Edit: /usr/include/boost/math/octonion.hpp (246465B)
// 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
#include
namespace boost
{
namespace math
{
#define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
type real() const \
{ \
return(a); \
} \
\
octonion unreal() const \
{ \
return( octonion(static_cast(0),b,c,d,e,f,g,h)); \
} \
\
type R_component_1() const \
{ \
return(a); \
} \
\
type R_component_2() const \
{ \
return(b); \
} \
\
type R_component_3() const \
{ \
return(c); \
} \
\
type R_component_4() const \
{ \
return(d); \
} \
\
type R_component_5() const \
{ \
return(e); \
} \
\
type R_component_6() const \
{ \
return(f); \
} \
\
type R_component_7() const \
{ \
return(g); \
} \
\
type R_component_8() const \
{ \
return(h); \
} \
\
::std::complex C_component_1() const \
{ \
return(::std::complex(a,b)); \
} \
\
::std::complex C_component_2() const \
{ \
return(::std::complex(c,d)); \
} \
\
::std::complex C_component_3() const \
{ \
return(::std::complex(e,f)); \
} \
\
::std::complex C_component_4() const \
{ \
return(::std::complex(g,h)); \
} \
\
::boost::math::quaternion H_component_1() const \
{ \
return(::boost::math::quaternion(a,b,c,d)); \
} \
\
::boost::math::quaternion H_component_2() const \
{ \
return(::boost::math::quaternion(e,f,g,h)); \
}
#define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
template \
octonion & operator = (octonion const & a_affecter) \
{ \
a = static_cast(a_affecter.R_component_1()); \
b = static_cast(a_affecter.R_component_2()); \
c = static_cast(a_affecter.R_component_3()); \
d = static_cast(a_affecter.R_component_4()); \
e = static_cast(a_affecter.R_component_5()); \
f = static_cast(a_affecter.R_component_6()); \
g = static_cast(a_affecter.R_component_7()); \
h = static_cast(a_affecter.R_component_8()); \
\
return(*this); \
} \
\
octonion & operator = (octonion const & a_affecter) \
{ \
a = a_affecter.a; \
b = a_affecter.b; \
c = a_affecter.c; \
d = a_affecter.d; \
e = a_affecter.e; \
f = a_affecter.f; \
g = a_affecter.g; \
h = a_affecter.h; \
\
return(*this); \
} \
\
octonion & operator = (type const & a_affecter) \
{ \
a = a_affecter; \
\
b = c = d = e = f= g = h = static_cast(0); \
\
return(*this); \
} \
\
octonion & operator = (::std::complex const & a_affecter) \
{ \
a = a_affecter.real(); \
b = a_affecter.imag(); \
\
c = d = e = f = g = h = static_cast(0); \
\
return(*this); \
} \
\
octonion & operator = (::boost::math::quaternion const & a_affecter) \
{ \
a = a_affecter.R_component_1(); \
b = a_affecter.R_component_2(); \
c = a_affecter.R_component_3(); \
d = a_affecter.R_component_4(); \
\
e = f = g = h = static_cast(0); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \
type a; \
type b; \
type c; \
type d; \
type e; \
type f; \
type g; \
type h; \
template
class octonion
{
public:
typedef T value_type;
// constructor for O seen as R^8
// (also default constructor)
explicit octonion( T const & requested_a = T(),
T const & requested_b = T(),
T const & requested_c = T(),
T const & requested_d = T(),
T const & requested_e = T(),
T const & requested_f = T(),
T const & requested_g = T(),
T const & requested_h = T())
: a(requested_a),
b(requested_b),
c(requested_c),
d(requested_d),
e(requested_e),
f(requested_f),
g(requested_g),
h(requested_h)
{
// nothing to do!
}
// constructor for H seen as C^4
explicit octonion( ::std::complex const & z0,
::std::complex const & z1 = ::std::complex(),
::std::complex const & z2 = ::std::complex(),
::std::complex const & z3 = ::std::complex())
: a(z0.real()),
b(z0.imag()),
c(z1.real()),
d(z1.imag()),
e(z2.real()),
f(z2.imag()),
g(z3.real()),
h(z3.imag())
{
// nothing to do!
