--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ossrv_pub/boost_apis/boost/math/octonion.hpp Tue Feb 02 02:01:42 2010 +0200
@@ -0,0 +1,4754 @@
+// boost octonion.hpp header file
+
+// (C) Copyright Hubert Holin 2001.
+// Distributed under the Boost Software License, Version 1.0. (See
+// accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+// See http://www.boost.org for updates, documentation, and revision history.
+
+
+#ifndef BOOST_OCTONION_HPP
+#define BOOST_OCTONION_HPP
+
+#include <boost/math/quaternion.hpp>
+
+
+namespace boost
+{
+ namespace math
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ // gcc 2.95.x uses expression templates for valarray calculations, but
+ // the result is not conforming. We need BOOST_GET_VALARRAY to get an
+ // actual valarray result when we need to call a member function
+ #define BOOST_GET_VALARRAY(T,x) ::std::valarray<T>(x)
+ // gcc 2.95.x has an "std::ios" class that is similar to
+ // "std::ios_base", so we just use a #define
+ #define BOOST_IOS_BASE ::std::ios
+ // gcc 2.x ignores function scope using declarations,
+ // put them in the scope of the enclosing namespace instead:
+ using ::std::valarray;
+ using ::std::sqrt;
+ using ::std::cos;
+ using ::std::sin;
+ using ::std::exp;
+ using ::std::cosh;
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+#define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
+ type real() const \
+ { \
+ return(a); \
+ } \
+ \
+ octonion<type> unreal() const \
+ { \
+ return( octonion<type>(static_cast<type>(0),b,c,d,e,f,g,h)); \
+ } \
+ \
+ type R_component_1() const \
+ { \
+ return(a); \
+ } \
+ \
+ type R_component_2() const \
+ { \
+ return(b); \
+ } \
+ \
+ type R_component_3() const \
+ { \
+ return(c); \
+ } \
+ \
+ type R_component_4() const \
+ { \
+ return(d); \
+ } \
+ \
+ type R_component_5() const \
+ { \
+ return(e); \
+ } \
+ \
+ type R_component_6() const \
+ { \
+ return(f); \
+ } \
+ \
+ type R_component_7() const \
+ { \
+ return(g); \
+ } \
+ \
+ type R_component_8() const \
+ { \
+ return(h); \
+ } \
+ \
+ ::std::complex<type> C_component_1() const \
+ { \
+ return(::std::complex<type>(a,b)); \
+ } \
+ \
+ ::std::complex<type> C_component_2() const \
+ { \
+ return(::std::complex<type>(c,d)); \
+ } \
+ \
+ ::std::complex<type> C_component_3() const \
+ { \
+ return(::std::complex<type>(e,f)); \
+ } \
+ \
+ ::std::complex<type> C_component_4() const \
+ { \
+ return(::std::complex<type>(g,h)); \
+ } \
+ \
+ ::boost::math::quaternion<type> H_component_1() const \
+ { \
+ return(::boost::math::quaternion<type>(a,b,c,d)); \
+ } \
+ \
+ ::boost::math::quaternion<type> H_component_2() const \
+ { \
+ return(::boost::math::quaternion<type>(e,f,g,h)); \
+ }
+
+
+#define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
+ template<typename X> \
+ octonion<type> & operator = (octonion<X> const & a_affecter) \
+ { \
+ a = static_cast<type>(a_affecter.R_component_1()); \
+ b = static_cast<type>(a_affecter.R_component_2()); \
+ c = static_cast<type>(a_affecter.R_component_3()); \
+ d = static_cast<type>(a_affecter.R_component_4()); \
+ e = static_cast<type>(a_affecter.R_component_5()); \
+ f = static_cast<type>(a_affecter.R_component_6()); \
+ g = static_cast<type>(a_affecter.R_component_7()); \
+ h = static_cast<type>(a_affecter.R_component_8()); \
+ \
+ return(*this); \
+ } \
+ \
+ octonion<type> & operator = (octonion<type> const & a_affecter) \
+ { \
+ a = a_affecter.a; \
+ b = a_affecter.b; \
+ c = a_affecter.c; \
+ d = a_affecter.d; \
+ e = a_affecter.e; \
+ f = a_affecter.f; \
+ g = a_affecter.g; \
+ h = a_affecter.h; \
+ \
+ return(*this); \
+ } \
+ \
+ octonion<type> & operator = (type const & a_affecter) \
+ { \
+ a = a_affecter; \
+ \
+ b = c = d = e = f= g = h = static_cast<type>(0); \
+ \
+ return(*this); \
+ } \
+ \
+ octonion<type> & operator = (::std::complex<type> const & a_affecter) \
+ { \
+ a = a_affecter.real(); \
+ b = a_affecter.imag(); \
+ \
+ c = d = e = f = g = h = static_cast<type>(0); \
+ \
+ return(*this); \
+ } \
+ \
+ octonion<type> & operator = (::boost::math::quaternion<type> const & a_affecter) \
+ { \
+ a = a_affecter.R_component_1(); \
+ b = a_affecter.R_component_2(); \
+ c = a_affecter.R_component_3(); \
+ d = a_affecter.R_component_4(); \
+ \
+ e = f = g = h = static_cast<type>(0); \
+ \
+ return(*this); \
+ }
+
+
+#define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \
+ type a; \
+ type b; \
+ type c; \
+ type d; \
+ type e; \
+ type f; \
+ type g; \
+ type h; \
+
+
+ template<typename T>
+ class octonion
+ {
+ public:
+
+ typedef T value_type;
+
+ // constructor for O seen as R^8
+ // (also default constructor)
+
+ explicit octonion( T const & requested_a = T(),
+ T const & requested_b = T(),
+ T const & requested_c = T(),
+ T const & requested_d = T(),
+ T const & requested_e = T(),
+ T const & requested_f = T(),
+ T const & requested_g = T(),
+ T const & requested_h = T())
+ : a(requested_a),
+ b(requested_b),
+ c(requested_c),
+ d(requested_d),
+ e(requested_e),
+ f(requested_f),
+ g(requested_g),
+ h(requested_h)
+ {
+ // nothing to do!
+ }
+
+
+ // constructor for H seen as C^4
+
+ explicit octonion( ::std::complex<T> const & z0,
+ ::std::complex<T> const & z1 = ::std::complex<T>(),
+ ::std::complex<T> const & z2 = ::std::complex<T>(),
+ ::std::complex<T> const & z3 = ::std::complex<T>())
+ : a(z0.real()),
+ b(z0.imag()),
+ c(z1.real()),
+ d(z1.imag()),
+ e(z2.real()),
+ f(z2.imag()),
+ g(z3.real()),
+ h(z3.imag())
+ {
+ // nothing to do!
+ }
+
+
+ // constructor for O seen as H^2
+
+ explicit octonion( ::boost::math::quaternion<T> const & q0,
+ ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
+ : a(q0.R_component_1()),
+ b(q0.R_component_2()),
+ c(q0.R_component_3()),
+ d(q0.R_component_4()),
+ e(q1.R_component_1()),
+ f(q1.R_component_2()),
+ g(q1.R_component_3()),
+ h(q1.R_component_4())
+ {
+ // nothing to do!
+ }
+
+
+ // UNtemplated copy constructor
+ // (this is taken care of by the compiler itself)
+
+
+ // templated copy constructor
+
+ template<typename X>
+ explicit octonion(octonion<X> const & a_recopier)
+ : a(static_cast<T>(a_recopier.R_component_1())),
+ b(static_cast<T>(a_recopier.R_component_2())),
+ c(static_cast<T>(a_recopier.R_component_3())),
+ d(static_cast<T>(a_recopier.R_component_4())),
+ e(static_cast<T>(a_recopier.R_component_5())),
+ f(static_cast<T>(a_recopier.R_component_6())),
+ g(static_cast<T>(a_recopier.R_component_7())),
+ h(static_cast<T>(a_recopier.R_component_8()))
+ {
+ // nothing to do!
+ }
+
+
+ // destructor
+ // (this is taken care of by the compiler itself)
+
+
+ // accessors
+ //
+ // Note: Like complex number, octonions do have a meaningful notion of "real part",
+ // but unlike them there is no meaningful notion of "imaginary part".
+ // Instead there is an "unreal part" which itself is an octonion, and usually
+ // nothing simpler (as opposed to the complex number case).
+ // However, for practicallity, there are accessors for the other components
+ // (these are necessary for the templated copy constructor, for instance).
