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boost/libs/multiprecision/test/test_eigen_interop.cpp
yangzuhao b199dd2a76 源码提交
2022-12-15 23:45:23 +08:00

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#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <iostream>
#include <Eigen/Dense>
#include <boost/multiprecision/mpfr.hpp>
#include <boost/multiprecision/logged_adaptor.hpp>
#include <boost/multiprecision/gmp.hpp>
#include <boost/multiprecision/mpc.hpp>
#include "test.hpp"
using namespace Eigen;
namespace Eigen
{
template <class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
struct NumTraits<boost::multiprecision::number<Backend, ExpressionTemplates> >
{
typedef boost::multiprecision::number<Backend, ExpressionTemplates> self_type;
typedef typename boost::multiprecision::scalar_result_from_possible_complex<self_type>::type Real;
typedef self_type NonInteger; // Not correct but we can't do much better??
typedef double Literal;
typedef self_type Nested;
enum {
IsComplex = boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_complex,
IsInteger = boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer,
ReadCost = 1,
AddCost = 4,
MulCost = 8,
IsSigned = std::numeric_limits<self_type>::is_specialized ? std::numeric_limits<self_type>::is_signed : true,
RequireInitialization = 1,
};
static Real epsilon()
{
return std::numeric_limits<Real>::epsilon();
}
static Real dummy_precision()
{
return sqrt(epsilon());
}
static Real highest()
{
return (std::numeric_limits<Real>::max)();
}
static Real lowest()
{
return (std::numeric_limits<Real>::min)();
}
static int digits10_imp(const boost::mpl::true_&)
{
return std::numeric_limits<Real>::digits10;
}
template <bool B>
static int digits10_imp(const boost::mpl::bool_<B>&)
{
return Real::default_precision();
}
static int digits10()
{
return digits10_imp(boost::mpl::bool_<std::numeric_limits<Real>::digits10 && (std::numeric_limits<Real>::digits10 != INT_MAX) ? true : false>());
}
};
#define BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(A)\
template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates, typename BinaryOp>\
struct ScalarBinaryOpTraits<boost::multiprecision::number<Backend, ExpressionTemplates>, A, BinaryOp>\
{\
static_assert(boost::multiprecision::is_compatible_arithmetic_type<A, boost::multiprecision::number<Backend, ExpressionTemplates> >::value, "Interoperability with this arithmetic type is not supported.");\
typedef boost::multiprecision::number<Backend, ExpressionTemplates> ReturnType;\
};\
template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates, typename BinaryOp>\
struct ScalarBinaryOpTraits<A, boost::multiprecision::number<Backend, ExpressionTemplates>, BinaryOp>\
{\
static_assert(boost::multiprecision::is_compatible_arithmetic_type<A, boost::multiprecision::number<Backend, ExpressionTemplates> >::value, "Interoperability with this arithmetic type is not supported.");\
typedef boost::multiprecision::number<Backend, ExpressionTemplates> ReturnType;\
};\
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(float)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(double)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(long double)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(char)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(unsigned char)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(signed char)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(short)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(unsigned short)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(int)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(unsigned int)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(long)
