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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/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> &)
- 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
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