}
// constructor for O seen as H^2
explicit octonion( ::boost::math::quaternion const & q0,
::boost::math::quaternion const & q1 = ::boost::math::quaternion())
: a(q0.R_component_1()),
b(q0.R_component_2()),
c(q0.R_component_3()),
d(q0.R_component_4()),
e(q1.R_component_1()),
f(q1.R_component_2()),
g(q1.R_component_3()),
h(q1.R_component_4())
{
// nothing to do!
}
// UNtemplated copy constructor
// (this is taken care of by the compiler itself)
// templated copy constructor
template
explicit octonion(octonion const & a_recopier)
: a(static_cast(a_recopier.R_component_1())),
b(static_cast(a_recopier.R_component_2())),
c(static_cast(a_recopier.R_component_3())),
d(static_cast(a_recopier.R_component_4())),
e(static_cast(a_recopier.R_component_5())),
f(static_cast(a_recopier.R_component_6())),
g(static_cast(a_recopier.R_component_7())),
h(static_cast(a_recopier.R_component_8()))
{
// nothing to do!
}
// destructor
// (this is taken care of by the compiler itself)
// accessors
//
// Note: Like complex number, octonions do have a meaningful notion of "real part",
// but unlike them there is no meaningful notion of "imaginary part".
// Instead there is an "unreal part" which itself is an octonion, and usually
// nothing simpler (as opposed to the complex number case).
// However, for practicality, there are accessors for the other components
// (these are necessary for the templated copy constructor, for instance).
BOOST_OCTONION_ACCESSOR_GENERATOR(T)
// assignment operators
BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
// other assignment-related operators
//
// NOTE: Octonion multiplication is *NOT* commutative;
// symbolically, "q *= rhs;" means "q = q * rhs;"
// and "q /= rhs;" means "q = q * inverse_of(rhs);";
// octonion multiplication is also *NOT* associative
octonion & operator += (T const & rhs)
{
T at = a + rhs; // exception guard
a = at;
return(*this);
}
octonion & operator += (::std::complex const & rhs)
{
T at = a + rhs.real(); // exception guard
T bt = b + rhs.imag(); // exception guard
a = at;
b = bt;
return(*this);
}
octonion & operator += (::boost::math::quaternion const & rhs)
{
T at = a + rhs.R_component_1(); // exception guard
T bt = b + rhs.R_component_2(); // exception guard
T ct = c + rhs.R_component_3(); // exception guard
T dt = d + rhs.R_component_4(); // exception guard
a = at;
b = bt;
c = ct;
d = dt;
return(*this);
}
template
octonion & operator += (octonion const & rhs)
{
T at = a + static_cast(rhs.R_component_1()); // exception guard
T bt = b + static_cast(rhs.R_component_2()); // exception guard
T ct = c + static_cast(rhs.R_component_3()); // exception guard
T dt = d + static_cast(rhs.R_component_4()); // exception guard
T et = e + static_cast(rhs.R_component_5()); // exception guard
T ft = f + static_cast(rhs.R_component_6()); // exception guard
T gt = g + static_cast(rhs.R_component_7()); // exception guard
T ht = h + static_cast(rhs.R_component_8()); // exception guard
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator -= (T const & rhs)
{
T at = a - rhs; // exception guard
a = at;
return(*this);
}
octonion & operator -= (::std::complex const & rhs)
{
T at = a - rhs.real(); // exception guard
T bt = b - rhs.imag(); // exception guard
a = at;
b = bt;
return(*this);
}
octonion & operator -= (::boost::math::quaternion const & rhs)
{
T at = a - rhs.R_component_1(); // exception guard
T bt = b - rhs.R_component_2(); // exception guard
T ct = c - rhs.R_component_3(); // exception guard
T dt = d - rhs.R_component_4(); // exception guard
a = at;
b = bt;
c = ct;
d = dt;
return(*this);
}
template
octonion & operator -= (octonion const & rhs)
{
T at = a - static_cast(rhs.R_component_1()); // exception guard
