Constants

Detailed Description

These functions allows access to scalar and SIMD values of some mathematical constants. In particular, all libc++ constants are here, sometimes with a different name.

All floating mathematical constants supports a regular call and two decorated calls:

• the regular call provides the floating point representation that is nearest to the mathematical value,
• eve::upward provides the least representable value that is greater than the mathematical value,
• eve::downward provides the greatest representable value that is less than the mathematical value,

About constants names:

• When a name contains an _ it means that preceding the underscore is a 'function or multiplication that must be applied to the following parts:
  • log_2 stands for \(\log(2)\) the natural logarithm of 2
  • log2_e stands for \(\log2(e)\) the logarithm in base 2 of the euler constant,
  • inv_pi is the inverse of \(\pi\).
  • four_pio_3 stands for \(4\pi/3\) (the o meanings over).

Variables
constexpr auto	eve::catalan = functor<catalan_t>
	Callable object computing the catalan constant \(\beta(2) = \sum_0^\infty \frac{(-1)^n}{(2n+1)^2}\).
constexpr auto	eve::cbrt_pi = functor<cbrt_pi_t>
	Callable object computing the constant \(\sqrt[3]\pi\).
constexpr auto	eve::cos_1 = functor<cos_1_t>
	Callable object computing the constant \(\cos1\).
constexpr auto	eve::cosh_1 = functor<cosh_1_t>
	Callable object computing the constant \(\cosh(1)\).
constexpr auto	eve::egamma = functor<egamma_t>
	Callable object computing the Euler-Mascheroni constant : \(\gamma = \lim_{n\to\infty}\left( \sum_{k = 0}^n \frac1k - \log n\right )\).
constexpr auto	eve::egamma_sqr = functor<egamma_sqr_t>
	Callable object computing the square of the [Euler-Mascheroni constant](eve::egamma).
constexpr auto	eve::epso_2 = functor<epso_2_t>
	Callable object computing the half of the machine epsilon.
constexpr auto	eve::euler = functor<euler_t>
	Callable object computing the constant e basis of the natural logarithms.
constexpr auto	eve::exp_pi = functor<exp_pi_t>
	Callable object computing the constant \(e^\pi\).
constexpr auto	eve::extreme_value_skewness = functor<extreme_value_skewness_t>
	Callable object computing the extreme value distribution skewness : \(12\sqrt6\zeta(3)/\pi^3\).
constexpr auto	eve::four_minus_pi = functor<four_minus_pi_t>
	Callable object computing the constant \(4-\pi\).
constexpr auto	eve::four_pio_3 = functor<four_pio_3_t>
	Callable object computing the constant \(4\pi/3\).
constexpr auto	eve::glaisher = functor<glaisher_t>
	Callable object computing the Glaisher-Kinkelin constant.
constexpr auto	eve::inv_2eps = functor<inv_2eps_t>
	Callable object computing half the inverse of the machine epsilon.
constexpr auto	eve::inv_2pi = functor<inv_2pi_t>
	Callable object computing the constant \(\frac{1}{2\pi}\).
constexpr auto	eve::inv_e = functor<inv_e_t>
	Callable object computing the constant \(e^{-1}\).
constexpr auto	eve::inv_egamma = functor<inv_egamma_t>
	Callable object computing the inverse of the [Euler-Mascheroni constant](eve::egamma).
constexpr auto	eve::inv_pi = functor<inv_pi_t>
	Callable object computing the constant \(\frac{1}{\pi}\).
constexpr auto	eve::invcbrt_pi = functor<invcbrt_pi_t>
	Callable object computing the constant \(\pi^{-1/3}\).
constexpr auto	eve::invlog10_2 = functor<invlog10_2_t>
	Callable object computing the constant \(1/\log_{10}2\).