+
+ BOOST_OCTONION_ACCESSOR_GENERATOR(T)
+
+ // assignment operators
+
+ BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
+
+ // other assignment-related operators
+ //
+ // NOTE: Octonion multiplication is *NOT* commutative;
+ // symbolically, "q *= rhs;" means "q = q * rhs;"
+ // and "q /= rhs;" means "q = q * inverse_of(rhs);";
+ // octonion multiplication is also *NOT* associative
+
+ octonion<T> & operator += (T const & rhs)
+ {
+ T at = a + rhs; // exception guard
+
+ a = at;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator += (::std::complex<T> const & rhs)
+ {
+ T at = a + rhs.real(); // exception guard
+ T bt = b + rhs.imag(); // exception guard
+
+ a = at;
+ b = bt;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator += (::boost::math::quaternion<T> const & rhs)
+ {
+ T at = a + rhs.R_component_1(); // exception guard
+ T bt = b + rhs.R_component_2(); // exception guard
+ T ct = c + rhs.R_component_3(); // exception guard
+ T dt = d + rhs.R_component_4(); // exception guard
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+
+ return(*this);
+ }
+
+
+ template<typename X>
+ octonion<T> & operator += (octonion<X> const & rhs)
+ {
+ T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
+ T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
+ T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
+ T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
+ T et = e + static_cast<T>(rhs.R_component_5()); // exception guard
+ T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard
+ T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard
+ T ht = h + static_cast<T>(rhs.R_component_8()); // exception guard
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+
+ octonion<T> & operator -= (T const & rhs)
+ {
+ T at = a - rhs; // exception guard
+
+ a = at;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator -= (::std::complex<T> const & rhs)
+ {
+ T at = a - rhs.real(); // exception guard
+ T bt = b - rhs.imag(); // exception guard
+
+ a = at;
+ b = bt;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs)
+ {
+ T at = a - rhs.R_component_1(); // exception guard
+ T bt = b - rhs.R_component_2(); // exception guard
+ T ct = c - rhs.R_component_3(); // exception guard
+ T dt = d - rhs.R_component_4(); // exception guard
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+
+ return(*this);
+ }
+
+
+ template<typename X>
+ octonion<T> & operator -= (octonion<X> const & rhs)
+ {
+ T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
+ T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
+ T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
+ T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
+ T et = e - static_cast<T>(rhs.R_component_5()); // exception guard
+ T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard
+ T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard
+ T ht = h - static_cast<T>(rhs.R_component_8()); // exception guard
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator *= (T const & rhs)
+ {
+ T at = a * rhs; // exception guard
+ T bt = b * rhs; // exception guard
+ T ct = c * rhs; // exception guard
+ T dt = d * rhs; // exception guard
+ T et = e * rhs; // exception guard
+ T ft = f * rhs; // exception guard
+ T gt = g * rhs; // exception guard
+ T ht = h * rhs; // exception guard
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator *= (::std::complex<T> const & rhs)
+ {
+ T ar = rhs.real();
+ T br = rhs.imag();
+
+ T at = +a*ar-b*br;
+ T bt = +a*br+b*ar;
+ T ct = +c*ar+d*br;
+ T dt = -c*br+d*ar;
+ T et = +e*ar+f*br;
+ T ft = -e*br+f*ar;
+ T gt = +g*ar-h*br;
+ T ht = +g*br+h*ar;
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs)
+ {
+ T ar = rhs.R_component_1();
+ T br = rhs.R_component_2();
+ T cr = rhs.R_component_2();
+ T dr = rhs.R_component_2();
+
+ T at = +a*ar-b*br-c*cr-d*dr;
+ T bt = +a*br+b*ar+c*dr-d*cr;
+ T ct = +a*cr-b*dr+c*ar+d*br;
+ T dt = +a*dr+b*cr-c*br+d*ar;
+ T et = +e*ar+f*br+g*cr+h*dr;
+ T ft = -e*br+f*ar-g*dr+h*cr;
+ T gt = -e*cr+f*dr+g*ar-h*br;
+ T ht = -e*dr-f*cr+g*br+h*ar;
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ template<typename X>
+ octonion<T> & operator *= (octonion<X> const & rhs)
+ {
+ T ar = static_cast<T>(rhs.R_component_1());
+ T br = static_cast<T>(rhs.R_component_2());
+ T cr = static_cast<T>(rhs.R_component_3());
+ T dr = static_cast<T>(rhs.R_component_4());
+ T er = static_cast<T>(rhs.R_component_5());
+ T fr = static_cast<T>(rhs.R_component_6());
+ T gr = static_cast<T>(rhs.R_component_7());
+ T hr = static_cast<T>(rhs.R_component_8());
+
+ T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr;
+ T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr;
+ T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr;
+ T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er;
+ T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr;
+ T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr;
+ T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br;
+ T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar;
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator /= (T const & rhs)
+ {
+ T at = a / rhs; // exception guard
+ T bt = b / rhs; // exception guard
+ T ct = c / rhs; // exception guard
+ T dt = d / rhs; // exception guard
+ T et = e / rhs; // exception guard
+ T ft = f / rhs; // exception guard
+ T gt = g / rhs; // exception guard
+ T ht = h / rhs; // exception guard
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator /= (::std::complex<T> const & rhs)
+ {
+ T ar = rhs.real();
+ T br = rhs.imag();
+
+ T denominator = ar*ar+br*br;
+
+ T at = (+a*ar-b*br)/denominator;
+ T bt = (-a*br+b*ar)/denominator;
+ T ct = (+c*ar-d*br)/denominator;
+ T dt = (+c*br+d*ar)/denominator;
+ T et = (+e*ar-f*br)/denominator;
+ T ft = (+e*br+f*ar)/denominator;
+ T gt = (+g*ar+h*br)/denominator;
+ T ht = (+g*br+h*ar)/denominator;
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs)
+ {
+ T ar = rhs.R_component_1();
+ T br = rhs.R_component_2();
+ T cr = rhs.R_component_2();
+ T dr = rhs.R_component_2();
+
+ T denominator = ar*ar+br*br+cr*cr+dr*dr;
+
+ T at = (+a*ar+b*br+c*cr+d*dr)/denominator;
+ T bt = (-a*br+b*ar-c*dr+d*cr)/denominator;
+ T ct = (-a*cr+b*dr+c*ar-d*br)/denominator;
+ T dt = (-a*dr-b*cr+c*br+d*ar)/denominator;
+ T et = (+e*ar-f*br-g*cr-h*dr)/denominator;
+ T ft = (+e*br+f*ar+g*dr-h*cr)/denominator;
+ T gt = (+e*cr-f*dr+g*ar+h*br)/denominator;
+ T ht = (+e*dr+f*cr-g*br+h*ar)/denominator;
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ template<typename X>
+ octonion<T> & operator /= (octonion<X> const & rhs)
+ {
+ T ar = static_cast<T>(rhs.R_component_1());
+ T br = static_cast<T>(rhs.R_component_2());
+ T cr = static_cast<T>(rhs.R_component_3());
+ T dr = static_cast<T>(rhs.R_component_4());
+ T er = static_cast<T>(rhs.R_component_5());
+ T fr = static_cast<T>(rhs.R_component_6());
+ T gr = static_cast<T>(rhs.R_component_7());
+ T hr = static_cast<T>(rhs.R_component_8());
+
+ T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr;
+
+ T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator;
+ T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator;
+ T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator;
+ T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator;
+ T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator;
+ T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator;