T bt = b - static_cast(rhs.R_component_2()); // exception guard
T ct = c - static_cast(rhs.R_component_3()); // exception guard
T dt = d - static_cast(rhs.R_component_4()); // exception guard
T et = e - static_cast(rhs.R_component_5()); // exception guard
T ft = f - static_cast(rhs.R_component_6()); // exception guard
T gt = g - static_cast(rhs.R_component_7()); // exception guard
T ht = h - static_cast(rhs.R_component_8()); // exception guard
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator *= (T const & rhs)
{
T at = a * rhs; // exception guard
T bt = b * rhs; // exception guard
T ct = c * rhs; // exception guard
T dt = d * rhs; // exception guard
T et = e * rhs; // exception guard
T ft = f * rhs; // exception guard
T gt = g * rhs; // exception guard
T ht = h * rhs; // exception guard
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator *= (::std::complex const & rhs)
{
T ar = rhs.real();
T br = rhs.imag();
T at = +a*ar-b*br;
T bt = +a*br+b*ar;
T ct = +c*ar+d*br;
T dt = -c*br+d*ar;
T et = +e*ar+f*br;
T ft = -e*br+f*ar;
T gt = +g*ar-h*br;
T ht = +g*br+h*ar;
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator *= (::boost::math::quaternion const & rhs)
{
T ar = rhs.R_component_1();
T br = rhs.R_component_2();
T cr = rhs.R_component_2();
T dr = rhs.R_component_2();
T at = +a*ar-b*br-c*cr-d*dr;
T bt = +a*br+b*ar+c*dr-d*cr;
T ct = +a*cr-b*dr+c*ar+d*br;
T dt = +a*dr+b*cr-c*br+d*ar;
T et = +e*ar+f*br+g*cr+h*dr;
T ft = -e*br+f*ar-g*dr+h*cr;
T gt = -e*cr+f*dr+g*ar-h*br;
T ht = -e*dr-f*cr+g*br+h*ar;
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
template
octonion & operator *= (octonion const & rhs)
{
T ar = static_cast(rhs.R_component_1());
T br = static_cast(rhs.R_component_2());
T cr = static_cast(rhs.R_component_3());
T dr = static_cast(rhs.R_component_4());
T er = static_cast(rhs.R_component_5());
T fr = static_cast(rhs.R_component_6());
T gr = static_cast(rhs.R_component_7());
T hr = static_cast(rhs.R_component_8());
T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr;
T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr;
T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr;
T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er;
T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr;
T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr;
T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br;
T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar;
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator /= (T const & rhs)
{
T at = a / rhs; // exception guard
T bt = b / rhs; // exception guard
T ct = c / rhs; // exception guard
T dt = d / rhs; // exception guard
T et = e / rhs; // exception guard
T ft = f / rhs; // exception guard
T gt = g / rhs; // exception guard
T ht = h / rhs; // exception guard
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator /= (::std::complex const & rhs)
{
T ar = rhs.real();
T br = rhs.imag();
T denominator = ar*ar+br*br;
T at = (+a*ar-b*br)/denominator;
T bt = (-a*br+b*ar)/denominator;
T ct = (+c*ar-d*br)/denominator;
T dt = (+c*br+d*ar)/denominator;
T et = (+e*ar-f*br)/denominator;
T ft = (+e*br+f*ar)/denominator;
T gt = (+g*ar+h*br)/denominator;
T ht = (+g*br+h*ar)/denominator;
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
octonion & operator /= (::boost::math::quaternion const & rhs)
{
T ar = rhs.R_component_1();
T br = rhs.R_component_2();
T cr = rhs.R_component_2();
T dr = rhs.R_component_2();
T denominator = ar*ar+br*br+cr*cr+dr*dr;
T at = (+a*ar+b*br+c*cr+d*dr)/denominator;
T bt = (-a*br+b*ar-c*dr+d*cr)/denominator;
T ct = (-a*cr+b*dr+c*ar-d*br)/denominator;
T dt = (-a*dr-b*cr+c*br+d*ar)/denominator;
T et = (+e*ar-f*br-g*cr-h*dr)/denominator;
T ft = (+e*br+f*ar+g*dr-h*cr)/denominator;
