octonion_test.cpp

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// test file for octonion.hpp

//  (C) Copyright Hubert Holin 2001.
//  Distributed under the Boost Software License, Version 1.0. (See
//  accompanying file LICENSE_1_0.txt or copy at
//  http://www.boost.org/LICENSE_1_0.txt)


#include <iomanip>


#include <boost/mpl/list.hpp>

#include <boost/test/unit_test.hpp>
#include <boost/test/unit_test_log.hpp>
#include <boost/test/test_case_template.hpp>


#include <boost/math/octonion.hpp>


template<typename T>
struct string_type_name;

#define DEFINE_TYPE_NAME(Type)              \
template<> struct string_type_name<Type>    \
{                                           \
    static char const * _()                 \
    {                                       \
        return #Type;                       \
    }                                       \
}

DEFINE_TYPE_NAME(float);
DEFINE_TYPE_NAME(double);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
DEFINE_TYPE_NAME(long double);
#endif

#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
typedef boost::mpl::list<float,double,long double>  test_types;
#else
typedef boost::mpl::list<float,double>  test_types;
#endif

// Apple GCC 4.0 uses the "double double" format for its long double,
// which means that epsilon is VERY small but useless for
// comparisons. So, don't do those comparisons.
#if (defined(__APPLE_CC__) && defined(__GNUC__) && __GNUC__ == 4) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
typedef boost::mpl::list<float,double>  near_eps_test_types;
#else
typedef boost::mpl::list<float,double,long double>  near_eps_test_types;
#endif

#if BOOST_WORKAROUND(__GNUC__, < 3)
    // gcc 2.x ignores function scope using declarations,
    // put them in the scope of the enclosing namespace instead:
using   ::std::sqrt;
using   ::std::atan;
using   ::std::log;
using   ::std::exp;
using   ::std::cos;
using   ::std::sin;
using   ::std::tan;
using   ::std::cosh;
using   ::std::sinh;
using   ::std::tanh;

using   ::std::numeric_limits;

using   ::boost::math::abs;
#endif  /* BOOST_WORKAROUND(__GNUC__, < 3) */


#ifdef  BOOST_NO_STDC_NAMESPACE
using   ::sqrt;
using   ::atan;
using   ::log;
using   ::exp;
using   ::cos;
using   ::sin;
using   ::tan;
using   ::cosh;
using   ::sinh;
using   ::tanh;
#endif  /* BOOST_NO_STDC_NAMESPACE */

#ifdef  BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
using   ::boost::math::real;
using   ::boost::math::unreal;
using   ::boost::math::sup;
using   ::boost::math::l1;
using   ::boost::math::abs;
using   ::boost::math::norm;
using   ::boost::math::conj;
using   ::boost::math::exp;
using   ::boost::math::pow;
using   ::boost::math::cos;
using   ::boost::math::sin;
using   ::boost::math::tan;
using   ::boost::math::cosh;
using   ::boost::math::sinh;
using   ::boost::math::tanh;
using   ::boost::math::sinc_pi;
using   ::boost::math::sinhc_pi;
#endif  /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
  
// Provide standard floating point abs() overloads if older Microsoft
// library is used with _MSC_EXTENSIONS defined. This code also works
// for the Intel compiler using the Microsoft library.
#if defined(_MSC_EXTENSIONS) && defined(_MSC_VER) && _MSC_VER < 1310
inline float        abs(float v)
{
    return(fabs(v));
}

inline double        abs(double v)
{
    return(fabs(v));
}

inline long double    abs(long double v)
{
    return(fabs(v));
}
#endif /* BOOST_WORKAROUND(BOOST_MSVC) */


// explicit (if ludicrous) instanciation
#if !BOOST_WORKAROUND(__GNUC__, < 3)
template    class ::boost::math::octonion<int>;
#else
// gcc doesn't like the absolutely-qualified namespace
template class boost::math::octonion<int>;
#endif /* !BOOST_WORKAROUND(__GNUC__) */


namespace
{
    template<typename T>
    ::boost::math::octonion<T>    index_i_element(int idx)
    {
        return(
            ::boost::math::octonion<T>(
                        (idx == 0) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 1) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 2) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 3) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 4) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 5) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 6) ?
                            static_cast<T>(1) :
                            static_cast<T>(0),
                        (idx == 7) ?
                            static_cast<T>(1) :
                            static_cast<T>(0)
            ));
    }
}



void    octonion_manual_test()
{
    // tests for evaluation by humans
    
    
    // using default constructor
    ::boost::math::octonion<float>            o0;
    
    ::boost::math::octonion<float>            oa[2];
    
    // using constructor "O seen as R^8"
    ::boost::math::octonion<float>            o1(1,2,3,4,5,6,7,8);
    
    ::std::complex<double>                    c0(9,10);
    
    // using constructor "O seen as C^4"
    ::boost::math::octonion<double>            o2(c0);
    
    ::boost::math::quaternion<long double>    q0(11,12,13,14);
    
    // using constructor "O seen as H^2"
    ::boost::math::octonion<long double>      o3(q0);
    
    // using UNtemplated copy constructor
    ::boost::math::octonion<float>            o4(o1);
    
