/external/boost/math/octonion.hpp
C++ Header | 4754 lines | 3781 code | 845 blank | 128 comment | 635 complexity | 52102af4d2065386029ec37667270515 MD5 | raw file
Possible License(s): LGPL-2.0, BSD-3-Clause
- // 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 <boost/math/quaternion.hpp>
- 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<T>(x)
- // gcc 2.95.x has an "std::ios" class that is similar to
- // "std::ios_base", so we just use a #define
- #define BOOST_IOS_BASE ::std::ios
- // gcc 2.x ignores function scope using declarations,
- // put them in the scope of the enclosing namespace instead:
- using ::std::valarray;
- using ::std::sqrt;
- using ::std::cos;
- using ::std::sin;
- using ::std::exp;
- using ::std::cosh;
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
-
- #define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
- type real() const \
- { \
- return(a); \
- } \
- \
- octonion<type> unreal() const \
- { \
- return( octonion<type>(static_cast<type>(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<type> C_component_1() const \
- { \
- return(::std::complex<type>(a,b)); \
- } \
- \
- ::std::complex<type> C_component_2() const \
- { \
- return(::std::complex<type>(c,d)); \
- } \
- \
- ::std::complex<type> C_component_3() const \
- { \
- return(::std::complex<type>(e,f)); \
- } \
- \
- ::std::complex<type> C_component_4() const \
- { \
- return(::std::complex<type>(g,h)); \
- } \
- \
- ::boost::math::quaternion<type> H_component_1() const \
- { \
- return(::boost::math::quaternion<type>(a,b,c,d)); \
- } \
- \
- ::boost::math::quaternion<type> H_component_2() const \
- { \
- return(::boost::math::quaternion<type>(e,f,g,h)); \
- }
-
-
- #define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
- template<typename X> \
- octonion<type> & operator = (octonion<X> const & a_affecter) \
- { \
- a = static_cast<type>(a_affecter.R_component_1()); \
- b = static_cast<type>(a_affecter.R_component_2()); \
- c = static_cast<type>(a_affecter.R_component_3()); \
- d = static_cast<type>(a_affecter.R_component_4()); \
- e = static_cast<type>(a_affecter.R_component_5()); \
- f = static_cast<type>(a_affecter.R_component_6()); \
- g = static_cast<type>(a_affecter.R_component_7()); \
- h = static_cast<type>(a_affecter.R_component_8()); \
- \
- return(*this); \
- } \
- \
- octonion<type> & operator = (octonion<type> 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<type> & operator = (type const & a_affecter) \
- { \
- a = a_affecter; \
- \
- b = c = d = e = f= g = h = static_cast<type>(0); \
- \
- return(*this); \
- } \
- \
- octonion<type> & operator = (::std::complex<type> const & a_affecter) \
- { \
- a = a_affecter.real(); \
- b = a_affecter.imag(); \
- \
- c = d = e = f = g = h = static_cast<type>(0); \
- \
- return(*this); \
- } \
- \
- octonion<type> & operator = (::boost::math::quaternion<type> 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<type>(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<typename T>
- 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<T> const & z0,
- ::std::complex<T> const & z1 = ::std::complex<T>(),
- ::std::complex<T> const & z2 = ::std::complex<T>(),
- ::std::complex<T> const & z3 = ::std::complex<T>())
- : 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<T> const & q0,
- ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
- : 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<typename X>
- explicit octonion(octonion<X> const & a_recopier)
- : a(static_cast<T>(a_recopier.R_component_1())),
- b(static_cast<T>(a_recopier.R_component_2())),
- c(static_cast<T>(a_recopier.R_component_3())),
- d(static_cast<T>(a_recopier.R_component_4())),
- e(static_cast<T>(a_recopier.R_component_5())),
- f(static_cast<T>(a_recopier.R_component_6())),
- g(static_cast<T>(a_recopier.R_component_7())),
- h(static_cast<T>(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<T> & operator += (T const & rhs)
- {
- T at = a + rhs; // exception guard
-
- a = at;
-
- return(*this);
- }
-
-
- octonion<T> & operator += (::std::complex<T> const & rhs)
- {
- T at = a + rhs.real(); // exception guard
- T bt = b + rhs.imag(); // exception guard
-
- a = at;
- b = bt;
-
- return(*this);
- }
-
-
- octonion<T> & operator += (::boost::math::quaternion<T> 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<typename X>
- octonion<T> & operator += (octonion<X> const & rhs)
- {
- T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
- T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
- T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
- T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
- T et = e + static_cast<T>(rhs.R_component_5()); // exception guard
- T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard
- T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard
- T ht = h + static_cast<T>(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<T> & operator -= (T const & rhs)
- {
- T at = a - rhs; // exception guard
-
- a = at;
-
- return(*this);
- }
-
-
- octonion<T> & operator -= (::std::complex<T> const & rhs)
- {
- T at = a - rhs.real(); // exception guard
- T bt = b - rhs.imag(); // exception guard
-
- a = at;
- b = bt;
-
- return(*this);
- }
-
-
- octonion<T> & operator -= (::boost::math::quaternion<T> 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<typename X>
- octonion<T> & operator -= (octonion<X> const & rhs)
- {
- T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
- T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
- T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
- T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
- T et = e - static_cast<T>(rhs.R_component_5()); // exception guard
- T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard
- T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard
- T ht = h - static_cast<T>(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<T> & operator *= (T const & rhs)
- {
- T at = a * rhs; // exception guard
- T bt = b * rhs; // exception guard
- T ct = c * rhs; // exception guard
- T dt = d * rhs; // exception guard
- T et = e * rhs; // exception guard
- T ft = f * rhs; // exception guard
- T gt = g * rhs; // exception guard
- T ht = h * rhs; // exception guard
-
- a = at;
- b = bt;
- c = ct;
- d = dt;
- e = et;
- f = ft;
- g = gt;
- h = ht;
-
- return(*this);
- }
-
-
- octonion<T> & operator *= (::std::complex<T> const & rhs)
- {
- T ar = rhs.real();
- T br = rhs.imag();
-
- T 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<T> & operator *= (::boost::math::quaternion<T> const & rhs)
- {
- T ar = rhs.R_component_1();
- T br = rhs.R_component_2();
- T cr = rhs.R_component_2();
- T dr = rhs.R_component_2();
-
- T 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<typename X>
- octonion<T> & operator *= (octonion<X> const & rhs)
- {
- T ar = static_cast<T>(rhs.R_component_1());
- T br = static_cast<T>(rhs.R_component_2());
- T cr = static_cast<T>(rhs.R_component_3());
- T dr = static_cast<T>(rhs.R_component_4());
- T er = static_cast<T>(rhs.R_component_5());
- T fr = static_cast<T>(rhs.R_component_6());
- T gr = static_cast<T>(rhs.R_component_7());
- T hr = static_cast<T>(rhs.R_component_8());
-
- T 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<T> & operator /= (T const & rhs)
- {
- T at = a / rhs; // exception guard
- T bt = b / rhs; // exception guard
- T ct = c / rhs; // exception guard
- T dt = d / rhs; // exception guard
- T et = e / rhs; // exception guard
