Boost C++ Libraries

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Numeric Constants

Synopsis

#include <boost/math/constants/constants.hpp>

namespace boost{ namespace math{ namespace constants{

template <class T> T pi();
template <class T> T root_pi();
template <class T> T root_half_pi();
template <class T> T root_two_pi();
template <class T> T root_ln_four();
template <class T> T e();
template <class T> T half();
template <class T> T euler();
template <class T> T root_two();
template <class T> T ln_two();
template <class T> T ln_ln_two();
template <class T> T third();
template <class T> T twothirds();
template <class T> T pi_minus_three();
template <class T> T four_minus_pi();

}}} // namespaces

Description

The header boost/math/constants/constants.hpp contains some numeric constants that we have found useful in the development of this library. New constants are added on an ad-hock basis based on need.

Usage is like this:

template <class T>
T circumference(T r)
{
   return 2 * boost::math::constants::pi<T>() * r;
}

All the constants are accurate to at least the 34 decimal digits required for 128-bit long doubles, and most are accurate to 100 digits or more when used with a suitable arbitrary precision type.

The following table summarises the constants we have at present:

Constant	Meaning	Value
pi	π	3.1415926535897932384...
root_pi	√π	1.772453850905516027...
root_half_pi	√(π/2)	1.253314137315500251...
root_two_pi	√(2*π)	2.506628274631000502...
root_ln_four	√(ln(4))	1.17741002251547469...
e	e	2.71828182845904523536...
half	0.5	0.5
euler	Euler's constant	0.577215664901532860606
root_two	√2	1.4142135623730950488...
ln_two	ln(2)	0.6931471805599453094...
ln_ln_two	ln(ln(2))	-0.3665129205816643...
third	1/3	0.333333333333333333...
twothirds	2/3	0.666666666666666666...
pi_minus_three	π-3	0.14159265358979323846...
four_minus_pi	4-π	0.85840734641020676153735...