octonion_test.cpp

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    f0 != o0;
    
    // using != (const octonion<T> &, const T &)
    o0 != f0;
    
    // using != (const ::std::complex<T> &, const octonion<T> &)
    c0 != o2;
    
    // using != (const octonion<T> &, const ::std::complex<T> &)
    o2 != c0;
    
    // using != (const ::boost::math::quaternion<T> &, const octonion<T> &)
    q0 != o3;
    
    // using != (const octonion<T> &, const ::boost::math::quaternion<T> &)
    o3 != q0;
    
    // using != (const octonion<T> &,const octonion<T> &)
    o0 != o4;
    
    BOOST_MESSAGE("Please input an octonion...");
    
#ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
    ::std::cin >> o0;
    
    if    (::std::cin.fail())
    {
        BOOST_MESSAGE("You have entered nonsense!");
    }
    else
    {
        BOOST_MESSAGE("You have entered the octonion " << o0 << " .");
    }
#else
    ::std::istringstream                bogus("(1,2,3,4,5,6,7,8)");
    
    bogus >> o0;
    
    BOOST_MESSAGE("You have entered the octonion " << o0 << " .");
#endif
    
    BOOST_MESSAGE("For this octonion:");
    
    BOOST_MESSAGE( "the value of the real part is "
                << real(o0));
    
    BOOST_MESSAGE( "the value of the unreal part is "
                << unreal(o0));
    
    BOOST_MESSAGE( "the value of the sup norm is "
                << sup(o0));
    
    BOOST_MESSAGE( "the value of the l1 norm is "
                << l1(o0));
    
    BOOST_MESSAGE( "the value of the magnitude (euclidian norm) is "
                << abs(o0));
    
    BOOST_MESSAGE( "the value of the (Cayley) norm is "
                << norm(o0));
    
    BOOST_MESSAGE( "the value of the conjugate is "
                << conj(o0));
    
    BOOST_MESSAGE( "the value of the exponential is "
                << exp(o0));
    
    BOOST_MESSAGE( "the value of the cube is "
                << pow(o0,3));
    
    BOOST_MESSAGE( "the value of the cosinus is "
                << cos(o0));
    
    BOOST_MESSAGE( "the value of the sinus is "
                << sin(o0));
    
    BOOST_MESSAGE( "the value of the tangent is "
                << tan(o0));
    
    BOOST_MESSAGE( "the value of the hyperbolic cosinus is "
                << cosh(o0));
    
    BOOST_MESSAGE( "the value of the hyperbolic sinus is "
                << sinh(o0));
    
    BOOST_MESSAGE( "the value of the hyperbolic tangent is "
                << tanh(o0));
    
#ifdef    BOOST_NO_TEMPLATE_TEMPLATES
    BOOST_MESSAGE( "no template templates, can't compute cardinal functions");
#else    /* BOOST_NO_TEMPLATE_TEMPLATES */
    BOOST_MESSAGE( "the value of the Sinus Cardinal (of index pi) is "
                << sinc_pi(o0));
    
    BOOST_MESSAGE( "the value of "
                << "the Hyperbolic Sinus Cardinal (of index pi) is "
                << sinhc_pi(o0));
#endif    /* BOOST_NO_TEMPLATE_TEMPLATES */
    
    BOOST_MESSAGE(" ");
    
    float                            rho = ::std::sqrt(4096.0f);
    float                            theta = ::std::atan(1.0f);
    float                            phi1 = ::std::atan(1.0f);
    float                            phi2 = ::std::atan(1.0f);
    float                            phi3 = ::std::atan(1.0f);
    float                            phi4 = ::std::atan(1.0f);
    float                            phi5 = ::std::atan(1.0f);
    float                            phi6 = ::std::atan(1.0f);
    
    BOOST_MESSAGE( "The value of the octonion represented "
                << "in spherical form by "
                << "rho = " << rho << " , theta = " << theta
                << " , phi1 = " << phi1 << " , phi2 = " << phi2
                << " , phi3 = " << phi3 << " , phi4 = " << phi4
                << " , phi5 = " << phi5 << " , phi6 = " << phi6
                << " is "
                << ::boost::math::spherical(rho, theta,
                        phi1, phi2, phi3, phi4, phi5, phi6));
    
    float                            rho1 = 1;
    float                            rho2 = 2;
    float                            rho3 = ::std::sqrt(2.0f);
    float                            rho4 = ::std::sqrt(8.0f);
    float                            theta1 = 0;
    float                            theta2 = ::std::atan(1.0f)*2;
    float                            theta3 = ::std::atan(1.0f);
    float                            theta4 = ::std::atan(::std::sqrt(3.0f));
    
    BOOST_MESSAGE( "The value of the octonion represented "
                << "in multipolar form by "
                << "rho1 = " << rho1 << " , theta1 = " << theta1
                << " , rho2 = " << rho2 << " , theta2 = " << theta2
                << "rho3 = " << rho3 << " , theta3 = " << theta3
                << " , rho4 = " << rho4 << " , theta4 = " << theta4
                << " is "
                << ::boost::math::multipolar(rho1, theta1, rho2, theta2,
                        rho3, theta3, rho4, theta4));
    
    float                            r = ::std::sqrt(2.0f);
    float                            angle = ::std::atan(1.0f);
    float                            h1 = 3;
    float                            h2 = 4;
    float                            h3 = 5;
    float                            h4 = 6;
    float                            h5 = 7;
    float                            h6 = 8;
    
