quaternion.hpp

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                return(*this);                                                       \
            }
    
#define    BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type)                      \
            template<typename X>                                              \
            quaternion<type> &        operator += (quaternion<X> const & rhs) \
            {                                                                 \
                a += static_cast<type>(rhs.R_component_1());                  \
                b += static_cast<type>(rhs.R_component_2());                  \
                c += static_cast<type>(rhs.R_component_3());                  \
                d += static_cast<type>(rhs.R_component_4());                  \
                                                                              \
                return(*this);                                                \
            }
    
#define    BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type)             \
            quaternion<type> &        operator -= (type const & rhs) \
            {                                                        \
                a -= rhs;                                            \
                                                                     \
                return(*this);                                       \
            }
    
#define    BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type)                             \
            quaternion<type> &        operator -= (::std::complex<type> const & rhs) \
            {                                                                        \
                a -= rhs.real();                                                     \
                b -= rhs.imag();                                                     \
                                                                                     \
                return(*this);                                                       \
            }
    
#define    BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type)                      \
            template<typename X>                                              \
            quaternion<type> &        operator -= (quaternion<X> const & rhs) \
            {                                                                 \
                a -= static_cast<type>(rhs.R_component_1());                  \
                b -= static_cast<type>(rhs.R_component_2());                  \
                c -= static_cast<type>(rhs.R_component_3());                  \
                d -= static_cast<type>(rhs.R_component_4());                  \
                                                                              \
                return(*this);                                                \
            }
    
#define    BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type)             \
            quaternion<type> &        operator *= (type const & rhs) \
            {                                                        \
                a *= rhs;                                            \
                b *= rhs;                                            \
                c *= rhs;                                            \
                d *= rhs;                                            \
                                                                     \
                return(*this);                                       \
            }
    
#define    BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type)                             \
            quaternion<type> &        operator *= (::std::complex<type> const & rhs) \
            {                                                                        \
                type    ar = rhs.real();                                             \
                type    br = rhs.imag();                                             \
                                                                                     \
                type    at = +a*ar-b*br;                                             \
                type    bt = +a*br+b*ar;                                             \
                type    ct = +c*ar+d*br;                                             \
                type    dt = -c*br+d*ar;                                             \
                                                                                     \
                a = at;                                                              \
                b = bt;                                                              \
                c = ct;                                                              \
                d = dt;                                                              \
                                                                                     \
                return(*this);                                                       \
            }
    
#define    BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type)                      \
            template<typename X>                                              \
            quaternion<type> &        operator *= (quaternion<X> const & rhs) \
            {                                                                 \
                type    ar = static_cast<type>(rhs.R_component_1());          \
                type    br = static_cast<type>(rhs.R_component_2());          \
                type    cr = static_cast<type>(rhs.R_component_3());          \
                type    dr = static_cast<type>(rhs.R_component_4());          \
                                                                              \
                type    at = +a*ar-b*br-c*cr-d*dr;                            \
                type    bt = +a*br+b*ar+c*dr-d*cr;                            \
                type    ct = +a*cr-b*dr+c*ar+d*br;                            \
                type    dt = +a*dr+b*cr-c*br+d*ar;                            \
                                                                              \
                a = at;                                                       \
                b = bt;                                                       \
                c = ct;                                                       \
                d = dt;                                                       \
                                                                              \
                return(*this);                                                \
            }
    
// There is quite a lot of repetition in the code below. This is intentional.
// The last conditional block is the normal form, and the others merely
// consist of workarounds for various compiler deficiencies. Hopefuly, when
// more compilers are conformant and we can retire support for those that are
// not, we will be able to remove the clutter. This is makes the situation
// (painfully) explicit.
    
#define    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type)             \
            quaternion<type> &        operator /= (type const & rhs) \
            {                                                        \
                a /= rhs;                                            \
                b /= rhs;                                            \
                c /= rhs;                                            \
                d /= rhs;                                            \
                                                                     \
                return(*this);                                       \
            }

