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// 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
{
#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(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
octonion<type> & operator /= (::std::complex<type> const & rhs) \
{ \
using ::std::valarray; \
using ::std::abs; \
\
valarray<type> tr(2); \
\
tr[0] = rhs.real(); \
tr[1] = rhs.imag(); \
\
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray<type> tt(8); \
\
tt[0] = +a*tr[0]-b*tr[1]; \
tt[1] = -a*tr[1]+b*tr[0]; \
tt[2] = +c*tr[0]-d*tr[1]; \
tt[3] = +c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]; \
tt[5] = +e*tr[1]+f*tr[0]; \
tt[6] = +g*tr[0]+h*tr[1]; \
tt[7] = +g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#else
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
octonion<type> & operator /= (::std::complex<type> const & rhs) \
{ \
using ::std::valarray; \
\
valarray<type> tr(2); \
\
tr[0] = rhs.real(); \
tr[1] = rhs.imag(); \
\
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray<type> tt(8); \
\
tt[0] = +a*tr[0]-b*tr[1]; \
tt[1] = -a*tr[1]+b*tr[0]; \
tt[2] = +c*tr[0]-d*tr[1]; \
tt[3] = +c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]; \
tt[5] = +e*tr[1]+f*tr[0]; \
tt[6] = +g*tr[0]+h*tr[1]; \
tt[7] = +g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
{ \
using ::std::valarray; \
using ::std::abs; \
\
valarray<type> tr(4); \
\
tr[0] = static_cast<type>(rhs.R_component_1()); \
tr[1] = static_cast<type>(rhs.R_component_2()); \
tr[2] = static_cast<type>(rhs.R_component_3()); \
tr[3] = static_cast<type>(rhs.R_component_4()); \
\
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray<type> tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#else
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
{ \
using ::std::valarray; \
\
valarray<type> tr(4); \
\
tr[0] = static_cast<type>(rhs.R_component_1()); \
tr[1] = static_cast<type>(rhs.R_component_2()); \
tr[2] = static_cast<type>(rhs.R_component_3()); \
tr[3] = static_cast<type>(rhs.R_component_4()); \
\
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray<type> tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
template<typename X> \
octonion<type> & operator /= (octonion<X> const & rhs) \
{ \
using ::std::valarray; \
using ::std::abs; \
\
valarray<type> tr(8); \
\
tr[0] = static_cast<type>(rhs.R_component_1()); \
tr[1] = static_cast<type>(rhs.R_component_2()); \
tr[2] = static_cast<type>(rhs.R_component_3()); \
tr[3] = static_cast<type>(rhs.R_component_4()); \
tr[4] = static_cast<type>(rhs.R_component_5()); \
tr[5] = static_cast<type>(rhs.R_component_6()); \
tr[6] = static_cast<type>(rhs.R_component_7()); \
tr[7] = static_cast<type>(rhs.R_component_8()); \
\
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray<type> tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#else
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
template<typename X> \
octonion<type> & operator /= (octonion<X> const & rhs) \
{ \
using ::std::valarray; \
\
valarray<type> tr(8); \
\
tr[0] = static_cast<type>(rhs.R_component_1()); \
tr[1] = static_cast<type>(rhs.R_component_2()); \
tr[2] = static_cast<type>(rhs.R_component_3()); \
tr[3] = static_cast<type>(rhs.R_component_4()); \
tr[4] = static_cast<type>(rhs.R_component_5()); \
tr[5] = static_cast<type>(rhs.R_component_6()); \
tr[6] = static_cast<type>(rhs.R_component_7()); \
tr[7] = static_cast<type>(rhs.R_component_8()); \
\
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray<type> tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
template<>
class octonion<float>
{
public:
typedef float value_type;
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
// UNtemplated copy constructor
// (this is taken care of by the compiler itself)
// explicit copy constructors (precision-loosing converters)
explicit octonion(octonion<double> const & a_recopier)
{
*this = detail::octonion_type_converter<float, double>(a_recopier);
}
explicit octonion(octonion<long double> const & a_recopier)
{
*this = detail::octonion_type_converter<float, long double>(a_recopier);
}
// destructor
// (this is taken care of by the compiler itself)
// accessors
//
// Note: Like complex number, octonions do have a meaningful notion of "real part",
// but unlike them there is no meaningful notion of "imaginary part".
