diff -r 666f914201fb -r 2fe1408b6811 epoc32/include/stdapis/boost/math/octonion.hpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/epoc32/include/stdapis/boost/math/octonion.hpp Tue Mar 16 16:12:26 2010 +0000 @@ -0,0 +1,4754 @@ +// boost octonion.hpp header file + +// (C) Copyright Hubert Holin 2001. +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +// See http://www.boost.org for updates, documentation, and revision history. + + +#ifndef BOOST_OCTONION_HPP +#define BOOST_OCTONION_HPP + +#include + + +namespace boost +{ + namespace math + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + // gcc 2.95.x uses expression templates for valarray calculations, but + // the result is not conforming. We need BOOST_GET_VALARRAY to get an + // actual valarray result when we need to call a member function + #define BOOST_GET_VALARRAY(T,x) ::std::valarray(x) + // gcc 2.95.x has an "std::ios" class that is similar to + // "std::ios_base", so we just use a #define + #define BOOST_IOS_BASE ::std::ios + // gcc 2.x ignores function scope using declarations, + // put them in the scope of the enclosing namespace instead: + using ::std::valarray; + using ::std::sqrt; + using ::std::cos; + using ::std::sin; + using ::std::exp; + using ::std::cosh; +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + +#define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \ + type real() const \ + { \ + return(a); \ + } \ + \ + octonion unreal() const \ + { \ + return( octonion(static_cast(0),b,c,d,e,f,g,h)); \ + } \ + \ + type R_component_1() const \ + { \ + return(a); \ + } \ + \ + type R_component_2() const \ + { \ + return(b); \ + } \ + \ + type R_component_3() const \ + { \ + return(c); \ + } \ + \ + type R_component_4() const \ + { \ + return(d); \ + } \ + \ + type R_component_5() const \ + { \ + return(e); \ + } \ + \ + type R_component_6() const \ + { \ + return(f); \ + } \ + \ + type R_component_7() const \ + { \ + return(g); \ + } \ + \ + type R_component_8() const \ + { \ + return(h); \ + } \ + \ + ::std::complex C_component_1() const \ + { \ + return(::std::complex(a,b)); \ + } \ + \ + ::std::complex C_component_2() const \ + { \ + return(::std::complex(c,d)); \ + } \ + \ + ::std::complex C_component_3() const \ + { \ + return(::std::complex(e,f)); \ + } \ + \ + ::std::complex C_component_4() const \ + { \ + return(::std::complex(g,h)); \ + } \ + \ + ::boost::math::quaternion H_component_1() const \ + { \ + return(::boost::math::quaternion(a,b,c,d)); \ + } \ + \ + ::boost::math::quaternion H_component_2() const \ + { \ + return(::boost::math::quaternion(e,f,g,h)); \ + } + + +#define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \ + template \ + octonion & operator = (octonion const & a_affecter) \ + { \ + a = static_cast(a_affecter.R_component_1()); \ + b = static_cast(a_affecter.R_component_2()); \ + c = static_cast(a_affecter.R_component_3()); \ + d = static_cast(a_affecter.R_component_4()); \ + e = static_cast(a_affecter.R_component_5()); \ + f = static_cast(a_affecter.R_component_6()); \ + g = static_cast(a_affecter.R_component_7()); \ + h = static_cast(a_affecter.R_component_8()); \ + \ + return(*this); \ + } \ + \ + octonion & operator = (octonion const & a_affecter) \ + { \ + a = a_affecter.a; \ + b = a_affecter.b; \ + c = a_affecter.c; \ + d = a_affecter.d; \ + e = a_affecter.e; \ + f = a_affecter.f; \ + g = a_affecter.g; \ + h = a_affecter.h; \ + \ + return(*this); \ + } \ + \ + octonion & operator = (type const & a_affecter) \ + { \ + a = a_affecter; \ + \ + b = c = d = e = f= g = h = static_cast(0); \ + \ + return(*this); \ + } \ + \ + octonion & operator = (::std::complex const & a_affecter) \ + { \ + a = a_affecter.real(); \ + b = a_affecter.imag(); \ + \ + c = d = e = f = g = h = static_cast(0); \ + \ + return(*this); \ + } \ + \ + octonion & operator = (::boost::math::quaternion const & a_affecter) \ + { \ + a = a_affecter.R_component_1(); \ + b = a_affecter.R_component_2(); \ + c = a_affecter.R_component_3(); \ + d = a_affecter.R_component_4(); \ + \ + e = f = g = h = static_cast(0); \ + \ + return(*this); \ + } + + +#define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \ + type a; \ + type b; \ + type c; \ + type d; \ + type e; \ + type f; \ + type g; \ + type h; \ + + + template + class octonion + { + public: + + typedef T value_type; + + // constructor for O seen as R^8 + // (also default constructor) + + explicit octonion( T const & requested_a = T(), + T const & requested_b = T(), + T const & requested_c = T(), + T const & requested_d = T(), + T const & requested_e = T(), + T const & requested_f = T(), + T const & requested_g = T(), + T const & requested_h = T()) + : a(requested_a), + b(requested_b), + c(requested_c), + d(requested_d), + e(requested_e), + f(requested_f), + g(requested_g), + h(requested_h) + { + // nothing to do! + } + + + // constructor for H seen as C^4 + + explicit octonion( ::std::complex const & z0, + ::std::complex const & z1 = ::std::complex(), + ::std::complex const & z2 = ::std::complex(), + ::std::complex const & z3 = ::std::complex()) + : a(z0.real()), + b(z0.imag()), + c(z1.real()), + d(z1.imag()), + e(z2.real()), + f(z2.imag()), + g(z3.real()), + h(z3.imag()) + { + // nothing to do! + } + + + // constructor for O seen as H^2 + + explicit octonion( ::boost::math::quaternion const & q0, + ::boost::math::quaternion const & q1 = ::boost::math::quaternion()) + : a(q0.R_component_1()), + b(q0.R_component_2()), + c(q0.R_component_3()), + d(q0.R_component_4()), + e(q1.R_component_1()), + f(q1.R_component_2()), + g(q1.R_component_3()), + h(q1.R_component_4()) + { + // nothing to do! + } + + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + + // templated copy constructor + + template + explicit octonion(octonion const & a_recopier) + : a(static_cast(a_recopier.R_component_1())), + b(static_cast(a_recopier.R_component_2())), + c(static_cast(a_recopier.R_component_3())), + d(static_cast(a_recopier.R_component_4())), + e(static_cast(a_recopier.R_component_5())), + f(static_cast(a_recopier.R_component_6())), + g(static_cast(a_recopier.R_component_7())), + h(static_cast(a_recopier.R_component_8())) + { + // nothing to do! + } + + + // destructor + // (this is taken care of by the compiler itself) + + + // accessors + // + // Note: Like complex number, octonions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is an octonion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_OCTONION_ACCESSOR_GENERATOR(T) + + // assignment operators + + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T) + + // other assignment-related operators + // + // NOTE: Octonion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);"; + // octonion multiplication is also *NOT* associative + + octonion & operator += (T const & rhs) + { + T at = a + rhs; // exception guard + + a = at; + + return(*this); + } + + + octonion & operator += (::std::complex const & rhs) + { + T at = a + rhs.real(); // exception guard + T bt = b + rhs.imag(); // exception guard + + a = at; + b = bt; + + return(*this); + } + + + octonion & operator += (::boost::math::quaternion const & rhs) + { + T at = a + rhs.R_component_1(); // exception guard + T bt = b + rhs.R_component_2(); // exception guard + T ct = c + rhs.R_component_3(); // exception guard + T dt = d + rhs.R_component_4(); // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + template + octonion & operator += (octonion const & rhs) + { + T at = a + static_cast(rhs.R_component_1()); // exception guard + T bt = b + static_cast(rhs.R_component_2()); // exception guard + T ct = c + static_cast(rhs.R_component_3()); // exception guard + T dt = d + static_cast(rhs.R_component_4()); // exception guard + T et = e + static_cast(rhs.R_component_5()); // exception guard + T ft = f + static_cast(rhs.R_component_6()); // exception guard + T gt = g + static_cast(rhs.R_component_7()); // exception guard + T ht = h + static_cast(rhs.R_component_8()); // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + + octonion & operator -= (T const & rhs) + { + T at = a - rhs; // exception guard + + a = at; + + return(*this); + } + + + octonion & operator -= (::std::complex const & rhs) + { + T at = a - rhs.real(); // exception guard + T bt = b - rhs.imag(); // exception guard + + a = at; + b = bt; + + return(*this); + } + + + octonion & operator -= (::boost::math::quaternion const & rhs) + { + T at = a - rhs.R_component_1(); // exception guard + T bt = b - rhs.R_component_2(); // exception guard + T ct = c - rhs.R_component_3(); // exception guard + T dt = d - rhs.R_component_4(); // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + template + octonion & operator -= (octonion const & rhs) + { + T at = a - static_cast(rhs.R_component_1()); // exception guard + T bt = b - static_cast(rhs.R_component_2()); // exception guard + T ct = c - static_cast(rhs.R_component_3()); // exception guard + T dt = d - static_cast(rhs.R_component_4()); // exception guard + T et = e - static_cast(rhs.R_component_5()); // exception guard + T ft = f - static_cast(rhs.R_component_6()); // exception guard + T gt = g - static_cast(rhs.R_component_7()); // exception guard + T ht = h - static_cast(rhs.R_component_8()); // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + octonion & operator *= (T const & rhs) + { + T at = a * rhs; // exception guard + T bt = b * rhs; // exception guard + T ct = c * rhs; // exception guard + T dt = d * rhs; // exception guard + T et = e * rhs; // exception