Mathematical Constants

Defines mathematical constants commonly in use. More...

Functions
template<typename T >
constexpr T	gears::math::pi () noexcept
	Computes pi with the precision needed.
template<typename T >
constexpr T	gears::math::half () noexcept
	Computes one half with the precision needed.
template<typename T >
constexpr T	gears::math::third () noexcept
	Computes one third with the precision needed.
template<typename T >
constexpr T	gears::math::root_two () noexcept
	Computes √2 with the precision needed.
template<typename T >
constexpr T	gears::math::ln_two () noexcept
	Computes pi with the precision needed.
template<typename T >
constexpr T	gears::math::half_pi () noexcept
	Computes half pi with the precision needed.
template<typename T >
constexpr T	gears::math::third_pi () noexcept
	Computes one third pi with the precision needed.
template<typename T >
constexpr T	gears::math::two_thirds_pi () noexcept
	Computes two thirds pi with the precision needed.
template<typename T >
constexpr T	gears::math::sixth_pi () noexcept
	Computes one sixth pi with the precision needed.
template<typename T >
constexpr T	gears::math::three_fourths_pi () noexcept
	Computes three fourths pi with the precision needed.
template<typename T >
constexpr T	gears::math::four_thirds_pi () noexcept
	Computes four thirds pi with the precision needed.
template<typename T >
constexpr T	gears::math::two_pi () noexcept
	Computes two pi with the precision needed.

Detailed Description

These functions compute their respective named constants up to the precision of the type given. The maximum valid precision that is guaranteed to be valid is std::numeric_limits<T>::digits10 + 2. This is to allow proper roundtrip calculations. For integer types the computed constant is floored. So pi<int>() would return 3. All constants provided are constexpr.

Example usage:

#include <gears/math/constants.hpp>

using namespace gears;

template<typename T>
constexpr T area(T radius) {
    return math::pi<T>() * radius * radius;
}

int main() {
    static_assert(area<double>(4) == 50.26548245743669, "...");
}