BOOST_MP_EIGEN_SCALAR_TRAITS_DECL(unsigned long)
#if 0
template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates, class Backend2, boost::multiprecision::expression_template_option ExpressionTemplates2, typename BinaryOp>
struct ScalarBinaryOpTraits<boost::multiprecision::number<Backend, ExpressionTemplates>, boost::multiprecision::number<Backend2, ExpressionTemplates2>, BinaryOp>
{
static_assert(
boost::multiprecision::is_compatible_arithmetic_type<boost::multiprecision::number<Backend2, ExpressionTemplates2>, boost::multiprecision::number<Backend, ExpressionTemplates> >::value
|| boost::multiprecision::is_compatible_arithmetic_type<boost::multiprecision::number<Backend, ExpressionTemplates>, boost::multiprecision::number<Backend2, ExpressionTemplates2> >::value, "Interoperability with this arithmetic type is not supported.");
typedef typename boost::mpl::if_c<boost::is_convertible<boost::multiprecision::number<Backend2, ExpressionTemplates2>, boost::multiprecision::number<Backend, ExpressionTemplates> >::value,
boost::multiprecision::number<Backend, ExpressionTemplates>, boost::multiprecision::number<Backend2, ExpressionTemplates2> >::type ReturnType;
};
template<unsigned D, typename BinaryOp>
struct ScalarBinaryOpTraits<boost::multiprecision::number<boost::multiprecision::backends::mpc_complex_backend<D>, boost::multiprecision::et_on>, boost::multiprecision::mpfr_float, BinaryOp>
{
typedef boost::multiprecision::number<boost::multiprecision::backends::mpc_complex_backend<D>, boost::multiprecision::et_on> ReturnType;
};
template<typename BinaryOp>
struct ScalarBinaryOpTraits<boost::multiprecision::mpfr_float, boost::multiprecision::mpc_complex, BinaryOp>
{
typedef boost::multiprecision::number<boost::multiprecision::backends::mpc_complex_backend<0>, boost::multiprecision::et_on> ReturnType;
};
template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates, typename BinaryOp>
struct ScalarBinaryOpTraits<boost::multiprecision::number<Backend, ExpressionTemplates>, boost::multiprecision::number<Backend, ExpressionTemplates>, BinaryOp>
{
typedef boost::multiprecision::number<Backend, ExpressionTemplates> ReturnType;
};
#endif
template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates, class tag, class Arg1, class Arg2, class Arg3, class Arg4, typename BinaryOp>
struct ScalarBinaryOpTraits<boost::multiprecision::number<Backend, ExpressionTemplates>, boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, BinaryOp>
{
static_assert(boost::is_convertible<typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, boost::multiprecision::number<Backend, ExpressionTemplates> >::value, "Interoperability with this arithmetic type is not supported.");
typedef boost::multiprecision::number<Backend, ExpressionTemplates> ReturnType;
};
template<class tag, class Arg1, class Arg2, class Arg3, class Arg4, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates, typename BinaryOp>
struct ScalarBinaryOpTraits<boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, boost::multiprecision::number<Backend, ExpressionTemplates>, BinaryOp>
{
static_assert(boost::is_convertible<typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, boost::multiprecision::number<Backend, ExpressionTemplates> >::value, "Interoperability with this arithmetic type is not supported.");
typedef boost::multiprecision::number<Backend, ExpressionTemplates> ReturnType;
};
}
template <class T>
struct related_number
{
typedef T type;
};
/*
template <>
struct related_number<boost::multiprecision::cpp_bin_float_50>
{
typedef boost::multiprecision::cpp_bin_float_quad type;