// Instead there is an "unreal part" which itself is an octonion, and usually
// nothing simpler (as opposed to the complex number case).
// However, for practicallity, there are accessors for the other components
// (these are necessary for the templated copy constructor, for instance).
BOOST_OCTONION_ACCESSOR_GENERATOR(float)
// assignment operators
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
// other assignment-related operators
//
// NOTE: Octonion multiplication is *NOT* commutative;
// symbolically, "q *= rhs;" means "q = q * rhs;"
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
// octonion multiplication is also *NOT* associative
BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
protected:
BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
private:
};
template<>
class octonion<double>
{
public:
typedef double value_type;
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
// UNtemplated copy constructor
// (this is taken care of by the compiler itself)
// converting copy constructor
explicit octonion(octonion<float> const & a_recopier)
{
*this = detail::octonion_type_converter<double, float>(a_recopier);
}
// explicit copy constructors (precision-loosing converters)
explicit octonion(octonion<long double> const & a_recopier)
{
*this = detail::octonion_type_converter<double, long double>(a_recopier);
}
// destructor
// (this is taken care of by the compiler itself)
// accessors
//
// Note: Like complex number, octonions do have a meaningful notion of "real part",
// but unlike them there is no meaningful notion of "imaginary part".
// Instead there is an "unreal part" which itself is an octonion, and usually
// nothing simpler (as opposed to the complex number case).
// However, for practicallity, there are accessors for the other components
// (these are necessary for the templated copy constructor, for instance).
BOOST_OCTONION_ACCESSOR_GENERATOR(double)
// assignment operators
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
// other assignment-related operators
//
// NOTE: Octonion multiplication is *NOT* commutative;
// symbolically, "q *= rhs;" means "q = q * rhs;"
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
// octonion multiplication is also *NOT* associative
BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
protected:
BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
private:
};
template<>
class octonion<long double>
{
public:
typedef long double value_type;
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
// UNtemplated copy constructor
// (this is taken care of by the compiler itself)
// converting copy constructor
explicit octonion(octonion<float> const & a_recopier)
{
*this = detail::octonion_type_converter<long double, float>(a_recopier);
}
explicit octonion(octonion<double> const & a_recopier)
{
*this = detail::octonion_type_converter<long double, double>(a_recopier);
}
// destructor
// (this is taken care of by the compiler itself)
// accessors
//
// Note: Like complex number, octonions do have a meaningful notion of "real part",
// but unlike them there is no meaningful notion of "imaginary part".
// Instead there is an "unreal part" which itself is an octonion, and usually
// nothing simpler (as opposed to the complex number case).
// However, for practicallity, there are accessors for the other components
// (these are necessary for the templated copy constructor, for instance).