    BOOST_MESSAGE( "The value of the octonion represented "
                << "in cylindrical form by "
                << "r = " << r << " , angle = " << angle
                << " , h1 = " << h1 << " , h2 = " << h2
                << " , h3 = " << h3 << " , h4 = " << h4
                << " , h5 = " << h5 << " , h6 = " << h6
                << " is " << ::boost::math::cylindrical(r, angle,
                        h1, h2, h3, h4, h5, h6));
    
    double                               real_1(1);
    ::std::complex<double>               complex_1(1);
    ::std::complex<double>               complex_i(0,1);
    ::boost::math::quaternion<double>    quaternion_1(1);
    ::boost::math::quaternion<double>    quaternion_i(0,1);
    ::boost::math::quaternion<double>    quaternion_j(0,0,1);
    ::boost::math::quaternion<double>    quaternion_k(0,0,0,1);
    ::boost::math::octonion<double>      octonion_1(1);
    ::boost::math::octonion<double>      octonion_i(0,1);
    ::boost::math::octonion<double>      octonion_j(0,0,1);
    ::boost::math::octonion<double>      octonion_k(0,0,0,1);
    ::boost::math::octonion<double>      octonion_e_prime(0,0,0,0,1);
    ::boost::math::octonion<double>      octonion_i_prime(0,0,0,0,0,1);
    ::boost::math::octonion<double>      octonion_j_prime(0,0,0,0,0,0,1);
    ::boost::math::octonion<double>      octonion_k_prime(0,0,0,0,0,0,0,1);
    
    
    BOOST_MESSAGE(" ");
    
    BOOST_MESSAGE( "Real 1: " << real_1
                << " ; Complex 1: " << complex_1
                << " ; Quaternion 1: " << quaternion_1
                << " ; Octonion 1: " << octonion_1 << " .");
                
    BOOST_MESSAGE( "Complex i: " << complex_i
                << " ; Quaternion i: " << quaternion_i
                << " ; Octonion i : " << octonion_i << " .");
                
    BOOST_MESSAGE( "Quaternion j: " << quaternion_j
                << " ; Octonion j: " << octonion_j << " .");
    
    BOOST_MESSAGE( "Quaternion k: " << quaternion_k
                << " ; Octonion k: " << octonion_k << " .");
    
    BOOST_MESSAGE( "Quaternion e\': " << octonion_e_prime << " .");
    
    BOOST_MESSAGE( "Quaternion i\': " << octonion_i_prime << " .");
    
    BOOST_MESSAGE( "Quaternion j\': " << octonion_j_prime << " .");
    
    BOOST_MESSAGE( "Quaternion k\': " << octonion_k_prime << " .");
    
    BOOST_MESSAGE(" ");
    
    BOOST_MESSAGE( octonion_1*octonion_1 << " ; "
                << octonion_1*octonion_i << " ; "
                << octonion_1*octonion_j << " ; "
                << octonion_1*octonion_k << " ; "
                << octonion_1*octonion_e_prime << " ; "
                << octonion_1*octonion_i_prime << " ; "
                << octonion_1*octonion_j_prime << " ; "
                << octonion_1*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_i*octonion_1 << " ; "
                << octonion_i*octonion_i << " ; "
                << octonion_i*octonion_j << " ; "
                << octonion_i*octonion_k << " ; "
                << octonion_i*octonion_e_prime << " ; "
                << octonion_i*octonion_i_prime << " ; "
                << octonion_i*octonion_j_prime << " ; "
                << octonion_i*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_j*octonion_1 << " ; "
                << octonion_j*octonion_i << " ; "
                << octonion_j*octonion_j << " ; "
                << octonion_j*octonion_k << " ; "
                << octonion_j*octonion_e_prime << " ; "
                << octonion_j*octonion_i_prime << " ; "
                << octonion_j*octonion_j_prime << " ; "
                << octonion_j*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_k*octonion_1 << " ; "
                << octonion_k*octonion_i << " ; "
                << octonion_k*octonion_j << " ; "
                << octonion_k*octonion_k << " ; "
                << octonion_k*octonion_e_prime << " ; "
                << octonion_k*octonion_i_prime << " ; "
                << octonion_k*octonion_j_prime << " ; "
                << octonion_k*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_e_prime*octonion_1 << " ; "
                << octonion_e_prime*octonion_i << " ; "
                << octonion_e_prime*octonion_j << " ; "
                << octonion_e_prime*octonion_k << " ; "
                << octonion_e_prime*octonion_e_prime << " ; "
                << octonion_e_prime*octonion_i_prime << " ; "
                << octonion_e_prime*octonion_j_prime << " ; "
                << octonion_e_prime*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_i_prime*octonion_1 << " ; "
                << octonion_i_prime*octonion_i << " ; "
                << octonion_i_prime*octonion_j << " ; "
                << octonion_i_prime*octonion_k << " ; "
                << octonion_i_prime*octonion_e_prime << " ; "
                << octonion_i_prime*octonion_i_prime << " ; "
                << octonion_i_prime*octonion_j_prime << " ; "
                << octonion_i_prime*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_j_prime*octonion_1 << " ; "
                << octonion_j_prime*octonion_i << " ; "
                << octonion_j_prime*octonion_j << " ; "
                << octonion_j_prime*octonion_k << " ; "
                << octonion_j_prime*octonion_e_prime << " ; "
                << octonion_j_prime*octonion_i_prime << " ; "
                << octonion_j_prime*octonion_j_prime << " ; "
                << octonion_j_prime*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE( octonion_k_prime*octonion_1 << " ; "
                << octonion_k_prime*octonion_i << " ; "
                << octonion_k_prime*octonion_j << " ; "
                << octonion_k_prime*octonion_k << " ; "
                << octonion_k_prime*octonion_e_prime << " ; "
                << octonion_k_prime*octonion_i_prime << " ; "
                << octonion_k_prime*octonion_j_prime << " ; "
                << octonion_k_prime*octonion_k_prime << " ; ");
    