+ T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator;
+ T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator;
+
+ a = at;
+ b = bt;
+ c = ct;
+ d = dt;
+ e = et;
+ f = ft;
+ g = gt;
+ h = ht;
+
+ return(*this);
+ }
+
+
+ protected:
+
+ BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
+
+
+ private:
+
+ };
+
+
+ // declaration of octonion specialization
+
+ template<> class octonion<float>;
+ template<> class octonion<double>;
+ template<> class octonion<long double>;
+
+
+ // helper templates for converting copy constructors (declaration)
+
+ namespace detail
+ {
+
+ template< typename T,
+ typename U
+ >
+ octonion<T> octonion_type_converter(octonion<U> const & rhs);
+ }
+
+
+ // implementation of octonion specialization
+
+
+#define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
+ explicit octonion( type const & requested_a = static_cast<type>(0), \
+ type const & requested_b = static_cast<type>(0), \
+ type const & requested_c = static_cast<type>(0), \
+ type const & requested_d = static_cast<type>(0), \
+ type const & requested_e = static_cast<type>(0), \
+ type const & requested_f = static_cast<type>(0), \
+ type const & requested_g = static_cast<type>(0), \
+ type const & requested_h = static_cast<type>(0)) \
+ : a(requested_a), \
+ b(requested_b), \
+ c(requested_c), \
+ d(requested_d), \
+ e(requested_e), \
+ f(requested_f), \
+ g(requested_g), \
+ h(requested_h) \
+ { \
+ } \
+ \
+ explicit octonion( ::std::complex<type> const & z0, \
+ ::std::complex<type> const & z1 = ::std::complex<type>(), \
+ ::std::complex<type> const & z2 = ::std::complex<type>(), \
+ ::std::complex<type> const & z3 = ::std::complex<type>()) \
+ : a(z0.real()), \
+ b(z0.imag()), \
+ c(z1.real()), \
+ d(z1.imag()), \
+ e(z2.real()), \
+ f(z2.imag()), \
+ g(z3.real()), \
+ h(z3.imag()) \
+ { \
+ } \
+ \
+ explicit octonion( ::boost::math::quaternion<type> const & q0, \
+ ::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \
+ : a(q0.R_component_1()), \
+ b(q0.R_component_2()), \
+ c(q0.R_component_3()), \
+ d(q0.R_component_4()), \
+ e(q1.R_component_1()), \
+ f(q1.R_component_2()), \
+ g(q1.R_component_3()), \
+ h(q1.R_component_4()) \
+ { \
+ }
+
+
+#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
+ octonion<type> & operator += (type const & rhs) \
+ { \
+ a += rhs; \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
+ octonion<type> & operator += (::std::complex<type> const & rhs) \
+ { \
+ a += rhs.real(); \
+ b += rhs.imag(); \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
+ octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \
+ { \
+ a += rhs.R_component_1(); \
+ b += rhs.R_component_2(); \
+ c += rhs.R_component_3(); \
+ d += rhs.R_component_4(); \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
+ template<typename X> \
+ octonion<type> & operator += (octonion<X> const & rhs) \
+ { \
+ a += static_cast<type>(rhs.R_component_1()); \
+ b += static_cast<type>(rhs.R_component_2()); \
+ c += static_cast<type>(rhs.R_component_3()); \
+ d += static_cast<type>(rhs.R_component_4()); \
+ e += static_cast<type>(rhs.R_component_5()); \
+ f += static_cast<type>(rhs.R_component_6()); \
+ g += static_cast<type>(rhs.R_component_7()); \
+ h += static_cast<type>(rhs.R_component_8()); \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
+ octonion<type> & operator -= (type const & rhs) \
+ { \
+ a -= rhs; \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
+ octonion<type> & operator -= (::std::complex<type> const & rhs) \
+ { \
+ a -= rhs.real(); \
+ b -= rhs.imag(); \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
+ octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \
+ { \
+ a -= rhs.R_component_1(); \
+ b -= rhs.R_component_2(); \
+ c -= rhs.R_component_3(); \
+ d -= rhs.R_component_4(); \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
+ template<typename X> \
+ octonion<type> & operator -= (octonion<X> const & rhs) \
+ { \
+ a -= static_cast<type>(rhs.R_component_1()); \
+ b -= static_cast<type>(rhs.R_component_2()); \
+ c -= static_cast<type>(rhs.R_component_3()); \
+ d -= static_cast<type>(rhs.R_component_4()); \
+ e -= static_cast<type>(rhs.R_component_5()); \
+ f -= static_cast<type>(rhs.R_component_6()); \
+ g -= static_cast<type>(rhs.R_component_7()); \
+ h -= static_cast<type>(rhs.R_component_8()); \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
+ octonion<type> & operator *= (type const & rhs) \
+ { \
+ a *= rhs; \
+ b *= rhs; \
+ c *= rhs; \
+ d *= rhs; \
+ e *= rhs; \
+ f *= rhs; \
+ g *= rhs; \
+ h *= rhs; \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
+ octonion<type> & operator *= (::std::complex<type> const & rhs) \
+ { \
+ type ar = rhs.real(); \
+ type br = rhs.imag(); \
+ \
+ type at = +a*ar-b*br; \
+ type bt = +a*br+b*ar; \
+ type ct = +c*ar+d*br; \
+ type dt = -c*br+d*ar; \
+ type et = +e*ar+f*br; \
+ type ft = -e*br+f*ar; \
+ type gt = +g*ar-h*br; \
+ type ht = +g*br+h*ar; \
+ \
+ a = at; \
+ b = bt; \
+ c = ct; \
+ d = dt; \
+ e = et; \
+ f = ft; \
+ g = gt; \
+ h = ht; \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
+ octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \
+ { \
+ type ar = rhs.R_component_1(); \
+ type br = rhs.R_component_2(); \
+ type cr = rhs.R_component_2(); \
+ type dr = rhs.R_component_2(); \
+ \
+ type at = +a*ar-b*br-c*cr-d*dr; \
+ type bt = +a*br+b*ar+c*dr-d*cr; \
+ type ct = +a*cr-b*dr+c*ar+d*br; \
+ type dt = +a*dr+b*cr-c*br+d*ar; \
+ type et = +e*ar+f*br+g*cr+h*dr; \
+ type ft = -e*br+f*ar-g*dr+h*cr; \
+ type gt = -e*cr+f*dr+g*ar-h*br; \
+ type ht = -e*dr-f*cr+g*br+h*ar; \
+ \
+ a = at; \
+ b = bt; \
+ c = ct; \
+ d = dt; \
+ e = et; \
+ f = ft; \
+ g = gt; \
+ h = ht; \
+ \
+ return(*this); \
+ }
+
+#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
+ template<typename X> \
+ octonion<type> & operator *= (octonion<X> const & rhs) \
+ { \
+ type ar = static_cast<type>(rhs.R_component_1()); \
+ type br = static_cast<type>(rhs.R_component_2()); \
+ type cr = static_cast<type>(rhs.R_component_3()); \
+ type dr = static_cast<type>(rhs.R_component_4()); \
+ type er = static_cast<type>(rhs.R_component_5()); \
+ type fr = static_cast<type>(rhs.R_component_6()); \
+ type gr = static_cast<type>(rhs.R_component_7()); \
+ type hr = static_cast<type>(rhs.R_component_8()); \
+ \
+ type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \
+ type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \
+ type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \
+ type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \
+ type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \
+ type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \
+ type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \
+ type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \
+ \
+ a = at; \
+ b = bt; \
+ c = ct; \
+ d = dt; \
+ e = et; \
+ f = ft; \
+ g = gt; \
+ h = ht; \
+ \
+ return(*this); \
+ }
+
+// There is quite a lot of repetition in the code below. This is intentional.
+// The last conditional block is the normal form, and the others merely
+// consist of workarounds for various compiler deficiencies. Hopefuly, when
+// more compilers are conformant and we can retire support for those that are
+// not, we will be able to remove the clutter. This is makes the situation
+// (painfully) explicit.
