E.V.E
v2023.02.15
 
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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:

About constants names:

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 \(\zeta(3)\).