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776 lines
25 KiB
C++
776 lines
25 KiB
C++
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// test file for octonion.hpp
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#include <iomanip>
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#include <boost/mpl/list.hpp>
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#include <boost/test/unit_test.hpp>
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#include <boost/test/unit_test_log.hpp>
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#include <boost/math/octonion.hpp>
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template<typename T>
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struct string_type_name;
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#define DEFINE_TYPE_NAME(Type) \
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template<> struct string_type_name<Type> \
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{ \
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static char const * _() \
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{ \
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return #Type; \
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} \
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}
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DEFINE_TYPE_NAME(float);
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DEFINE_TYPE_NAME(double);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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DEFINE_TYPE_NAME(long double);
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#endif
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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typedef boost::mpl::list<float,double,long double> test_types;
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#else
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typedef boost::mpl::list<float,double> test_types;
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#endif
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// Apple GCC 4.0 uses the "double double" format for its long double,
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// which means that epsilon is VERY small but useless for
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// comparisons. So, don't do those comparisons.
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#if (defined(__APPLE_CC__) && defined(__GNUC__) && __GNUC__ == 4) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
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typedef boost::mpl::list<float,double> near_eps_test_types;
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#else
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typedef boost::mpl::list<float,double,long double> near_eps_test_types;
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#endif
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#if BOOST_WORKAROUND(__GNUC__, < 3)
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// gcc 2.x ignores function scope using declarations,
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// put them in the scope of the enclosing namespace instead:
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using ::std::sqrt;
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using ::std::atan;
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using ::std::log;
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using ::std::exp;
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using ::std::cos;
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using ::std::sin;
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using ::std::tan;
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using ::std::cosh;
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using ::std::sinh;
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using ::std::tanh;
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using ::std::numeric_limits;
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using ::boost::math::abs;
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#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
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#ifdef BOOST_NO_STDC_NAMESPACE
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using ::sqrt;
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using ::atan;
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using ::log;
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using ::exp;
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using ::cos;
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using ::sin;
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using ::tan;
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using ::cosh;
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using ::sinh;
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using ::tanh;
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#endif /* BOOST_NO_STDC_NAMESPACE */
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#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
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using ::boost::math::real;
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using ::boost::math::unreal;
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using ::boost::math::sup;
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using ::boost::math::l1;
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using ::boost::math::abs;
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using ::boost::math::norm;
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using ::boost::math::conj;
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using ::boost::math::exp;
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using ::boost::math::pow;
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using ::boost::math::cos;
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using ::boost::math::sin;
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using ::boost::math::tan;
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using ::boost::math::cosh;
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using ::boost::math::sinh;
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using ::boost::math::tanh;
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using ::boost::math::sinc_pi;
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using ::boost::math::sinhc_pi;
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#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
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// Provide standard floating point abs() overloads if older Microsoft
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// library is used with _MSC_EXTENSIONS defined. This code also works
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// for the Intel compiler using the Microsoft library.
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#if defined(_MSC_EXTENSIONS) && defined(_MSC_VER) && _MSC_VER < 1310
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inline float abs(float v)
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{
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return(fabs(v));
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}
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inline double abs(double v)
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{
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return(fabs(v));
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}
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inline long double abs(long double v)
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{
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return(fabs(v));
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}
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#endif /* BOOST_WORKAROUND(BOOST_MSVC) */
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// explicit (if ludicrous) instanciation
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#if !BOOST_WORKAROUND(__GNUC__, < 3)
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template class ::boost::math::octonion<int>;
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#else
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// gcc doesn't like the absolutely-qualified namespace
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template class boost::math::octonion<int>;
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#endif /* !BOOST_WORKAROUND(__GNUC__) */
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namespace
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{
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template<typename T>
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::boost::math::octonion<T> index_i_element(int idx)
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{
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return(
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::boost::math::octonion<T>(
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(idx == 0) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 1) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 2) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 3) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 4) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 5) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 6) ?
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static_cast<T>(1) :
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static_cast<T>(0),
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(idx == 7) ?