    // using templated copy constructor
    ::boost::math::octonion<long double>      o5(o2);
    
    // using UNtemplated assignment operator
    o5 = o3;
    oa[0] = o0;
    
    // using templated assignment operator
    o5 = o2;
    oa[1] = o5;
    
    float                                     f0(15);
    
    // using converting assignment operator
    o0 = f0;
    
    // using converting assignment operator
    o2 = c0;
    
    // using converting assignment operator
    o5 = q0;
    
    // using += (const T &)
    o4 += f0;
    
    // using += (const ::std::complex<T> &)
    o2 += c0;
    
    // using += (const ::boost::math::quaternion<T> &)
    o3 += q0;
    
    // using += (const quaternion<X> &)
    o5 += o4;
    
    // using -= (const T &)
    o1 -= f0;
    
    // using -= (const ::std::complex<T> &)
    o2 -= c0;
    
    // using -= (const ::boost::math::quaternion<T> &)
    o5 -= q0;
    
    // using -= (const octonion<X> &)
    o3 -= o4;
    
    double                                    d0(16);
    ::std::complex<double>                    c1(17,18);
    ::boost::math::quaternion<double>         q1(19,20,21,22);
    
    // using *= (const T &)
    o2 *= d0;
    
    // using *= (const ::std::complex<T> &)
    o2 *= c1;
    
    // using *= (const ::boost::math::quaternion<T> &)
    o2 *= q1;
    
    // using *= (const octonion<X> &)
    o2 *= o4;
    
    long double                               l0(23);
    ::std::complex<long double>               c2(24,25);
    
    // using /= (const T &)
    o5 /= l0;
    
    // using /= (const ::std::complex<T> &)
    o5 /= c2;
    
    // using /= (const quaternion<X> &)
    o5 /= q0;
    
    // using /= (const octonion<X> &)
    o5 /= o5;
    
    // using + (const T &, const octonion<T> &)
    ::boost::math::octonion<float>            o6 = f0+o0;
    
    // using + (const octonion<T> &, const T &)
    ::boost::math::octonion<float>            o7 = o0+f0;
    
    // using + (const ::std::complex<T> &, const quaternion<T> &)
    ::boost::math::octonion<double>           o8 = c0+o2;
    
    // using + (const octonion<T> &, const ::std::complex<T> &)
    ::boost::math::octonion<double>           o9 = o2+c0;
    
    // using + (const ::boost::math::quaternion<T>, const octonion<T> &)
    ::boost::math::octonion<long double>      o10 = q0+o3;
    
    // using + (const octonion<T> &, const ::boost::math::quaternion<T> &)
    ::boost::math::octonion<long double>      o11 = o3+q0;
    
    // using + (const quaternion<T> &,const quaternion<T> &)
    ::boost::math::octonion<float>            o12 = o0+o4;
    
    // using - (const T &, const octonion<T> &)
    o6 = f0-o0;
    
    // using - (const octonion<T> &, const T &)
    o7 = o0-f0;
    
    // using - (const ::std::complex<T> &, const octonion<T> &)
    o8 = c0-o2;
    
    // using - (const octonion<T> &, const ::std::complex<T> &)
    o9 = o2-c0;
    
    // using - (const quaternion<T> &,const octonion<T> &)
    o10 = q0-o3;
    
    // using - (const octonion<T> &,const quaternion<T> &)
    o11 = o3-q0;
    
    // using - (const octonion<T> &,const octonion<T> &)
    o12 = o0-o4;
    
    // using * (const T &, const octonion<T> &)
    o6 = f0*o0;
    
    // using * (const octonion<T> &, const T &)
    o7 = o0*f0;
    
    // using * (const ::std::complex<T> &, const octonion<T> &)
    o8 = c0*o2;
    
    // using * (const octonion<T> &, const ::std::complex<T> &)
    o9 = o2*c0;
    
    // using * (const quaternion<T> &,const octonion<T> &)
    o10 = q0*o3;
    
    // using * (const octonion<T> &,const quaternion<T> &)
    o11 = o3*q0;
    
    // using * (const octonion<T> &,const octonion<T> &)
    o12 = o0*o4;
    
    // using / (const T &, const octonion<T> &)
    o6 = f0/o0;
    
    // using / (const octonion<T> &, const T &)
    o7 = o0/f0;
    
    // using / (const ::std::complex<T> &, const octonion<T> &)
    o8 = c0/o2;
    
    // using / (const octonion<T> &, const ::std::complex<T> &)
    o9 = o2/c0;
    
    // using / (const ::boost::math::quaternion<T> &, const octonion<T> &)
    o10 = q0/o3;
    
    // using / (const octonion<T> &, const ::boost::math::quaternion<T> &)
    o11 = o3/q0;
    
    // using / (const octonion<T> &,const octonion<T> &)
    o12 = o0/o4;
    
    // using + (const octonion<T> &)
    o4 = +o0;
    
    // using - (const octonion<T> &)
    o0 = -o4;
    
    // using == (const T &, const octonion<T> &)
    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;
    
    // using != (const T &, const octonion<T> &)