    BOOST_MESSAGE(" ");
    
    BOOST_MESSAGE("i\'*(e\'*j) : "
    << octonion_i_prime*(octonion_e_prime*octonion_j) << " ;");
    
    BOOST_MESSAGE("(i\'*e\')*j : "
    << (octonion_i_prime*octonion_e_prime)*octonion_j << " ;");
    
    BOOST_MESSAGE(" ");
}


BOOST_TEST_CASE_TEMPLATE_FUNCTION(multiplication_test, T)
{
#if     BOOST_WORKAROUND(__GNUC__, < 3)
#else   /* BOOST_WORKAROUND(__GNUC__, < 3) */
    using ::std::numeric_limits;
    
    using ::boost::math::abs;
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
    
    
    BOOST_MESSAGE("Testing multiplication for "
        << string_type_name<T>::_() << ".");
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
        (abs(::boost::math::octonion<T>(1,0,0,0,0,0,0,0)*
             ::boost::math::octonion<T>(1,0,0,0,0,0,0,0)-
             static_cast<T>(1)))
        (numeric_limits<T>::epsilon()));
    
    for    (int idx = 1; idx < 8; ++idx)
    {
        ::boost::math::octonion<T>    toto = index_i_element<T>(idx);
        
        BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
            (abs(toto*toto+static_cast<T>(1)))
            (numeric_limits<T>::epsilon()));
    }
}


BOOST_TEST_CASE_TEMPLATE_FUNCTION(exp_test, T)
{
#if     BOOST_WORKAROUND(__GNUC__, < 3)
#else   /* BOOST_WORKAROUND(__GNUC__, < 3) */
    using ::std::numeric_limits;
    
    using ::std::atan;
    
    using ::boost::math::abs;
#endif  /* BOOST_WORKAROUND(__GNUC__, < 3) */
    
    
    BOOST_MESSAGE("Testing exp for "
        << string_type_name<T>::_() << ".");
    
    for    (int idx = 1; idx < 8; ++idx)
    {
        ::boost::math::octonion<T>    toto =
            static_cast<T>(4)*atan(static_cast<T>(1))*index_i_element<T>(idx);
            
        BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
            (abs(exp(toto)+static_cast<T>(1)))
            (2*numeric_limits<T>::epsilon()));
    }
}


boost::unit_test_framework::test_suite *    init_unit_test_suite(int, char *[])
{
    ::boost::unit_test::unit_test_log.
        set_threshold_level(::boost::unit_test::log_messages);
    
    boost::unit_test_framework::test_suite *    test =
        BOOST_TEST_SUITE("octonion_test");
    
    BOOST_MESSAGE("Results of octonion test.");
    BOOST_MESSAGE(" ");
    BOOST_MESSAGE("(C) Copyright Hubert Holin 2003-2005.");
    BOOST_MESSAGE("Distributed under the Boost Software License, Version 1.0.");
    BOOST_MESSAGE("(See accompanying file LICENSE_1_0.txt or copy at");
    BOOST_MESSAGE("http://www.boost.org/LICENSE_1_0.txt)");
    BOOST_MESSAGE(" ");
    
#define    BOOST_OCTONION_COMMON_GENERATOR(fct) \
    test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, test_types));
    
#define    BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(fct) \
    test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, near_eps_test_types));
    
    
#define    BOOST_OCTONION_TEST                      \
    BOOST_OCTONION_COMMON_GENERATOR(multiplication) \
    BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(exp)
    
    
    BOOST_OCTONION_TEST
    
    
#undef    BOOST_OCTONION_TEST
    
#undef    BOOST_OCTONION_COMMON_GENERATOR
#undef BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS
    
#ifdef BOOST_OCTONION_TEST_VERBOSE
    
    test->add(BOOST_TEST_CASE(octonion_manual_test));
    
#endif    /* BOOST_OCTONION_TEST_VERBOSE */
    
    return test;
}

#undef DEFINE_TYPE_NAME