BOOST_OCTONION_ACCESSOR_GENERATOR(long double)
// assignment operators
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
// other assignment-related operators
//
// NOTE: Octonion multiplication is *NOT* commutative;
// symbolically, "q *= rhs;" means "q = q * rhs;"
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
// octonion multiplication is also *NOT* associative
BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
protected:
BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
private:
};
#undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
#undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
#undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
#undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
#undef BOOST_OCTONION_ACCESSOR_GENERATOR
// operators
#define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
{ \
octonion<T> res(lhs); \
res op##= rhs; \
return(res); \
}
#define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
template<typename T> \
inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
template<typename T> \
inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
template<typename T> \
inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
template<typename T> \
inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
template<typename T> \
inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
template<typename T> \
inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
template<typename T> \
inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
#define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
BOOST_OCTONION_OPERATOR_GENERATOR(+)
BOOST_OCTONION_OPERATOR_GENERATOR(-)
BOOST_OCTONION_OPERATOR_GENERATOR(*)
BOOST_OCTONION_OPERATOR_GENERATOR(/)
#undef BOOST_OCTONION_OPERATOR_GENERATOR
#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
#undef BOOST_OCTONION_OPERATOR_GENERATOR_4
#undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
template<typename T>
inline octonion<T> operator + (octonion<T> const & o)
{
return(o);
}
template<typename T>
inline octonion<T> operator - (octonion<T> const & o)
{
return(octonion<T>(-o.R_component_1(),-o.R_component_2(),-o.R_component_3(),-o.R_component_4(),-o.R_component_5(),-o.R_component_6(),-o.R_component_7(),-o.R_component_8()));
}
template<typename T>
inline bool operator == (T const & lhs, octonion<T> const & rhs)
{
return(
(rhs.R_component_1() == lhs)&&
(rhs.R_component_2() == static_cast<T>(0))&&
(rhs.R_component_3() == static_cast<T>(0))&&
(rhs.R_component_4() == static_cast<T>(0))&&
(rhs.R_component_5() == static_cast<T>(0))&&
(rhs.R_component_6() == static_cast<T>(0))&&
(rhs.R_component_7() == static_cast<T>(0))&&
(rhs.R_component_8() == static_cast<T>(0))
);
}
template<typename T>
inline bool operator == (octonion<T> const & lhs, T const & rhs)
{
return(
(lhs.R_component_1() == rhs)&&
(lhs.R_component_2() == static_cast<T>(0))&&
(lhs.R_component_3() == static_cast<T>(0))&&
(lhs.R_component_4() == static_cast<T>(0))&&
(lhs.R_component_5() == static_cast<T>(0))&&
(lhs.R_component_6() == static_cast<T>(0))&&
(lhs.R_component_7() == static_cast<T>(0))&&
(lhs.R_component_8() == static_cast<T>(0))
);
}
template<typename T>
inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
{
return(
(rhs.R_component_1() == lhs.real())&&
(rhs.R_component_2() == lhs.imag())&&
(rhs.R_component_3() == static_cast<T>(0))&&
(rhs.R_component_4() == static_cast<T>(0))&&
(rhs.R_component_5() == static_cast<T>(0))&&
(rhs.R_component_6() == static_cast<T>(0))&&
(rhs.R_component_7() == static_cast<T>(0))&&
(rhs.R_component_8() == static_cast<T>(0))
);
}
template<typename T>
inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
{
return(
(lhs.R_component_1() == rhs.real())&&
(lhs.R_component_2() == rhs.imag())&&
(lhs.R_component_3() == static_cast<T>(0))&&
(lhs.R_component_4() == static_cast<T>(0))&&
(lhs.R_component_5() == static_cast<T>(0))&&
(lhs.R_component_6() == static_cast<T>(0))&&
(lhs.R_component_7() == static_cast<T>(0))&&
(lhs.R_component_8() == static_cast<T>(0))
);
}
template<typename T>
inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
{
return(
(rhs.R_component_1() == lhs.R_component_1())&&
(rhs.R_component_2() == lhs.R_component_2())&&
(rhs.R_component_3() == lhs.R_component_3())&&
(rhs.R_component_4() == lhs.R_component_4())&&
(rhs.R_component_5() == static_cast<T>(0))&&
(rhs.R_component_6() == static_cast<T>(0))&&
(rhs.R_component_7() == static_cast<T>(0))&&
(rhs.R_component_8() == static_cast<T>(0))
);
}
template<typename T>
inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
{
return(
(lhs.R_component_1() == rhs.R_component_1())&&
(lhs.R_component_2() == rhs.R_component_2())&&
(lhs.R_component_3() == rhs.R_component_3())&&
(lhs.R_component_4() == rhs.R_component_4())&&
(lhs.R_component_5() == static_cast<T>(0))&&
(lhs.R_component_6() == static_cast<T>(0))&&
(lhs.R_component_7() == static_cast<T>(0))&&
(lhs.R_component_8() == static_cast<T>(0))
);
}
template<typename T>
inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
{
return(
(rhs.R_component_1() == lhs.R_component_1())&&
(rhs.R_component_2() == lhs.R_component_2())&&
(rhs.R_component_3() == lhs.R_component_3())&&
(rhs.R_component_4() == lhs.R_component_4())&&
(rhs.R_component_5() == lhs.R_component_5())&&
(rhs.R_component_6() == lhs.R_component_6())&&
(rhs.R_component_7() == lhs.R_component_7())&&
(rhs.R_component_8() == lhs.R_component_8())
);
}
#define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
{ \
return(!(lhs == rhs)); \
}
template<typename T>
inline bool operator != (T const & lhs, octonion<T> const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
template<typename T>
inline bool operator != (octonion<T> const & lhs, T const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
template<typename T>
inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
template<typename T>
inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
template<typename T>
inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
template<typename T>
inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
template<typename T>
inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
BOOST_OCTONION_NOT_EQUAL_GENERATOR
#undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
// Note: the default values in the constructors of the complex and quaternions make for
// a very complex and ambiguous situation; we have made choices to disambiguate.
