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WSJT-X/boost/libs/math/test/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/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_TEST_MESSAGE("Please input a quaternion...");
#ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
::std::cin >> q0;
if (::std::cin.fail())
{
BOOST_TEST_MESSAGE("You have entered nonsense!");
}
else
{
BOOST_TEST_MESSAGE("You have entered the quaternion "<< q0 << " .");
}
#else
::std::istringstream bogus("(1,2,3,4)");
bogus >> q0;
BOOST_TEST_MESSAGE("You have entered the quaternion " << q0 << " .");
#endif
BOOST_TEST_MESSAGE("For this quaternion:");
BOOST_TEST_MESSAGE( "the value of the real part is "
<< real(q0));
BOOST_TEST_MESSAGE( "the value of the unreal part is "
<< unreal(q0));
BOOST_TEST_MESSAGE( "the value of the sup norm is "
<< sup(q0));
BOOST_TEST_MESSAGE( "the value of the l1 norm is "
<< l1(q0));
BOOST_TEST_MESSAGE( "the value of the magnitude (euclidian norm) is "
<< abs(q0));
BOOST_TEST_MESSAGE( "the value of the (Cayley) norm is "
<< norm(q0));
BOOST_TEST_MESSAGE( "the value of the conjugate is "
<< conj(q0));
BOOST_TEST_MESSAGE( "the value of the exponential is "
<< exp(q0));
BOOST_TEST_MESSAGE( "the value of the cube is "
<< pow(q0,3));
BOOST_TEST_MESSAGE( "the value of the cosinus is "
<< cos(q0));
BOOST_TEST_MESSAGE( "the value of the sinus is "
<< sin(q0));
BOOST_TEST_MESSAGE( "the value of the tangent is "
<< tan(q0));
BOOST_TEST_MESSAGE( "the value of the hyperbolic cosinus is "
<< cosh(q0));
BOOST_TEST_MESSAGE( "the value of the hyperbolic sinus is "
<< sinh(q0));
BOOST_TEST_MESSAGE( "the value of the hyperbolic tangent is "
<< tanh(q0));
#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(q0));
BOOST_TEST_MESSAGE( "the value of "
<< "the Hyperbolic Sinus Cardinal (of index pi) is "
<< sinhc_pi(q0));
#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
BOOST_TEST_MESSAGE(" ");
float rho = ::std::sqrt(8.0f);
float theta = ::std::atan(1.0f);
float phi1 = ::std::atan(1.0f);
float phi2 = ::std::atan(1.0f);
BOOST_TEST_MESSAGE( "The value of the quaternion represented "
<< "in spherical form by "
<< "rho = " << rho << " , theta = " << theta
<< " , phi1 = " << phi1 << " , phi2 = " << phi2
<< " is "
<< ::boost::math::spherical(rho, theta, phi1, phi2));
float alpha = ::std::atan(1.0f);
BOOST_TEST_MESSAGE( "The value of the quaternion represented "
<< "in semipolar form by "
<< "rho = " << rho << " , alpha = " << alpha
<< " , phi1 = " << phi1 << " , phi2 = " << phi2
<< " is "
<< ::boost::math::semipolar(rho, alpha, phi1, phi2));
float rho1 = 1;
float rho2 = 2;
float theta1 = 0;
float theta2 = ::std::atan(1.0f)*2;
BOOST_TEST_MESSAGE( "The value of the quaternion represented "
<< "in multipolar form by "
<< "rho1 = " << rho1 << " , theta1 = " << theta1
<< " , rho2 = " << rho2 << " , theta2 = " << theta2
<< " is "
<< ::boost::math::multipolar(rho1, theta1, rho2, theta2));
float t = 5;
float radius = ::std::sqrt(2.0f);
float longitude = ::std::atan(1.0f);
float lattitude = ::std::atan(::std::sqrt(3.0f));
BOOST_TEST_MESSAGE( "The value of the quaternion represented "
<< "in cylindrospherical form by "
<< "t = " << t << " , radius = " << radius
<< " , longitude = " << longitude << " , latitude = "
<< lattitude << " is "
<< ::boost::math::cylindrospherical(t, radius,
longitude, lattitude));
float r = ::std::sqrt(2.0f);
float angle = ::std::atan(1.0f);
float h1 = 3;
float h2 = 4;
BOOST_TEST_MESSAGE( "The value of the quaternion represented "
<< "in cylindrical form by "
<< "r = " << r << " , angle = " << angle