+
+#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
+ octonion<type> & operator /= (type const & rhs) \
+ { \
+ a /= rhs; \
+ b /= rhs; \
+ c /= rhs; \
+ d /= rhs; \
+ \
+ return(*this); \
+ }
+
+#if defined(__GNUC__) && (__GNUC__ < 3)
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
+ octonion<type> & operator /= (::std::complex<type> const & rhs) \
+ { \
+ using ::std::valarray; \
+ \
+ valarray<type> tr(2); \
+ \
+ tr[0] = rhs.real(); \
+ tr[1] = rhs.imag(); \
+ \
+ type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]-b*tr[1]; \
+ tt[1] = -a*tr[1]+b*tr[0]; \
+ tt[2] = +c*tr[0]-d*tr[1]; \
+ tt[3] = +c*tr[1]+d*tr[0]; \
+ tt[4] = +e*tr[0]-f*tr[1]; \
+ tt[5] = +e*tr[1]+f*tr[0]; \
+ tt[6] = +g*tr[0]+h*tr[1]; \
+ tt[7] = +g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
+ octonion<type> & operator /= (::std::complex<type> const & rhs) \
+ { \
+ using ::std::valarray; \
+ using ::std::abs; \
+ \
+ valarray<type> tr(2); \
+ \
+ tr[0] = rhs.real(); \
+ tr[1] = rhs.imag(); \
+ \
+ type mixam = static_cast<type>(1)/(abs(tr).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]-b*tr[1]; \
+ tt[1] = -a*tr[1]+b*tr[0]; \
+ tt[2] = +c*tr[0]-d*tr[1]; \
+ tt[3] = +c*tr[1]+d*tr[0]; \
+ tt[4] = +e*tr[0]-f*tr[1]; \
+ tt[5] = +e*tr[1]+f*tr[0]; \
+ tt[6] = +g*tr[0]+h*tr[1]; \
+ tt[7] = +g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#else
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
+ octonion<type> & operator /= (::std::complex<type> const & rhs) \
+ { \
+ using ::std::valarray; \
+ \
+ valarray<type> tr(2); \
+ \
+ tr[0] = rhs.real(); \
+ tr[1] = rhs.imag(); \
+ \
+ type mixam = static_cast<type>(1)/(abs(tr).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]-b*tr[1]; \
+ tt[1] = -a*tr[1]+b*tr[0]; \
+ tt[2] = +c*tr[0]-d*tr[1]; \
+ tt[3] = +c*tr[1]+d*tr[0]; \
+ tt[4] = +e*tr[0]-f*tr[1]; \
+ tt[5] = +e*tr[1]+f*tr[0]; \
+ tt[6] = +g*tr[0]+h*tr[1]; \
+ tt[7] = +g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+#if defined(__GNUC__) && (__GNUC__ < 3)
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
+ octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
+ { \
+ using ::std::valarray; \
+ \
+ valarray<type> tr(4); \
+ \
+ tr[0] = static_cast<type>(rhs.R_component_1()); \
+ tr[1] = static_cast<type>(rhs.R_component_2()); \
+ tr[2] = static_cast<type>(rhs.R_component_3()); \
+ tr[3] = static_cast<type>(rhs.R_component_4()); \
+ \
+ type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
+ tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
+ tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
+ tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
+ tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
+ tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
+ tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
+ tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
+ octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
+ { \
+ using ::std::valarray; \
+ using ::std::abs; \
+ \
+ valarray<type> tr(4); \
+ \
+ tr[0] = static_cast<type>(rhs.R_component_1()); \
+ tr[1] = static_cast<type>(rhs.R_component_2()); \
+ tr[2] = static_cast<type>(rhs.R_component_3()); \
+ tr[3] = static_cast<type>(rhs.R_component_4()); \
+ \
+ type mixam = static_cast<type>(1)/(abs(tr).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
+ tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
+ tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
+ tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
+ tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
+ tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
+ tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
+ tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#else
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
+ octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
+ { \
+ using ::std::valarray; \
+ \
+ valarray<type> tr(4); \
+ \
+ tr[0] = static_cast<type>(rhs.R_component_1()); \
+ tr[1] = static_cast<type>(rhs.R_component_2()); \
+ tr[2] = static_cast<type>(rhs.R_component_3()); \
+ tr[3] = static_cast<type>(rhs.R_component_4()); \
+ \
+ type mixam = static_cast<type>(1)/(abs(tr).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
+ tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
+ tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
+ tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
+ tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
+ tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
+ tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
+ tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+#if defined(__GNUC__) && (__GNUC__ < 3)
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
+ template<typename X> \
+ octonion<type> & operator /= (octonion<X> const & rhs) \
+ { \
+ using ::std::valarray; \
+ \
+ valarray<type> tr(8); \
+ \
+ tr[0] = static_cast<type>(rhs.R_component_1()); \
+ tr[1] = static_cast<type>(rhs.R_component_2()); \
+ tr[2] = static_cast<type>(rhs.R_component_3()); \
+ tr[3] = static_cast<type>(rhs.R_component_4()); \
+ tr[4] = static_cast<type>(rhs.R_component_5()); \
+ tr[5] = static_cast<type>(rhs.R_component_6()); \
+ tr[6] = static_cast<type>(rhs.R_component_7()); \
+ tr[7] = static_cast<type>(rhs.R_component_8()); \
+ \
+ type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
+ tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
+ tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
+ tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
+ tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
+ tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
+ tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
+ tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
+ template<typename X> \
+ octonion<type> & operator /= (octonion<X> const & rhs) \
+ { \
+ using ::std::valarray; \
+ using ::std::abs; \
+ \
+ valarray<type> tr(8); \
+ \
+ tr[0] = static_cast<type>(rhs.R_component_1()); \
+ tr[1] = static_cast<type>(rhs.R_component_2()); \
+ tr[2] = static_cast<type>(rhs.R_component_3()); \
+ tr[3] = static_cast<type>(rhs.R_component_4()); \
+ tr[4] = static_cast<type>(rhs.R_component_5()); \
+ tr[5] = static_cast<type>(rhs.R_component_6()); \
+ tr[6] = static_cast<type>(rhs.R_component_7()); \
+ tr[7] = static_cast<type>(rhs.R_component_8()); \
+ \
+ type mixam = static_cast<type>(1)/(abs(tr).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
+ tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
+ tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
+ tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
+ tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
+ tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
+ tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
+ tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#else
+ #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
+ template<typename X> \
+ octonion<type> & operator /= (octonion<X> const & rhs) \
+ { \
+ using ::std::valarray; \
+ \
+ valarray<type> tr(8); \
+ \
+ tr[0] = static_cast<type>(rhs.R_component_1()); \
+ tr[1] = static_cast<type>(rhs.R_component_2()); \
+ tr[2] = static_cast<type>(rhs.R_component_3()); \
+ tr[3] = static_cast<type>(rhs.R_component_4()); \
+ tr[4] = static_cast<type>(rhs.R_component_5()); \
+ tr[5] = static_cast<type>(rhs.R_component_6()); \
+ tr[6] = static_cast<type>(rhs.R_component_7()); \
+ tr[7] = static_cast<type>(rhs.R_component_8()); \
+ \
+ type mixam = static_cast<type>(1)/(abs(tr).max)(); \
+ \
+ tr *= mixam; \
+ \
+ valarray<type> tt(8); \
+ \
+ tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
+ tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
+ tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
+ tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
+ tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
+ tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
+ tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
+ tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
+ \
+ tr *= tr; \
+ \
+ tt *= (mixam/tr.sum()); \
+ \
+ a = tt[0]; \
+ b = tt[1]; \
+ c = tt[2]; \
+ d = tt[3]; \
+ e = tt[4]; \
+ f = tt[5]; \
+ g = tt[6]; \
+ h = tt[7]; \
+ \
+ return(*this); \
+ }
+#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+
+#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
+ BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
+ BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
+ BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
+
+#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
+ BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
+ BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
+ BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
+
+#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
+ BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
+ BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
+ BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
+
+#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
+ BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
+ BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
+ BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
+
+#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
+ BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
+
+
+ template<>
+ class octonion<float>
+ {
+ public:
+
+ typedef float value_type;
+
+ BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
+
+ // UNtemplated copy constructor
+ // (this is taken care of by the compiler itself)
+
+ // explicit copy constructors (precision-loosing converters)
+
+ explicit octonion(octonion<double> const & a_recopier)
+ {
+ *this = detail::octonion_type_converter<float, double>(a_recopier);
+ }
+
+ explicit octonion(octonion<long double> const & a_recopier)
+ {
+ *this = detail::octonion_type_converter<float, long double>(a_recopier);
+ }
+
+ // destructor
+ // (this is taken care of by the compiler itself)
+
+ // accessors
+ //
+ // Note: Like complex number, octonions do have a meaningful notion of "real part",
+ // but unlike them there is no meaningful notion of "imaginary part".
+ // Instead there is an "unreal part" which itself is an octonion, and usually
+ // nothing simpler (as opposed to the complex number case).
+ // However, for practicallity, there are accessors for the other components
+ // (these are necessary for the templated copy constructor, for instance).
+
+ BOOST_OCTONION_ACCESSOR_GENERATOR(float)
+
+ // assignment operators
+
+ BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
+
+ // other assignment-related operators
+ //
+ // NOTE: Octonion multiplication is *NOT* commutative;
+ // symbolically, "q *= rhs;" means "q = q * rhs;"
+ // and "q /= rhs;" means "q = q * inverse_of(rhs);";
+ // octonion multiplication is also *NOT* associative
+
+ BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
+
+
+ protected:
+
+ BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
+
+
+ private:
+
+ };
+
+
+ template<>
+ class octonion<double>
+ {
+ public:
+
+ typedef double value_type;
+
+ BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
+
+ // UNtemplated copy constructor
+ // (this is taken care of by the compiler itself)
+
+ // converting copy constructor
+
+ explicit octonion(octonion<float> const & a_recopier)
+ {
+ *this = detail::octonion_type_converter<double, float>(a_recopier);
+ }
+
+ // explicit copy constructors (precision-loosing converters)
+
+ explicit octonion(octonion<long double> const & a_recopier)
+ {
+ *this = detail::octonion_type_converter<double, long double>(a_recopier);
+ }
+
+ // destructor
+ // (this is taken care of by the compiler itself)
+
+ // accessors
+ //
+ // Note: Like complex number, octonions do have a meaningful notion of "real part",
+ // but unlike them there is no meaningful notion of "imaginary part".
