octonion.hpp

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                type    ct = +c*ar+d*br;                                                \
                type    dt = -c*br+d*ar;                                                \
                type    et = +e*ar+f*br;                                                \
                type    ft = -e*br+f*ar;                                                \
                type    gt = +g*ar-h*br;                                                \
                type    ht = +g*br+h*ar;                                                \
                                                                                        \
                a = at;                                                                 \
                b = bt;                                                                 \
                c = ct;                                                                 \
                d = dt;                                                                 \
                e = et;                                                                 \
                f = ft;                                                                 \
                g = gt;                                                                 \
                h = ht;                                                                 \
                                                                                        \
                return(*this);                                                          \
            }
    
#define    BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type)                                                    \
            octonion<type> &            operator *= (::boost::math::quaternion<type> const & rhs)   \
            {                                                                                       \
                type    ar = rhs.R_component_1();                                                   \
                type    br = rhs.R_component_2();                                                   \
                type    cr = rhs.R_component_2();                                                   \
                type    dr = rhs.R_component_2();                                                   \
                                                                                                    \
                type    at = +a*ar-b*br-c*cr-d*dr;                                                  \
                type    bt = +a*br+b*ar+c*dr-d*cr;                                                  \
                type    ct = +a*cr-b*dr+c*ar+d*br;                                                  \
                type    dt = +a*dr+b*cr-c*br+d*ar;                                                  \
                type    et = +e*ar+f*br+g*cr+h*dr;                                                  \
                type    ft = -e*br+f*ar-g*dr+h*cr;                                                  \
                type    gt = -e*cr+f*dr+g*ar-h*br;                                                  \
                type    ht = -e*dr-f*cr+g*br+h*ar;                                                  \
                                                                                                    \
                a = at;                                                                             \
                b = bt;                                                                             \
                c = ct;                                                                             \
                d = dt;                                                                             \
                e = et;                                                                             \
                f = ft;                                                                             \
                g = gt;                                                                             \
                h = ht;                                                                             \
                                                                                                    \
                return(*this);                                                                      \
            }
    
#define    BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)                          \
            template<typename X>                                                \
            octonion<type> &            operator *= (octonion<X> const & rhs)   \
            {                                                                   \
                type    ar = static_cast<type>(rhs.R_component_1());            \
                type    br = static_cast<type>(rhs.R_component_2());            \
                type    cr = static_cast<type>(rhs.R_component_3());            \
                type    dr = static_cast<type>(rhs.R_component_4());            \
                type    er = static_cast<type>(rhs.R_component_5());            \
                type    fr = static_cast<type>(rhs.R_component_6());            \
                type    gr = static_cast<type>(rhs.R_component_7());            \
                type    hr = static_cast<type>(rhs.R_component_8());            \
                                                                                \
                type    at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr;          \
                type    bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr;          \
                type    ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr;          \
                type    dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er;          \
                type    et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr;          \
                type    ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr;          \
                type    gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br;          \
                type    ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar;          \
                                                                                \
                a = at;                                                         \
                b = bt;                                                         \
                c = ct;                                                         \
                d = dt;                                                         \
                e = et;                                                         \
                f = ft;                                                         \
                g = gt;                                                         \
                h = ht;                                                         \
                                                                                \
                return(*this);                                                  \
            }
    
// There is quite a lot of repetition in the code below. This is intentional.
// The last conditional block is the normal form, and the others merely
// consist of workarounds for various compiler deficiencies. Hopefuly, when
// more compilers are conformant and we can retire support for those that are
// not, we will be able to remove the clutter. This is makes the situation
// (painfully) explicit.
    
#define    BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type)                  \
            octonion<type> &            operator /= (type const & rhs)  \
            {                                                           \
                a /= rhs;                                               \
                b /= rhs;                                               \
                c /= rhs;                                               \
                d /= rhs;                                               \
                                                                        \
                return(*this);                                          \
            }
    