T gt = (+e*cr-f*dr+g*ar+h*br)/denominator;
T ht = (+e*dr+f*cr-g*br+h*ar)/denominator;
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
template
octonion & operator /= (octonion const & rhs)
{
T ar = static_cast(rhs.R_component_1());
T br = static_cast(rhs.R_component_2());
T cr = static_cast(rhs.R_component_3());
T dr = static_cast(rhs.R_component_4());
T er = static_cast(rhs.R_component_5());
T fr = static_cast(rhs.R_component_6());
T gr = static_cast(rhs.R_component_7());
T hr = static_cast(rhs.R_component_8());
T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr;
T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator;
T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator;
T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator;
T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator;
T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator;
T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator;
T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator;
T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator;
a = at;
b = bt;
c = ct;
d = dt;
e = et;
f = ft;
g = gt;
h = ht;
return(*this);
}
protected:
BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
private:
};
// declaration of octonion specialization
template<> class octonion;
template<> class octonion;
template<> class octonion;
// helper templates for converting copy constructors (declaration)
namespace detail
{
template< typename T,
typename U
>
octonion octonion_type_converter(octonion const & rhs);
}
// implementation of octonion specialization
#define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
explicit octonion( type const & requested_a = static_cast(0), \
type const & requested_b = static_cast(0), \
type const & requested_c = static_cast(0), \
type const & requested_d = static_cast(0), \
type const & requested_e = static_cast(0), \
type const & requested_f = static_cast(0), \
type const & requested_g = static_cast(0), \
type const & requested_h = static_cast(0)) \
: a(requested_a), \
b(requested_b), \
c(requested_c), \
d(requested_d), \
e(requested_e), \
f(requested_f), \
g(requested_g), \
h(requested_h) \
{ \
} \
\
explicit octonion( ::std::complex const & z0, \
::std::complex const & z1 = ::std::complex(), \
::std::complex const & z2 = ::std::complex(), \
::std::complex const & z3 = ::std::complex()) \
: a(z0.real()), \
b(z0.imag()), \
c(z1.real()), \
d(z1.imag()), \
e(z2.real()), \
f(z2.imag()), \
g(z3.real()), \
h(z3.imag()) \
{ \
} \
\
explicit octonion( ::boost::math::quaternion const & q0, \
::boost::math::quaternion const & q1 = ::boost::math::quaternion()) \
: a(q0.R_component_1()), \
b(q0.R_component_2()), \
c(q0.R_component_3()), \
d(q0.R_component_4()), \
e(q1.R_component_1()), \
f(q1.R_component_2()), \
g(q1.R_component_3()), \
h(q1.R_component_4()) \
{ \
}
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
octonion & operator += (type const & rhs) \
{ \
a += rhs; \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
octonion & operator += (::std::complex const & rhs) \
{ \
a += rhs.real(); \
b += rhs.imag(); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
octonion & operator += (::boost::math::quaternion const & rhs) \
{ \
a += rhs.R_component_1(); \
b += rhs.R_component_2(); \
c += rhs.R_component_3(); \
d += rhs.R_component_4(); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
template \
octonion & operator += (octonion const & rhs) \
{ \
a += static_cast(rhs.R_component_1()); \
b += static_cast(rhs.R_component_2()); \
c += static_cast(rhs.R_component_3()); \
d += static_cast(rhs.R_component_4()); \
e += static_cast(rhs.R_component_5()); \
f += static_cast(rhs.R_component_6()); \
g += static_cast(rhs.R_component_7()); \