};
template <>
struct related_number<boost::multiprecision::cpp_dec_float_100>
{
typedef boost::multiprecision::cpp_dec_float_50 type;
};*/
template <class Num>
void example1()
{
// expected results first:
Matrix<Num, 2, 2> r1, r2;
r1 << 3, 5, 4, 8;
r2 << -1, -1, 2, 0;
Matrix<Num, 3, 1> r3;
r3 << -1, -4, -6;
Matrix<Num, 2, 2> a;
a << 1, 2, 3, 4;
Matrix<Num, Dynamic, Dynamic> b(2,2);
b << 2, 3, 1, 4;
std::cout << "a + b =\n" << a + b << std::endl;
BOOST_CHECK_EQUAL(a + b, r1);
std::cout << "a - b =\n" << a - b << std::endl;
BOOST_CHECK_EQUAL(a - b, r2);
std::cout << "Doing a += b;" << std::endl;
a += b;
std::cout << "Now a =\n" << a << std::endl;
Matrix<Num, 3, 1> v(1,2,3);
Matrix<Num, 3, 1> w(1,0,0);
std::cout << "-v + w - v =\n" << -v + w - v << std::endl;
BOOST_CHECK_EQUAL(-v + w - v, r3);
}
template <class Num>
void example2()
{
Matrix<Num, 2, 2> a;
a << 1, 2, 3, 4;
Matrix<Num, 3, 1> v(1, 2, 3);
std::cout << "a * 2.5 =\n" << a * 2.5 << std::endl;
std::cout << "0.1 * v =\n" << 0.1 * v << std::endl;
std::cout << "Doing v *= 2;" << std::endl;
v *= 2;
std::cout << "Now v =\n" << v << std::endl;
Num n(4);
std::cout << "Doing v *= Num;" << std::endl;
v *= n;
std::cout << "Now v =\n" << v << std::endl;
typedef typename related_number<Num>::type related_type;
related_type r(6);
std::cout << "Doing v *= RelatedType;" << std::endl;
v *= r;
std::cout << "Now v =\n" << v << std::endl;
std::cout << "RelatedType * v =\n" << r * v << std::endl;
std::cout << "Doing v *= RelatedType^2;" << std::endl;
v *= r * r;
std::cout << "Now v =\n" << v << std::endl;
std::cout << "RelatedType^2 * v =\n" << r * r * v << std::endl;
static_assert(boost::is_same<typename Eigen::ScalarBinaryOpTraits<Num, related_type, Eigen::internal::scalar_product_op<Num, related_type> >::ReturnType, Num>::value, "Incorrect type.");
}
template <class Num>
void example3()
{
using namespace std;
Matrix<Num, Dynamic, Dynamic> a = Matrix<Num, Dynamic, Dynamic>::Random(2, 2);
cout << "Here is the matrix a\n" << a << endl;
cout << "Here is the matrix a^T\n" << a.transpose() << endl;
cout << "Here is the conjugate of a\n" << a.conjugate() << endl;
cout << "Here is the matrix a^*\n" << a.adjoint() << endl;
}
template <class Num>
void example4()
{
Matrix<Num, 2, 2> mat;
mat << 1, 2,
3, 4;
Matrix<Num, 2, 1> u(-1, 1), v(2, 0);
std::cout << "Here is mat*mat:\n" << mat * mat << std::endl;
std::cout << "Here is mat*u:\n" << mat * u << std::endl;
std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl;
std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl;
std::cout << "Here is u*v^T:\n" << u * v.transpose() << std::endl;
std::cout << "Let's multiply mat by itself" << std::endl;
mat = mat * mat;
std::cout << "Now mat is mat:\n" << mat << std::endl;
}
template <class Num>
void example5()
{
using namespace std;
Matrix<Num, 3, 1> v(1, 2, 3);
Matrix<Num, 3, 1> w(0, 1, 2);
cout << "Dot product: " << v.dot(w) << endl;
Num dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar
cout << "Dot product via a matrix product: " << dp << endl;
cout << "Cross product:\n" << v.cross(w) << endl;
}
template <class Num>
void example6()
{
using namespace std;
Matrix<Num, 2, 2> mat;
mat << 1, 2,
3, 4;
cout << "Here is mat.sum(): " << mat.sum() << endl;
cout << "Here is mat.prod(): " << mat.prod() << endl;
cout << "Here is mat.mean(): " << mat.mean() << endl;
cout << "Here is mat.minCoeff(): " << mat.minCoeff() << endl;
cout << "Here is mat.maxCoeff(): " << mat.maxCoeff() << endl;
cout << "Here is mat.trace(): " << mat.trace() << endl;
}
template <class Num>
void example7()
{
using namespace std;
Array<Num, Dynamic, Dynamic> m(2, 2);