template<typename T, typename charT, class traits>
::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
octonion<T> & o)
{
#ifdef BOOST_NO_STD_LOCALE
#else
const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
#endif /* BOOST_NO_STD_LOCALE */
T a = T();
T b = T();
T c = T();
T d = T();
T e = T();
T f = T();
T g = T();
T h = T();
::std::complex<T> u = ::std::complex<T>();
::std::complex<T> v = ::std::complex<T>();
::std::complex<T> x = ::std::complex<T>();
::std::complex<T> y = ::std::complex<T>();
::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
charT ch = charT();
char cc;
is >> ch; // get the first lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "("
{
is >> ch; // get the second lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "(("
{
is >> ch; // get the third lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((("
{
is.putback(ch);
is >> u; // read "((u"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((u)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // format: (((a))), (((a,b)))
{
o = octonion<T>(u);
}
else if (cc == ',') // read "((u),"
{
p = ::boost::math::quaternion<T>(u);
is >> q; // read "((u),q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // format: (((a)),q), (((a,b)),q)
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc ==',') // read "((u,"
{
is >> v; // read "((u,v"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((u,v)"
{
p = ::boost::math::quaternion<T>(u,v);
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // format: (((a),v)), (((a,b),v))
{
o = octonion<T>(p);
}
else if (cc == ',') // read "((u,v),"
{
is >> q; // read "(p,q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "((a"
{
is.putback(ch);
is >> a; // we extract the first component
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a))"
{
o = octonion<T>(a);
}
else if (cc == ',') // read "((a),"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a),("
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a),(("
{
is.putback(ch);
is.putback(ch); // we backtrack twice, with the same value!
is >> q; // read "((a),q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),q)"
{
p = ::boost::math::quaternion<T>(a);
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "((a),(c" or "((a),(e"
{
is.putback(ch);
is >> c;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c)" (ambiguity resolution)
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c))"
{
o = octonion<T>(a,b,c);
}
else if (cc == ',') // read "((a),(c),"
{
u = ::std::complex<T>(a);
v = ::std::complex<T>(c);
is >> x; // read "((a),(c),x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c),x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "((a),(c),x,"
{
is >> y; // read "((a),(c),x,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c),x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a),(c," or "((a),(e,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
{
p = ::boost::math::quaternion<T>(a);
x = ::std::complex<T>(c); // "c" was actually "e"
is.putback(ch); // we can only backtrace once
is >> y; // read "((a),(e,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(e,y)"
{
q = ::boost::math::quaternion<T>(x,y);
is >> ch; // get the next lexeme
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(e,y))"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "((a),(c,d" or "((a),(e,f"
{
is.putback(ch);
is >> d;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c,d))"
{
o = octonion<T>(a,b,c,d);
}
else if (cc == ',') // read "((a),(c,d),"
{
u = ::std::complex<T>(a);
v = ::std::complex<T>(c,d);
is >> x; // read "((a),(c,d),x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c,d),x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "((a),(c,d),x,"
{
is >> y; // read "((a),(c,d),x,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(c,d),x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
{
p = ::boost::math::quaternion<T>(a);
is >> g; // read "((a),(e,f,g" (too late to backtrack)
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(e,f,g)"
{
q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(e,f,g))"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a),(e,f,g,"
{
is >> h; // read "((a),(e,f,g,h"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(e,f,g,h)"
