libs/math/example/constants_eg1.cpp
// Copyright Paul Bristow 2013. // Copyright John Maddock 2010. // Use, modification and distribution are subject to 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) /*! \brief Examples of using the enhanced math constants. \details This allows for access to constants via functions like @c pi(), and also via namespaces, @c using @c namespace boost::math::double_constants; called simply @c pi. */ #include <boost/math/constants/constants.hpp> #include <iostream> using std::cout; using std::endl; #include <limits> using std::numeric_limits; /*! \brief Examples of a template function using constants. \details This example shows using of constants from function calls like @c pi(), rather than the 'cute' plain @c pi use in non-template applications. \tparam Real radius parameter that can be a built-in like float, double, or a user-defined type like multiprecision. \returns Area = pi * radius ^ 2 */ //[math_constants_eg1 template<class Real> Real area(Real r) { using namespace boost::math::constants; return pi<Real>() * r * r; } //] [/math_constants_eg1] int main() { { // Boost.Math constants using function calls like pi(). // using namespace boost::math::constants; using boost::math::constants::pi; using boost::math::constants::one_div_two_pi; #ifdef BOOST_NO_CXX11_NUMERIC_LIMITS std::size_t max_digits10 = 2 + std::numeric_limits<double>::digits * 3010/10000; #else std::size_t max_digits10 = std::numeric_limits<double>::max_digits10; #endif std::cout.precision(max_digits10); cout << "double pi = boost::math::double_constants::pi = " << pi<double>() << endl; // double pi = boost::math::double_constants::pi = 3.1415926535897931 double r = 1.234567890123456789; double d = pi<double>() * r * r; cout << "d = " << d << ", r = " << r << endl; float rf = 0.987654321987654321f; float pif = boost::math::constants::pi<float>(); cout << "pidf = boost::math::constants::pi() = " << pif << endl; // pidf = boost::math::float_constants::pi = 3.1415927410125732 //float df = pi * rf * rf; // conversion from 'const double' to 'float', possible loss of data. float df = pif * rf * rf; cout << "df = " << df << ", rf = " << rf << endl; cout << "one_div_two_pi " << one_div_two_pi<double>() << endl; using boost::math::constants::one_div_two_pi; cout << "one_div_root_two_pi " << one_div_two_pi<double>() << endl; } { // Boost math new constants using namespace selected values, like pi. //using namespace boost::math::float_constants; using namespace boost::math::double_constants; double my2pi = two_pi; // Uses boost::math::double_constants::two_pi; cout << "double my2pi = " << my2pi << endl; using boost::math::float_constants::e; float my_e = e; cout << "float my_e " << my_e << endl; double my_pi = boost::math::double_constants::pi; cout << "double my_pi = boost::math::double_constants::pi = " << my_pi << endl; // If you try to use two namespaces, this may, of course, create ambiguity: // it is not too difficult to do this inadvertently. using namespace boost::math::float_constants; //cout << pi << endl; // error C2872: 'pi' : ambiguous symbol. } { //[math_constants_ambiguity // If you use more than one namespace, this will, of course, create ambiguity: using namespace boost::math::double_constants; using namespace boost::math::constants; //double my_pi = pi(); // error C2872: 'pi' : ambiguous symbol //double my_pi2 = pi; // Context does not allow for disambiguation of overloaded function // It is also possible to create ambiguity inadvertently, // perhaps in other peoples code, // by making the scope of a namespace declaration wider than necessary, // therefore is it prudent to avoid this risk by localising the scope of such definitions. //] [/math_constants_ambiguity] } { // You can, of course, use both methods of access if both are fully qualified, for examples: //cout.precision(std::numeric_limits<double>::max_digits10);// Ideally. cout.precision(2 + std::numeric_limits<double>::digits * 3010/10000); // If no max_digits10. double my_pi1 = boost::math::constants::pi<double>(); double my_pid = boost::math::double_constants::pi; cout << "boost::math::constants::pi<double>() = " << my_pi1 << endl << "boost::math::double_constants::pi = " << my_pid << endl; // cout.precision(std::numeric_limits<float>::max_digits10); // Ideally. cout.precision(2 + std::numeric_limits<double>::digits * 3010/10000); // If no max_digits10. float my_pif = boost::math::float_constants::pi; cout << "boost::math::float_constants::pi = " << my_pif << endl; } { // Use with templates // \warning it is important to be very careful with the type provided as parameter. // For example, naively providing an @b integer instead of a floating-point type can be disastrous. // cout << "Area = " << area(2) << endl; // warning : 'return' : conversion from 'double' to 'int', possible loss of data // Failure to heed this warning can lead to very wrong answers! // Area = 12 !! = 3 * 2 * 2 //[math_constants_template_integer_type //cout << "Area = " << area(2) << endl; // Area = 12! cout << "Area = " << area(2.) << endl; // Area = 12.566371 // You can also avoid this by being explicit about the type of @c area. cout << "Area = " << area<double>(2) << endl; //] [/math_constants_template_integer_type] } /* { using boost::math::constants::pi; //double my_pi3 = pi<double>(); // OK //double my_pi4 = pi<>(); cannot find template type. //double my_pi4 = pi(); // Can't find a function. } */ } // int main() /*[constants_eq1_output Output: double pi = boost::math::double_constants::pi = 3.1415926535897931 d = 4.7882831840285398, r = 1.2345678901234567 pidf = boost::math::constants::pi() = 3.1415927410125732 df = 3.0645015239715576, rf = 0.98765432834625244 one_div_two_pi 0.15915494309189535 one_div_root_two_pi 0.15915494309189535 double my2pi = 6.2831853071795862 float my_e 2.7182817459106445 double my_pi = boost::math::double_constants::pi = 3.1415926535897931 boost::math::constants::pi<double>() = 3.1415926535897931 boost::math::double_constants::pi = 3.1415926535897931 boost::math::float_constants::pi = 3.1415927410125732 Area = 12.566370614359172 Area = 12.566370614359172 ] [/constants_eq1_output] */