+ // Instead there is an "unreal part" which itself is an octonion, and usually
+ // nothing simpler (as opposed to the complex number case).
+ // However, for practicallity, there are accessors for the other components
+ // (these are necessary for the templated copy constructor, for instance).
+
+ BOOST_OCTONION_ACCESSOR_GENERATOR(double)
+
+ // assignment operators
+
+ BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
+
+ // other assignment-related operators
+ //
+ // NOTE: Octonion multiplication is *NOT* commutative;
+ // symbolically, "q *= rhs;" means "q = q * rhs;"
+ // and "q /= rhs;" means "q = q * inverse_of(rhs);";
+ // octonion multiplication is also *NOT* associative
+
+ BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
+
+
+ protected:
+
+ BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
+
+
+ private:
+
+ };
+
+
+ template<>
+ class octonion<long double>
+ {
+ public:
+
+ typedef long double value_type;
+
+ BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
+
+ // UNtemplated copy constructor
+ // (this is taken care of by the compiler itself)
+
+ // converting copy constructor
+
+ explicit octonion(octonion<float> const & a_recopier)
+ {
+ *this = detail::octonion_type_converter<long double, float>(a_recopier);
+ }
+
+
+ explicit octonion(octonion<double> const & a_recopier)
+ {
+ *this = detail::octonion_type_converter<long double, double>(a_recopier);
+ }
+
+
+ // destructor
+ // (this is taken care of by the compiler itself)
+
+ // accessors
+ //
+ // Note: Like complex number, octonions do have a meaningful notion of "real part",
+ // but unlike them there is no meaningful notion of "imaginary part".
+ // Instead there is an "unreal part" which itself is an octonion, and usually
+ // nothing simpler (as opposed to the complex number case).
+ // However, for practicallity, there are accessors for the other components
+ // (these are necessary for the templated copy constructor, for instance).
+
+ BOOST_OCTONION_ACCESSOR_GENERATOR(long double)
+
+ // assignment operators
+
+ BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
+
+ // other assignment-related operators
+ //
+ // NOTE: Octonion multiplication is *NOT* commutative;
+ // symbolically, "q *= rhs;" means "q = q * rhs;"
+ // and "q /= rhs;" means "q = q * inverse_of(rhs);";
+ // octonion multiplication is also *NOT* associative
+
+ BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
+
+
+ protected:
+
+ BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
+
+
+ private:
+
+ };
+
+
+#undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
+
+#undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
+
+#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
+#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
+#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
+#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
+
+#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
+#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
+#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
+#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
+#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
+#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
+#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
+#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
+#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
+#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
+#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
+#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
+#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
+#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
+#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
+#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
+
+
+#undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
+
+#undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
+
+#undef BOOST_OCTONION_ACCESSOR_GENERATOR
+
+
+ // operators
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
+ { \
+ octonion<T> res(lhs); \
+ res op##= rhs; \
+ return(res); \
+ }
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
+ template<typename T> \
+ inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
+ template<typename T> \
+ inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
+ template<typename T> \
+ inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
+ template<typename T> \
+ inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
+ template<typename T> \
+ inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
+ template<typename T> \
+ inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
+ template<typename T> \
+ inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
+
+#define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
+ BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
+
+
+ BOOST_OCTONION_OPERATOR_GENERATOR(+)
+ BOOST_OCTONION_OPERATOR_GENERATOR(-)
+ BOOST_OCTONION_OPERATOR_GENERATOR(*)
+ BOOST_OCTONION_OPERATOR_GENERATOR(/)
+
+
+#undef BOOST_OCTONION_OPERATOR_GENERATOR
+
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_4
+
+#undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
+
+
+ template<typename T>
+ inline octonion<T> operator + (octonion<T> const & o)
+ {
+ return(o);
+ }
+
+
+ template<typename T>
+ inline octonion<T> operator - (octonion<T> const & o)
+ {
+ return(octonion<T>(-o.R_component_1(),-o.R_component_2(),-o.R_component_3(),-o.R_component_4(),-o.R_component_5(),-o.R_component_6(),-o.R_component_7(),-o.R_component_8()));
+ }
+
+
+ template<typename T>
+ inline bool operator == (T const & lhs, octonion<T> const & rhs)
+ {
+ return(
+ (rhs.R_component_1() == lhs)&&
+ (rhs.R_component_2() == static_cast<T>(0))&&
+ (rhs.R_component_3() == static_cast<T>(0))&&
+ (rhs.R_component_4() == static_cast<T>(0))&&
+ (rhs.R_component_5() == static_cast<T>(0))&&
+ (rhs.R_component_6() == static_cast<T>(0))&&
+ (rhs.R_component_7() == static_cast<T>(0))&&
+ (rhs.R_component_8() == static_cast<T>(0))
+ );
+ }
+
+
+ template<typename T>
+ inline bool operator == (octonion<T> const & lhs, T const & rhs)
+ {
+ return(
+ (lhs.R_component_1() == rhs)&&
+ (lhs.R_component_2() == static_cast<T>(0))&&
+ (lhs.R_component_3() == static_cast<T>(0))&&
+ (lhs.R_component_4() == static_cast<T>(0))&&
+ (lhs.R_component_5() == static_cast<T>(0))&&
+ (lhs.R_component_6() == static_cast<T>(0))&&
+ (lhs.R_component_7() == static_cast<T>(0))&&
+ (lhs.R_component_8() == static_cast<T>(0))
+ );
+ }
+
+
+ template<typename T>
+ inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
+ {
+ return(
+ (rhs.R_component_1() == lhs.real())&&
+ (rhs.R_component_2() == lhs.imag())&&
+ (rhs.R_component_3() == static_cast<T>(0))&&
+ (rhs.R_component_4() == static_cast<T>(0))&&
+ (rhs.R_component_5() == static_cast<T>(0))&&
+ (rhs.R_component_6() == static_cast<T>(0))&&
+ (rhs.R_component_7() == static_cast<T>(0))&&
+ (rhs.R_component_8() == static_cast<T>(0))
+ );
+ }
+
+
+ template<typename T>
+ inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
+ {
+ return(
+ (lhs.R_component_1() == rhs.real())&&
+ (lhs.R_component_2() == rhs.imag())&&
+ (lhs.R_component_3() == static_cast<T>(0))&&
+ (lhs.R_component_4() == static_cast<T>(0))&&
+ (lhs.R_component_5() == static_cast<T>(0))&&
+ (lhs.R_component_6() == static_cast<T>(0))&&
+ (lhs.R_component_7() == static_cast<T>(0))&&
+ (lhs.R_component_8() == static_cast<T>(0))
+ );
+ }
+
+
+ template<typename T>
+ inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
+ {
+ return(
+ (rhs.R_component_1() == lhs.R_component_1())&&
+ (rhs.R_component_2() == lhs.R_component_2())&&
+ (rhs.R_component_3() == lhs.R_component_3())&&
+ (rhs.R_component_4() == lhs.R_component_4())&&
+ (rhs.R_component_5() == static_cast<T>(0))&&
+ (rhs.R_component_6() == static_cast<T>(0))&&
+ (rhs.R_component_7() == static_cast<T>(0))&&
+ (rhs.R_component_8() == static_cast<T>(0))
+ );
+ }
+
+
+ template<typename T>
+ inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
+ {
+ return(
+ (lhs.R_component_1() == rhs.R_component_1())&&
+ (lhs.R_component_2() == rhs.R_component_2())&&
+ (lhs.R_component_3() == rhs.R_component_3())&&
+ (lhs.R_component_4() == rhs.R_component_4())&&
+ (lhs.R_component_5() == static_cast<T>(0))&&
+ (lhs.R_component_6() == static_cast<T>(0))&&
+ (lhs.R_component_7() == static_cast<T>(0))&&
+ (lhs.R_component_8() == static_cast<T>(0))
+ );
+ }
+
+
+ template<typename T>
+ inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
+ {
+ return(
+ (rhs.R_component_1() == lhs.R_component_1())&&
+ (rhs.R_component_2() == lhs.R_component_2())&&
+ (rhs.R_component_3() == lhs.R_component_3())&&
+ (rhs.R_component_4() == lhs.R_component_4())&&
+ (rhs.R_component_5() == lhs.R_component_5())&&
+ (rhs.R_component_6() == lhs.R_component_6())&&
+ (rhs.R_component_7() == lhs.R_component_7())&&
+ (rhs.R_component_8() == lhs.R_component_8())
+ );
+ }
+
+
+#define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
+ { \
+ return(!(lhs == rhs)); \
+ }
+
+ template<typename T>
+ inline bool operator != (T const & lhs, octonion<T> const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ template<typename T>
+ inline bool operator != (octonion<T> const & lhs, T const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ template<typename T>
+ inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ template<typename T>
+ inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ template<typename T>
+ inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ template<typename T>
+ inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ template<typename T>
+ inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
+ BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+ #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
+
+
+ // Note: the default values in the constructors of the complex and quaternions make for
+ // a very complex and ambiguous situation; we have made choices to disambiguate.