- T ft = f / rhs; // exception guard
- T gt = g / rhs; // exception guard
- T ht = h / rhs; // exception guard
-
- a = at;
- b = bt;
- c = ct;
- d = dt;
- e = et;
- f = ft;
- g = gt;
- h = ht;
-
- return(*this);
- }
-
-
- octonion<T> & operator /= (::std::complex<T> const & rhs)
- {
- T ar = rhs.real();
- T br = rhs.imag();
-
- T denominator = ar*ar+br*br;
-
- T at = (+a*ar-b*br)/denominator;
- T bt = (-a*br+b*ar)/denominator;
- T ct = (+c*ar-d*br)/denominator;
- T dt = (+c*br+d*ar)/denominator;
- T et = (+e*ar-f*br)/denominator;
- T ft = (+e*br+f*ar)/denominator;
- T gt = (+g*ar+h*br)/denominator;
- T ht = (+g*br+h*ar)/denominator;
-
- a = at;
- b = bt;
- c = ct;
- d = dt;
- e = et;
- f = ft;
- g = gt;
- h = ht;
-
- return(*this);
- }
-
-
- octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs)
- {
- T ar = rhs.R_component_1();
- T br = rhs.R_component_2();
- T cr = rhs.R_component_2();
- T dr = rhs.R_component_2();
-
- T denominator = ar*ar+br*br+cr*cr+dr*dr;
-
- T at = (+a*ar+b*br+c*cr+d*dr)/denominator;
- T bt = (-a*br+b*ar-c*dr+d*cr)/denominator;
- T ct = (-a*cr+b*dr+c*ar-d*br)/denominator;
- T dt = (-a*dr-b*cr+c*br+d*ar)/denominator;
- T et = (+e*ar-f*br-g*cr-h*dr)/denominator;
- T ft = (+e*br+f*ar+g*dr-h*cr)/denominator;
- T gt = (+e*cr-f*dr+g*ar+h*br)/denominator;
- T ht = (+e*dr+f*cr-g*br+h*ar)/denominator;
-
- a = at;
- b = bt;
- c = ct;
- d = dt;
- e = et;
- f = ft;
- g = gt;
- h = ht;
-
- return(*this);
- }
-
-
- template<typename X>
- octonion<T> & operator /= (octonion<X> const & rhs)
- {
- T ar = static_cast<T>(rhs.R_component_1());
- T br = static_cast<T>(rhs.R_component_2());
- T cr = static_cast<T>(rhs.R_component_3());
- T dr = static_cast<T>(rhs.R_component_4());
- T er = static_cast<T>(rhs.R_component_5());
- T fr = static_cast<T>(rhs.R_component_6());
- T gr = static_cast<T>(rhs.R_component_7());
- T hr = static_cast<T>(rhs.R_component_8());
-
- T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr;
-
- T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator;
- T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator;
- T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator;
- T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator;
- T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator;
- T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator;
- T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator;
- T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator;
-
- a = at;
- b = bt;
- c = ct;
- d = dt;
- e = et;
- f = ft;
- g = gt;
- h = ht;
-
- return(*this);
- }
-
-
- protected:
-
- BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
-
-
- private:
-
- };
-
-
- // declaration of octonion specialization
-
- template<> class octonion<float>;
- template<> class octonion<double>;
- template<> class octonion<long double>;
-
-
- // helper templates for converting copy constructors (declaration)
-
- namespace detail
- {
-
- template< typename T,
- typename U
- >
- octonion<T> octonion_type_converter(octonion<U> const & rhs);
- }
-
-
- // implementation of octonion specialization
-
-
- #define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
- explicit octonion( type const & requested_a = static_cast<type>(0), \
- type const & requested_b = static_cast<type>(0), \
- type const & requested_c = static_cast<type>(0), \
- type const & requested_d = static_cast<type>(0), \
- type const & requested_e = static_cast<type>(0), \
- type const & requested_f = static_cast<type>(0), \
- type const & requested_g = static_cast<type>(0), \
- type const & requested_h = static_cast<type>(0)) \
- : a(requested_a), \
- b(requested_b), \
- c(requested_c), \
- d(requested_d), \
- e(requested_e), \
- f(requested_f), \
- g(requested_g), \
- h(requested_h) \
- { \
- } \
- \
- explicit octonion( ::std::complex<type> const & z0, \
- ::std::complex<type> const & z1 = ::std::complex<type>(), \
- ::std::complex<type> const & z2 = ::std::complex<type>(), \
- ::std::complex<type> const & z3 = ::std::complex<type>()) \
- : a(z0.real()), \
- b(z0.imag()), \
- c(z1.real()), \
- d(z1.imag()), \
- e(z2.real()), \
- f(z2.imag()), \
- g(z3.real()), \
- h(z3.imag()) \
- { \
- } \
- \
- explicit octonion( ::boost::math::quaternion<type> const & q0, \
- ::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \
- : a(q0.R_component_1()), \
- b(q0.R_component_2()), \
- c(q0.R_component_3()), \
- d(q0.R_component_4()), \
- e(q1.R_component_1()), \
- f(q1.R_component_2()), \
- g(q1.R_component_3()), \
- h(q1.R_component_4()) \
- { \
- }
-
-
- #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
- octonion<type> & operator += (type const & rhs) \
- { \
- a += rhs; \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
- octonion<type> & operator += (::std::complex<type> const & rhs) \
- { \
- a += rhs.real(); \
- b += rhs.imag(); \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
- octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \
- { \
- a += rhs.R_component_1(); \
- b += rhs.R_component_2(); \
- c += rhs.R_component_3(); \
- d += rhs.R_component_4(); \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
- template<typename X> \
- octonion<type> & operator += (octonion<X> const & rhs) \
- { \
- a += static_cast<type>(rhs.R_component_1()); \
- b += static_cast<type>(rhs.R_component_2()); \
- c += static_cast<type>(rhs.R_component_3()); \
- d += static_cast<type>(rhs.R_component_4()); \
- e += static_cast<type>(rhs.R_component_5()); \
- f += static_cast<type>(rhs.R_component_6()); \
- g += static_cast<type>(rhs.R_component_7()); \
- h += static_cast<type>(rhs.R_component_8()); \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
- octonion<type> & operator -= (type const & rhs) \
- { \
- a -= rhs; \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
- octonion<type> & operator -= (::std::complex<type> const & rhs) \
- { \
- a -= rhs.real(); \
- b -= rhs.imag(); \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
- octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \
- { \
- a -= rhs.R_component_1(); \
- b -= rhs.R_component_2(); \
- c -= rhs.R_component_3(); \
- d -= rhs.R_component_4(); \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
- template<typename X> \
- octonion<type> & operator -= (octonion<X> const & rhs) \
- { \
- a -= static_cast<type>(rhs.R_component_1()); \
- b -= static_cast<type>(rhs.R_component_2()); \
- c -= static_cast<type>(rhs.R_component_3()); \
- d -= static_cast<type>(rhs.R_component_4()); \
- e -= static_cast<type>(rhs.R_component_5()); \
- f -= static_cast<type>(rhs.R_component_6()); \
- g -= static_cast<type>(rhs.R_component_7()); \
- h -= static_cast<type>(rhs.R_component_8()); \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
- octonion<type> & operator *= (type const & rhs) \
- { \
- a *= rhs; \
- b *= rhs; \
- c *= rhs; \
- d *= rhs; \
- e *= rhs; \
- f *= rhs; \
- g *= rhs; \
- h *= rhs; \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
- octonion<type> & operator *= (::std::complex<type> const & rhs) \
- { \
- type ar = rhs.real(); \
- type br = rhs.imag(); \
- \
- type at = +a*ar-b*br; \
- type bt = +a*br+b*ar; \
- type ct = +c*ar+d*br; \
- type dt = -c*br+d*ar; \
- type et = +e*ar+f*br; \
- type ft = -e*br+f*ar; \
- type gt = +g*ar-h*br; \
- type ht = +g*br+h*ar; \
- \
- a = at; \
- b = bt; \
- c = ct; \
- d = dt; \
- e = et; \
- f = ft; \
- g = gt; \
- h = ht; \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
- octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \
- { \
- type ar = rhs.R_component_1(); \
- type br = rhs.R_component_2(); \
- type cr = rhs.R_component_2(); \
- type dr = rhs.R_component_2(); \
- \
- type at = +a*ar-b*br-c*cr-d*dr; \
- type bt = +a*br+b*ar+c*dr-d*cr; \
- type ct = +a*cr-b*dr+c*ar+d*br; \
- type dt = +a*dr+b*cr-c*br+d*ar; \
- type et = +e*ar+f*br+g*cr+h*dr; \
- type ft = -e*br+f*ar-g*dr+h*cr; \
- type gt = -e*cr+f*dr+g*ar-h*br; \
- type ht = -e*dr-f*cr+g*br+h*ar; \
- \
- a = at; \
- b = bt; \
- c = ct; \
- d = dt; \
- e = et; \
- f = ft; \
- g = gt; \
- h = ht; \
- \
- return(*this); \
- }
-
- #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
- template<typename X> \
- octonion<type> & operator *= (octonion<X> const & rhs) \
- { \
- type ar = static_cast<type>(rhs.R_component_1()); \
- type br = static_cast<type>(rhs.R_component_2()); \
- type cr = static_cast<type>(rhs.R_component_3()); \
- type dr = static_cast<type>(rhs.R_component_4()); \
- type er = static_cast<type>(rhs.R_component_5()); \
- type fr = static_cast<type>(rhs.R_component_6()); \
- type gr = static_cast<type>(rhs.R_component_7()); \
- type hr = static_cast<type>(rhs.R_component_8()); \
- \
- type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \
- type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \
- type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \
- type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \
- type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \
- type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \
- type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \
- type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \
- \
- a = at; \
- b = bt; \
- c = ct; \
- d = dt; \
- e = et; \
- f = ft; \
- g = gt; \
- h = ht; \
- \
- return(*this); \
- }
-
- // There is quite a lot of repetition in the code below. This is intentional.
- // The last conditional block is the normal form, and the others merely
- // consist of workarounds for various compiler deficiencies. Hopefuly, when
- // more compilers are conformant and we can retire support for those that are
- // not, we will be able to remove the clutter. This is makes the situation
- // (painfully) explicit.
-
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
- octonion<type> & operator /= (type const & rhs) \
- { \
- a /= rhs; \
- b /= rhs; \
- c /= rhs; \
- d /= rhs; \
- \
- return(*this); \
- }
-
- #if defined(__GNUC__) && (__GNUC__ < 3)
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
- octonion<type> & operator /= (::std::complex<type> const & rhs) \
- { \
- using ::std::valarray; \
- \
- valarray<type> tr(2); \
- \
- tr[0] = rhs.real(); \
- tr[1] = rhs.imag(); \
- \
- type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]-b*tr[1]; \
- tt[1] = -a*tr[1]+b*tr[0]; \
- tt[2] = +c*tr[0]-d*tr[1]; \
- tt[3] = +c*tr[1]+d*tr[0]; \
- tt[4] = +e*tr[0]-f*tr[1]; \
- tt[5] = +e*tr[1]+f*tr[0]; \
- tt[6] = +g*tr[0]+h*tr[1]; \
- tt[7] = +g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
- octonion<type> & operator /= (::std::complex<type> const & rhs) \
- { \
- using ::std::valarray; \
- using ::std::abs; \
- \
- valarray<type> tr(2); \
- \
- tr[0] = rhs.real(); \
- tr[1] = rhs.imag(); \
- \
- type mixam = static_cast<type>(1)/(abs(tr).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]-b*tr[1]; \
- tt[1] = -a*tr[1]+b*tr[0]; \
- tt[2] = +c*tr[0]-d*tr[1]; \
- tt[3] = +c*tr[1]+d*tr[0]; \
- tt[4] = +e*tr[0]-f*tr[1]; \
- tt[5] = +e*tr[1]+f*tr[0]; \
- tt[6] = +g*tr[0]+h*tr[1]; \
- tt[7] = +g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #else
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
- octonion<type> & operator /= (::std::complex<type> const & rhs) \
- { \
- using ::std::valarray; \
- \
- valarray<type> tr(2); \
- \
- tr[0] = rhs.real(); \
- tr[1] = rhs.imag(); \
- \
- type mixam = static_cast<type>(1)/(abs(tr).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]-b*tr[1]; \
- tt[1] = -a*tr[1]+b*tr[0]; \
- tt[2] = +c*tr[0]-d*tr[1]; \
- tt[3] = +c*tr[1]+d*tr[0]; \
- tt[4] = +e*tr[0]-f*tr[1]; \
- tt[5] = +e*tr[1]+f*tr[0]; \
- tt[6] = +g*tr[0]+h*tr[1]; \
- tt[7] = +g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
-
- #if defined(__GNUC__) && (__GNUC__ < 3)
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
- octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
- { \
- using ::std::valarray; \
- \
- valarray<type> tr(4); \
- \
- tr[0] = static_cast<type>(rhs.R_component_1()); \
- tr[1] = static_cast<type>(rhs.R_component_2()); \
- tr[2] = static_cast<type>(rhs.R_component_3()); \
- tr[3] = static_cast<type>(rhs.R_component_4()); \
- \
- type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
- tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
- tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
- tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
- tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
- tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
- tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
- tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
- octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
- { \
- using ::std::valarray; \
- using ::std::abs; \
- \
- valarray<type> tr(4); \
- \
- tr[0] = static_cast<type>(rhs.R_component_1()); \
- tr[1] = static_cast<type>(rhs.R_component_2()); \
- tr[2] = static_cast<type>(rhs.R_component_3()); \
- tr[3] = static_cast<type>(rhs.R_component_4()); \
- \
- type mixam = static_cast<type>(1)/(abs(tr).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
- tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
- tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
- tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
- tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
- tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
- tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
- tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #else
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
- octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
- { \
- using ::std::valarray; \
- \
- valarray<type> tr(4); \
- \
- tr[0] = static_cast<type>(rhs.R_component_1()); \
- tr[1] = static_cast<type>(rhs.R_component_2()); \
- tr[2] = static_cast<type>(rhs.R_component_3()); \
- tr[3] = static_cast<type>(rhs.R_component_4()); \
- \
- type mixam = static_cast<type>(1)/(abs(tr).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
- tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
- tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
- tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
- tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
- tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
- tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
- tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
-
- #if defined(__GNUC__) && (__GNUC__ < 3)
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
- template<typename X> \
- octonion<type> & operator /= (octonion<X> const & rhs) \
- { \
- using ::std::valarray; \
- \
- valarray<type> tr(8); \
- \
- tr[0] = static_cast<type>(rhs.R_component_1()); \
- tr[1] = static_cast<type>(rhs.R_component_2()); \
- tr[2] = static_cast<type>(rhs.R_component_3()); \
- tr[3] = static_cast<type>(rhs.R_component_4()); \
- tr[4] = static_cast<type>(rhs.R_component_5()); \
- tr[5] = static_cast<type>(rhs.R_component_6()); \
- tr[6] = static_cast<type>(rhs.R_component_7()); \
- tr[7] = static_cast<type>(rhs.R_component_8()); \
- \
