WSJT-X/boost/libs/math/example/constants_eg1.cpp

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// 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]
*/