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ template<typename T>
+ ::std::istream & operator >> ( ::std::istream & is,
+ octonion<T>& o)
+#else
+ template<typename T, typename charT, class traits>
+ ::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
+ octonion<T> & o)
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ typedef char charT;
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+#ifdef BOOST_NO_STD_LOCALE
+#else
+ const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ T a = T();
+ T b = T();
+ T c = T();
+ T d = T();
+ T e = T();
+ T f = T();
+ T g = T();
+ T h = T();
+
+ ::std::complex<T> u = ::std::complex<T>();
+ ::std::complex<T> v = ::std::complex<T>();
+ ::std::complex<T> x = ::std::complex<T>();
+ ::std::complex<T> y = ::std::complex<T>();
+
+ ::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
+ ::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
+
+ charT ch = charT();
+ char cc;
+
+ is >> ch; // get the first lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "("
+ {
+ is >> ch; // get the second lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "(("
+ {
+ is >> ch; // get the third lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((("
+ {
+ is.putback(ch);
+
+ is >> u; // read "((u"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((u)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // format: (((a))), (((a,b)))
+ {
+ o = octonion<T>(u);
+ }
+ else if (cc == ',') // read "((u),"
+ {
+ p = ::boost::math::quaternion<T>(u);
+
+ is >> q; // read "((u),q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // format: (((a)),q), (((a,b)),q)
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc ==',') // read "((u,"
+ {
+ is >> v; // read "((u,v"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((u,v)"
+ {
+ p = ::boost::math::quaternion<T>(u,v);
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // format: (((a),v)), (((a,b),v))
+ {
+ o = octonion<T>(p);
+ }
+ else if (cc == ',') // read "((u,v),"
+ {
+ is >> q; // read "(p,q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "((a"
+ {
+ is.putback(ch);
+
+ is >> a; // we extract the first component
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a))"
+ {
+ o = octonion<T>(a);
+ }
+ else if (cc == ',') // read "((a),"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a),("
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a),(("
+ {
+ is.putback(ch);
+
+ is.putback(ch); // we backtrack twice, with the same value!
+
+ is >> q; // read "((a),q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),q)"
+ {
+ p = ::boost::math::quaternion<T>(a);
+
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "((a),(c" or "((a),(e"
+ {
+ is.putback(ch);
+
+ is >> c;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c)" (ambiguity resolution)
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c))"
+ {
+ o = octonion<T>(a,b,c);
+ }
+ else if (cc == ',') // read "((a),(c),"
+ {
+ u = ::std::complex<T>(a);
+
+ v = ::std::complex<T>(c);
+
+ is >> x; // read "((a),(c),x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c),x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "((a),(c),x,"
+ {
+ is >> y; // read "((a),(c),x,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c),x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a),(c," or "((a),(e,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
+ {
+ p = ::boost::math::quaternion<T>(a);
+
+ x = ::std::complex<T>(c); // "c" was actually "e"
+
+ is.putback(ch); // we can only backtrace once
+
+ is >> y; // read "((a),(e,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(e,y)"
+ {
+ q = ::boost::math::quaternion<T>(x,y);
+
+ is >> ch; // get the next lexeme
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(e,y))"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "((a),(c,d" or "((a),(e,f"
+ {
+ is.putback(ch);
+
+ is >> d;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c,d))"
+ {
+ o = octonion<T>(a,b,c,d);
+ }
+ else if (cc == ',') // read "((a),(c,d),"
+ {
+ u = ::std::complex<T>(a);
+
+ v = ::std::complex<T>(c,d);
+
+ is >> x; // read "((a),(c,d),x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c,d),x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "((a),(c,d),x,"
+ {
+ is >> y; // read "((a),(c,d),x,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(c,d),x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
+ {
+ p = ::boost::math::quaternion<T>(a);
+
+ is >> g; // read "((a),(e,f,g" (too late to backtrack)
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(e,f,g)"
+ {
+ q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(e,f,g))"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a),(e,f,g,"
+ {
+ is >> h; // read "((a),(e,f,g,h"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(e,f,g,h)"
+ {
+ q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),(e,f,g,h))"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // read "((a),c" (ambiguity resolution)
+ {
+ is.putback(ch);
+
+ is >> c; // we extract the third component
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),c)"
+ {
+ o = octonion<T>(a,b,c);
+ }
+ else if (cc == ',') // read "((a),c,"
+ {
+ is >> x; // read "((a),c,x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),c,x)"
+ {
+ o = octonion<T>(a,b,c,d,x.real(),x.imag());
+ }
+ else if (cc == ',') // read "((a),c,x,"
+ {
+ is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a),c,x,y)"
+ {
+ o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc ==',') // read "((a,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a,("
+ {
+ u = ::std::complex<T>(a);
+
+ is.putback(ch); // can only backtrack so much
+
+ is >> v; // read "((a,v"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,v)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,v))"
+ {
+ o = octonion<T>(u,v);
+ }
+ else if (cc == ',') // read "((a,v),"
+ {
+ p = ::boost::math::quaternion<T>(u,v);
+
+ is >> q; // read "((a,v),q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,v),q)"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else
+ {
+ is.putback(ch);
+
+ is >> b; // read "((a,b"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b))"
+ {
+ o = octonion<T>(a,b);
+ }
+ else if (cc == ',') // read "((a,b),"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a,b),("
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a,b),(("
+ {
+ p = ::boost::math::quaternion<T>(a,b);
+
+ is.putback(ch);
+
+ is.putback(ch); // we backtrack twice, with the same value
+
+ is >> q; // read "((a,b),q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),q)"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "((a,b),(c" or "((a,b),(e"
+ {
+ is.putback(ch);
+
+ is >> c;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c))"
+ {
+ o = octonion<T>(a,b,c);
+ }
+ else if (cc == ',') // read "((a,b),(c),"
+ {
+ u = ::std::complex<T>(a,b);
+
+ v = ::std::complex<T>(c);
+
+ is >> x; // read "((a,b),(c),x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c),x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "((a,b),(c),x,"
+ {
+ is >> y; // read "((a,b),(c),x,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c),x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
+ {
+ u = ::std::complex<T>(a,b);
+
+ x = ::std::complex<T>(c); // "c" is actually "e"
+
+ is.putback(ch);
+
+ is >> y; // read "((a,b),(e,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(e,y)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(e,y))"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "((a,b),(c,d" or "((a,b),(e,f"
+ {
+ is.putback(ch);
+
+ is >> d;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
+ {
+ u = ::std::complex<T>(a,b);
+
+ v = ::std::complex<T>(c,d);
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c,d))"
+ {
+ o = octonion<T>(u,v);
+ }
+ else if (cc == ',') // read "((a,b),(c,d),"
+ {
+ is >> x; // read "((a,b),(c,d),x
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c,d),x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "((a,b),(c,d),x,"
+ {
+ is >> y; // read "((a,b),(c,d),x,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(c,d),x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
+ {
+ p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
+
+ is >> g; // read "((a,b),(e,f,g"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(e,f,g)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(e,f,g))"
+ {
+ q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
+
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a,b),(e,f,g,"
+ {
+ is >> h; // read "((a,b),(e,f,g,h"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b),(e,f,g,h)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read ((a,b),(e,f,g,h))"
+ {
+ q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
+
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a,b,"
+ {
+ is >> c; // read "((a,b,c"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b,c)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b,c))"
+ {
+ o = octonion<T>(a,b,c);
+ }
+ else if (cc == ',') // read "((a,b,c),"
+ {
+ p = ::boost::math::quaternion<T>(a,b,c);
+
+ is >> q; // read "((a,b,c),q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b,c),q)"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "((a,b,c,"
+ {
+ is >> d; // read "((a,b,c,d"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b,c,d)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b,c,d))"