guard + T ft = f * rhs; // exception guard + T gt = g * rhs; // exception guard + T ht = h * rhs; // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + octonion & operator *= (::std::complex const & rhs) + { + T ar = rhs.real(); + T br = rhs.imag(); + + T at = +a*ar-b*br; + T bt = +a*br+b*ar; + T ct = +c*ar+d*br; + T dt = -c*br+d*ar; + T et = +e*ar+f*br; + T ft = -e*br+f*ar; + T gt = +g*ar-h*br; + T ht = +g*br+h*ar; + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + octonion & operator *= (::boost::math::quaternion const & rhs) + { + T ar = rhs.R_component_1(); + T br = rhs.R_component_2(); + T cr = rhs.R_component_2(); + T dr = rhs.R_component_2(); + + T at = +a*ar-b*br-c*cr-d*dr; + T bt = +a*br+b*ar+c*dr-d*cr; + T ct = +a*cr-b*dr+c*ar+d*br; + T dt = +a*dr+b*cr-c*br+d*ar; + T et = +e*ar+f*br+g*cr+h*dr; + T ft = -e*br+f*ar-g*dr+h*cr; + T gt = -e*cr+f*dr+g*ar-h*br; + T ht = -e*dr-f*cr+g*br+h*ar; + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + template + octonion & operator *= (octonion const & rhs) + { + T ar = static_cast(rhs.R_component_1()); + T br = static_cast(rhs.R_component_2()); + T cr = static_cast(rhs.R_component_3()); + T dr = static_cast(rhs.R_component_4()); + T er = static_cast(rhs.R_component_5()); + T fr = static_cast(rhs.R_component_6()); + T gr = static_cast(rhs.R_component_7()); + T hr = static_cast(rhs.R_component_8()); + + T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; + T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; + T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; + T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; + T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; + T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; + T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; + T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + octonion & operator /= (T const & rhs) + { + T at = a / rhs; // exception guard + T bt = b / rhs; // exception guard + T ct = c / rhs; // exception guard + T dt = d / rhs; // exception guard + T et = e / rhs; // exception guard + T ft = f / rhs; // exception guard + T gt = g / rhs; // exception guard + T ht = h / rhs; // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + octonion & operator /= (::std::complex const & rhs) + { + T ar = rhs.real(); + T br = rhs.imag(); + + T denominator = ar*ar+br*br; + + T at = (+a*ar-b*br)/denominator; + T bt = (-a*br+b*ar)/denominator; + T ct = (+c*ar-d*br)/denominator; + T dt = (+c*br+d*ar)/denominator; + T et = (+e*ar-f*br)/denominator; + T ft = (+e*br+f*ar)/denominator; + T gt = (+g*ar+h*br)/denominator; + T ht = (+g*br+h*ar)/denominator; + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + octonion & operator /= (::boost::math::quaternion const & rhs) + { + T ar = rhs.R_component_1(); + T br = rhs.R_component_2(); + T cr = rhs.R_component_2(); + T dr = rhs.R_component_2(); + + T denominator = ar*ar+br*br+cr*cr+dr*dr; + + T at = (+a*ar+b*br+c*cr+d*dr)/denominator; + T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; + T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; + T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; + T et = (+e*ar-f*br-g*cr-h*dr)/denominator; + T ft = (+e*br+f*ar+g*dr-h*cr)/denominator; + T gt = (+e*cr-f*dr+g*ar+h*br)/denominator; + T ht = (+e*dr+f*cr-g*br+h*ar)/denominator; + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + template + octonion & operator /= (octonion const & rhs) + { + T ar = static_cast(rhs.R_component_1()); + T br = static_cast(rhs.R_component_2()); + T cr = static_cast(rhs.R_component_3()); + T dr = static_cast(rhs.R_component_4()); + T er = static_cast(rhs.R_component_5()); + T fr = static_cast(rhs.R_component_6()); + T gr = static_cast(rhs.R_component_7()); + T hr = static_cast(rhs.R_component_8()); + + T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr; + + T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator; + T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator; + T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator; + T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator; + T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator; + T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator; + T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator; + T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator; + + a = at; + b = bt; + c = ct; + d = dt; + e = et; + f = ft; + g = gt; + h = ht; + + return(*this); + } + + + protected: + + BOOST_OCTONION_MEMBER_DATA_GENERATOR(T) + + + private: + + }; + + + // declaration of octonion specialization + + template<> class octonion; + template<> class octonion; + template<> class octonion; + + + // helper templates for converting copy constructors (declaration) + + namespace