::math::quaternion(u,v); Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (((a),v)), (((a,b),v)) Chris@16: { Chris@16: o = octonion(p); Chris@16: } Chris@16: else if (cc == ',') // read "((u,v)," Chris@16: { Chris@16: is >> q; // read "(p,q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (((a),v),q), (((a,b),v),q) Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "((a" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> a; // we extract the first component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a))" Chris@16: { Chris@16: o = octonion(a); Chris@16: } Chris@16: else if (cc == ',') // read "((a)," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a),(" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a),((" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is.putback(ch); // we backtrack twice, with the same value! Chris@16: Chris@16: is >> q; // read "((a),q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),q)" Chris@16: { Chris@16: p = ::boost::math::quaternion(a); Chris@16: Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "((a),(c" or "((a),(e" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> c; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c)" (ambiguity resolution) Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c))" Chris@16: { Chris@16: o = octonion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "((a),(c)," Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: v = ::std::complex(c); Chris@16: Chris@16: is >> x; // read "((a),(c),x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c),x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "((a),(c),x," Chris@16: { Chris@16: is >> y; // read "((a),(c),x,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c),x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a),(c," or "((a),(e," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a),(e,(" (ambiguity resolution) Chris@16: { Chris@16: p = ::boost::math::quaternion(a); Chris@16: Chris@16: x = ::std::complex(c); // "c" was actually "e" Chris@16: Chris@16: is.putback(ch); // we can only backtrace once Chris@16: Chris@16: is >> y; // read "((a),(e,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(e,y)" Chris@16: { Chris@16: q = ::boost::math::quaternion(x,y); Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(e,y))" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "((a),(c,d" or "((a),(e,f" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> d; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c,d)" (ambiguity resolution) Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c,d))" Chris@16: { Chris@16: o = octonion(a,b,c,d); Chris@16: } Chris@16: else if (cc == ',') // read "((a),(c,d)," Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: v = ::std::complex(c,d); Chris@16: Chris@16: is >> x; // read "((a),(c,d),x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c,d),x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "((a),(c,d),x," Chris@16: { Chris@16: is >> y; // read "((a),(c,d),x,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(c,d),x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a),(e,f," (ambiguity resolution) Chris@16: { Chris@16: p = ::boost::math::quaternion(a); Chris@16: Chris@16: is >> g; // read "((a),(e,f,g" (too late to backtrack) Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(e,f,g)" Chris@16: { Chris@16: q = ::boost::math::quaternion(c,d,g); // "c" was actually "e", and "d" was actually "f" Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(e,f,g))" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a),(e,f,g," Chris@16: { Chris@16: is >> h; // read "((a),(e,f,g,h" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(e,f,g,h)" Chris@16: { Chris@16: q = ::boost::math::quaternion(c,d,g,h); // "c" was actually "e", and "d" was actually "f" Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),(e,f,g,h))" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // read "((a),c" (ambiguity resolution) Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> c; // we extract the third component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),c)" Chris@16: { Chris@16: o = octonion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "((a),c," Chris@16: { Chris@16: is >> x; // read "((a),c,x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),c,x)" Chris@16: { Chris@16: o = octonion(a,b,c,d,x.real(),x.imag()); Chris@16: } Chris@16: else if (cc == ',') // read "((a),c,x," Chris@16: { Chris@16: is >> y;if (!is.good()) goto finish; // read "((a),c,x,y" Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a),c,x,y)" Chris@16: { Chris@16: o = octonion(a,b,c,d,x.real(),x.imag(),y.real(),y.imag()); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc ==',') // read "((a," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a,(" Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: is.putback(ch); // can only backtrack so much Chris@16: Chris@16: is >> v; // read "((a,v" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,v)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,v))" Chris@16: { Chris@16: o = octonion(u,v); Chris@16: } Chris@16: else if (cc == ',') // read "((a,v)," Chris@16: { Chris@16: p = ::boost::math::quaternion(u,v); Chris@16: Chris@16: is >> q; // read "((a,v),q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,v),q)" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> b; // read "((a,b" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b))" Chris@16: { Chris@16: o = octonion(a,b); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b)," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a,b),(" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a,b),((" Chris@16: { Chris@16: p = ::boost::math::quaternion(a,b); Chris@16: Chris@16: is.putback(ch); Chris@16: Chris@16: is.putback(ch); // we backtrack twice, with the same value Chris@16: Chris@16: is >> q; // read "((a,b),q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),q)" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "((a,b),(c" or "((a,b),(e" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> c; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c)" (ambiguity resolution) Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c))" Chris@16: { Chris@16: o = octonion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(c)," Chris@16: { Chris@16: u = ::std::complex(a,b); Chris@16: Chris@16: v = ::std::complex(c); Chris@16: Chris@16: is >> x; // read "((a,b),(c),x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c),x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(c),x," Chris@16: { Chris@16: is >> y; // read "((a,b),(c),x,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c),x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(c," or "((a,b),(e," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution) Chris@16: { Chris@16: u = ::std::complex(a,b); Chris@16: Chris@16: x = ::std::complex(c); // "c" is actually "e" Chris@16: Chris@16: is.putback(ch); Chris@16: Chris@16: is >> y; // read "((a,b),(e,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(e,y)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(e,y))" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "((a,b),(c,d" or "((a,b),(e,f" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> d; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution) Chris@16: { Chris@16: u = ::std::complex(a,b); Chris@16: Chris@16: v = ::std::complex(c,d); Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c,d))" Chris@16: { Chris@16: o = octonion(u,v); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(c,d)," Chris@16: { Chris@16: is >> x; // read "((a,b),(c,d),x Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c,d),x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(c,d),x," Chris@16: { Chris@16: is >> y; // read "((a,b),(c,d),x,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(c,d),x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution) Chris@16: { Chris@16: p = ::boost::math::quaternion(a,b); // too late to backtrack Chris@16: Chris@16: is >> g; // read "((a,b),(e,f,g" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(e,f,g)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(e,f,g))" Chris@16: { Chris@16: q = ::boost::math::quaternion(c,d,g); // "c" is actually "e" and "d" is actually "f" Chris@16: Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a,b),(e,f,g," Chris@16: { Chris@16: is >> h; // read "((a,b),(e,f,g,h" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b),(e,f,g,h)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read ((a,b),(e,f,g,h))" Chris@16: { Chris@16: q = ::boost::math::quaternion(c,d,g,h); // "c" is actually "e" and "d" is actually "f" Chris@16: Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a,b," Chris@16: { Chris@16: is >> c; // read "((a,b,c" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b,c)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b,c))" Chris@16: { Chris@16: o = octonion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b,c)," Chris@16: { Chris@16: p = ::boost::math::quaternion(a,b,c); Chris@16: Chris@16: is >> q; // read "((a,b,c),q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b,c),q)" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "((a,b,c," Chris@16: { Chris@16: is >> d; // read "((a,b,c,d" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b,c,d)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b,c,d))" Chris@16: { Chris@16: o = octonion(a,b,c,d); Chris@16: } Chris@16: else if (cc == ',') // read "((a,b,c,d)," Chris@16: { Chris@16: p = ::boost::math::quaternion(a,b,c,d); Chris@16: Chris@16: is >> q; // read "((a,b,c,d),q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "((a,b,c,d),q)" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // read "(a" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> a; // we extract the first component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a)" Chris@16: { Chris@16: o = octonion(a); Chris@16: } Chris@16: else if (cc == ',') // read "(a," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(a,(" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(a,((" Chris@16: { Chris@16: p = ::boost::math::quaternion(a); Chris@16: Chris@16: is.putback(ch); Chris@16: Chris@16: is.putback(ch); // we backtrack twice, with the same value Chris@16: Chris@16: is >> q; // read "(a,q" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,q)" Chris@16: { Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "(a,(c" or "(a,(e" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> c; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c)" (ambiguity resolution) Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c))" Chris@16: { Chris@16: o = octonion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "(a,(c)," Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: v = ::std::complex(c); Chris@16: Chris@16: is >> x; // read "(a,(c),x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c),x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "(a,(c),x," Chris@16: { Chris@16: is >> y; // read "(a,(c),x,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c),x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "(a,(c," or "(a,(e," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(a,(e,(" (ambiguity resolution) Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: x = ::std::complex(c); // "c" is actually "e" Chris@16: Chris@16: is.putback(ch); // we backtrack Chris@16: Chris@16: is >> y; // read "(a,(e,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(e,y)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(e,y))" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "(a,(c,d" or "(a,(e,f" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> d; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c,d)" (ambiguity resolution) Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c,d))" Chris@16: { Chris@16: o = octonion(a,b,c,d); Chris@16: } Chris@16: else if (cc == ',') // read "(a,(c,d)," Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: v = ::std::complex(c,d); Chris@16: Chris@16: is >> x; // read "(a,(c,d),x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c,d),x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "(a,(c,d),x," Chris@16: { Chris@16: is >> y; // read "(a,(c,d),x,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(c,d),x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "(a,(e,f," (ambiguity resolution) Chris@16: { Chris@16: p = ::boost::math::quaternion(a); Chris@16: Chris@16: is >> g; // read "(a,(e,f,g" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(e,f,g)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(e,f,g))" Chris@16: { Chris@16: q = ::boost::math::quaternion(c,d,g); // "c" is actually "e" and "d" is actually "f" Chris@16: Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else if (cc == ',') // read "(a,(e,f,g," Chris@16: { Chris@16: is >> h; // read "(a,(e,f,g,h" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(e,f,g,h)" Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,(e,f,g,h))" Chris@16: { Chris@16: q = ::boost::math::quaternion(c,d,g,h); // "c" is actually "e" and "d" is actually "f" Chris@16: Chris@16: o = octonion(p,q); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // read "(a,b" or "(a,c" (ambiguity resolution) Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> b; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b)" (ambiguity resolution) Chris@16: { Chris@16: o = octonion(a,b); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b," or "(a,c," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(a,c,(" (ambiguity resolution) Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: v = ::std::complex(b); // "b" is actually "c" Chris@16: Chris@16: is.putback(ch); // we backtrack Chris@16: Chris@16: is >> x; // read "(a,c,x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,c,x)" Chris@16: { Chris@16: o = octonion(u,v,x); Chris@16: } Chris@16: else if (cc == ',') // read "(a,c,x," Chris@16: { Chris@16: is >> y; // read "(a,c,x,y" // read "(a,c,x" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,c,x,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "(a,b,c" or "(a,c,e" Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> c; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b,c)" (ambiguity resolution) Chris@16: { Chris@16: o = octonion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,c," or "(a,c,e," Chris@16: { Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(a,c,e,(") (ambiguity resolution) Chris@16: { Chris@16: u = ::std::complex(a); Chris@16: Chris@16: v = ::std::complex(b); // "b" is actually "c" Chris@16: Chris@16: x = ::std::complex(c); // "c" is actually "e" Chris@16: Chris@16: is.putback(ch); // we backtrack Chris@16: Chris@16: is >> y; // read "(a,c,e,y" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,c,e,y)" Chris@16: { Chris@16: o = octonion(u,v,x,y); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "(a,b,c,d" (ambiguity resolution) Chris@16: { Chris@16: is.putback(ch); // we backtrack Chris@16: Chris@16: is >> d; Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b,c,d)" Chris@16: { Chris@16: o = octonion(a,b,c,d); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,c,d," Chris@16: { Chris@16: is >> e; // read "(a,b,c,d,e" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b,c,d,e)" Chris@16: { Chris@16: o = octonion(a,b,c,d,e); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,c,d,e," Chris@16: { Chris@16: is >> f; // read "(a,b,c,d,e,f" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b,c,d,e,f)" Chris@16: { Chris@16: o = octonion(a,b,c,d,e,f); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,c,d,e,f," Chris@16: { Chris@16: is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b,c,d,e,f,g)" Chris@16: { Chris@16: o = octonion(a,b,c,d,e,f,g); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,c,d,e,f,g," Chris@16: { Chris@16: 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" Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // read "(a,b,c,d,e,f,g,h)" Chris@16: { Chris@16: o = octonion(a,b,c,d,e,f,g,h); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // format: a Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> a; // we extract the first component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: o = octonion(a); Chris@16: } Chris@16: Chris@16: finish: Chris@16: return(is); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: ::std::basic_ostream & operator << ( ::std::basic_ostream & os, Chris@16: octonion const & o) Chris@16: { Chris@16: ::std::basic_ostringstream s; Chris@16: Chris@16: s.flags(os.flags()); Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: #else Chris@16: s.imbue(os.getloc()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: s.precision(os.precision()); Chris@16: Chris@16: s << '(' << o.R_component_1() << ',' Chris@16: << o.R_component_2() << ',' Chris@16: << o.R_component_3() << ',' Chris@16: << o.R_component_4() << ',' Chris@16: << o.R_component_5() << ',' Chris@16: << o.R_component_6() << ',' Chris@16: << o.R_component_7() << ',' Chris@16: << o.R_component_8() << ')'; Chris@16: Chris@16: return os << s.str(); Chris@16: } Chris@16: Chris@16: Chris@16: // values Chris@16: Chris@16: template Chris@16: inline T real(octonion const & o) Chris@16: { Chris@16: return(o.real()); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion unreal(octonion const & o) Chris@16: { Chris@16: return(o.unreal()); Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_OCTONION_VALARRAY_LOADER \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray temp(8); \ Chris@16: \ Chris@16: temp[0] = o.R_component_1(); \ Chris@16: temp[1] = o.R_component_2(); \ Chris@16: temp[2] = o.R_component_3(); \ Chris@16: temp[3] = o.R_component_4(); \ Chris@16: temp[4] = o.R_component_5(); \ Chris@16: temp[5] = o.R_component_6(); \ Chris@16: temp[6] = o.R_component_7(); \ Chris@16: temp[7] = o.R_component_8(); Chris@16: Chris@16: Chris@16: template Chris@16: inline T sup(octonion const & o) Chris@16: { Chris@16: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP Chris@16: using ::std::abs; Chris@16: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: BOOST_OCTONION_VALARRAY_LOADER Chris@16: Chris@16: return((abs(temp).max)()); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline T l1(octonion const & o) Chris@16: { Chris@16: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP Chris@16: using ::std::abs; Chris@16: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: BOOST_OCTONION_VALARRAY_LOADER Chris@16: Chris@16: return(abs(temp).sum()); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline T abs(const octonion & o) Chris@16: { Chris@16: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP Chris@16: using ::std::abs; Chris@16: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: using ::std::sqrt; Chris@16: Chris@16: BOOST_OCTONION_VALARRAY_LOADER Chris@16: Chris@16: T maxim = (abs(temp).max)(); // overflow protection Chris@16: Chris@16: if (maxim == static_cast(0)) Chris@16: { Chris@16: return(maxim); Chris@16: } Chris@16: else Chris@16: { Chris@16: T mixam = static_cast(1)/maxim; // prefer multiplications over divisions Chris@16: Chris@16: temp *= mixam; Chris@16: Chris@16: temp *= temp; Chris@16: Chris@16: return(maxim*sqrt(temp.sum())); Chris@16: } Chris@16: Chris@16: //return(::std::sqrt(norm(o))); Chris@16: } Chris@16: Chris@16: Chris@16: #undef BOOST_OCTONION_VALARRAY_LOADER Chris@16: Chris@16: Chris@16: // Note: This is the Cayley norm, not the Euclidian norm... Chris@16: Chris@16: template Chris@16: inline T norm(octonion const & o) Chris@16: { Chris@16: return(real(o*conj(o))); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion conj(octonion const & o) Chris@16: { Chris@16: return(octonion( +o.R_component_1(), Chris@16: -o.R_component_2(), Chris@16: -o.R_component_3(), Chris@16: -o.R_component_4(), Chris@16: -o.R_component_5(), Chris@16: -o.R_component_6(), Chris@16: -o.R_component_7(), Chris@16: -o.R_component_8())); Chris@16: } Chris@16: Chris@16: Chris@16: // Note: There is little point, for the octonions, to introduce the equivalents Chris@16: // to the complex "arg" and the quaternionic "cylindropolar". Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion spherical(T const & rho, Chris@16: T const & theta, Chris@16: T const & phi1, Chris@16: T const & phi2, Chris@16: T const & phi3, Chris@16: T const & phi4, Chris@16: T const & phi5, Chris@16: T const & phi6) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: //T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); Chris@16: //T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); Chris@16: //T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); Chris@16: //T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); Chris@16: //T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6); Chris@16: //T f = sin(phi4)*cos(phi5)*cos(phi6); Chris@16: //T g = sin(phi5)*cos(phi6); Chris@16: //T h = sin(phi6); Chris@16: Chris@16: T courrant = static_cast(1); Chris@16: Chris@16: T h = sin(phi6); Chris@16: Chris@16: courrant *= cos(phi6); Chris@16: Chris@16: T g = sin(phi5)*courrant; Chris@16: Chris@16: courrant *= cos(phi5); Chris@16: Chris@16: T f = sin(phi4)*courrant; Chris@16: Chris@16: courrant *= cos(phi4); Chris@16: Chris@16: T e = sin(phi3)*courrant; Chris@16: Chris@16: courrant *= cos(phi3); Chris@16: Chris@16: T d = sin(phi2)*courrant; Chris@16: Chris@16: courrant *= cos(phi2); Chris@16: Chris@16: T c = sin(phi1)*courrant; Chris@16: Chris@16: courrant *= cos(phi1); Chris@16: Chris@16: T b = sin(theta)*courrant; Chris@16: T a = cos(theta)*courrant; Chris@16: Chris@16: return(rho*octonion(a,b,c,d,e,f,g,h)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion multipolar(T const & rho1, Chris@16: T const & theta1, Chris@16: T const & rho2, Chris@16: T const & theta2, Chris@16: T const & rho3, Chris@16: T const & theta3, Chris@16: T const & rho4, Chris@16: T const & theta4) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: T a = rho1*cos(theta1); Chris@16: T b = rho1*sin(theta1); Chris@16: T c = rho2*cos(theta2); Chris@16: T d = rho2*sin(theta2); Chris@16: T e = rho3*cos(theta3); Chris@16: T f = rho3*sin(theta3); Chris@16: T g = rho4*cos(theta4); Chris@16: T h = rho4*sin(theta4); Chris@16: Chris@16: return(octonion(a,b,c,d,e,f,g,h)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion cylindrical(T const & r, Chris@16: T const & angle, Chris@16: T const & h1, Chris@16: T const & h2, Chris@16: T const & h3, Chris@16: T const & h4, Chris@16: T const & h5, Chris@16: T const & h6) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: T a = r*cos(angle); Chris@16: T b = r*sin(angle); Chris@16: Chris@16: return(octonion(a,b,h1,h2,h3,h4,h5,h6)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion exp(octonion const & o) Chris@16: { Chris@16: using ::std::exp; Chris@16: using ::std::cos; Chris@16: Chris@16: using ::boost::math::sinc_pi; Chris@16: Chris@16: T u = exp(real(o)); Chris@16: Chris@16: T z = abs(unreal(o)); Chris@16: Chris@16: T w = sinc_pi(z); Chris@16: Chris@16: return(u*octonion(cos(z), Chris@16: w*o.R_component_2(), w*o.R_component_3(), Chris@16: w*o.R_component_4(), w*o.R_component_5(), Chris@16: w*o.R_component_6(), w*o.R_component_7(), Chris@16: w*o.R_component_8())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion cos(octonion const & o) Chris@16: { Chris@16: using ::std::sin; Chris@16: using ::std::cos; Chris@16: using ::std::cosh; Chris@16: Chris@16: using ::boost::math::sinhc_pi; Chris@16: Chris@16: T z = abs(unreal(o)); Chris@16: Chris@16: T w = -sin(o.real())*sinhc_pi(z); Chris@16: Chris@16: return(octonion(cos(o.real())*cosh(z), Chris@16: w*o.R_component_2(), w*o.R_component_3(), Chris@16: w*o.R_component_4(), w*o.R_component_5(), Chris@16: w*o.R_component_6(), w*o.R_component_7(), Chris@16: w*o.R_component_8())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion sin(octonion const & o) Chris@16: { Chris@16: using ::std::sin; Chris@16: using ::std::cos; Chris@16: using ::std::cosh; Chris@16: Chris@16: using ::boost::math::sinhc_pi; Chris@16: Chris@16: T z = abs(unreal(o)); Chris@16: Chris@16: T w = +cos(o.real())*sinhc_pi(z); Chris@16: Chris@16: return(octonion(sin(o.real())*cosh(z), Chris@16: w*o.R_component_2(), w*o.R_component_3(), Chris@16: w*o.R_component_4(), w*o.R_component_5(), Chris@16: w*o.R_component_6(), w*o.R_component_7(), Chris@16: w*o.R_component_8())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion tan(octonion const & o) Chris@16: { Chris@16: return(sin(o)/cos(o)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion cosh(octonion const & o) Chris@16: { Chris@16: return((exp(+o)+exp(-o))/static_cast(2)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion sinh(octonion const & o) Chris@16: { Chris@16: return((exp(+o)-exp(-o))/static_cast(2)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline octonion tanh(octonion const & o) Chris@16: { Chris@16: return(sinh(o)/cosh(o)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: octonion pow(octonion const & o, Chris@16: int n) Chris@16: { Chris@16: if (n > 1) Chris@16: { Chris@16: int m = n>>1; Chris@16: Chris@16: octonion result = pow(o, m); Chris@16: Chris@16: result *= result; Chris@16: Chris@16: if (n != (m<<1)) Chris@16: { Chris@16: result *= o; // n odd Chris@16: } Chris@16: Chris@16: return(result); Chris@16: } Chris@16: else if (n == 1) Chris@16: { Chris@16: return(o); Chris@16: } Chris@16: else if (n == 0) Chris@16: { Chris@16: return(octonion(static_cast(1))); Chris@16: } Chris@16: else /* n < 0 */ Chris@16: { Chris@16: return(pow(octonion(static_cast(1))/o,-n)); Chris@16: } Chris@16: } Chris@16: Chris@16: Chris@16: // helper templates for converting copy constructors (definition) Chris@16: Chris@16: namespace detail Chris@16: { Chris@16: Chris@16: template< typename T, Chris@16: typename U Chris@16: > Chris@16: octonion octonion_type_converter(octonion const & rhs) Chris@16: { Chris@16: return(octonion( static_cast(rhs.R_component_1()), Chris@16: static_cast(rhs.R_component_2()), Chris@16: static_cast(rhs.R_component_3()), Chris@16: static_cast(rhs.R_component_4()), Chris@16: static_cast(rhs.R_component_5()), Chris@16: static_cast(rhs.R_component_6()), Chris@16: static_cast(rhs.R_component_7()), Chris@16: static_cast(rhs.R_component_8()))); Chris@16: } Chris@16: } Chris@16: } Chris@16: } Chris@16: Chris@16: #endif /* BOOST_OCTONION_HPP */