// 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 */ |