// assign some values coefficient by coefficient
m(0, 0) = 1.0; m(0, 1) = 2.0;
m(1, 0) = 3.0; m(1, 1) = m(0, 1) + m(1, 0);
// print values to standard output
cout << m << endl << endl;
// using the comma-initializer is also allowed
m << 1.0, 2.0,
3.0, 4.0;
// print values to standard output
cout << m << endl;
}
template <class Num>
void example8()
{
using namespace std;
Array<Num, Dynamic, Dynamic> a(3, 3);
Array<Num, Dynamic, Dynamic> b(3, 3);
a << 1, 2, 3,
4, 5, 6,
7, 8, 9;
b << 1, 2, 3,
1, 2, 3,
1, 2, 3;
// Adding two arrays
cout << "a + b = " << endl << a + b << endl << endl;
// Subtracting a scalar from an array
cout << "a - 2 = " << endl << a - 2 << endl;
}
template <class Num>
void example9()
{
using namespace std;
Array<Num, Dynamic, Dynamic> a(2, 2);
Array<Num, Dynamic, Dynamic> b(2, 2);
a << 1, 2,
3, 4;
b << 5, 6,
7, 8;
cout << "a * b = " << endl << a * b << endl;
}
template <class Num>
void example10()
{
using namespace std;
Array<Num, Dynamic, 1> a = Array<Num, Dynamic, 1>::Random(5);
a *= 2;
cout << "a =" << endl
<< a << endl;
cout << "a.abs() =" << endl
<< a.abs() << endl;
cout << "a.abs().sqrt() =" << endl
<< a.abs().sqrt() << endl;
cout << "a.min(a.abs().sqrt()) =" << endl
<< a.min(a.abs().sqrt()) << endl;
}
template <class Num>
void example11()
{
using namespace std;
Matrix<Num, Dynamic, Dynamic> m(2, 2);
Matrix<Num, Dynamic, Dynamic> n(2, 2);
Matrix<Num, Dynamic, Dynamic> result(2, 2);
m << 1, 2,
3, 4;
n << 5, 6,
7, 8;
result = m * n;
cout << "-- Matrix m*n: --" << endl << result << endl << endl;
result = m.array() * n.array();
cout << "-- Array m*n: --" << endl << result << endl << endl;
result = m.cwiseProduct(n);
cout << "-- With cwiseProduct: --" << endl << result << endl << endl;
result = m.array() + 4;
cout << "-- Array m + 4: --" << endl << result << endl << endl;
}
template <class Num>
void example12()
{
using namespace std;
Matrix<Num, Dynamic, Dynamic> m(2, 2);
Matrix<Num, Dynamic, Dynamic> n(2, 2);
Matrix<Num, Dynamic, Dynamic> result(2, 2);
m << 1, 2,
3, 4;
n << 5, 6,
7, 8;
result = (m.array() + 4).matrix() * m;
cout << "-- Combination 1: --" << endl << result << endl << endl;
result = (m.array() * n.array()).matrix() * m;
cout << "-- Combination 2: --" << endl << result << endl << endl;
}
template <class Num>
void example13()
{
using namespace std;
Matrix<Num, Dynamic, Dynamic> m(4, 4);
m << 1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16;
cout << "Block in the middle" << endl;
cout << m.template block<2, 2>(1, 1) << endl << endl;
for (int i = 1; i <= 3; ++i)
{
cout << "Block of size " << i << "x" << i << endl;
cout << m.block(0, 0, i, i) << endl << endl;
}
}
template <class Num>
void example14()
{
using namespace std;
Array<Num, 2, 2> m;
m << 1, 2,
3, 4;
Array<Num, 4, 4> a = Array<Num, 4, 4>::Constant(0.6);
cout << "Here is the array a:" << endl << a << endl << endl;
a.template block<2, 2>(1, 1) = m;
cout << "Here is now a with m copied into its central 2x2 block:" << endl << a << endl << endl;
a.block(0, 0, 2, 3) = a.block(2, 1, 2, 3);
cout << "Here is now a with bottom-right 2x3 block copied into top-left 2x2 block:" << endl << a << endl << endl;
}
template <class Num>
void example15()
{
using namespace std;
Eigen::Matrix<Num, Dynamic, Dynamic> m(3, 3);
m << 1, 2, 3,
4, 5, 6,
7, 8, 9;
cout << "Here is the matrix m:" << endl << m << endl;
cout << "2nd Row: " << m.row(1) << endl;
m.col(2) += 3 * m.col(0);
cout << "After adding 3 times the first column into the third column, the matrix m is:\n";
cout << m << endl;
}
template <class Num>
void example16()
{
using namespace std;
Matrix<Num, 4, 4> m;