- type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
- tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
- tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
- tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
- tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
- tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
- tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
- tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
- template<typename X> \
- octonion<type> & operator /= (octonion<X> const & rhs) \
- { \
- using ::std::valarray; \
- using ::std::abs; \
- \
- valarray<type> tr(8); \
- \
- tr[0] = static_cast<type>(rhs.R_component_1()); \
- tr[1] = static_cast<type>(rhs.R_component_2()); \
- tr[2] = static_cast<type>(rhs.R_component_3()); \
- tr[3] = static_cast<type>(rhs.R_component_4()); \
- tr[4] = static_cast<type>(rhs.R_component_5()); \
- tr[5] = static_cast<type>(rhs.R_component_6()); \
- tr[6] = static_cast<type>(rhs.R_component_7()); \
- tr[7] = static_cast<type>(rhs.R_component_8()); \
- \
- type mixam = static_cast<type>(1)/(abs(tr).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
- tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
- tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
- tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
- tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
- tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
- tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
- tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #else
- #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
- template<typename X> \
- octonion<type> & operator /= (octonion<X> const & rhs) \
- { \
- using ::std::valarray; \
- \
- valarray<type> tr(8); \
- \
- tr[0] = static_cast<type>(rhs.R_component_1()); \
- tr[1] = static_cast<type>(rhs.R_component_2()); \
- tr[2] = static_cast<type>(rhs.R_component_3()); \
- tr[3] = static_cast<type>(rhs.R_component_4()); \
- tr[4] = static_cast<type>(rhs.R_component_5()); \
- tr[5] = static_cast<type>(rhs.R_component_6()); \
- tr[6] = static_cast<type>(rhs.R_component_7()); \
- tr[7] = static_cast<type>(rhs.R_component_8()); \
- \
- type mixam = static_cast<type>(1)/(abs(tr).max)(); \
- \
- tr *= mixam; \
- \
- valarray<type> tt(8); \
- \
- tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
- tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
- tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
- tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
- tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
- tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
- tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
- tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
- \
- tr *= tr; \
- \
- tt *= (mixam/tr.sum()); \
- \
- a = tt[0]; \
- b = tt[1]; \
- c = tt[2]; \
- d = tt[3]; \
- e = tt[4]; \
- f = tt[5]; \
- g = tt[6]; \
- h = tt[7]; \
- \
- return(*this); \
- }
- #endif /* 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<float>
- {
- public:
-
- typedef float value_type;
-
- BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
-
- // UNtemplated copy constructor
- // (this is taken care of by the compiler itself)
-
- // explicit copy constructors (precision-loosing converters)
-
- explicit octonion(octonion<double> const & a_recopier)
- {
- *this = detail::octonion_type_converter<float, double>(a_recopier);
- }
-
- explicit octonion(octonion<long double> const & a_recopier)
- {
- *this = detail::octonion_type_converter<float, long double>(a_recopier);
- }
-
- // destructor
- // (this is taken care of by the compiler itself)
-
- // accessors
- //
- // Note: Like complex number, octonions do have a meaningful notion of "real part",
- // but unlike them there is no meaningful notion of "imaginary part".
- // Instead there is an "unreal part" which itself is an octonion, and usually
- // nothing simpler (as opposed to the complex number case).
- // However, for practicallity, there are accessors for the other components
- // (these are necessary for the templated copy constructor, for instance).
-
- BOOST_OCTONION_ACCESSOR_GENERATOR(float)
-
- // assignment operators
-
- BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
-
- // other assignment-related operators
- //
- // NOTE: Octonion multiplication is *NOT* commutative;
- // symbolically, "q *= rhs;" means "q = q * rhs;"
- // and "q /= rhs;" means "q = q * inverse_of(rhs);";
- // octonion multiplication is also *NOT* associative
-
- BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
-
-
- protected:
-
- BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
-
-
- private:
-
- };
-
-
- template<>
- class octonion<double>
- {
- public:
-
- typedef double value_type;
-
- BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
-
- // UNtemplated copy constructor
- // (this is taken care of by the compiler itself)
-
- // converting copy constructor
-
- explicit octonion(octonion<float> const & a_recopier)
- {
- *this = detail::octonion_type_converter<double, float>(a_recopier);
- }
-
- // explicit copy constructors (precision-loosing converters)
-
- explicit octonion(octonion<long double> const & a_recopier)
- {
- *this = detail::octonion_type_converter<double, long double>(a_recopier);
- }
-
- // destructor
- // (this is taken care of by the compiler itself)
-
- // accessors
- //
- // Note: Like complex number, octonions do have a meaningful notion of "real part",
- // but unlike them there is no meaningful notion of "imaginary part".
- // Instead there is an "unreal part" which itself is an octonion, and usually
- // nothing simpler (as opposed to the complex number case).
- // However, for practicallity, there are accessors for the other components
- // (these are necessary for the templated copy constructor, for instance).
-
- BOOST_OCTONION_ACCESSOR_GENERATOR(double)
-
- // assignment operators
-
- BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
-
- // other assignment-related operators
- //
- // NOTE: Octonion multiplication is *NOT* commutative;
- // symbolically, "q *= rhs;" means "q = q * rhs;"
- // and "q /= rhs;" means "q = q * inverse_of(rhs);";
- // octonion multiplication is also *NOT* associative
-
- BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
-
-
- protected:
-
- BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
-
-
- private:
-
- };
-
-
- template<>
- class octonion<long double>
- {
- public:
-
- typedef long double value_type;
-
- BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
-
- // UNtemplated copy constructor
- // (this is taken care of by the compiler itself)
-
- // converting copy constructor
-
- explicit octonion(octonion<float> const & a_recopier)
- {
- *this = detail::octonion_type_converter<long double, float>(a_recopier);
- }
-
-
- explicit octonion(octonion<double> const & a_recopier)
- {
- *this = detail::octonion_type_converter<long double, double>(a_recopier);
- }
-
-
- // destructor
- // (this is taken care of by the compiler itself)
-
- // accessors
- //
- // Note: Like complex number, octonions do have a meaningful notion of "real part",
- // but unlike them there is no meaningful notion of "imaginary part".
- // Instead there is an "unreal part" which itself is an octonion, and usually
- // nothing simpler (as opposed to the complex number case).
- // However, for practicallity, there are accessors for the other components
- // (these are necessary for the templated copy constructor, for instance).
