// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
-// This example requires C++17.
+#if !defined(__cpp_structured_bindings) || (__cpp_structured_bindings < 201606L)
+# error "This example requires a C++17 compiler that supports 'structured bindings'. Try /std:c++17 or -std=c++17 or later."
+#endif
-#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostic output.
+//#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostic output.
#include <boost/math/quadrature/ooura_fourier_integrals.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp> // for cpp_bin_float_quad, cpp_bin_float_50...
int main()
{
- try
- {
- typedef boost::multiprecision::cpp_bin_float_quad Real;
-
- std::cout.precision(std::numeric_limits<Real>::max_digits10); // Show all potentially significant digits.
-
- using boost::math::quadrature::ooura_fourier_cos;
- using boost::math::constants::half_pi;
- using boost::math::constants::e;
-
- //[ooura_fourier_integrals_multiprecision_example_1
-
- // Use the default parameters for tolerance root_epsilon and eight levels for a type of 8 bytes.
- //auto integrator = ooura_fourier_cos<Real>();
- // Decide on a (tight) tolerance.
- const Real tol = 2 * std::numeric_limits<Real>::epsilon();
- auto integrator = ooura_fourier_cos<Real>(tol, 8); // Loops or gets worse for more than 8.
-
- auto f = [](Real x)
- { // More complex example function.
- return 1 / (x * x + 1);
- };
-
- double omega = 1;
- auto [result, relative_error] = integrator.integrate(f, omega);
-
- //] [/ooura_fourier_integrals_multiprecision_example_1]
-
- //[ooura_fourier_integrals_multiprecision_example_2
- std::cout << "Integral = " << result << ", relative error estimate " << relative_error << std::endl;
-
- const Real expected = half_pi<Real>() / e<Real>(); // Expect integral = 1/(2e)
- std::cout << "pi/(2e) = " << expected << ", difference " << result - expected << std::endl;
- //] [/ooura_fourier_integrals_multiprecision_example_2]
- }
- catch (std::exception const & ex)
- {
- // Lacking try&catch blocks, the program will abort after any throw, whereas the
- // message below from the thrown exception will give some helpful clues as to the cause of the problem.
- std::cout << "\n""Message from thrown exception was:\n " << ex.what() << std::endl;
- }
+ try
+ {
+ typedef boost::multiprecision::cpp_bin_float_quad Real;
+
+ std::cout.precision(std::numeric_limits<Real>::max_digits10); // Show all potentially significant digits.
+
+ using boost::math::quadrature::ooura_fourier_cos;
+ using boost::math::constants::half_pi;
+ using boost::math::constants::e;
+
+ //[ooura_fourier_integrals_multiprecision_example_1
+
+ // Use the default parameters for tolerance root_epsilon and eight levels for a type of 8 bytes.
+ //auto integrator = ooura_fourier_cos<Real>();
+ // Decide on a (tight) tolerance.
+ const Real tol = 2 * std::numeric_limits<Real>::epsilon();
+ auto integrator = ooura_fourier_cos<Real>(tol, 8); // Loops or gets worse for more than 8.
+
+ auto f = [](Real x)
+ { // More complex example function.
+ return 1 / (x * x + 1);
+ };
+
+ double omega = 1;
+ auto [result, relative_error] = integrator.integrate(f, omega);
+
+ //] [/ooura_fourier_integrals_multiprecision_example_1]
+
+ //[ooura_fourier_integrals_multiprecision_example_2
+ std::cout << "Integral = " << result << ", relative error estimate " << relative_error << std::endl;
+
+ const Real expected = half_pi<Real>() / e<Real>(); // Expect integral = 1/(2e)
+ std::cout << "pi/(2e) = " << expected << ", difference " << result - expected << std::endl;
+ //] [/ooura_fourier_integrals_multiprecision_example_2]
+ }
+ catch (std::exception const & ex)
+ {
+ // Lacking try&catch blocks, the program will abort after any throw, whereas the
+ // message below from the thrown exception will give some helpful clues as to the cause of the problem.
+ std::cout << "\n""Message from thrown exception was:\n " << ex.what() << std::endl;
+ }
} // int main()
/*
``
//] [/ooura_fourier_integrals_example_multiprecision_diagnostic_output_1]
-
-Example of it going wrong below
-
->ooura_fourier_cos with relative error goal 1.925929944387235853055977942584927319e-34 & 15 levels.
-1>epsilon for type = 1.925929944387235853055977942584927319e-34
-1>h = 1.000000000000000000000000000000000, I_h = 0.588268622591776615359568690603776 = 0.5882686225917766153595686906037760, absolute error estimate = nan
-1>h = 0.500000000000000000000000000000000, I_h = 0.577871642184837461311756940493259 = 0.5778716421848374613117569404932595, absolute error estimate = 1.039698040693915404781175011051656e-02
-1>h = 0.250000000000000000000000000000000, I_h = 0.577863671186882539559996800783122 = 0.5778636711868825395599968007831220, absolute error estimate = 7.970997954921751760139710137450075e-06
-1>h = 0.125000000000000000000000000000000, I_h = 0.577863674895460885593491133506723 = 0.5778636748954608855934911335067232, absolute error estimate = 3.708578346033494332723601147051768e-09
-1>h = 0.062500000000000000000000000000000, I_h = 0.577863674895460858955046591656350 = 0.5778636748954608589550465916563502, absolute error estimate = 2.663844454185037302771663314961535e-17
-1>h = 0.031250000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563484, absolute error estimate = 1.733336949948512267750380148326435e-33
-1>h = 0.015625000000000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563479, absolute error estimate = 4.814824860968089632639944856462318e-34
-1>h = 0.007812500000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563473, absolute error estimate = 6.740754805355325485695922799047246e-34
-1>h = 0.003906250000000000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563475, absolute error estimate = 1.925929944387235853055977942584927e-34
-1>h = 0.001953125000000000000000000000000, I_h = 0.577863674895460858955046591656346 = 0.5778636748954608589550465916563463, absolute error estimate = 1.155557966632341511833586765550956e-33
-1>h = 0.000976562500000000000000000000000, I_h = 0.577863674895460858955046591656350 = 0.5778636748954608589550465916563504, absolute error estimate = 4.140749380432557084070352576557594e-33
-1>h = 0.000488281250000000000000000000000, I_h = 0.577863674895460858955046591656348 = 0.5778636748954608589550465916563478, absolute error estimate = 2.600005424922768401625570222489652e-33
-1>h = 0.000244140625000000000000000000000, I_h = 0.577863674895460858955046591656342 = 0.5778636748954608589550465916563418, absolute error estimate = 6.066679324819792937126330519142521e-33
-1>h = 0.000122070312500000000000000000000, I_h = 0.577863674895460858955046591656347 = 0.5778636748954608589550465916563467, absolute error estimate = 4.911121358187451425292743753591565e-33
-1>h = 0.000061035156250000000000000000000, I_h = 0.577863674895460858955046591656342 = 0.5778636748954608589550465916563424, absolute error estimate = 4.333342374871280669375950370816086e-33
-1>h = 0.000030517578125000000000000000000, I_h = 0.577863674895460858955046591656328 = 0.5778636748954608589550465916563282, absolute error estimate = 1.415558509124618351996143787799922e-32
-
-
-
-
-
*/
projects / platform / upstream / boost.git / blobdiff