m << 1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16;
cout << "m.leftCols(2) =" << endl << m.leftCols(2) << endl << endl;
cout << "m.bottomRows<2>() =" << endl << m.template bottomRows<2>() << endl << endl;
m.topLeftCorner(1, 3) = m.bottomRightCorner(3, 1).transpose();
cout << "After assignment, m = " << endl << m << endl;
}
template <class Num>
void example17()
{
using namespace std;
Array<Num, Dynamic, 1> v(6);
v << 1, 2, 3, 4, 5, 6;
cout << "v.head(3) =" << endl << v.head(3) << endl << endl;
cout << "v.tail<3>() = " << endl << v.template tail<3>() << endl << endl;
v.segment(1, 4) *= 2;
cout << "after 'v.segment(1,4) *= 2', v =" << endl << v << endl;
}
template <class Num>
void example18()
{
using namespace std;
Matrix<Num, 2, 2> mat;
mat << 1, 2,
3, 4;
cout << "Here is mat.sum(): " << mat.sum() << endl;
cout << "Here is mat.prod(): " << mat.prod() << endl;
cout << "Here is mat.mean(): " << mat.mean() << endl;
cout << "Here is mat.minCoeff(): " << mat.minCoeff() << endl;
cout << "Here is mat.maxCoeff(): " << mat.maxCoeff() << endl;
cout << "Here is mat.trace(): " << mat.trace() << endl;
BOOST_CHECK_EQUAL(mat.sum(), 10);
BOOST_CHECK_EQUAL(mat.prod(), 24);
BOOST_CHECK_EQUAL(mat.mean(), Num(5) / 2);
BOOST_CHECK_EQUAL(mat.minCoeff(), 1);
BOOST_CHECK_EQUAL(mat.maxCoeff(), 4);
BOOST_CHECK_EQUAL(mat.trace(), 5);
}
template <class Num>
void example18a()
{
using namespace std;
Matrix<Num, 2, 2> mat;
mat << 1, 2,
3, 4;
cout << "Here is mat.sum(): " << mat.sum() << endl;
cout << "Here is mat.prod(): " << mat.prod() << endl;
cout << "Here is mat.mean(): " << mat.mean() << endl;
//cout << "Here is mat.minCoeff(): " << mat.minCoeff() << endl;
//cout << "Here is mat.maxCoeff(): " << mat.maxCoeff() << endl;
cout << "Here is mat.trace(): " << mat.trace() << endl;
}
template <class Num>
void example19()
{
using namespace std;
Matrix<Num, Dynamic, 1> v(2);
Matrix<Num, Dynamic, Dynamic> m(2, 2), n(2, 2);
v << -1,
2;
m << 1, -2,
-3, 4;
cout << "v.squaredNorm() = " << v.squaredNorm() << endl;
cout << "v.norm() = " << v.norm() << endl;
cout << "v.lpNorm<1>() = " << v.template lpNorm<1>() << endl;
cout << "v.lpNorm<Infinity>() = " << v.template lpNorm<Infinity>() << endl;
cout << endl;
cout << "m.squaredNorm() = " << m.squaredNorm() << endl;
cout << "m.norm() = " << m.norm() << endl;
cout << "m.lpNorm<1>() = " << m.template lpNorm<1>() << endl;
cout << "m.lpNorm<Infinity>() = " << m.template lpNorm<Infinity>() << endl;
}
template <class Num>
void example20()
{
using namespace std;
Matrix<Num, 3, 3> A;
Matrix<Num, 3, 1> b;
A << 1, 2, 3, 4, 5, 6, 7, 8, 10;
b << 3, 3, 4;
cout << "Here is the matrix A:\n" << A << endl;
cout << "Here is the vector b:\n" << b << endl;
Matrix<Num, 3, 1> x = A.colPivHouseholderQr().solve(b);
cout << "The solution is:\n" << x << endl;
}
template <class Num>
void example21()
{
using namespace std;
Matrix<Num, 2, 2> A, b;
A << 2, -1, -1, 3;
b << 1, 2, 3, 1;
cout << "Here is the matrix A:\n" << A << endl;
cout << "Here is the right hand side b:\n" << b << endl;
Matrix<Num, 2, 2> x = A.ldlt().solve(b);
cout << "The solution is:\n" << x << endl;
}
template <class Num>
void example22()
{
using namespace std;
Matrix<Num, Dynamic, Dynamic> A = Matrix<Num, Dynamic, Dynamic>::Random(100, 100);
Matrix<Num, Dynamic, Dynamic> b = Matrix<Num, Dynamic, Dynamic>::Random(100, 50);
Matrix<Num, Dynamic, Dynamic> x = A.fullPivLu().solve(b);
Matrix<Num, Dynamic, Dynamic> axmb = A * x - b;
double relative_error = static_cast<double>(abs(axmb.norm() / b.norm())); // norm() is L2 norm
cout << "norm1 = " << axmb.norm() << endl;
cout << "norm2 = " << b.norm() << endl;
cout << "The relative error is:\n" << relative_error << endl;