-
- BOOST_OCTONION_ACCESSOR_GENERATOR(long double)
-
- // assignment operators
-
- BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
-
- // other assignment-related operators
- //
- // NOTE: Octonion multiplication is *NOT* commutative;
- // symbolically, "q *= rhs;" means "q = q * rhs;"
- // and "q /= rhs;" means "q = q * inverse_of(rhs);";
- // octonion multiplication is also *NOT* associative
-
- BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
-
-
- protected:
-
- BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
-
-
- private:
-
- };
-
-
- #undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
-
- #undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
-
- #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
- #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
- #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
- #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
-
- #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
- #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
- #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
- #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
- #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
- #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
- #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
- #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
- #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
- #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
- #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
- #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
- #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
- #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
- #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
- #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
-
-
- #undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
-
- #undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
-
- #undef BOOST_OCTONION_ACCESSOR_GENERATOR
-
-
- // operators
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
- { \
- octonion<T> res(lhs); \
- res op##= rhs; \
- return(res); \
- }
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
- template<typename T> \
- inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
- template<typename T> \
- inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
- template<typename T> \
- inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
- template<typename T> \
- inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
- template<typename T> \
- inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
- template<typename T> \
- inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
- template<typename T> \
- inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
- BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
-
- #define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
- BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
-
-
- BOOST_OCTONION_OPERATOR_GENERATOR(+)
- BOOST_OCTONION_OPERATOR_GENERATOR(-)
- BOOST_OCTONION_OPERATOR_GENERATOR(*)
- BOOST_OCTONION_OPERATOR_GENERATOR(/)
-
-
- #undef BOOST_OCTONION_OPERATOR_GENERATOR
-
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_4
-
- #undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
-
-
- template<typename T>
- inline octonion<T> operator + (octonion<T> const & o)
- {
- return(o);
- }
-
-
- template<typename T>
- inline octonion<T> operator - (octonion<T> const & o)
- {
- return(octonion<T>(-o.R_component_1(),-o.R_component_2(),-o.R_component_3(),-o.R_component_4(),-o.R_component_5(),-o.R_component_6(),-o.R_component_7(),-o.R_component_8()));
- }
-
-
- template<typename T>
- inline bool operator == (T const & lhs, octonion<T> const & rhs)
- {
- return(
- (rhs.R_component_1() == lhs)&&
- (rhs.R_component_2() == static_cast<T>(0))&&
- (rhs.R_component_3() == static_cast<T>(0))&&
- (rhs.R_component_4() == static_cast<T>(0))&&
- (rhs.R_component_5() == static_cast<T>(0))&&
- (rhs.R_component_6() == static_cast<T>(0))&&
- (rhs.R_component_7() == static_cast<T>(0))&&
- (rhs.R_component_8() == static_cast<T>(0))
- );
- }
-
-
- template<typename T>
- inline bool operator == (octonion<T> const & lhs, T const & rhs)
- {
- return(
- (lhs.R_component_1() == rhs)&&
- (lhs.R_component_2() == static_cast<T>(0))&&
- (lhs.R_component_3() == static_cast<T>(0))&&
- (lhs.R_component_4() == static_cast<T>(0))&&
- (lhs.R_component_5() == static_cast<T>(0))&&
- (lhs.R_component_6() == static_cast<T>(0))&&
- (lhs.R_component_7() == static_cast<T>(0))&&
- (lhs.R_component_8() == static_cast<T>(0))
- );
- }
-
-
- template<typename T>
- inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
- {
- return(
- (rhs.R_component_1() == lhs.real())&&
- (rhs.R_component_2() == lhs.imag())&&
- (rhs.R_component_3() == static_cast<T>(0))&&
- (rhs.R_component_4() == static_cast<T>(0))&&
- (rhs.R_component_5() == static_cast<T>(0))&&
- (rhs.R_component_6() == static_cast<T>(0))&&
- (rhs.R_component_7() == static_cast<T>(0))&&
- (rhs.R_component_8() == static_cast<T>(0))
- );
- }
-
-
- template<typename T>
- inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
- {
- return(
- (lhs.R_component_1() == rhs.real())&&
- (lhs.R_component_2() == rhs.imag())&&
- (lhs.R_component_3() == static_cast<T>(0))&&
- (lhs.R_component_4() == static_cast<T>(0))&&
- (lhs.R_component_5() == static_cast<T>(0))&&
- (lhs.R_component_6() == static_cast<T>(0))&&
- (lhs.R_component_7() == static_cast<T>(0))&&
- (lhs.R_component_8() == static_cast<T>(0))
- );
- }
-
-
- template<typename T>
- inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
- {
- return(
- (rhs.R_component_1() == lhs.R_component_1())&&
- (rhs.R_component_2() == lhs.R_component_2())&&
- (rhs.R_component_3() == lhs.R_component_3())&&
- (rhs.R_component_4() == lhs.R_component_4())&&
- (rhs.R_component_5() == static_cast<T>(0))&&
- (rhs.R_component_6() == static_cast<T>(0))&&
- (rhs.R_component_7() == static_cast<T>(0))&&
- (rhs.R_component_8() == static_cast<T>(0))
- );
- }
-
-
- template<typename T>
- inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
- {
- return(
- (lhs.R_component_1() == rhs.R_component_1())&&
- (lhs.R_component_2() == rhs.R_component_2())&&
- (lhs.R_component_3() == rhs.R_component_3())&&
- (lhs.R_component_4() == rhs.R_component_4())&&
- (lhs.R_component_5() == static_cast<T>(0))&&
- (lhs.R_component_6() == static_cast<T>(0))&&
- (lhs.R_component_7() == static_cast<T>(0))&&
- (lhs.R_component_8() == static_cast<T>(0))
- );
- }
-
-
- template<typename T>
- inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
- {
- return(
- (rhs.R_component_1() == lhs.R_component_1())&&
- (rhs.R_component_2() == lhs.R_component_2())&&
- (rhs.R_component_3() == lhs.R_component_3())&&
- (rhs.R_component_4() == lhs.R_component_4())&&
- (rhs.R_component_5() == lhs.R_component_5())&&
- (rhs.R_component_6() == lhs.R_component_6())&&
- (rhs.R_component_7() == lhs.R_component_7())&&
- (rhs.R_component_8() == lhs.R_component_8())
- );
- }
-
-
- #define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
- { \
- return(!(lhs == rhs)); \
- }
-
- template<typename T>
- inline bool operator != (T const & lhs, octonion<T> const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- template<typename T>
- inline bool operator != (octonion<T> const & lhs, T const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- template<typename T>
- inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- template<typename T>
- inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- template<typename T>
- inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- template<typename T>
- inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- template<typename T>
- inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
- BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
- #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
-
-
- // Note: the default values in the constructors of the complex and quaternions make for
- // a very complex and ambiguous situation; we have made choices to disambiguate.