constexpr auto	eve::invlog10_e = functor<invlog10_e_t>
	Callable object computing the constant \(1/\log_{10}e\).
constexpr auto	eve::invlog_10 = functor<invlog_10_t>
	Callable object computing \(1/\log10\).
constexpr auto	eve::invlog_2 = functor<invlog_2_t>
	Callable object computing the constant \(1/\log2\).
constexpr auto	eve::invlog_phi = functor<invlog_phi_t>
	Callable object computing the inverse of the logarithm of the golden ratio : \(1/\log((1+\sqrt5)/2)\).
constexpr auto	eve::invsqrt_2 = functor<invsqrt_2_t>
	Callable object computing the constant \(2^{-1/2}\).
constexpr auto	eve::khinchin = functor<khinchin_t>
	Callable object computing the Khinchin constant.
constexpr auto	eve::log10_e = functor<log10_e_t>
	Callable object computing the constant \(\log_{10}e\).
constexpr auto	eve::log2_e = functor<log2_e_t>
	Callable object computing the constant \(\log_2 e\).
constexpr auto	eve::log_10 = functor<log_10_t>
	Callable object computing the constant \(\log 10\).
constexpr auto	eve::log_2 = functor<log_2_t>
	Callable object computing the constant \(\log 2\).
constexpr auto	eve::log_phi = functor<log_phi_t>
	Callable object computing the logarithm of the golden ratio : \(\log((1+\sqrt5)/2)\).
constexpr auto	eve::loglog_2 = functor<loglog_2_t>
	Callable object computing the constant \(\log(\log2)\).
constexpr auto	eve::maxlog = functor<maxlog_t>
	Callable object computing the greatest positive value for which eve::exp is finite.
constexpr auto	eve::maxlog10 = functor<maxlog10_t>
	Callable object computing the greatest positive value for which eve::exp10 is finite.
constexpr auto	eve::maxlog2 = functor<maxlog2_t>
	Callable object computing the greatest positive value for which eve::exp2 is finite.
constexpr auto	eve::minlog = functor<minlog_t>
	Callable object computing the least value for which eve::exp is not zero.
constexpr auto	eve::minlog10 = functor<minlog10_t>
	Callable object computing the least value for which eve::exp10 is not zero.
constexpr auto	eve::minlog10denormal = functor<minlog10denormal_t>
	Callable object computing the least value for which eve::exp10 is not zero.
constexpr auto	eve::minlog2 = functor<minlog2_t>
	Callable object computing the least value for which eve::exp2 is not zero.
constexpr auto	eve::minlog2denormal = functor<minlog2denormal_t>
	Callable object computing the least value for which eve::exp2 is not denormal.
constexpr auto	eve::minlogdenormal = functor<minlogdenormal_t>
	Callable object computing the least value for which eve::exp is not denormal.
constexpr auto	eve::phi = functor<phi_t>
	Callable object computing the golden ratio : \(\frac{1+\sqrt5}2\).
constexpr auto	eve::pi = functor<pi_t>
	Callable object computing the constant \(\pi\).
constexpr auto	eve::pi2 = functor<pi2_t>
	Callable object computing the square of \(\pi\).
constexpr auto	eve::pi2o_16 = functor<pi2o_16_t>
	Callable object computing the constant \(\pi^2/16\).
constexpr auto	eve::pi2o_6 = functor<pi2o_6_t>
	Callable object computing the constant \(\pi^2/6\).
constexpr auto	eve::pi3 = functor<pi3_t>
	Callable object computing the pi cubed value : \(\pi^3\).
constexpr auto	eve::pi_minus_3 = functor<pi_minus_3_t>
	Callable object computing the constant \(\pi-3\).
constexpr auto	eve::pi_pow_e = functor<pi_pow_e_t>
	Callable object computing the constant \(\pi^e\).
constexpr auto	eve::pio_2 = functor<pio_2_t>