h += static_cast(rhs.R_component_8()); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
octonion & operator -= (type const & rhs) \
{ \
a -= rhs; \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
octonion & operator -= (::std::complex const & rhs) \
{ \
a -= rhs.real(); \
b -= rhs.imag(); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
octonion & operator -= (::boost::math::quaternion const & rhs) \
{ \
a -= rhs.R_component_1(); \
b -= rhs.R_component_2(); \
c -= rhs.R_component_3(); \
d -= rhs.R_component_4(); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
template \
octonion & operator -= (octonion const & rhs) \
{ \
a -= static_cast(rhs.R_component_1()); \
b -= static_cast(rhs.R_component_2()); \
c -= static_cast(rhs.R_component_3()); \
d -= static_cast(rhs.R_component_4()); \
e -= static_cast(rhs.R_component_5()); \
f -= static_cast(rhs.R_component_6()); \
g -= static_cast(rhs.R_component_7()); \
h -= static_cast(rhs.R_component_8()); \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
octonion & operator *= (type const & rhs) \
{ \
a *= rhs; \
b *= rhs; \
c *= rhs; \
d *= rhs; \
e *= rhs; \
f *= rhs; \
g *= rhs; \
h *= rhs; \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
octonion & operator *= (::std::complex const & rhs) \
{ \
type ar = rhs.real(); \
type br = rhs.imag(); \
\
type at = +a*ar-b*br; \
type bt = +a*br+b*ar; \
type ct = +c*ar+d*br; \
type dt = -c*br+d*ar; \
type et = +e*ar+f*br; \
type ft = -e*br+f*ar; \
type gt = +g*ar-h*br; \
type ht = +g*br+h*ar; \
\
a = at; \
b = bt; \
c = ct; \
d = dt; \
e = et; \
f = ft; \
g = gt; \
h = ht; \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
octonion & operator *= (::boost::math::quaternion const & rhs) \
{ \
type ar = rhs.R_component_1(); \
type br = rhs.R_component_2(); \
type cr = rhs.R_component_2(); \
type dr = rhs.R_component_2(); \
\
type at = +a*ar-b*br-c*cr-d*dr; \
type bt = +a*br+b*ar+c*dr-d*cr; \
type ct = +a*cr-b*dr+c*ar+d*br; \
type dt = +a*dr+b*cr-c*br+d*ar; \
type et = +e*ar+f*br+g*cr+h*dr; \
type ft = -e*br+f*ar-g*dr+h*cr; \
type gt = -e*cr+f*dr+g*ar-h*br; \
type ht = -e*dr-f*cr+g*br+h*ar; \
\
a = at; \
b = bt; \
c = ct; \
d = dt; \
e = et; \
f = ft; \
g = gt; \
h = ht; \
\
return(*this); \
}
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
template \
octonion & operator *= (octonion const & rhs) \
{ \
type ar = static_cast(rhs.R_component_1()); \
type br = static_cast(rhs.R_component_2()); \
type cr = static_cast(rhs.R_component_3()); \
type dr = static_cast(rhs.R_component_4()); \
type er = static_cast(rhs.R_component_5()); \
type fr = static_cast(rhs.R_component_6()); \
type gr = static_cast(rhs.R_component_7()); \
type hr = static_cast(rhs.R_component_8()); \
\
type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \
type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \
type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \
type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \
type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \
type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \
type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \
type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \
\
a = at; \
b = bt; \
c = ct; \
d = dt; \
e = et; \
f = ft; \
g = gt; \
h = ht; \
\
return(*this); \
}
// There is quite a lot of repetition in the code below. This is intentional.
// The last conditional block is the normal form, and the others merely
// consist of workarounds for various compiler deficiencies. Hopefully, when
// more compilers are conformant and we can retire support for those that are
// not, we will be able to remove the clutter. This is makes the situation
// (painfully) explicit.