-
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- template<typename T>
- ::std::istream & operator >> ( ::std::istream & is,
- octonion<T>& o)
- #else
- template<typename T, typename charT, class traits>
- ::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
- octonion<T> & o)
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- typedef char charT;
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
-
- #ifdef BOOST_NO_STD_LOCALE
- #else
- const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
- #endif /* BOOST_NO_STD_LOCALE */
-
- T a = T();
- T b = T();
- T c = T();
- T d = T();
- T e = T();
- T f = T();
- T g = T();
- T h = T();
-
- ::std::complex<T> u = ::std::complex<T>();
- ::std::complex<T> v = ::std::complex<T>();
- ::std::complex<T> x = ::std::complex<T>();
- ::std::complex<T> y = ::std::complex<T>();
-
- ::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
- ::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
-
- charT ch = charT();
- char cc;
-
- is >> ch; // get the first lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "("
- {
- is >> ch; // get the second lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "(("
- {
- is >> ch; // get the third lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((("
- {
- is.putback(ch);
-
- is >> u; // read "((u"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((u)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // format: (((a))), (((a,b)))
- {
- o = octonion<T>(u);
- }
- else if (cc == ',') // read "((u),"
- {
- p = ::boost::math::quaternion<T>(u);
-
- is >> q; // read "((u),q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // format: (((a)),q), (((a,b)),q)
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc ==',') // read "((u,"
- {
- is >> v; // read "((u,v"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((u,v)"
- {
- p = ::boost::math::quaternion<T>(u,v);
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // format: (((a),v)), (((a,b),v))
- {
- o = octonion<T>(p);
- }
- else if (cc == ',') // read "((u,v),"
- {
- is >> q; // read "(p,q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "((a"
- {
- is.putback(ch);
-
- is >> a; // we extract the first component
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a))"
- {
- o = octonion<T>(a);
- }
- else if (cc == ',') // read "((a),"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a),("
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a),(("
- {
- is.putback(ch);
-
- is.putback(ch); // we backtrack twice, with the same value!
-
- is >> q; // read "((a),q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),q)"
- {
- p = ::boost::math::quaternion<T>(a);
-
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "((a),(c" or "((a),(e"
- {
- is.putback(ch);
-
- is >> c;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c)" (ambiguity resolution)
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c))"
- {
- o = octonion<T>(a,b,c);
- }
- else if (cc == ',') // read "((a),(c),"
- {
- u = ::std::complex<T>(a);
-
- v = ::std::complex<T>(c);
-
- is >> x; // read "((a),(c),x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c),x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "((a),(c),x,"
- {
- is >> y; // read "((a),(c),x,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c),x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a),(c," or "((a),(e,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
- {
- p = ::boost::math::quaternion<T>(a);
-
- x = ::std::complex<T>(c); // "c" was actually "e"
-
- is.putback(ch); // we can only backtrace once
-
- is >> y; // read "((a),(e,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(e,y)"
- {
- q = ::boost::math::quaternion<T>(x,y);
-
- is >> ch; // get the next lexeme
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(e,y))"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "((a),(c,d" or "((a),(e,f"
- {
- is.putback(ch);
-
- is >> d;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c,d))"
- {
- o = octonion<T>(a,b,c,d);
- }
- else if (cc == ',') // read "((a),(c,d),"
- {
- u = ::std::complex<T>(a);
-
- v = ::std::complex<T>(c,d);
-
- is >> x; // read "((a),(c,d),x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c,d),x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "((a),(c,d),x,"
- {
- is >> y; // read "((a),(c,d),x,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(c,d),x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
- {
- p = ::boost::math::quaternion<T>(a);
-
- is >> g; // read "((a),(e,f,g" (too late to backtrack)
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(e,f,g)"
- {
- q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(e,f,g))"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a),(e,f,g,"
- {
- is >> h; // read "((a),(e,f,g,h"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(e,f,g,h)"
- {
- q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),(e,f,g,h))"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // read "((a),c" (ambiguity resolution)
- {
- is.putback(ch);
-
- is >> c; // we extract the third component
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),c)"
- {
- o = octonion<T>(a,b,c);
- }
- else if (cc == ',') // read "((a),c,"
- {
- is >> x; // read "((a),c,x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),c,x)"
- {
- o = octonion<T>(a,b,c,d,x.real(),x.imag());
- }
- else if (cc == ',') // read "((a),c,x,"
- {
- is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a),c,x,y)"
- {
- o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc ==',') // read "((a,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a,("
- {
- u = ::std::complex<T>(a);
-
- is.putback(ch); // can only backtrack so much
-
- is >> v; // read "((a,v"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,v)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,v))"
- {
- o = octonion<T>(u,v);
- }
- else if (cc == ',') // read "((a,v),"
- {
- p = ::boost::math::quaternion<T>(u,v);
-
- is >> q; // read "((a,v),q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,v),q)"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else
- {
- is.putback(ch);
-
- is >> b; // read "((a,b"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b))"
- {
- o = octonion<T>(a,b);
- }
- else if (cc == ',') // read "((a,b),"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a,b),("
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a,b),(("
- {
- p = ::boost::math::quaternion<T>(a,b);
-
- is.putback(ch);
-
- is.putback(ch); // we backtrack twice, with the same value
-
- is >> q; // read "((a,b),q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),q)"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "((a,b),(c" or "((a,b),(e"
- {
- is.putback(ch);
-
- is >> c;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c))"
- {
- o = octonion<T>(a,b,c);
- }
- else if (cc == ',') // read "((a,b),(c),"
- {
- u = ::std::complex<T>(a,b);
-
- v = ::std::complex<T>(c);
-
- is >> x; // read "((a,b),(c),x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c),x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "((a,b),(c),x,"
- {
- is >> y; // read "((a,b),(c),x,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c),x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
- {
- u = ::std::complex<T>(a,b);
-
- x = ::std::complex<T>(c); // "c" is actually "e"
-
- is.putback(ch);
-
- is >> y; // read "((a,b),(e,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(e,y)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(e,y))"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "((a,b),(c,d" or "((a,b),(e,f"
- {
- is.putback(ch);
-
- is >> d;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
- {
- u = ::std::complex<T>(a,b);
-
- v = ::std::complex<T>(c,d);
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c,d))"
- {
- o = octonion<T>(u,v);
- }
- else if (cc == ',') // read "((a,b),(c,d),"
- {
- is >> x; // read "((a,b),(c,d),x
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c,d),x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "((a,b),(c,d),x,"
- {
- is >> y; // read "((a,b),(c,d),x,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(c,d),x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
- {
- p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
-
- is >> g; // read "((a,b),(e,f,g"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(e,f,g)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(e,f,g))"
- {
- q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
-
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a,b),(e,f,g,"
- {
- is >> h; // read "((a,b),(e,f,g,h"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b),(e,f,g,h)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read ((a,b),(e,f,g,h))"
- {
- q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
-
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a,b,"
- {
- is >> c; // read "((a,b,c"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b,c)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b,c))"
- {
- o = octonion<T>(a,b,c);
- }
- else if (cc == ',') // read "((a,b,c),"
- {
- p = ::boost::math::quaternion<T>(a,b,c);
-
- is >> q; // read "((a,b,c),q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b,c),q)"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "((a,b,c,"
- {
- is >> d; // read "((a,b,c,d"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b,c,d)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b,c,d))"