{
q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),(e,f,g,h))"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // read "((a),c" (ambiguity resolution)
{
is.putback(ch);
is >> c; // we extract the third component
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),c)"
{
o = octonion<T>(a,b,c);
}
else if (cc == ',') // read "((a),c,"
{
is >> x; // read "((a),c,x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),c,x)"
{
o = octonion<T>(a,b,c,d,x.real(),x.imag());
}
else if (cc == ',') // read "((a),c,x,"
{
is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a),c,x,y)"
{
o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc ==',') // read "((a,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a,("
{
u = ::std::complex<T>(a);
is.putback(ch); // can only backtrack so much
is >> v; // read "((a,v"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,v)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,v))"
{
o = octonion<T>(u,v);
}
else if (cc == ',') // read "((a,v),"
{
p = ::boost::math::quaternion<T>(u,v);
is >> q; // read "((a,v),q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,v),q)"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else
{
is.putback(ch);
is >> b; // read "((a,b"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b))"
{
o = octonion<T>(a,b);
}
else if (cc == ',') // read "((a,b),"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a,b),("
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a,b),(("
{
p = ::boost::math::quaternion<T>(a,b);
is.putback(ch);
is.putback(ch); // we backtrack twice, with the same value
is >> q; // read "((a,b),q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),q)"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "((a,b),(c" or "((a,b),(e"
{
is.putback(ch);
is >> c;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c))"
{
o = octonion<T>(a,b,c);
}
else if (cc == ',') // read "((a,b),(c),"
{
u = ::std::complex<T>(a,b);
v = ::std::complex<T>(c);
is >> x; // read "((a,b),(c),x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c),x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "((a,b),(c),x,"
{
is >> y; // read "((a,b),(c),x,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c),x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
{
u = ::std::complex<T>(a,b);
x = ::std::complex<T>(c); // "c" is actually "e"
is.putback(ch);
is >> y; // read "((a,b),(e,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(e,y)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(e,y))"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "((a,b),(c,d" or "((a,b),(e,f"
{
is.putback(ch);
is >> d;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
{
u = ::std::complex<T>(a,b);
v = ::std::complex<T>(c,d);
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c,d))"
{
o = octonion<T>(u,v);
}
else if (cc == ',') // read "((a,b),(c,d),"
{
is >> x; // read "((a,b),(c,d),x
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c,d),x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "((a,b),(c,d),x,"
{
is >> y; // read "((a,b),(c,d),x,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(c,d),x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
{
p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
is >> g; // read "((a,b),(e,f,g"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(e,f,g)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(e,f,g))"
{
q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a,b),(e,f,g,"
{
is >> h; // read "((a,b),(e,f,g,h"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b),(e,f,g,h)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read ((a,b),(e,f,g,h))"
{
q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a,b,"
{
is >> c; // read "((a,b,c"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b,c)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b,c))"
{
o = octonion<T>(a,b,c);
}
else if (cc == ',') // read "((a,b,c),"
{
p = ::boost::math::quaternion<T>(a,b,c);
is >> q; // read "((a,b,c),q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b,c),q)"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "((a,b,c,"
{