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
octonion & operator /= (type const & rhs) \
{ \
a /= rhs; \
b /= rhs; \
c /= rhs; \
d /= rhs; \
\
return(*this); \
}
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
octonion & operator /= (::std::complex const & rhs) \
{ \
using ::std::valarray; \
using ::std::abs; \
\
valarray tr(2); \
\
tr[0] = rhs.real(); \
tr[1] = rhs.imag(); \
\
type mixam = static_cast(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray tt(8); \
\
tt[0] = +a*tr[0]-b*tr[1]; \
tt[1] = -a*tr[1]+b*tr[0]; \
tt[2] = +c*tr[0]-d*tr[1]; \
tt[3] = +c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]; \
tt[5] = +e*tr[1]+f*tr[0]; \
tt[6] = +g*tr[0]+h*tr[1]; \
tt[7] = +g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#else
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
octonion & operator /= (::std::complex const & rhs) \
{ \
using ::std::valarray; \
\
valarray tr(2); \
\
tr[0] = rhs.real(); \
tr[1] = rhs.imag(); \
\
type mixam = static_cast(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray tt(8); \
\
tt[0] = +a*tr[0]-b*tr[1]; \
tt[1] = -a*tr[1]+b*tr[0]; \
tt[2] = +c*tr[0]-d*tr[1]; \
tt[3] = +c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]; \
tt[5] = +e*tr[1]+f*tr[0]; \
tt[6] = +g*tr[0]+h*tr[1]; \
tt[7] = +g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
octonion & operator /= (::boost::math::quaternion const & rhs) \
{ \
using ::std::valarray; \
using ::std::abs; \
\
valarray tr(4); \
\
tr[0] = static_cast(rhs.R_component_1()); \
tr[1] = static_cast(rhs.R_component_2()); \
tr[2] = static_cast(rhs.R_component_3()); \
tr[3] = static_cast(rhs.R_component_4()); \
\
type mixam = static_cast(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#else
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
octonion & operator /= (::boost::math::quaternion const & rhs) \
{ \
using ::std::valarray; \
\
valarray tr(4); \
\
tr[0] = static_cast(rhs.R_component_1()); \
tr[1] = static_cast(rhs.R_component_2()); \
tr[2] = static_cast(rhs.R_component_3()); \
tr[3] = static_cast(rhs.R_component_4()); \
\
type mixam = static_cast(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
template \
octonion & operator /= (octonion const & rhs) \
{ \
using ::std::valarray; \
using ::std::abs; \
\
valarray tr(8); \
\
tr[0] = static_cast(rhs.R_component_1()); \
tr[1] = static_cast(rhs.R_component_2()); \
tr[2] = static_cast(rhs.R_component_3()); \
tr[3] = static_cast(rhs.R_component_4()); \
tr[4] = static_cast(rhs.R_component_5()); \
tr[5] = static_cast(rhs.R_component_6()); \
tr[6] = static_cast(rhs.R_component_7()); \
tr[7] = static_cast(rhs.R_component_8()); \
\
type mixam = static_cast(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#else
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
template \
octonion & operator /= (octonion const & rhs) \
{ \
using ::std::valarray; \
\
valarray tr(8); \
\
tr[0] = static_cast(rhs.R_component_1()); \
tr[1] = static_cast(rhs.R_component_2()); \
tr[2] = static_cast(rhs.R_component_3()); \
tr[3] = static_cast(rhs.R_component_4()); \
tr[4] = static_cast(rhs.R_component_5()); \
tr[5] = static_cast(rhs.R_component_6()); \
tr[6] = static_cast(rhs.R_component_7()); \
tr[7] = static_cast(rhs.R_component_8()); \
\
type mixam = static_cast(1)/(abs(tr).max)(); \
\
tr *= mixam; \
\
valarray tt(8); \
\
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
\
tr *= tr; \
\
tt *= (mixam/tr.sum()); \
\
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
e = tt[4]; \
f = tt[5]; \
g = tt[6]; \
h = tt[7]; \
\
return(*this); \
}
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
template<>
class octonion
{
public:
typedef float value_type;
BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
// UNtemplated copy constructor
// (this is taken care of by the compiler itself)
// explicit copy constructors (precision-losing converters)
explicit octonion(octonion