- {
- o = octonion<T>(a,b,c,d);
- }
- else if (cc == ',') // read "((a,b,c,d),"
- {
- p = ::boost::math::quaternion<T>(a,b,c,d);
-
- is >> q; // read "((a,b,c,d),q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "((a,b,c,d),q)"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // read "(a"
- {
- is.putback(ch);
-
- is >> a; // we extract the first component
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a)"
- {
- o = octonion<T>(a);
- }
- else if (cc == ',') // read "(a,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "(a,("
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "(a,(("
- {
- p = ::boost::math::quaternion<T>(a);
-
- is.putback(ch);
-
- is.putback(ch); // we backtrack twice, with the same value
-
- is >> q; // read "(a,q"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,q)"
- {
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "(a,(c" or "(a,(e"
- {
- is.putback(ch);
-
- is >> c;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c)" (ambiguity resolution)
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c))"
- {
- o = octonion<T>(a,b,c);
- }
- else if (cc == ',') // read "(a,(c),"
- {
- u = ::std::complex<T>(a);
-
- v = ::std::complex<T>(c);
-
- is >> x; // read "(a,(c),x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c),x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "(a,(c),x,"
- {
- is >> y; // read "(a,(c),x,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c),x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "(a,(c," or "(a,(e,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
- {
- u = ::std::complex<T>(a);
-
- x = ::std::complex<T>(c); // "c" is actually "e"
-
- is.putback(ch); // we backtrack
-
- is >> y; // read "(a,(e,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(e,y)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(e,y))"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "(a,(c,d" or "(a,(e,f"
- {
- is.putback(ch);
-
- is >> d;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c,d))"
- {
- o = octonion<T>(a,b,c,d);
- }
- else if (cc == ',') // read "(a,(c,d),"
- {
- u = ::std::complex<T>(a);
-
- v = ::std::complex<T>(c,d);
-
- is >> x; // read "(a,(c,d),x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c,d),x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "(a,(c,d),x,"
- {
- is >> y; // read "(a,(c,d),x,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(c,d),x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
- {
- p = ::boost::math::quaternion<T>(a);
-
- is >> g; // read "(a,(e,f,g"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(e,f,g)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(e,f,g))"
- {
- q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
-
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else if (cc == ',') // read "(a,(e,f,g,"
- {
- is >> h; // read "(a,(e,f,g,h"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(e,f,g,h)"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,(e,f,g,h))"
- {
- q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
-
- o = octonion<T>(p,q);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // read "(a,b" or "(a,c" (ambiguity resolution)
- {
- is.putback(ch);
-
- is >> b;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b)" (ambiguity resolution)
- {
- o = octonion<T>(a,b);
- }
- else if (cc == ',') // read "(a,b," or "(a,c,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "(a,c,(" (ambiguity resolution)
- {
- u = ::std::complex<T>(a);
-
- v = ::std::complex<T>(b); // "b" is actually "c"
-
- is.putback(ch); // we backtrack
-
- is >> x; // read "(a,c,x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,c,x)"
- {
- o = octonion<T>(u,v,x);
- }
- else if (cc == ',') // read "(a,c,x,"
- {
- is >> y; // read "(a,c,x,y" // read "(a,c,x"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,c,x,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "(a,b,c" or "(a,c,e"
- {
- is.putback(ch);
-
- is >> c;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
- {
- o = octonion<T>(a,b,c);
- }
- else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
- {
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
- {
- u = ::std::complex<T>(a);
-
- v = ::std::complex<T>(b); // "b" is actually "c"
-
- x = ::std::complex<T>(c); // "c" is actually "e"
-
- is.putback(ch); // we backtrack
-
- is >> y; // read "(a,c,e,y"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,c,e,y)"
- {
- o = octonion<T>(u,v,x,y);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // read "(a,b,c,d" (ambiguity resolution)
- {
- is.putback(ch); // we backtrack
-
- is >> d;
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b,c,d)"
- {
- o = octonion<T>(a,b,c,d);
- }
- else if (cc == ',') // read "(a,b,c,d,"
- {
- is >> e; // read "(a,b,c,d,e"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b,c,d,e)"
- {
- o = octonion<T>(a,b,c,d,e);
- }
- else if (cc == ',') // read "(a,b,c,d,e,"
- {
- is >> f; // read "(a,b,c,d,e,f"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b,c,d,e,f)"
- {
- o = octonion<T>(a,b,c,d,e,f);
- }
- else if (cc == ',') // read "(a,b,c,d,e,f,"
- {
- is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b,c,d,e,f,g)"
- {
- o = octonion<T>(a,b,c,d,e,f,g);
- }
- else if (cc == ',') // read "(a,b,c,d,e,f,g,"
- {
- is >> h; // read "(a,b,c,d,e,f,g,h" // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
-
- if (!is.good()) goto finish;
-
- is >> ch; // get the next lexeme
-
- if (!is.good()) goto finish;
-
- #ifdef BOOST_NO_STD_LOCALE
- cc = ch;
- #else
- cc = ct.narrow(ch, char());
- #endif /* BOOST_NO_STD_LOCALE */
-
- if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
- {
- o = octonion<T>(a,b,c,d,e,f,g,h);
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // error
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- is.setstate(::std::ios::failbit);
- #else
- is.setstate(::std::ios_base::failbit);
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
- }
- }
- else // format: a
- {
- is.putback(ch);
-
- is >> a; // we extract the first component
-
- if (!is.good()) goto finish;
-
- o = octonion<T>(a);
- }
-
- finish:
- return(is);
- }
-
-
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- template<typename T>
- ::std::ostream & operator << ( ::std::ostream & os,
- octonion<T> const & o)
- #else
- template<typename T, typename charT, class traits>
- ::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
- octonion<T> const & o)
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- {
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- ::std::ostringstream s;
- #else
- ::std::basic_ostringstream<charT,traits> s;
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
-
- s.flags(os.flags());
- #ifdef BOOST_NO_STD_LOCALE
- #else
- s.imbue(os.getloc());
- #endif /* BOOST_NO_STD_LOCALE */
- s.precision(os.precision());
-
- s << '(' << o.R_component_1() << ','
- << o.R_component_2() << ','
- << o.R_component_3() << ','
- << o.R_component_4() << ','
- << o.R_component_5() << ','
- << o.R_component_6() << ','
- << o.R_component_7() << ','
- << o.R_component_8() << ')';
-
- return os << s.str();
- }
-
-
- // values
-
- template<typename T>
- inline T real(octonion<T> const & o)
- {
- return(o.real());
- }
-
-
- template<typename T>
- inline octonion<T> unreal(octonion<T> const & o)
- {
- return(o.unreal());
- }
-
-
- #define BOOST_OCTONION_VALARRAY_LOADER \
- using ::std::valarray; \
- \
- valarray<T> temp(8); \
- \
- temp[0] = o.R_component_1(); \
- temp[1] = o.R_component_2(); \
- temp[2] = o.R_component_3(); \
- temp[3] = o.R_component_4(); \
- temp[4] = o.R_component_5(); \
- temp[5] = o.R_component_6(); \
- temp[6] = o.R_component_7(); \
- temp[7] = o.R_component_8();
-
-
- template<typename T>
- inline T sup(octonion<T> const & o)
- {
- #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
- using ::std::abs;
- #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
-
- BOOST_OCTONION_VALARRAY_LOADER
-
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- return((BOOST_GET_VALARRAY(T, abs(temp)).max)());
- #else
- return((abs(temp).max)());
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
-
-
- template<typename T>
- inline T l1(octonion<T> const & o)
- {
- #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
- using ::std::abs;
- #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
-
- BOOST_OCTONION_VALARRAY_LOADER
-
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- return(BOOST_GET_VALARRAY(T, abs(temp)).sum());
- #else
- return(abs(temp).sum());
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- }
-
-
- template<typename T>
- inline T abs(const octonion<T> & o)
- {
- #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
- using ::std::abs;
- #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
-
- using ::std::sqrt;
-
- BOOST_OCTONION_VALARRAY_LOADER
-
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- T maxim = (BOOST_GET_VALARRAY(T,abs(temp)).max)(); // overflow protection
- #else
- T maxim = (abs(temp).max)(); // overflow protection
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
-
- if (maxim == static_cast<T>(0))
- {
- return(maxim);
- }
- else
- {
- T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
-
- temp *= mixam;
-
- temp *= temp;
-
- return(maxim*sqrt(temp.sum()));
- }
-
- //return(::std::sqrt(norm(o)));
- }
-
-
- #undef BOOST_OCTONION_VALARRAY_LOADER
-
-
- // Note: This is the Cayley norm, not the Euclidian norm...