is >> d; // read "((a,b,c,d"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b,c,d)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b,c,d))"
{
o = octonion<T>(a,b,c,d);
}
else if (cc == ',') // read "((a,b,c,d),"
{
p = ::boost::math::quaternion<T>(a,b,c,d);
is >> q; // read "((a,b,c,d),q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "((a,b,c,d),q)"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // read "(a"
{
is.putback(ch);
is >> a; // we extract the first component
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a)"
{
o = octonion<T>(a);
}
else if (cc == ',') // read "(a,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "(a,("
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "(a,(("
{
p = ::boost::math::quaternion<T>(a);
is.putback(ch);
is.putback(ch); // we backtrack twice, with the same value
is >> q; // read "(a,q"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,q)"
{
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "(a,(c" or "(a,(e"
{
is.putback(ch);
is >> c;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c)" (ambiguity resolution)
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c))"
{
o = octonion<T>(a,b,c);
}
else if (cc == ',') // read "(a,(c),"
{
u = ::std::complex<T>(a);
v = ::std::complex<T>(c);
is >> x; // read "(a,(c),x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c),x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "(a,(c),x,"
{
is >> y; // read "(a,(c),x,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c),x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "(a,(c," or "(a,(e,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
{
u = ::std::complex<T>(a);
x = ::std::complex<T>(c); // "c" is actually "e"
is.putback(ch); // we backtrack
is >> y; // read "(a,(e,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(e,y)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(e,y))"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "(a,(c,d" or "(a,(e,f"
{
is.putback(ch);
is >> d;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c,d))"
{
o = octonion<T>(a,b,c,d);
}
else if (cc == ',') // read "(a,(c,d),"
{
u = ::std::complex<T>(a);
v = ::std::complex<T>(c,d);
is >> x; // read "(a,(c,d),x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c,d),x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "(a,(c,d),x,"
{
is >> y; // read "(a,(c,d),x,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(c,d),x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
{
p = ::boost::math::quaternion<T>(a);
is >> g; // read "(a,(e,f,g"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(e,f,g)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(e,f,g))"
{
q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else if (cc == ',') // read "(a,(e,f,g,"
{
is >> h; // read "(a,(e,f,g,h"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(e,f,g,h)"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,(e,f,g,h))"
{
q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
o = octonion<T>(p,q);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // read "(a,b" or "(a,c" (ambiguity resolution)
{
is.putback(ch);
is >> b;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b)" (ambiguity resolution)
{
o = octonion<T>(a,b);
}
else if (cc == ',') // read "(a,b," or "(a,c,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "(a,c,(" (ambiguity resolution)
{
u = ::std::complex<T>(a);
v = ::std::complex<T>(b); // "b" is actually "c"
is.putback(ch); // we backtrack
is >> x; // read "(a,c,x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,c,x)"
{
o = octonion<T>(u,v,x);
}
else if (cc == ',') // read "(a,c,x,"
{
is >> y; // read "(a,c,x,y" // read "(a,c,x"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,c,x,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "(a,b,c" or "(a,c,e"
{
is.putback(ch);
is >> c;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
{
o = octonion<T>(a,b,c);
}
else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
{
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
{
u = ::std::complex<T>(a);
v = ::std::complex<T>(b); // "b" is actually "c"
x = ::std::complex<T>(c); // "c" is actually "e"
is.putback(ch); // we backtrack
is >> y; // read "(a,c,e,y"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,c,e,y)"
{