+ {
+ o = octonion<T>(a,b,c,d);
+ }
+ else if (cc == ',') // read "((a,b,c,d),"
+ {
+ p = ::boost::math::quaternion<T>(a,b,c,d);
+
+ is >> q; // read "((a,b,c,d),q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "((a,b,c,d),q)"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // read "(a"
+ {
+ is.putback(ch);
+
+ is >> a; // we extract the first component
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a)"
+ {
+ o = octonion<T>(a);
+ }
+ else if (cc == ',') // read "(a,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "(a,("
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "(a,(("
+ {
+ p = ::boost::math::quaternion<T>(a);
+
+ is.putback(ch);
+
+ is.putback(ch); // we backtrack twice, with the same value
+
+ is >> q; // read "(a,q"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,q)"
+ {
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "(a,(c" or "(a,(e"
+ {
+ is.putback(ch);
+
+ is >> c;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c)" (ambiguity resolution)
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c))"
+ {
+ o = octonion<T>(a,b,c);
+ }
+ else if (cc == ',') // read "(a,(c),"
+ {
+ u = ::std::complex<T>(a);
+
+ v = ::std::complex<T>(c);
+
+ is >> x; // read "(a,(c),x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c),x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "(a,(c),x,"
+ {
+ is >> y; // read "(a,(c),x,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c),x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "(a,(c," or "(a,(e,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
+ {
+ u = ::std::complex<T>(a);
+
+ x = ::std::complex<T>(c); // "c" is actually "e"
+
+ is.putback(ch); // we backtrack
+
+ is >> y; // read "(a,(e,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(e,y)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(e,y))"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "(a,(c,d" or "(a,(e,f"
+ {
+ is.putback(ch);
+
+ is >> d;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c,d))"
+ {
+ o = octonion<T>(a,b,c,d);
+ }
+ else if (cc == ',') // read "(a,(c,d),"
+ {
+ u = ::std::complex<T>(a);
+
+ v = ::std::complex<T>(c,d);
+
+ is >> x; // read "(a,(c,d),x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c,d),x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "(a,(c,d),x,"
+ {
+ is >> y; // read "(a,(c,d),x,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(c,d),x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
+ {
+ p = ::boost::math::quaternion<T>(a);
+
+ is >> g; // read "(a,(e,f,g"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(e,f,g)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(e,f,g))"
+ {
+ q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
+
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else if (cc == ',') // read "(a,(e,f,g,"
+ {
+ is >> h; // read "(a,(e,f,g,h"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(e,f,g,h)"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,(e,f,g,h))"
+ {
+ q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
+
+ o = octonion<T>(p,q);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // read "(a,b" or "(a,c" (ambiguity resolution)
+ {
+ is.putback(ch);
+
+ is >> b;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b)" (ambiguity resolution)
+ {
+ o = octonion<T>(a,b);
+ }
+ else if (cc == ',') // read "(a,b," or "(a,c,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "(a,c,(" (ambiguity resolution)
+ {
+ u = ::std::complex<T>(a);
+
+ v = ::std::complex<T>(b); // "b" is actually "c"
+
+ is.putback(ch); // we backtrack
+
+ is >> x; // read "(a,c,x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,c,x)"
+ {
+ o = octonion<T>(u,v,x);
+ }
+ else if (cc == ',') // read "(a,c,x,"
+ {
+ is >> y; // read "(a,c,x,y" // read "(a,c,x"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,c,x,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "(a,b,c" or "(a,c,e"
+ {
+ is.putback(ch);
+
+ is >> c;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
+ {
+ o = octonion<T>(a,b,c);
+ }
+ else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
+ {
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
+ {
+ u = ::std::complex<T>(a);
+
+ v = ::std::complex<T>(b); // "b" is actually "c"
+
+ x = ::std::complex<T>(c); // "c" is actually "e"
+
+ is.putback(ch); // we backtrack
+
+ is >> y; // read "(a,c,e,y"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,c,e,y)"
+ {
+ o = octonion<T>(u,v,x,y);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // read "(a,b,c,d" (ambiguity resolution)
+ {
+ is.putback(ch); // we backtrack
+
+ is >> d;
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b,c,d)"
+ {
+ o = octonion<T>(a,b,c,d);
+ }
+ else if (cc == ',') // read "(a,b,c,d,"
+ {
+ is >> e; // read "(a,b,c,d,e"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b,c,d,e)"
+ {
+ o = octonion<T>(a,b,c,d,e);
+ }
+ else if (cc == ',') // read "(a,b,c,d,e,"
+ {
+ is >> f; // read "(a,b,c,d,e,f"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b,c,d,e,f)"
+ {
+ o = octonion<T>(a,b,c,d,e,f);
+ }
+ else if (cc == ',') // read "(a,b,c,d,e,f,"
+ {
+ is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b,c,d,e,f,g)"
+ {
+ o = octonion<T>(a,b,c,d,e,f,g);
+ }
+ else if (cc == ',') // read "(a,b,c,d,e,f,g,"
+ {
+ is >> h; // read "(a,b,c,d,e,f,g,h" // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
+
+ if (!is.good()) goto finish;
+
+ is >> ch; // get the next lexeme
+
+ if (!is.good()) goto finish;
+
+#ifdef BOOST_NO_STD_LOCALE
+ cc = ch;
+#else
+ cc = ct.narrow(ch, char());
+#endif /* BOOST_NO_STD_LOCALE */
+
+ if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
+ {
+ o = octonion<T>(a,b,c,d,e,f,g,h);
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // error
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ is.setstate(::std::ios::failbit);
+#else
+ is.setstate(::std::ios_base::failbit);
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+ }
+ }
+ else // format: a
+ {
+ is.putback(ch);
+
+ is >> a; // we extract the first component
+
+ if (!is.good()) goto finish;
+
+ o = octonion<T>(a);
+ }
+
+ finish:
+ return(is);
+ }
+
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ template<typename T>
+ ::std::ostream & operator << ( ::std::ostream & os,
+ octonion<T> const & o)
+#else
+ template<typename T, typename charT, class traits>
+ ::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
+ octonion<T> const & o)
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ {
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ ::std::ostringstream s;
+#else
+ ::std::basic_ostringstream<charT,traits> s;
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+ s.flags(os.flags());
+#ifdef BOOST_NO_STD_LOCALE
+#else
+ s.imbue(os.getloc());
+#endif /* BOOST_NO_STD_LOCALE */
+ s.precision(os.precision());
+
+ s << '(' << o.R_component_1() << ','
+ << o.R_component_2() << ','
+ << o.R_component_3() << ','
+ << o.R_component_4() << ','
+ << o.R_component_5() << ','
+ << o.R_component_6() << ','
+ << o.R_component_7() << ','
+ << o.R_component_8() << ')';
+
+ return os << s.str();
+ }
+
+
+ // values
+
+ template<typename T>
+ inline T real(octonion<T> const & o)
+ {
+ return(o.real());
+ }
+
+
+ template<typename T>
+ inline octonion<T> unreal(octonion<T> const & o)
+ {
+ return(o.unreal());
+ }
+
+
+#define BOOST_OCTONION_VALARRAY_LOADER \
+ using ::std::valarray; \
+ \
+ valarray<T> temp(8); \
+ \
+ temp[0] = o.R_component_1(); \
+ temp[1] = o.R_component_2(); \
+ temp[2] = o.R_component_3(); \
+ temp[3] = o.R_component_4(); \
+ temp[4] = o.R_component_5(); \
+ temp[5] = o.R_component_6(); \
+ temp[6] = o.R_component_7(); \
+ temp[7] = o.R_component_8();
+
+
+ template<typename T>
+ inline T sup(octonion<T> const & o)
+ {
+#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
+ using ::std::abs;
+#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+ BOOST_OCTONION_VALARRAY_LOADER
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ return((BOOST_GET_VALARRAY(T, abs(temp)).max)());
+#else
+ return((abs(temp).max)());
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+
+
+ template<typename T>
+ inline T l1(octonion<T> const & o)
+ {
+#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
+ using ::std::abs;
+#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+ BOOST_OCTONION_VALARRAY_LOADER
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ return(BOOST_GET_VALARRAY(T, abs(temp)).sum());
+#else
+ return(abs(temp).sum());
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ }
+
+
+ template<typename T>
+ inline T abs(const octonion<T> & o)
+ {
+#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
+ using ::std::abs;
+#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+ using ::std::sqrt;
+
+ BOOST_OCTONION_VALARRAY_LOADER
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ T maxim = (BOOST_GET_VALARRAY(T,abs(temp)).max)(); // overflow protection
+#else
+ T maxim = (abs(temp).max)(); // overflow protection
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+ if (maxim == static_cast<T>(0))
+ {
+ return(maxim);
+ }
+ else
+ {
+ T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
+
+ temp *= mixam;
+
+ temp *= temp;
+
+ return(maxim*sqrt(temp.sum()));
+ }
+
+ //return(::std::sqrt(norm(o)));
+ }
+
+
+#undef BOOST_OCTONION_VALARRAY_LOADER
+
+
+ // Note: This is the Cayley norm, not the Euclidian norm...
