quaternion_test.cpp

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// test file for quaternion.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/quaternion.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);
DEFINE_TYPE_NAME(long double);


#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) && BOOST_WORKAROUND(_MSC_VER, < 1310)
#if !((__INTEL__ && _WIN32) && BOOST_WORKAROUND(__MWERKS__, >= 0x3201))
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 /* !((__INTEL__ && _WIN32) && BOOST_WORKAROUND(__MWERKS__, >= 0x3201)) */
#endif /* defined(_MSC_EXTENSIONS) && BOOST_WORKAROUND(_MSC_VER, < 1310) */


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



void    quaternion_manual_test()
{
    // tests for evaluation by humans
    
    
    // using default constructor
    ::boost::math::quaternion<float>        q0;
    
    ::boost::math::quaternion<float>        qa[2];
    
    // using constructor "H seen as R^4"
    ::boost::math::quaternion<double>       q1(1,2,3,4);
    
    ::std::complex<float>                   c0(5,6);
    
    // using constructor "H seen as C^2"
    ::boost::math::quaternion<float>        q2(c0);
    
    // using UNtemplated copy constructor
    ::boost::math::quaternion<float>        q3(q2);
    
    // using templated copy constructor
    ::boost::math::quaternion<long double>  q4(q3);
    
    // using UNtemplated assignment operator
    q3 = q0;
    qa[0] = q0;
    
    // using templated assignment operator
    q4 = q0;
    qa[1] = q1;
    
    float                                   f0(7);
    
    // using converting assignment operator
    q2 = f0;
    
    // using converting assignment operator
    q3 = c0;
    
    // using += (const T &)
    q2 += f0;
    
    // using += (const ::std::complex<T> &)
    q2 += c0;
    
    // using += (const quaternion<X> &)
    q2 += q3;
    
    // using -= (const T &)
    q3 -= f0;
    
    // using -= (const ::std::complex<T> &)
    q3 -= c0;
    
    // using -= (const quaternion<X> &)
    q3 -= q2;
    
    double                                  d0(8);
    ::std::complex<double>                  c1(9,10);
    
    // using *= (const T &)
    q1 *= d0;
    
    // using *= (const ::std::complex<T> &)
    q1 *= c1;
    
    // using *= (const quaternion<X> &)
    q1 *= q1;
    
    long double                             l0(11);
    ::std::complex<long double>             c2(12,13);
    
    // using /= (const T &)
    q4 /= l0;
    
    // using /= (const ::std::complex<T> &)
    q4 /= c2;
    
    // using /= (const quaternion<X> &)
    q4 /= q1;
    
    // using + (const T &, const quaternion<T> &)
    ::boost::math::quaternion<float>        q5 = f0+q2;
    
    // using + (const quaternion<T> &, const T &)
    ::boost::math::quaternion<float>        q6 = q2+f0;
    
    // using + (const ::std::complex<T> &, const quaternion<T> &)
    ::boost::math::quaternion<float>        q7 = c0+q2;
    
    // using + (const quaternion<T> &, const ::std::complex<T> &)
    ::boost::math::quaternion<float>        q8 = q2+c0;
    
    // using + (const quaternion<T> &,const quaternion<T> &)
    ::boost::math::quaternion<float>        q9 = q2+q3;
    
    // using - (const T &, const quaternion<T> &)
    q5 = f0-q2;
    
    // using - (const quaternion<T> &, const T &)
    q6 = q2-f0;
    
    // using - (const ::std::complex<T> &, const quaternion<T> &)
    q7 = c0-q2;
    
    // using - (const quaternion<T> &, const ::std::complex<T> &)
    q8 = q2-c0;
    
    // using - (const quaternion<T> &,const quaternion<T> &)
    q9 = q2-q3;
    
    // using * (const T &, const quaternion<T> &)
    q5 = f0*q2;
    
    // using * (const quaternion<T> &, const T &)
    q6 = q2*f0;
    