o = octonion<T>(u,v,x,y);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // read "(a,b,c,d" (ambiguity resolution)
{
is.putback(ch); // we backtrack
is >> d;
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b,c,d)"
{
o = octonion<T>(a,b,c,d);
}
else if (cc == ',') // read "(a,b,c,d,"
{
is >> e; // read "(a,b,c,d,e"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b,c,d,e)"
{
o = octonion<T>(a,b,c,d,e);
}
else if (cc == ',') // read "(a,b,c,d,e,"
{
is >> f; // read "(a,b,c,d,e,f"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b,c,d,e,f)"
{
o = octonion<T>(a,b,c,d,e,f);
}
else if (cc == ',') // read "(a,b,c,d,e,f,"
{
is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b,c,d,e,f,g)"
{
o = octonion<T>(a,b,c,d,e,f,g);
}
else if (cc == ',') // read "(a,b,c,d,e,f,g,"
{
is >> h; // read "(a,b,c,d,e,f,g,h" // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
if (!is.good()) goto finish;
is >> ch; // get the next lexeme
if (!is.good()) goto finish;
#ifdef BOOST_NO_STD_LOCALE
cc = ch;
#else
cc = ct.narrow(ch, char());
#endif /* BOOST_NO_STD_LOCALE */
if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
{
o = octonion<T>(a,b,c,d,e,f,g,h);
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // error
{
is.setstate(::std::ios_base::failbit);
}
}
}
else // format: a
{
is.putback(ch);
is >> a; // we extract the first component
if (!is.good()) goto finish;
o = octonion<T>(a);
}
finish:
return(is);
}
template<typename T, typename charT, class traits>
::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
octonion<T> const & o)
{
::std::basic_ostringstream<charT,traits> s;
s.flags(os.flags());
#ifdef BOOST_NO_STD_LOCALE
#else
s.imbue(os.getloc());
#endif /* BOOST_NO_STD_LOCALE */
s.precision(os.precision());
s << '(' << o.R_component_1() << ','
<< o.R_component_2() << ','
<< o.R_component_3() << ','
<< o.R_component_4() << ','
<< o.R_component_5() << ','
<< o.R_component_6() << ','
<< o.R_component_7() << ','
<< o.R_component_8() << ')';
return os << s.str();
}
// values
template<typename T>
inline T real(octonion<T> const & o)
{
return(o.real());
}
template<typename T>
inline octonion<T> unreal(octonion<T> const & o)
{
return(o.unreal());
}
#define BOOST_OCTONION_VALARRAY_LOADER \
using ::std::valarray; \
\
valarray<T> temp(8); \
\
temp[0] = o.R_component_1(); \
temp[1] = o.R_component_2(); \
temp[2] = o.R_component_3(); \
temp[3] = o.R_component_4(); \
temp[4] = o.R_component_5(); \
temp[5] = o.R_component_6(); \
temp[6] = o.R_component_7(); \
temp[7] = o.R_component_8();
template<typename T>
inline T sup(octonion<T> const & o)
{
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
using ::std::abs;
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
BOOST_OCTONION_VALARRAY_LOADER
return((abs(temp).max)());
}
template<typename T>
inline T l1(octonion<T> const & o)
{
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
using ::std::abs;
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
BOOST_OCTONION_VALARRAY_LOADER
return(abs(temp).sum());
}
template<typename T>
inline T abs(const octonion<T> & o)
{
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
using ::std::abs;
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
using ::std::sqrt;
BOOST_OCTONION_VALARRAY_LOADER
T maxim = (abs(temp).max)(); // overflow protection
if (maxim == static_cast<T>(0))
{
return(maxim);
}
else
{
T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
temp *= mixam;
temp *= temp;
return(maxim*sqrt(temp.sum()));
}
//return(::std::sqrt(norm(o)));
}
#undef BOOST_OCTONION_VALARRAY_LOADER
// Note: This is the Cayley norm, not the Euclidian norm...
template<typename T>
inline T norm(octonion<T> const & o)
{
return(real(o*conj(o)));
}
template<typename T>
inline octonion<T> conj(octonion<T> const & o)
{
return(octonion<T>( +o.R_component_1(),
-o.R_component_2(),
-o.R_component_3(),
-o.R_component_4(),
-o.R_component_5(),
-o.R_component_6(),
-o.R_component_7(),
-o.R_component_8()));
}
// Note: There is little point, for the octonions, to introduce the equivalents
// to the complex "arg" and the quaternionic "cylindropolar".
template<typename T>
inline octonion<T> spherical(T const & rho,
T const & theta,
T const & phi1,
T const & phi2,
T const & phi3,