+
+ template<typename T>
+ inline T norm(octonion<T> const & o)
+ {
+ return(real(o*conj(o)));
+ }
+
+
+ template<typename T>
+ inline octonion<T> conj(octonion<T> const & o)
+ {
+ return(octonion<T>( +o.R_component_1(),
+ -o.R_component_2(),
+ -o.R_component_3(),
+ -o.R_component_4(),
+ -o.R_component_5(),
+ -o.R_component_6(),
+ -o.R_component_7(),
+ -o.R_component_8()));
+ }
+
+
+ // Note: There is little point, for the octonions, to introduce the equivalents
+ // to the complex "arg" and the quaternionic "cylindropolar".
+
+
+ template<typename T>
+ inline octonion<T> spherical(T const & rho,
+ T const & theta,
+ T const & phi1,
+ T const & phi2,
+ T const & phi3,
+ T const & phi4,
+ T const & phi5,
+ T const & phi6)
+ {
+ using ::std::cos;
+ using ::std::sin;
+
+ //T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
+ //T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
+ //T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
+ //T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
+ //T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
+ //T f = sin(phi4)*cos(phi5)*cos(phi6);
+ //T g = sin(phi5)*cos(phi6);
+ //T h = sin(phi6);
+
+ T courrant = static_cast<T>(1);
+
+ T h = sin(phi6);
+
+ courrant *= cos(phi6);
+
+ T g = sin(phi5)*courrant;
+
+ courrant *= cos(phi5);
+
+ T f = sin(phi4)*courrant;
+
+ courrant *= cos(phi4);
+
+ T e = sin(phi3)*courrant;
+
+ courrant *= cos(phi3);
+
+ T d = sin(phi2)*courrant;
+
+ courrant *= cos(phi2);
+
+ T c = sin(phi1)*courrant;
+
+ courrant *= cos(phi1);
+
+ T b = sin(theta)*courrant;
+ T a = cos(theta)*courrant;
+
+ return(rho*octonion<T>(a,b,c,d,e,f,g,h));
+ }
+
+
+ template<typename T>
+ inline octonion<T> multipolar(T const & rho1,
+ T const & theta1,
+ T const & rho2,
+ T const & theta2,
+ T const & rho3,
+ T const & theta3,
+ T const & rho4,
+ T const & theta4)
+ {
+ using ::std::cos;
+ using ::std::sin;
+
+ T a = rho1*cos(theta1);
+ T b = rho1*sin(theta1);
+ T c = rho2*cos(theta2);
+ T d = rho2*sin(theta2);
+ T e = rho3*cos(theta3);
+ T f = rho3*sin(theta3);
+ T g = rho4*cos(theta4);
+ T h = rho4*sin(theta4);
+
+ return(octonion<T>(a,b,c,d,e,f,g,h));
+ }
+
+
+ template<typename T>
+ inline octonion<T> cylindrical(T const & r,
+ T const & angle,
+ T const & h1,
+ T const & h2,
+ T const & h3,
+ T const & h4,
+ T const & h5,
+ T const & h6)
+ {
+ using ::std::cos;
+ using ::std::sin;
+
+ T a = r*cos(angle);
+ T b = r*sin(angle);
+
+ return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
+ }
+
+
+ template<typename T>
+ inline octonion<T> exp(octonion<T> const & o)
+ {
+ using ::std::exp;
+ using ::std::cos;
+
+ using ::boost::math::sinc_pi;
+
+ T u = exp(real(o));
+
+ T z = abs(unreal(o));
+
+ T w = sinc_pi(z);
+
+ return(u*octonion<T>(cos(z),
+ w*o.R_component_2(), w*o.R_component_3(),
+ w*o.R_component_4(), w*o.R_component_5(),
+ w*o.R_component_6(), w*o.R_component_7(),
+ w*o.R_component_8()));
+ }
+
+
+ template<typename T>
+ inline octonion<T> cos(octonion<T> const & o)
+ {
+ using ::std::sin;
+ using ::std::cos;
+ using ::std::cosh;
+
+ using ::boost::math::sinhc_pi;
+
+ T z = abs(unreal(o));
+
+ T w = -sin(o.real())*sinhc_pi(z);
+
+ return(octonion<T>(cos(o.real())*cosh(z),
+ w*o.R_component_2(), w*o.R_component_3(),
+ w*o.R_component_4(), w*o.R_component_5(),
+ w*o.R_component_6(), w*o.R_component_7(),
+ w*o.R_component_8()));
+ }
+
+
+ template<typename T>
+ inline octonion<T> sin(octonion<T> const & o)
+ {
+ using ::std::sin;
+ using ::std::cos;
+ using ::std::cosh;
+
+ using ::boost::math::sinhc_pi;
+
+ T z = abs(unreal(o));
+
+ T w = +cos(o.real())*sinhc_pi(z);
+
+ return(octonion<T>(sin(o.real())*cosh(z),
+ w*o.R_component_2(), w*o.R_component_3(),
+ w*o.R_component_4(), w*o.R_component_5(),
+ w*o.R_component_6(), w*o.R_component_7(),
+ w*o.R_component_8()));
+ }
+
+
+ template<typename T>
+ inline octonion<T> tan(octonion<T> const & o)
+ {
+ return(sin(o)/cos(o));
+ }
+
+
+ template<typename T>
+ inline octonion<T> cosh(octonion<T> const & o)
+ {
+ return((exp(+o)+exp(-o))/static_cast<T>(2));
+ }
+
+
+ template<typename T>
+ inline octonion<T> sinh(octonion<T> const & o)
+ {
+ return((exp(+o)-exp(-o))/static_cast<T>(2));
+ }
+
+
+ template<typename T>
+ inline octonion<T> tanh(octonion<T> const & o)
+ {
+ return(sinh(o)/cosh(o));
+ }
+
+
+ template<typename T>
+ octonion<T> pow(octonion<T> const & o,
+ int n)
+ {
+ if (n > 1)
+ {
+ int m = n>>1;
+
+ octonion<T> result = pow(o, m);
+
+ result *= result;
+
+ if (n != (m<<1))
+ {
+ result *= o; // n odd
+ }
+
+ return(result);
+ }
+ else if (n == 1)
+ {
+ return(o);
+ }
+ else if (n == 0)
+ {
+ return(octonion<T>(1));
+ }
+ else /* n < 0 */
+ {
+ return(pow(octonion<T>(1)/o,-n));
+ }
+ }
+
+
+ // helper templates for converting copy constructors (definition)
+
+ namespace detail
+ {
+
+ template< typename T,
+ typename U
+ >
+ octonion<T> octonion_type_converter(octonion<U> const & rhs)
+ {
+ return(octonion<T>( static_cast<T>(rhs.R_component_1()),
+ static_cast<T>(rhs.R_component_2()),
+ static_cast<T>(rhs.R_component_3()),
+ static_cast<T>(rhs.R_component_4()),
+ static_cast<T>(rhs.R_component_5()),
+ static_cast<T>(rhs.R_component_6()),
+ static_cast<T>(rhs.R_component_7()),
+ static_cast<T>(rhs.R_component_8())));
+ }
+ }
+ }
+}
+
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ #undef BOOST_GET_VALARRAY
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+
+#endif /* BOOST_OCTONION_HPP */