-
- template<typename T>
- inline T norm(octonion<T> const & o)
- {
- return(real(o*conj(o)));
- }
-
-
- template<typename T>
- inline octonion<T> conj(octonion<T> const & o)
- {
- return(octonion<T>( +o.R_component_1(),
- -o.R_component_2(),
- -o.R_component_3(),
- -o.R_component_4(),
- -o.R_component_5(),
- -o.R_component_6(),
- -o.R_component_7(),
- -o.R_component_8()));
- }
-
-
- // Note: There is little point, for the octonions, to introduce the equivalents
- // to the complex "arg" and the quaternionic "cylindropolar".
-
-
- template<typename T>
- inline octonion<T> spherical(T const & rho,
- T const & theta,
- T const & phi1,
- T const & phi2,
- T const & phi3,
- T const & phi4,
- T const & phi5,
- T const & phi6)
- {
- using ::std::cos;
- using ::std::sin;
-
- //T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
- //T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
- //T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
- //T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
- //T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
- //T f = sin(phi4)*cos(phi5)*cos(phi6);
- //T g = sin(phi5)*cos(phi6);
- //T h = sin(phi6);
-
- T courrant = static_cast<T>(1);
-
- T h = sin(phi6);
-
- courrant *= cos(phi6);
-
- T g = sin(phi5)*courrant;
-
- courrant *= cos(phi5);
-
- T f = sin(phi4)*courrant;
-
- courrant *= cos(phi4);
-
- T e = sin(phi3)*courrant;
-
- courrant *= cos(phi3);
-
- T d = sin(phi2)*courrant;
-
- courrant *= cos(phi2);
-
- T c = sin(phi1)*courrant;
-
- courrant *= cos(phi1);
-
- T b = sin(theta)*courrant;
- T a = cos(theta)*courrant;
-
- return(rho*octonion<T>(a,b,c,d,e,f,g,h));
- }
-
-
- template<typename T>
- inline octonion<T> multipolar(T const & rho1,
- T const & theta1,
- T const & rho2,
- T const & theta2,
- T const & rho3,
- T const & theta3,
- T const & rho4,
- T const & theta4)
- {
- using ::std::cos;
- using ::std::sin;
-
- T a = rho1*cos(theta1);
- T b = rho1*sin(theta1);
- T c = rho2*cos(theta2);
- T d = rho2*sin(theta2);
- T e = rho3*cos(theta3);
- T f = rho3*sin(theta3);
- T g = rho4*cos(theta4);
- T h = rho4*sin(theta4);
-
- return(octonion<T>(a,b,c,d,e,f,g,h));
- }
-
-
- template<typename T>
- inline octonion<T> cylindrical(T const & r,
- T const & angle,
- T const & h1,
- T const & h2,
- T const & h3,
- T const & h4,
- T const & h5,
- T const & h6)
- {
- using ::std::cos;
- using ::std::sin;
-
- T a = r*cos(angle);
- T b = r*sin(angle);
-
- return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
- }
-
-
- template<typename T>
- inline octonion<T> exp(octonion<T> const & o)
- {
- using ::std::exp;
- using ::std::cos;
-
- using ::boost::math::sinc_pi;
-
- T u = exp(real(o));
-
- T z = abs(unreal(o));
-
- T w = sinc_pi(z);
-
- return(u*octonion<T>(cos(z),
- w*o.R_component_2(), w*o.R_component_3(),
- w*o.R_component_4(), w*o.R_component_5(),
- w*o.R_component_6(), w*o.R_component_7(),
- w*o.R_component_8()));
- }
-
-
- template<typename T>
- inline octonion<T> cos(octonion<T> const & o)
- {
- using ::std::sin;
- using ::std::cos;
- using ::std::cosh;
-
- using ::boost::math::sinhc_pi;
-
- T z = abs(unreal(o));
-
- T w = -sin(o.real())*sinhc_pi(z);
-
- return(octonion<T>(cos(o.real())*cosh(z),
- w*o.R_component_2(), w*o.R_component_3(),
- w*o.R_component_4(), w*o.R_component_5(),
- w*o.R_component_6(), w*o.R_component_7(),
- w*o.R_component_8()));
- }
-
-
- template<typename T>
- inline octonion<T> sin(octonion<T> const & o)
- {
- using ::std::sin;
- using ::std::cos;
- using ::std::cosh;
-
- using ::boost::math::sinhc_pi;
-
- T z = abs(unreal(o));
-
- T w = +cos(o.real())*sinhc_pi(z);
-
- return(octonion<T>(sin(o.real())*cosh(z),
- w*o.R_component_2(), w*o.R_component_3(),
- w*o.R_component_4(), w*o.R_component_5(),
- w*o.R_component_6(), w*o.R_component_7(),
- w*o.R_component_8()));
- }
-
-
- template<typename T>
- inline octonion<T> tan(octonion<T> const & o)
- {
- return(sin(o)/cos(o));
- }
-
-
- template<typename T>
- inline octonion<T> cosh(octonion<T> const & o)
- {
- return((exp(+o)+exp(-o))/static_cast<T>(2));
- }
-
-
- template<typename T>
- inline octonion<T> sinh(octonion<T> const & o)
- {
- return((exp(+o)-exp(-o))/static_cast<T>(2));
- }
-
-
- template<typename T>
- inline octonion<T> tanh(octonion<T> const & o)
- {
- return(sinh(o)/cosh(o));
- }
-
-
- template<typename T>
- octonion<T> pow(octonion<T> const & o,
- int n)
- {
- if (n > 1)
- {
- int m = n>>1;
-
- octonion<T> result = pow(o, m);
-
- result *= result;
-
- if (n != (m<<1))
- {
- result *= o; // n odd
- }
-
- return(result);
- }
- else if (n == 1)
- {
- return(o);
- }
- else if (n == 0)
- {
- return(octonion<T>(1));
- }
- else /* n < 0 */
- {
- return(pow(octonion<T>(1)/o,-n));
- }
- }
-
-
- // helper templates for converting copy constructors (definition)
-
- namespace detail
- {
-
- template< typename T,
- typename U
- >
- octonion<T> octonion_type_converter(octonion<U> const & rhs)
- {
- return(octonion<T>( static_cast<T>(rhs.R_component_1()),
- static_cast<T>(rhs.R_component_2()),
- static_cast<T>(rhs.R_component_3()),
- static_cast<T>(rhs.R_component_4()),
- static_cast<T>(rhs.R_component_5()),
- static_cast<T>(rhs.R_component_6()),
- static_cast<T>(rhs.R_component_7()),
- static_cast<T>(rhs.R_component_8())));
- }
- }
- }
- }
- #if BOOST_WORKAROUND(__GNUC__, < 3)
- #undef BOOST_GET_VALARRAY
- #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
- #endif /* BOOST_OCTONION_HPP */