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static_cast<T>(1) :
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static_cast<T>(0)
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));
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}
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}
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void octonion_manual_test()
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{
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// tests for evaluation by humans
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// using default constructor
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::boost::math::octonion<float> o0;
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::boost::math::octonion<float> oa[2];
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// using constructor "O seen as R^8"
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::boost::math::octonion<float> o1(1,2,3,4,5,6,7,8);
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::std::complex<double> c0(9,10);
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// using constructor "O seen as C^4"
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::boost::math::octonion<double> o2(c0);
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::boost::math::quaternion<long double> q0(11,12,13,14);
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// using constructor "O seen as H^2"
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::boost::math::octonion<long double> o3(q0);
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// using UNtemplated copy constructor
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::boost::math::octonion<float> o4(o1);
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// using templated copy constructor
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::boost::math::octonion<long double> o5(o2);
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// using UNtemplated assignment operator
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o5 = o3;
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oa[0] = o0;
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// using templated assignment operator
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o5 = o2;
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oa[1] = o5;
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float f0(15);
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// using converting assignment operator
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o0 = f0;
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// using converting assignment operator
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o2 = c0;
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// using converting assignment operator
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o5 = q0;
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// using += (const T &)
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o4 += f0;
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// using += (const ::std::complex<T> &)
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o2 += c0;
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// using += (const ::boost::math::quaternion<T> &)
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o3 += q0;
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// using += (const quaternion<X> &)
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o5 += o4;
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// using -= (const T &)
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o1 -= f0;
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// using -= (const ::std::complex<T> &)
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o2 -= c0;
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// using -= (const ::boost::math::quaternion<T> &)
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o5 -= q0;
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// using -= (const octonion<X> &)
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o3 -= o4;
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double d0(16);
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::std::complex<double> c1(17,18);
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::boost::math::quaternion<double> q1(19,20,21,22);
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// using *= (const T &)
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o2 *= d0;
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// using *= (const ::std::complex<T> &)
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o2 *= c1;
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// using *= (const ::boost::math::quaternion<T> &)
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o2 *= q1;
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// using *= (const octonion<X> &)
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o2 *= o4;
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long double l0(23);
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::std::complex<long double> c2(24,25);
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// using /= (const T &)
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o5 /= l0;
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// using /= (const ::std::complex<T> &)
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o5 /= c2;
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// using /= (const quaternion<X> &)
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o5 /= q0;
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// using /= (const octonion<X> &)
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o5 /= o5;
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// using + (const T &, const octonion<T> &)
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::boost::math::octonion<float> o6 = f0+o0;
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// using + (const octonion<T> &, const T &)
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::boost::math::octonion<float> o7 = o0+f0;
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// using + (const ::std::complex<T> &, const quaternion<T> &)
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::boost::math::octonion<double> o8 = c0+o2;
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// using + (const octonion<T> &, const ::std::complex<T> &)
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::boost::math::octonion<double> o9 = o2+c0;
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// using + (const ::boost::math::quaternion<T>, const octonion<T> &)
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::boost::math::octonion<long double> o10 = q0+o3;
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// using + (const octonion<T> &, const ::boost::math::quaternion<T> &)
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::boost::math::octonion<long double> o11 = o3+q0;
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// using + (const quaternion<T> &,const quaternion<T> &)
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::boost::math::octonion<float> o12 = o0+o4;
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// using - (const T &, const octonion<T> &)
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o6 = f0-o0;
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// using - (const octonion<T> &, const T &)
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o7 = o0-f0;
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// using - (const ::std::complex<T> &, const octonion<T> &)
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o8 = c0-o2;
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// using - (const octonion<T> &, const ::std::complex<T> &)
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o9 = o2-c0;
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// using - (const quaternion<T> &,const octonion<T> &)
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o10 = q0-o3;
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// using - (const octonion<T> &,const quaternion<T> &)
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o11 = o3-q0;
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// using - (const octonion<T> &,const octonion<T> &)
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o12 = o0-o4;
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// using * (const T &, const octonion<T> &)
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o6 = f0*o0;
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// using * (const octonion<T> &, const T &)
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o7 = o0*f0;