<< " , h1 = " << h1 << " , h2 = " << h2
<< " is "
<< ::boost::math::cylindrical(r, angle, h1, h2));
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_TEST_MESSAGE(" ");
BOOST_TEST_MESSAGE( "Real 1: " << real_1 << " ; "
<< "Complex 1: " << complex_1 << " ; "
<< "Quaternion 1: " << quaternion_1 << " .");
BOOST_TEST_MESSAGE( "Complex i: " << complex_i << " ; "
<< "Quaternion i: " << quaternion_i << " .");
BOOST_TEST_MESSAGE( "Quaternion j: " << quaternion_j << " .");
BOOST_TEST_MESSAGE( "Quaternion k: " << quaternion_k << " .");
BOOST_TEST_MESSAGE(" ");
BOOST_TEST_MESSAGE( "i*i: " << quaternion_i*quaternion_i << " ; "
<< "j*j: " << quaternion_j*quaternion_j << " ; "
<< "k*k: " << quaternion_k*quaternion_k << " .");
BOOST_TEST_MESSAGE( "i*j: " << quaternion_i*quaternion_j << " ; "
<< "j*i: " << quaternion_j*quaternion_i << " .");
BOOST_TEST_MESSAGE( "j*k: " << quaternion_j*quaternion_k << " ; "
<< "k*j: " << quaternion_k*quaternion_j << " .");
BOOST_TEST_MESSAGE( "k*i: " << quaternion_k*quaternion_i << " ; "
<< "i*k: " << quaternion_i*quaternion_k << " .");
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::quaternion<T>(1,0,0,0)*
::boost::math::quaternion<T>(1,0,0,0)-static_cast<T>(1)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,1,0,0)*
::boost::math::quaternion<T>(0,1,0,0)+static_cast<T>(1)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,0,1,0)*
::boost::math::quaternion<T>(0,0,1,0)+static_cast<T>(1)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,0,0,1)*
::boost::math::quaternion<T>(0,0,0,1)+static_cast<T>(1)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,1,0,0)*
::boost::math::quaternion<T>(0,0,1,0)-
::boost::math::quaternion<T>(0,0,0,1)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,0,1,0)*
::boost::math::quaternion<T>(0,1,0,0)+
::boost::math::quaternion<T>(0,0,0,1)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,0,1,0)*
::boost::math::quaternion<T>(0,0,0,1)-
::boost::math::quaternion<T>(0,1,0,0)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,0,0,1)*
::boost::math::quaternion<T>(0,0,1,0)+
::boost::math::quaternion<T>(0,1,0,0)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,0,0,1)*
::boost::math::quaternion<T>(0,1,0,0)-
::boost::math::quaternion<T>(0,0,1,0)))
(numeric_limits<T>::epsilon()));
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
(abs(::boost::math::quaternion<T>(0,1,0,0)*
::boost::math::quaternion<T>(0,0,0,1)+
::boost::math::quaternion<T>(0,0,1,0)))
(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>::_() << ".");
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(exp(::boost::math::quaternion<T>
(0,4*atan(static_cast<T>(1)),0,0))+static_cast<T>(1)))
(2*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(exp(::boost::math::quaternion<T>
(0,0,4*atan(static_cast<T>(1)),0))+static_cast<T>(1)))
(2*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(exp(::boost::math::quaternion<T>
(0,0,0,4*atan(static_cast<T>(1))))+static_cast<T>(1)))
(2*numeric_limits<T>::epsilon()));
}
BOOST_TEST_CASE_TEMPLATE_FUNCTION(cos_test, T)
{
#if BOOST_WORKAROUND(__GNUC__, < 3)
#else /* BOOST_WORKAROUND(__GNUC__, < 3) */
using ::std::numeric_limits;
using ::std::log;
using ::boost::math::abs;
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
BOOST_TEST_MESSAGE("Testing cos for "
<< string_type_name<T>::_() << ".");
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(static_cast<T>(4)*cos(::boost::math::quaternion<T>
(0,log(static_cast<T>(2)),0,0))-static_cast<T>(5)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(static_cast<T>(4)*cos(::boost::math::quaternion<T>