	Callable object computing the constant \(\pi/2\).
constexpr auto	eve::pio_3 = functor<pio_3_t>
	Callable object computing the constant \(\pi/3\).
constexpr auto	eve::pio_4 = functor<pio_4_t>
	Callable object computing the constant \(\pi/4\).
constexpr auto	eve::pio_6 = functor<pio_6_t>
	Callable object computing the constant \(\pi/6\).
constexpr auto	eve::quarter = functor<quarter_t>
	Callable object computing the constant \(1/3\).
constexpr auto	eve::rayleigh_kurtosis = functor<rayleigh_kurtosis_t>
	Callable object computing the Rayleigh kurtosis value : \(3+(6\pi^2-24\pi+16)/(4-\pi^2)\).
constexpr auto	eve::rayleigh_kurtosis_excess = functor<rayleigh_kurtosis_excess_t>
	Callable object computing the Rayleigh kurtosis excess value : \(-(6\pi^2-24\pi+16)/(4-\pi^2)\).
constexpr auto	eve::rayleigh_skewness = functor<rayleigh_skewness_t>
	Callable object computing the Rayleigh skewness value : \(2\sqrt\pi(\pi-3)/(4-\pi^{3/2})\).
constexpr auto	eve::rsqrt_2pi = functor<rsqrt_2pi_t>
	Callable object computing the constant \(1/\sqrt{2\pi}\).
constexpr auto	eve::rsqrt_e = functor<rsqrt_e_t>
	Callable object computing the constant \(1/\sqrt{e}\).
constexpr auto	eve::rsqrt_pi = functor<rsqrt_pi_t>
	Callable object computing the constant \(\pi^{-1/2}\).
constexpr auto	eve::rsqrt_pio_2 = functor<rsqrt_pio_2_t>
	Callable object computing the constant \((\pi/2)^{-1/2}\).
constexpr auto	eve::sin_1 = functor<sin_1_t>
	Callable object computing the constant \(\sin(1)\).
constexpr auto	eve::sinh_1 = functor<sinh_1_t>
	Callable object computing the constant \(\sinh(1)\).
constexpr auto	eve::sixth = functor<sixth_t>
	Callable object computing the constant \(1/6\).
constexpr auto	eve::sqrt_2 = functor<sqrt_2_t>
	Callable object computing the constant \(\sqrt2\).
constexpr auto	eve::sqrt_2pi = functor<sqrt_2pi_t>
	Callable object computing the constant \(\sqrt{2\pi}\).
constexpr auto	eve::sqrt_3 = functor<sqrt_3_t>
	Callable object computing constant \(\sqrt{3}\).
constexpr auto	eve::sqrt_e = functor<sqrt_e_t>
	Callable object computing the constant \(\sqrt{e}\).
constexpr auto	eve::sqrt_pi = functor<sqrt_pi_t>
	Callable object computing the constant \(\sqrt{\pi}\).
constexpr auto	eve::sqrt_pio_2 = functor<sqrt_pio_2_t>
	Callable object computing the constant \(\sqrt{\pi/2}\).
constexpr auto	eve::sqrtlog_4 = functor<sqrtlog_4_t>
	Callable object computing the constant \(\sqrt{\log4}\).
constexpr auto	eve::third = functor<third_t>
	Callable object computing the constant \(1/3\).
constexpr auto	eve::three_o_4 = functor<three_o_4_t>
	Callable object computing the constant \(3/4\).
constexpr auto	eve::three_pio_4 = functor<three_pio_4_t>
	Callable object computing the constant \(3\pi/4\).
constexpr auto	eve::two_o_3 = functor<two_o_3_t>
	Callable object computing the constant \(2/3\).
constexpr auto	eve::two_o_pi = functor<two_o_pi_t>
	Callable object computing the constant \(2/\pi\).
constexpr auto	eve::two_o_sqrt_pi = functor<two_o_sqrt_pi_t>
	Callable object computing the constant \(2/\sqrt\pi\).
constexpr auto	eve::two_pi = functor<two_pi_t>
	Callable object computing the constant \(2\pi\).
constexpr auto	eve::two_pio_3 = functor<two_pio_3_t>
	Callable object computing the constant \(2\pi/3\).
constexpr auto	eve::zeta_2 = functor<zeta_2_t>
	Callable object computing the constant \(\zeta(2)\).
constexpr auto	eve::zeta_3 = functor<zeta_3_t>
	Callable object computing the constant \(\zeta(3)\).