detail + { + + template< typename T, + typename U + > + octonion octonion_type_converter(octonion const & rhs); + } + + + // implementation of octonion specialization + + +#define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \ + explicit octonion( type const & requested_a = static_cast(0), \ + type const & requested_b = static_cast(0), \ + type const & requested_c = static_cast(0), \ + type const & requested_d = static_cast(0), \ + type const & requested_e = static_cast(0), \ + type const & requested_f = static_cast(0), \ + type const & requested_g = static_cast(0), \ + type const & requested_h = static_cast(0)) \ + : a(requested_a), \ + b(requested_b), \ + c(requested_c), \ + d(requested_d), \ + e(requested_e), \ + f(requested_f), \ + g(requested_g), \ + h(requested_h) \ + { \ + } \ + \ + explicit octonion( ::std::complex const & z0, \ + ::std::complex const & z1 = ::std::complex(), \ + ::std::complex const & z2 = ::std::complex(), \ + ::std::complex const & z3 = ::std::complex()) \ + : a(z0.real()), \ + b(z0.imag()), \ + c(z1.real()), \ + d(z1.imag()), \ + e(z2.real()), \ + f(z2.imag()), \ + g(z3.real()), \ + h(z3.imag()) \ + { \ + } \ + \ + explicit octonion( ::boost::math::quaternion const & q0, \ + ::boost::math::quaternion const & q1 = ::boost::math::quaternion()) \ + : a(q0.R_component_1()), \ + b(q0.R_component_2()), \ + c(q0.R_component_3()), \ + d(q0.R_component_4()), \ + e(q1.R_component_1()), \ + f(q1.R_component_2()), \ + g(q1.R_component_3()), \ + h(q1.R_component_4()) \ + { \ + } + + +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \ + octonion & operator += (type const & rhs) \ + { \ + a += rhs; \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \ + octonion & operator += (::std::complex const & rhs) \ + { \ + a += rhs.real(); \ + b += rhs.imag(); \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \ + octonion & operator += (::boost::math::quaternion const & rhs) \ + { \ + a += rhs.R_component_1(); \ + b += rhs.R_component_2(); \ + c += rhs.R_component_3(); \ + d += rhs.R_component_4(); \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \ + template \ + octonion & operator += (octonion const & rhs) \ + { \ + a += static_cast(rhs.R_component_1()); \ + b += static_cast(rhs.R_component_2()); \ + c += static_cast(rhs.R_component_3()); \ + d += static_cast(rhs.R_component_4()); \ + e += static_cast(rhs.R_component_5()); \ + f += static_cast(rhs.R_component_6()); \ + g += static_cast(rhs.R_component_7()); \ + h += static_cast(rhs.R_component_8()); \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \ + octonion & operator -= (type const & rhs) \ + { \ + a -= rhs; \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \ + octonion & operator -= (::std::complex const & rhs) \ + { \ + a -= rhs.real(); \ + b -= rhs.imag(); \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \ + octonion & operator -= (::boost::math::quaternion const & rhs) \ + { \ + a -= rhs.R_component_1(); \ + b -= rhs.R_component_2(); \ + c -= rhs.R_component_3(); \ + d -= rhs.R_component_4(); \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \ + template \ + octonion & operator -= (octonion const & rhs) \ + { \ + a -= static_cast(rhs.R_component_1()); \ + b -= static_cast(rhs.R_component_2()); \ + c -= static_cast(rhs.R_component_3()); \ + d -= static_cast(rhs.R_component_4()); \ + e -= static_cast(rhs.R_component_5()); \ + f -= static_cast(rhs.R_component_6()); \ + g -= static_cast(rhs.R_component_7()); \ + h -= static_cast(rhs.R_component_8()); \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \ + octonion & operator *= (type const & rhs) \ + { \ + a *= rhs; \ + b *= rhs; \ + c *= rhs; \ + d *= rhs; \ + e *= rhs; \ + f *= rhs; \ + g *= rhs; \ + h *= rhs; \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \ + octonion & operator *= (::std::complex const & rhs) \ + { \ + type ar = rhs.real(); \ + type br = rhs.imag(); \ + \ + type at = +a*ar-b*br; \ + type bt = +a*br+b*ar; \ + type ct = +c*ar+d*br; \ + type dt = -c*br+d*ar; \ + type et = +e*ar+f*br; \ + type ft = -e*br+f*ar; \ + type gt = +g*ar-h*br; \ + type ht = +g*br+h*ar; \ + \ + a = at; \ + b = bt; \ + c = ct; \ + d = dt; \ + e = et; \ + f = ft; \ + g = gt; \ + h = ht; \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \ + octonion & operator *= (::boost::math::quaternion const & rhs) \ + { \ + type ar = rhs.R_component_1(); \ + type br = rhs.R_component_2(); \ + type cr = rhs.R_component_2(); \ + type dr = rhs.R_component_2(); \ + \ + type at = +a*ar-b*br-c*cr-d*dr; \ + type bt = +a*br+b*ar+c*dr-d*cr; \ + type ct = +a*cr-b*dr+c*ar+d*br; \ + type dt = +a*dr+b*cr-c*br+d*ar; \ + type et = +e*ar+f*br+g*cr+h*dr; \ + type ft = -e*br+f*ar-g*dr+h*cr; \ + type gt = -e*cr+f*dr+g*ar-h*br; \ + type ht = -e*dr-f*cr+g*br+h*ar; \ + \ + a = at; \ + b = bt; \ + c = ct; \ + d = dt; \ + e = et; \ + f = ft; \ + g = gt; \ + h = ht; \ + \ + return(*this); \ + } + +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \ + template \ + octonion & operator *= (octonion const & rhs) \ + { \ + type ar = static_cast(rhs.R_component_1()); \ + type br = static_cast(rhs.R_component_2()); \ + type cr = static_cast(rhs.R_component_3()); \ + type dr = static_cast(rhs.R_component_4()); \ + type er = static_cast(rhs.R_component_5()); \ + type fr = static_cast(rhs.R_component_6()); \ + type gr = static_cast(rhs.R_component_7()); \ + type hr = static_cast(rhs.R_component_8()); \ + \ + type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \ + type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \ + type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \ + type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \ + type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \ + type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \ + type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \ + type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \ + \ + a = at; \ + b = bt; \ + c = ct; \ + d = dt; \ + e = et; \ + f = ft; \ + g = gt; \ + h = ht; \ + \ + return(*this); \ + } + +// There is quite a lot of repetition in the code below. This is intentional. +// The last conditional block is the normal form, and the others merely +// consist of workarounds for various compiler deficiencies. Hopefuly, when +// more compilers are conformant and we can retire support for those that are +// not, we will be able to remove the clutter. This is makes the situation +// (painfully) explicit. + +#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \ + octonion & operator /= (type const & rhs) \ + { \ + a /= rhs; \ + b /= rhs; \ + c /= rhs; \ + d /= rhs; \ + \ + return(*this); \ + } + +#if defined(__GNUC__) && (__GNUC__ < 3) + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ + octonion & operator /= (::std::complex const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(2); \ + \ + tr[0] = rhs.real(); \ + tr[1] = rhs.imag(); \ + \ + type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]-b*tr[1]; \ + tt[1] = -a*tr[1]+b*tr[0]; \ + tt[2] = +c*tr[0]-d*tr[1]; \ + tt[3] = +c*tr[1]+d*tr[0]; \ + tt[4] = +e*tr[0]-f*tr[1]; \ + tt[5] = +e*tr[1]+f*tr[0]; \ + tt[6] = +g*tr[0]+h*tr[1]; \ + tt[7] = +g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ + octonion & operator /= (::std::complex const & rhs) \ + { \ + using ::std::valarray; \ + using ::std::abs; \ + \ + valarray tr(2); \ + \ + tr[0] = rhs.real(); \ + tr[1] = rhs.imag(); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]-b*tr[1]; \ + tt[1] = -a*tr[1]+b*tr[0]; \ + tt[2] = +c*tr[0]-d*tr[1]; \ + tt[3] = +c*tr[1]+d*tr[0]; \ + tt[4] = +e*tr[0]-f*tr[1]; \ + tt[5] = +e*tr[1]+f*tr[0]; \ + tt[6] = +g*tr[0]+h*tr[1]; \ + tt[7] = +g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#else + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ + octonion & operator /= (::std::complex const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(2); \ + \ + tr[0] = rhs.real(); \ + tr[1] = rhs.imag(); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]-b*tr[1]; \ + tt[1] = -a*tr[1]+b*tr[0]; \ + tt[2] = +c*tr[0]-d*tr[1]; \ + tt[3] = +c*tr[1]+d*tr[0]; \ + tt[4] = +e*tr[0]-f*tr[1]; \ + tt[5] = +e*tr[1]+f*tr[0]; \ + tt[6] = +g*tr[0]+h*tr[1]; \ + tt[7] = +g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + +#if defined(__GNUC__) && (__GNUC__ < 3) + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ + octonion & operator /= (::boost::math::quaternion const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(4); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + \ + type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)();\ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ + tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ + tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ + tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ + tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ + octonion & operator /= (::boost::math::quaternion const & rhs) \ + { \ + using ::std::valarray; \ + using ::std::abs; \ + \ + valarray tr(4); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ + tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ + tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ + tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ + tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#else + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ + octonion & operator /= (::boost::math::quaternion const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(4); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ + tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ + tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ + tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ + tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + +#if defined(__GNUC__) && (__GNUC__ < 3) + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ + template \ + octonion & operator /= (octonion const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(8); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + tr[4] = static_cast(rhs.R_component_5()); \ + tr[5] = static_cast(rhs.R_component_6()); \ + tr[6] = static_cast(rhs.R_component_7()); \ + tr[7] = static_cast(rhs.R_component_8()); \ + \ + type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)();\ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \ + tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ + tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ + tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ + tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ + template \ + octonion & operator /= (octonion const & rhs) \ + { \ + using ::std::valarray; \ + using ::std::abs; \ + \ + valarray tr(8); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + tr[4] = static_cast(rhs.R_component_5()); \ + tr[5] = static_cast(rhs.R_component_6()); \ + tr[6] = static_cast(rhs.R_component_7()); \ + tr[7] = static_cast(rhs.R_component_8()); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \ + tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ + tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ + tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ + tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#else + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ + template \ + octonion & operator /= (octonion const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(8); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + tr[4] = static_cast(rhs.R_component_5()); \ + tr[5] = static_cast(rhs.R_component_6()); \ + tr[6] = static_cast(rhs.R_component_7()); \ + tr[7] = static_cast(rhs.R_component_8()); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(8); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \ + tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ + tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ + tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ + tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + e = tt[4]; \ + f = tt[5]; \ + g = tt[6]; \ + h = tt[7]; \ + \ + return(*this); \ + } +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + + +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \ + BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \ + BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \ + BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) + +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \ + BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \ + BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \ + BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) + +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \ + BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \ + BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \ + BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) + +#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \ + BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ + BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ + BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) + +#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \ + BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) + + + template<> + class octonion + { + public: + + typedef float value_type; + + BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float) + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + // explicit copy constructors (precision-loosing converters) + + explicit octonion(octonion const & a_recopier) + { + *this = detail::octonion_type_converter(a_recopier); + } + + explicit octonion(octonion const & a_recopier) + { + *this = detail::octonion_type_converter(a_recopier); + } + + // destructor + // (this is taken care of by the compiler itself) + + // accessors + // + // Note: Like complex number, octonions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is an octonion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_OCTONION_ACCESSOR_GENERATOR(float) + + // assignment operators + + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float) + + // other assignment-related operators + // + // NOTE: Octonion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);"; + // octonion multiplication is also *NOT* associative + + BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float) + + + protected: + + BOOST_OCTONION_MEMBER_DATA_GENERATOR(float) + + + private: + + }; + + + template<> + class octonion + { + public: + + typedef double value_type; + + BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double) + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + // converting copy constructor + + explicit octonion(octonion const & a_recopier) + { + *this = detail::octonion_type_converter(a_recopier); + } + + // explicit copy constructors (precision-loosing converters) + + explicit octonion(octonion const & a_recopier) + { + *this = detail::octonion_type_converter(a_recopier); + } + + // destructor + // (this is taken care of by the compiler itself) + + // accessors + // + // Note: Like complex number, octonions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is an octonion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_OCTONION_ACCESSOR_GENERATOR(double) + + // assignment operators + + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double) + + // other assignment-related operators + // + // NOTE: Octonion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);"; + // octonion multiplication is also *NOT* associative + + BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double) + + + protected: + + BOOST_OCTONION_MEMBER_DATA_GENERATOR(double) + + + private: + + }; + + + template<> + class octonion + { + public: + + typedef long double value_type; + + BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double) + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + // converting copy constructor + + explicit octonion(octonion const & a_recopier) + { + *this = detail::octonion_type_converter(a_recopier); + } + + + explicit octonion(octonion const & a_recopier) + { + *this = detail::octonion_type_converter(a_recopier); + } + + + // destructor + // (this is taken care of by the compiler itself) + + // accessors + // + // Note: Like complex number, octonions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is an octonion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_OCTONION_ACCESSOR_GENERATOR(long double) + + // assignment operators + + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double) + + // other assignment-related operators + // + // NOTE: Octonion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);"; + // octonion multiplication is also *NOT* associative + + BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double) + + + protected: + + BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double) + + + private: + + }; + + +#undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR + +#undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR + +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR + +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4 + + +#undef BOOST_OCTONION_MEMBER_DATA_GENERATOR + +#undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR + +#undef BOOST_OCTONION_ACCESSOR_GENERATOR + + + // operators + +#define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \ + { \ + octonion res(lhs); \ + res op##= rhs; \ + return(res); \ + } + +#define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \ + template \ + inline octonion operator op (T const & lhs, octonion const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \ + template \ + inline octonion operator op (octonion const & lhs, T const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \ + template \ + inline octonion operator op (::std::complex const & lhs, octonion const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \ + template \ + inline octonion operator op (octonion const & lhs, ::std::complex const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \ + template \ + inline octonion operator op (::boost::math::quaternion const & lhs, octonion const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \ + template \ + inline octonion operator op (octonion const & lhs, ::boost::math::quaternion const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \ + template \ + inline octonion operator op (octonion const & lhs, octonion const & rhs) \ + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_OCTONION_OPERATOR_GENERATOR(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \ + BOOST_OCTONION_OPERATOR_GENERATOR_4(op) + + + BOOST_OCTONION_OPERATOR_GENERATOR(+) + BOOST_OCTONION_OPERATOR_GENERATOR(-) + BOOST_OCTONION_OPERATOR_GENERATOR(*) + BOOST_OCTONION_OPERATOR_GENERATOR(/) + + +#undef BOOST_OCTONION_OPERATOR_GENERATOR + +#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L +#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R +#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L +#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R +#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L +#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R +#undef BOOST_OCTONION_OPERATOR_GENERATOR_4 + +#undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY + + + template + inline octonion operator + (octonion const & o) + { + return(o); + } + + + template + inline octonion operator - (octonion const & o) + { + 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())); + } + + + template + inline bool operator == (T const & lhs, octonion const & rhs) + { + return( + (rhs.R_component_1() == lhs)&& + (rhs.R_component_2() == static_cast(0))&& + (rhs.R_component_3() == static_cast(0))&& + (rhs.R_component_4() == static_cast(0))&& + (rhs.R_component_5() == static_cast(0))&& + (rhs.R_component_6() == static_cast(0))&& + (rhs.R_component_7() == static_cast(0))&& + (rhs.R_component_8() == static_cast(0)) + ); + } + + + template + inline bool operator == (octonion const & lhs, T const & rhs) + { + return( + (lhs.R_component_1() == rhs)&& + (lhs.R_component_2() == static_cast(0))&& + (lhs.R_component_3() == static_cast(0))&& + (lhs.R_component_4() == static_cast(0))&& + (lhs.R_component_5() == static_cast(0))&& + (lhs.R_component_6() == static_cast(0))&& + (lhs.R_component_7() == static_cast(0))&& + (lhs.R_component_8() == static_cast(0)) + ); + } + + + template + inline bool operator == (::std::complex const & lhs, octonion const & rhs) + { + return( + (rhs.R_component_1() == lhs.real())&& + (rhs.R_component_2() == lhs.imag())&& + (rhs.R_component_3() == static_cast(0))&& + (rhs.R_component_4() == static_cast(0))&& + (rhs.R_component_5() == static_cast(0))&& + (rhs.R_component_6() == static_cast(0))&& + (rhs.R_component_7() == static_cast(0))&& + (rhs.R_component_8() == static_cast(0)) + ); + } + + + template + inline bool operator == (octonion const & lhs, ::std::complex const & rhs) + { + return( + (lhs.R_component_1() == rhs.real())&& + (lhs.R_component_2() == rhs.imag())&& + (lhs.R_component_3() == static_cast(0))&& + (lhs.R_component_4() == static_cast(0))&& + (lhs.R_component_5() == static_cast(0))&& + (lhs.R_component_6() == static_cast(0))&& + (lhs.R_component_7() == static_cast(0))&& + (lhs.R_component_8() == static_cast(0)) + ); + } + + + template + inline bool operator == (::boost::math::quaternion const & lhs, octonion const & rhs) + { + return( + (rhs.R_component_1() == lhs.R_component_1())&& + (rhs.R_component_2() == lhs.R_component_2())&& + (rhs.R_component_3() == lhs.R_component_3())&& + (rhs.R_component_4() == lhs.R_component_4())&& + (rhs.R_component_5() == static_cast(0))&& + (rhs.R_component_6() == static_cast(0))&& + (rhs.R_component_7() == static_cast(0))&& + (rhs.R_component_8() == static_cast(0)) + ); + } + + + template + inline bool operator == (octonion const & lhs, ::boost::math::quaternion const & rhs) + { + return( + (lhs.R_component_1() == rhs.R_component_1())&& + (lhs.R_component_2() == rhs.R_component_2())&& + (lhs.R_component_3() == rhs.R_component_3())&& + (lhs.R_component_4() == rhs.R_component_4())&& + (lhs.R_component_5() == static_cast(0))&& + (lhs.R_component_6() == static_cast(0))&& + (lhs.R_component_7() == static_cast(0))&& + (lhs.R_component_8() == static_cast(0)) + ); + } + + + template + inline bool operator == (octonion const & lhs, octonion const & rhs) + { + return( + (rhs.R_component_1() == lhs.R_component_1())&& + (rhs.R_component_2() == lhs.R_component_2())&& + (rhs.R_component_3() == lhs.R_component_3())&& + (rhs.R_component_4() == lhs.R_component_4())&& + (rhs.R_component_5() == lhs.R_component_5())&& + (rhs.R_component_6() == lhs.R_component_6())&& + (rhs.R_component_7() == lhs.R_component_7())&& + (rhs.R_component_8() == lhs.R_component_8()) + ); + } + + +#define BOOST_OCTONION_NOT_EQUAL_GENERATOR \ + { \ + return(!(lhs == rhs)); \ + } + + template + inline bool operator != (T const & lhs, octonion const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (octonion const & lhs, T const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (::std::complex const & lhs, octonion const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (octonion const & lhs, ::std::complex const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (::boost::math::quaternion const & lhs, octonion const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (octonion const & lhs, ::boost::math::quaternion const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (octonion const & lhs, octonion const & rhs) + BOOST_OCTONION_NOT_EQUAL_GENERATOR + + #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR + + + // Note: the default values in the constructors of the complex and quaternions make for + // a very complex and ambiguous situation; we have made choices to disambiguate. + +#if BOOST_WORKAROUND(__GNUC__, < 3) + template