(0,0,log(static_cast<T>(2)),0))-static_cast<T>(5)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(static_cast<T>(4)*cos(::boost::math::quaternion<T>
(0,0,0,log(static_cast<T>(2))))-static_cast<T>(5)))
(4*numeric_limits<T>::epsilon()));
}
BOOST_TEST_CASE_TEMPLATE_FUNCTION(sin_test, T)
{
#if BOOST_WORKAROUND(__GNUC__, < 3)
#else /* BOOST_WORKAROUND(__GNUC__, < 3) */
using ::std::numeric_limits;
using ::std::log;
using ::boost::math::abs;
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
BOOST_TEST_MESSAGE("Testing sin for "
<< string_type_name<T>::_() << ".");
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(static_cast<T>(4)*sin(::boost::math::quaternion<T>
(0,log(static_cast<T>(2)),0,0))
-::boost::math::quaternion<T>(0,3,0,0)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(static_cast<T>(4)*sin(::boost::math::quaternion<T>
(0,0,log(static_cast<T>(2)),0))
-::boost::math::quaternion<T>(0,0,3,0)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(static_cast<T>(4)*sin(::boost::math::quaternion<T>
(0,0,0,log(static_cast<T>(2))))
-::boost::math::quaternion<T>(0,0,0,3)))
(4*numeric_limits<T>::epsilon()));
}
BOOST_TEST_CASE_TEMPLATE_FUNCTION(cosh_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 cosh for "
<< string_type_name<T>::_() << ".");
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(cosh(::boost::math::quaternion<T>
(0,4*atan(static_cast<T>(1)),0,0))
+static_cast<T>(1)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(cosh(::boost::math::quaternion<T>
(0,0,4*atan(static_cast<T>(1)),0))
+static_cast<T>(1)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(cosh(::boost::math::quaternion<T>
(0,0,0,4*atan(static_cast<T>(1))))
+static_cast<T>(1)))
(4*numeric_limits<T>::epsilon()));
}
BOOST_TEST_CASE_TEMPLATE_FUNCTION(sinh_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 sinh for "
<< string_type_name<T>::_() << ".");
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(sinh(::boost::math::quaternion<T>
(0,2*atan(static_cast<T>(1)),0,0))
-::boost::math::quaternion<T>(0,1,0,0)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(sinh(::boost::math::quaternion<T>
(0,0,2*atan(static_cast<T>(1)),0))
-::boost::math::quaternion<T>(0,0,1,0)))
(4*numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(sinh(::boost::math::quaternion<T>
(0,0,0,2*atan(static_cast<T>(1))))
-::boost::math::quaternion<T>(0,0,0,1)))
(4*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("quaternion_test");
BOOST_TEST_MESSAGE("Results of quaternion 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_QUATERNION_COMMON_GENERATOR(fct) \
test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, test_types));
#define BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS(fct) \
test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, near_eps_test_types));
#define BOOST_QUATERNION_TEST \
BOOST_QUATERNION_COMMON_GENERATOR(multiplication) \
BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS(exp) \
BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS(cos) \
BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS(sin) \
BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS(cosh) \
BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS(sinh)
BOOST_QUATERNION_TEST
#undef BOOST_QUATERNION_TEST
#undef BOOST_QUATERNION_COMMON_GENERATOR
#undef BOOST_QUATERNION_COMMON_GENERATOR_NEAR_EPS
#ifdef BOOST_QUATERNION_TEST_VERBOSE
test->add(BOOST_TEST_CASE(quaternion_manual_test));
#endif /* BOOST_QUATERNION_TEST_VERBOSE */
return test;
}
#undef DEFINE_TYPE_NAME
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