#if defined(__GNUC__) && (__GNUC__ < 3)
    #define    BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type)                                              \
            octonion<type> &            operator /= (::std::complex<type> const & rhs)                  \
            {                                                                                           \
                using    ::std::valarray;                                                               \
                                                                                                        \
                valarray<type>    tr(2);                                                                \
                                                                                                        \
                tr[0] = rhs.real();                                                                     \
                tr[1] = rhs.imag();                                                                     \
                                                                                                        \
                type            mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();  \
                                                                                                        \
                tr *= mixam;                                                                            \
                                                                                                        \
                valarray<type>    tt(8);                                                                \
                                                                                                        \
                tt[0] = +a*tr[0]-b*tr[1];                                                               \
                tt[1] = -a*tr[1]+b*tr[0];                                                               \
                tt[2] = +c*tr[0]-d*tr[1];                                                               \
                tt[3] = +c*tr[1]+d*tr[0];                                                               \
                tt[4] = +e*tr[0]-f*tr[1];                                                               \
                tt[5] = +e*tr[1]+f*tr[0];                                                               \
                tt[6] = +g*tr[0]+h*tr[1];                                                               \
                tt[7] = +g*tr[1]+h*tr[0];                                                               \
                                                                                                        \
                tr *= tr;                                                                               \
                                                                                                        \
                tt *= (mixam/tr.sum());                                                                 \
                                                                                                        \
                a = tt[0];                                                                              \
                b = tt[1];                                                                              \
                c = tt[2];                                                                              \
                d = tt[3];                                                                              \
                e = tt[4];                                                                              \
                f = tt[5];                                                                              \
                g = tt[6];                                                                              \
                h = tt[7];                                                                              \
                                                                                                        \
                return(*this);                                                                          \
            }
#elif    defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
    #define    BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type)                              \
            octonion<type> &            operator /= (::std::complex<type> const & rhs)  \
            {                                                                           \
                using    ::std::valarray;                                               \
                using    ::std::abs;                                                    \
                                                                                        \
                valarray<type>    tr(2);                                                \
                                                                                        \
                tr[0] = rhs.real();                                                     \
                tr[1] = rhs.imag();                                                     \
                                                                                        \
                type            mixam = static_cast<type>(1)/(abs(tr).max)();           \
                                                                                        \
                tr *= mixam;                                                            \
                                                                                        \
                valarray<type>    tt(8);                                                \
                                                                                        \
                tt[0] = +a*tr[0]-b*tr[1];                                               \
                tt[1] = -a*tr[1]+b*tr[0];                                               \
                tt[2] = +c*tr[0]-d*tr[1];                                               \
                tt[3] = +c*tr[1]+d*tr[0];                                               \
                tt[4] = +e*tr[0]-f*tr[1];                                               \
                tt[5] = +e*tr[1]+f*tr[0];                                               \
                tt[6] = +g*tr[0]+h*tr[1];                                               \
                tt[7] = +g*tr[1]+h*tr[0];                                               \
                                                                                        \
                tr *= tr;                                                               \
                                                                                        \
                tt *= (mixam/tr.sum());                                                 \
                                                                                        \
                a = tt[0];                                                              \
                b = tt[1];                                                              \
                c = tt[2];                                                              \
                d = tt[3];                                                              \
                e = tt[4];                                                              \
                f = tt[5];                                                              \
                g = tt[6];                                                              \
                h = tt[7];                                                              \
                                                                                        \
                return(*this);                                                          \
            }
#else
    #define    BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type)                              \
            octonion<type> &            operator /= (::std::complex<type> const & rhs)  \
            {                                                                           \
                using    ::std::valarray;                                               \
                                                                                        \
                valarray<type>    tr(2);                                                \
                                                                                        \
                tr[0] = rhs.real();                                                     \
                tr[1] = rhs.imag();                                                     \
                                                                                        \
                type            mixam = static_cast<type>(1)/(abs(tr).max)();           \
                                                                                        \
                tr *= mixam;                                                            \
                                                                                        \
                valarray<type>    tt(8);                                                \
                                                                                        \
                tt[0] = +a*tr[0]-b*tr[1];                                               \
                tt[1] = -a*tr[1]+b*tr[0];                                               \
                tt[2] = +c*tr[0]-d*tr[1];                                               \
                tt[3] = +c*tr[1]+d*tr[0];                                               \
                tt[4] = +e*tr[0]-f*tr[1];                                               \
                tt[5] = +e*tr[1]+f*tr[0];                                               \
                tt[6] = +g*tr[0]+h*tr[1];                                               \
                tt[7] = +g*tr[1]+h*tr[0];                                               \
                                                                                        \
                tr *= tr;                                                               \