#if defined(__GNUC__) && (__GNUC__ < 3)
    #define    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type)                                            \
            quaternion<type> &        operator /= (::std::complex<type> const & rhs)                    \
            {                                                                                           \
                using    ::std::valarray;                                                               \
                                                                                                        \
                valarray<type>    tr(2);                                                                \
                                                                                                        \
                tr[0] = rhs.real();                                                                     \
                tr[1] = rhs.imag();                                                                     \
                                                                                                        \
                type            mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();  \
                                                                                                        \
                tr *= mixam;                                                                            \
                                                                                                        \
                valarray<type>    tt(4);                                                                \
                                                                                                        \
                tt[0] = +a*tr[0]+b*tr[1];                                                               \
                tt[1] = -a*tr[1]+b*tr[0];                                                               \
                tt[2] = +c*tr[0]-d*tr[1];                                                               \
                tt[3] = +c*tr[1]+d*tr[0];                                                               \
                                                                                                        \
                tr *= tr;                                                                               \
                                                                                                        \
                tt *= (mixam/tr.sum());                                                                 \
                                                                                                        \
                a = tt[0];                                                                              \
                b = tt[1];                                                                              \
                c = tt[2];                                                                              \
                d = tt[3];                                                                              \
                                                                                                        \
                return(*this);                                                                          \
            }
#elif    defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
    #define    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type)                         \
            quaternion<type> &        operator /= (::std::complex<type> const & rhs) \
            {                                                                        \
                using    ::std::valarray;                                            \
                using    ::std::abs;                                                 \
                                                                                     \
                valarray<type>    tr(2);                                             \
                                                                                     \
                tr[0] = rhs.real();                                                  \
                tr[1] = rhs.imag();                                                  \
                                                                                     \
                type            mixam = static_cast<type>(1)/(abs(tr).max)();        \
                                                                                     \
                tr *= mixam;                                                         \
                                                                                     \
                valarray<type>    tt(4);                                             \
                                                                                     \
                tt[0] = +a*tr[0]+b*tr[1];                                            \
                tt[1] = -a*tr[1]+b*tr[0];                                            \
                tt[2] = +c*tr[0]-d*tr[1];                                            \
                tt[3] = +c*tr[1]+d*tr[0];                                            \
                                                                                     \
                tr *= tr;                                                            \
                                                                                     \
                tt *= (mixam/tr.sum());                                              \
                                                                                     \
                a = tt[0];                                                           \
                b = tt[1];                                                           \
                c = tt[2];                                                           \
                d = tt[3];                                                           \
                                                                                     \
                return(*this);                                                       \
            }
#else
    #define    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type)                         \
            quaternion<type> &        operator /= (::std::complex<type> const & rhs) \
            {                                                                        \
                using    ::std::valarray;                                            \
                                                                                     \
                valarray<type>    tr(2);                                             \
                                                                                     \
                tr[0] = rhs.real();                                                  \
                tr[1] = rhs.imag();                                                  \
                                                                                     \
                type            mixam = static_cast<type>(1)/(abs(tr).max)();        \
                                                                                     \
                tr *= mixam;                                                         \
                                                                                     \
                valarray<type>    tt(4);                                             \
                                                                                     \
                tt[0] = +a*tr[0]+b*tr[1];                                            \
                tt[1] = -a*tr[1]+b*tr[0];                                            \
                tt[2] = +c*tr[0]-d*tr[1];                                            \
                tt[3] = +c*tr[1]+d*tr[0];                                            \
                                                                                     \
                tr *= tr;                                                            \
                                                                                     \
                tt *= (mixam/tr.sum());                                              \
                                                                                     \
                a = tt[0];                                                           \
                b = tt[1];                                                           \
                c = tt[2];                                                           \
                d = tt[3];                                                           \
                                                                                     \
                return(*this);                                                       \
            }
#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
    
#if defined(__GNUC__) && (__GNUC__ < 3)
    #define    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type)                                            \
            template<typename X>                                                                        \
            quaternion<type> &        operator /= (quaternion<X> const & rhs)                           \
            {                                                                                           \
                using    ::std::valarray;                                                               \
                                                                                                        \
                valarray<type>    tr(4);                                                                \
                                                                                                        \
                tr[0] = static_cast<type>(rhs.R_component_1());                                         \
                tr[1] = static_cast<type>(rhs.R_component_2());                                         \
                tr[2] = static_cast<type>(rhs.R_component_3());                                         \
                tr[3] = static_cast<type>(rhs.R_component_4());                                         \
                                                                                                        \
                type            mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();  \
                                                                                                        \
                tr *= mixam;                                                                            \
                                                                                                        \
                valarray<type>    tt(4);                                                                \
                                                                                                        \
                tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3];                                               \
                tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2];                                               \
                tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1];                                               \
                tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0];                                               \
                                                                                                        \
                tr *= tr;                                                                               \
                                                                                                        \
                tt *= (mixam/tr.sum());                                                                 \