    // using * (const ::std::complex<T> &, const quaternion<T> &)
    q7 = c0*q2;
    
    // using * (const quaternion<T> &, const ::std::complex<T> &)
    q8 = q2*c0;
    
    // using * (const quaternion<T> &,const quaternion<T> &)
    q9 = q2*q3;
    
    // using / (const T &, const quaternion<T> &)
    q5 = f0/q2;
    
    // using / (const quaternion<T> &, const T &)
    q6 = q2/f0;
    
    // using / (const ::std::complex<T> &, const quaternion<T> &)
    q7 = c0/q2;
    
    // using / (const quaternion<T> &, const ::std::complex<T> &)
    q8 = q2/c0;
    
    // using / (const quaternion<T> &,const quaternion<T> &)
    q9 = q2/q3;
    
    // using + (const quaternion<T> &)
    q2 = +q0;
    
    // using - (const quaternion<T> &)
    q2 = -q3;
    
    // using == (const T &, const quaternion<T> &)
    f0 == q2;
    
    // using == (const quaternion<T> &, const T &)
    q2 == f0;
    
    // using == (const ::std::complex<T> &, const quaternion<T> &)
    c0 == q2;
    
    // using == (const quaternion<T> &, const ::std::complex<T> &)
    q2 == c0;
    
    // using == (const quaternion<T> &,const quaternion<T> &)
    q2 == q3;
    
    // using != (const T &, const quaternion<T> &)
    f0 != q2;
    
    // using != (const quaternion<T> &, const T &)
    q2 != f0;
    
    // using != (const ::std::complex<T> &, const quaternion<T> &)
    c0 != q2;
    
    // using != (const quaternion<T> &, const ::std::complex<T> &)
    q2 != c0;
    
    // using != (const quaternion<T> &,const quaternion<T> &)
    q2 != q3;
    
    BOOST_MESSAGE("Please input a quaternion...");
    
#ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
    ::std::cin >> q0;
    
    if    (::std::cin.fail())
    {
        BOOST_MESSAGE("You have entered nonsense!");
    }
    else
    {
        BOOST_MESSAGE("You have entered the quaternion "<< q0 << " .");
    }
#else
    ::std::istringstream                bogus("(1,2,3,4)");
    
    bogus >> q0;
    
    BOOST_MESSAGE("You have entered the quaternion " << q0 << " .");
#endif
    
    BOOST_MESSAGE("For this quaternion:");
    
    BOOST_MESSAGE( "the value of the real part is "
                << real(q0));
    
    BOOST_MESSAGE( "the value of the unreal part is "
                << unreal(q0));
    
    BOOST_MESSAGE( "the value of the sup norm is "
                << sup(q0));
    
    BOOST_MESSAGE( "the value of the l1 norm is "
                << l1(q0));
    
    BOOST_MESSAGE( "the value of the magnitude (euclidian norm) is "
                << abs(q0));
    
    BOOST_MESSAGE( "the value of the (Cayley) norm is "
                << norm(q0));
    
    BOOST_MESSAGE( "the value of the conjugate is "
                << conj(q0));
    
    BOOST_MESSAGE( "the value of the exponential is "
                << exp(q0));
    
    BOOST_MESSAGE( "the value of the cube is "
                << pow(q0,3));
    
    BOOST_MESSAGE( "the value of the cosinus is "
                << cos(q0));
    
    BOOST_MESSAGE( "the value of the sinus is "
                << sin(q0));
    
    BOOST_MESSAGE( "the value of the tangent is "
                << tan(q0));
    
    BOOST_MESSAGE( "the value of the hyperbolic cosinus is "
                << cosh(q0));
    
    BOOST_MESSAGE( "the value of the hyperbolic sinus is "
                << sinh(q0));
    
    BOOST_MESSAGE( "the value of the hyperbolic tangent is "
                << tanh(q0));
    
#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(q0));
    
    BOOST_MESSAGE( "the value of "
                << "the Hyperbolic Sinus Cardinal (of index pi) is "