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// using * (const ::std::complex<T> &, const octonion<T> &)
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o8 = c0*o2;
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// using * (const octonion<T> &, const ::std::complex<T> &)
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o9 = o2*c0;
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// using * (const quaternion<T> &,const octonion<T> &)
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o10 = q0*o3;
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// using * (const octonion<T> &,const quaternion<T> &)
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o11 = o3*q0;
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// using * (const octonion<T> &,const octonion<T> &)
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o12 = o0*o4;
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// using / (const T &, const octonion<T> &)
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o6 = f0/o0;
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// using / (const octonion<T> &, const T &)
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o7 = o0/f0;
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// using / (const ::std::complex<T> &, const octonion<T> &)
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o8 = c0/o2;
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// using / (const octonion<T> &, const ::std::complex<T> &)
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o9 = o2/c0;
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// using / (const ::boost::math::quaternion<T> &, const octonion<T> &)
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o10 = q0/o3;
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// using / (const octonion<T> &, const ::boost::math::quaternion<T> &)
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o11 = o3/q0;
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// using / (const octonion<T> &,const octonion<T> &)
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o12 = o0/o4;
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// using + (const octonion<T> &)
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o4 = +o0;
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// using - (const octonion<T> &)
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o0 = -o4;
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// using == (const T &, const octonion<T> &)
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f0 == o0;
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// using == (const octonion<T> &, const T &)
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o0 == f0;
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// using == (const ::std::complex<T> &, const octonion<T> &)
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c0 == o2;
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// using == (const octonion<T> &, const ::std::complex<T> &)
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o2 == c0;
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// using == (const ::boost::math::quaternion<T> &, const octonion<T> &)
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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> &)
|
||
|
|
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_TEST_MESSAGE("Please input an octonion...");
|
||
|
|
|
||
|
|
#ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
|
||
|
|
::std::cin >> o0;
|
||
|
|
|
||
|
|
if (::std::cin.fail())
|
||
|
|
{
|
||
|
|
BOOST_TEST_MESSAGE("You have entered nonsense!");
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
|
||
|
|
}
|
||
|
|
#else
|
||
|
|
::std::istringstream bogus("(1,2,3,4,5,6,7,8)");
|
||
|
|
|
||
|
|
bogus >> o0;
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
|
||
|
|
#endif
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE("For this octonion:");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the real part is "
|
||
|
|
<< real(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the unreal part is "
|
||
|
|
<< unreal(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the sup norm is "
|
||
|
|
<< sup(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the l1 norm is "
|
||
|
|
<< l1(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the magnitude (euclidian norm) is "
|
||
|
|
<< abs(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the (Cayley) norm is "
|
||
|
|
<< norm(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the conjugate is "
|
||
|
|
<< conj(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the exponential is "
|
||
|
|
<< exp(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the cube is "
|
||
|
|
<< pow(o0,3));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the cosinus is "
|
||
|
|
<< cos(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the sinus is "
|
||
|
|
<< sin(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the tangent is "
|
||
|
|
<< tan(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the hyperbolic cosinus is "
|
||
|
|
<< cosh(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the hyperbolic sinus is "
|
||
|
|
<< sinh(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the hyperbolic tangent is "
|
||
|
|
<< tanh(o0));
|
||
|
|
|
||
|
|
#ifdef BOOST_NO_TEMPLATE_TEMPLATES
|
||
|
|
BOOST_TEST_MESSAGE( "no template templates, can't compute cardinal functions");
|
||
|
|
#else /* BOOST_NO_TEMPLATE_TEMPLATES */
|
||
|
|
BOOST_TEST_MESSAGE( "the value of the Sinus Cardinal (of index pi) is "
|
||
|
|
<< sinc_pi(o0));
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "the value of "
|
||
|
|
<< "the Hyperbolic Sinus Cardinal (of index pi) is "
|
||
|
|
<< sinhc_pi(o0));
|
||
|
|
#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
|
||
|
|
|
||
|
|
BOOST_TEST_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_TEST_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_TEST_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_TEST_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_TEST_MESSAGE(" ");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Real 1: " << real_1
|
||
|
|
<< " ; Complex 1: " << complex_1
|
||
|
|
<< " ; Quaternion 1: " << quaternion_1
|
||
|
|
<< " ; Octonion 1: " << octonion_1 << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Complex i: " << complex_i
|
||
|
|
<< " ; Quaternion i: " << quaternion_i
|
||
|
|
<< " ; Octonion i : " << octonion_i << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Quaternion j: " << quaternion_j
|
||
|
|
<< " ; Octonion j: " << octonion_j << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Quaternion k: " << quaternion_k
|
||
|
|
<< " ; Octonion k: " << octonion_k << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Quaternion e\': " << octonion_e_prime << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Quaternion i\': " << octonion_i_prime << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Quaternion j\': " << octonion_j_prime << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE( "Quaternion k\': " << octonion_k_prime << " .");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE(" ");
|
||
|
|
|
||
|
|
BOOST_TEST_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_TEST_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_TEST_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_TEST_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_TEST_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_TEST_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_TEST_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_TEST_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_TEST_MESSAGE(" ");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE("i\'*(e\'*j) : "
|
||
|
|
<< octonion_i_prime*(octonion_e_prime*octonion_j) << " ;");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE("(i\'*e\')*j : "
|
||
|
|
<< (octonion_i_prime*octonion_e_prime)*octonion_j << " ;");
|
||
|
|
|
||
|
|
BOOST_TEST_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_TEST_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_TEST_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::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::test_suite * test =
|
||
|
|
BOOST_TEST_SUITE("octonion_test");
|
||
|
|
|
||
|
|
BOOST_TEST_MESSAGE("Results of octonion test.");
|
||
|
|
BOOST_TEST_MESSAGE(" ");
|
||
|
|
BOOST_TEST_MESSAGE("(C) Copyright Hubert Holin 2003-2005.");
|
||
|
|
BOOST_TEST_MESSAGE("Distributed under the Boost Software License, Version 1.0.");
|
||
|
|
BOOST_TEST_MESSAGE("(See accompanying file LICENSE_1_0.txt or copy at");
|
||
|
|
BOOST_TEST_MESSAGE("http://www.boost.org/LICENSE_1_0.txt)");
|
||
|
|
BOOST_TEST_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
|