T const & phi4,
T const & phi5,
T const & phi6)
{
using ::std::cos;
using ::std::sin;
//T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
//T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
//T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
//T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
//T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
//T f = sin(phi4)*cos(phi5)*cos(phi6);
//T g = sin(phi5)*cos(phi6);
//T h = sin(phi6);
T courrant = static_cast<T>(1);
T h = sin(phi6);
courrant *= cos(phi6);
T g = sin(phi5)*courrant;
courrant *= cos(phi5);
T f = sin(phi4)*courrant;
courrant *= cos(phi4);
T e = sin(phi3)*courrant;
courrant *= cos(phi3);
T d = sin(phi2)*courrant;
courrant *= cos(phi2);
T c = sin(phi1)*courrant;
courrant *= cos(phi1);
T b = sin(theta)*courrant;
T a = cos(theta)*courrant;
return(rho*octonion<T>(a,b,c,d,e,f,g,h));
}
template<typename T>
inline octonion<T> multipolar(T const & rho1,
T const & theta1,
T const & rho2,
T const & theta2,
T const & rho3,
T const & theta3,
T const & rho4,
T const & theta4)
{
using ::std::cos;
using ::std::sin;
T a = rho1*cos(theta1);
T b = rho1*sin(theta1);
T c = rho2*cos(theta2);
T d = rho2*sin(theta2);
T e = rho3*cos(theta3);
T f = rho3*sin(theta3);
T g = rho4*cos(theta4);
T h = rho4*sin(theta4);
return(octonion<T>(a,b,c,d,e,f,g,h));
}
template<typename T>
inline octonion<T> cylindrical(T const & r,
T const & angle,
T const & h1,
T const & h2,
T const & h3,
T const & h4,
T const & h5,
T const & h6)
{
using ::std::cos;
using ::std::sin;
T a = r*cos(angle);
T b = r*sin(angle);
return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
}
template<typename T>
inline octonion<T> exp(octonion<T> const & o)
{
using ::std::exp;
using ::std::cos;
using ::boost::math::sinc_pi;
T u = exp(real(o));
T z = abs(unreal(o));
T w = sinc_pi(z);
return(u*octonion<T>(cos(z),
w*o.R_component_2(), w*o.R_component_3(),
w*o.R_component_4(), w*o.R_component_5(),
w*o.R_component_6(), w*o.R_component_7(),
w*o.R_component_8()));
}
template<typename T>
inline octonion<T> cos(octonion<T> const & o)
{
using ::std::sin;
using ::std::cos;
using ::std::cosh;
using ::boost::math::sinhc_pi;
T z = abs(unreal(o));
T w = -sin(o.real())*sinhc_pi(z);
return(octonion<T>(cos(o.real())*cosh(z),
w*o.R_component_2(), w*o.R_component_3(),
w*o.R_component_4(), w*o.R_component_5(),
w*o.R_component_6(), w*o.R_component_7(),
w*o.R_component_8()));
}
template<typename T>
inline octonion<T> sin(octonion<T> const & o)
{
using ::std::sin;
using ::std::cos;
using ::std::cosh;
using ::boost::math::sinhc_pi;
T z = abs(unreal(o));
T w = +cos(o.real())*sinhc_pi(z);
return(octonion<T>(sin(o.real())*cosh(z),
w*o.R_component_2(), w*o.R_component_3(),
w*o.R_component_4(), w*o.R_component_5(),
w*o.R_component_6(), w*o.R_component_7(),
w*o.R_component_8()));
}
template<typename T>
inline octonion<T> tan(octonion<T> const & o)
{
return(sin(o)/cos(o));
}
template<typename T>
inline octonion<T> cosh(octonion<T> const & o)
{
return((exp(+o)+exp(-o))/static_cast<T>(2));
}
template<typename T>
inline octonion<T> sinh(octonion<T> const & o)
{
return((exp(+o)-exp(-o))/static_cast<T>(2));
}
template<typename T>
inline octonion<T> tanh(octonion<T> const & o)
{
return(sinh(o)/cosh(o));
}
template<typename T>
octonion<T> pow(octonion<T> const & o,
int n)
{
if (n > 1)
{
int m = n>>1;
octonion<T> result = pow(o, m);
result *= result;
if (n != (m<<1))
{
result *= o; // n odd
}
return(result);
}
else if (n == 1)
{
return(o);
}
else if (n == 0)
{
return(octonion<T>(static_cast<T>(1)));
}
else /* n < 0 */
{
return(pow(octonion<T>(static_cast<T>(1))/o,-n));
}
}
// helper templates for converting copy constructors (definition)
namespace detail
{
template< typename T,
typename U
>
octonion<T> octonion_type_converter(octonion<U> const & rhs)
{
return(octonion<T>( static_cast<T>(rhs.R_component_1()),
static_cast<T>(rhs.R_component_2()),
static_cast<T>(rhs.R_component_3()),
static_cast<T>(rhs.R_component_4()),
static_cast<T>(rhs.R_component_5()),
static_cast<T>(rhs.R_component_6()),
static_cast<T>(rhs.R_component_7()),
static_cast<T>(rhs.R_component_8())));
}
}
}
}
#endif /* BOOST_OCTONION_HPP */
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