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