}
template <class Num>
void example23()
{
using namespace std;
Matrix<Num, 2, 2> A;
A << 1, 2, 2, 3;
cout << "Here is the matrix A:\n" << A << endl;
SelfAdjointEigenSolver<Matrix<Num, 2, 2> > eigensolver(A);
if (eigensolver.info() != Success)
{
std::cout << "Eigenvalue solver failed!" << endl;
}
else
{
cout << "The eigenvalues of A are:\n" << eigensolver.eigenvalues() << endl;
cout << "Here's a matrix whose columns are eigenvectors of A \n"
<< "corresponding to these eigenvalues:\n"
<< eigensolver.eigenvectors() << endl;
}
}
template <class Num>
void example24()
{
using namespace std;
Matrix<Num, 3, 3> A;
A << 1, 2, 1,
2, 1, 0,
-1, 1, 2;
cout << "Here is the matrix A:\n" << A << endl;
cout << "The determinant of A is " << A.determinant() << endl;
cout << "The inverse of A is:\n" << A.inverse() << endl;
}
template <class Num>
void test_integer_type()
{
example1<Num>();
//example2<Num>();
example18<Num>();
}
template <class Num>
void test_float_type()
{
std::cout << "Epsilon = " << Eigen::NumTraits<Num>::epsilon() << std::endl;
std::cout << "Dummy Prec = " << Eigen::NumTraits<Num>::dummy_precision() << std::endl;
std::cout << "Highest = " << Eigen::NumTraits<Num>::highest() << std::endl;
std::cout << "Lowest = " << Eigen::NumTraits<Num>::lowest() << std::endl;
std::cout << "Digits10 = " << Eigen::NumTraits<Num>::digits10() << std::endl;
example1<Num>();
example2<Num>();
example4<Num>();
example5<Num>();
example6<Num>();
example7<Num>();
example8<Num>();
example9<Num>();
example10<Num>();
example11<Num>();
example12<Num>();
example13<Num>();
example14<Num>();
example15<Num>();
example16<Num>();
example17<Num>();
example18<Num>();
example19<Num>();
example20<Num>();
example21<Num>();
example22<Num>();
example23<Num>();
example24<Num>();
}
template <class Num>
void test_complex_type()
{
std::cout << "Epsilon = " << Eigen::NumTraits<Num>::epsilon() << std::endl;
std::cout << "Dummy Prec = " << Eigen::NumTraits<Num>::dummy_precision() << std::endl;
std::cout << "Highest = " << Eigen::NumTraits<Num>::highest() << std::endl;
std::cout << "Lowest = " << Eigen::NumTraits<Num>::lowest() << std::endl;
std::cout << "Digits10 = " << Eigen::NumTraits<Num>::digits10() << std::endl;
example1<Num>();
example2<Num>();
example3<Num>();
example4<Num>();
example5<Num>();
example7<Num>();
example8<Num>();
example9<Num>();
example11<Num>();
example12<Num>();
example13<Num>();
example14<Num>();
example15<Num>();
example16<Num>();
example17<Num>();
example18a<Num>();
example19<Num>();
example20<Num>();
example21<Num>();
example22<Num>();
// example23<Num>(); //requires comparisons.
example24<Num>();
}
namespace boost {
namespace multiprecision {
template <unsigned D>
inline void log_postfix_event(const mpc_complex_backend<D>& val, const char* event_description)
{
if (mpfr_nan_p(mpc_realref(val.data())))
{
std::cout << "Found a NaN! " << event_description << std::endl;
}
}
}
}
int main()
{
using namespace boost::multiprecision;
test_complex_type<mpc_complex>();
#if 0
test_integer_type<int>();
test_float_type<double>();
test_complex_type<std::complex<double> >();
test_float_type<boost::multiprecision::cpp_dec_float_100>();
test_float_type<boost::multiprecision::cpp_bin_float_50>();
test_float_type<boost::multiprecision::mpfr_float>();
test_integer_type<boost::multiprecision::int256_t>();
test_integer_type<boost::multiprecision::cpp_int>();
test_integer_type<boost::multiprecision::cpp_rational>();
test_integer_type<boost::multiprecision::mpz_int>();
test_integer_type<boost::multiprecision::mpq_rational>();
#endif
return 0;
}
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