E.V.E
v2022.09.01
Elliptic functions

Detailed Description

Elliptic functions.

This module provides implementation for scalar and SIMD versions of elliptic functions.

Convenience header:

#include <eve/module/elliptic.hpp>

Variables

constexpr callable_ellint_1_ eve::ellint_1 = {}
 Computes the elliptic integrals of the first kind : \(\mathbf{F}(\phi, k) = \int_0^{\phi} \frac{\mathrm{d}t}{\sqrt{1-k^2\sin^2 t}}\) and \(\mathbf{K}(k) = \int_0^{\pi/2} \frac{\mathrm{d}t}{\sqrt{1-k^2\sin^2 t}}\). More...
 
constexpr callable_ellint_2_ eve::ellint_2 = {}
 Computes the elliptic integrals of the second kind : \( \mathbf{E}(\phi, k) = \int_0^{\phi} \scriptstyle \sqrt{1-k^2\sin^2 t} \scriptstyle\;\mathrm{d}t\) and \(\mathbf{E}(k) = \int_0^{\pi/2} \scriptstyle \sqrt{1-k^2\sin^2 t} \scriptstyle\;\mathrm{d}t\). More...
 
constexpr callable_ellint_d_ eve::ellint_d = {}
 Computes the \(\mbox{D}\) elliptic integrals : \( \mathbf{D}(\phi, k) = \int_0^{\phi} \frac{\sin^2 t}{\sqrt{1-k^2\sin^2 t}} \scriptstyle\;\mathrm{d}t\) and \( \mathbf{D}(k) = \int_0^{\pi/2} \frac{\sin^2 t}{\sqrt{1-k^2\sin^2 t}} \scriptstyle\;\mathrm{d}t\). More...
 
constexpr callable_ellint_rc_ eve::ellint_rc = {}
 computes the degenerate Carlson's elliptic integral \( \mathbf{R}_\mathbf{C}(x, y) = \frac12 \int_{0}^{\infty} \scriptstyle(t+x)^{-1/2}(t+y)^{-1}\scriptstyle\;\mathrm{d}t\). More...
 
constexpr callable_ellint_rd_ eve::ellint_rd = {}
 Computes the Carlson's elliptic integral. More...
 
constexpr callable_ellint_rf_ eve::ellint_rf = {}
 Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{F}(x, y) = \mathbf{R}_\mathbf{D}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)]^{-1/2} (t+z)^{-3/2}\scriptstyle\;\mathrm{d}t\). More...
 
constexpr callable_ellint_rg_ eve::ellint_rg = {}
 Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{G}(x, y) = \frac1{4\pi} \int_{0}^{2\pi}\int_{0}^{\pi} \scriptstyle\sqrt{x\sin^2\theta\cos^2\phi +y\sin^2\theta\sin^2\phi +z\cos^2\theta} \scriptstyle\;\mathrm{d}\theta\;\mathrm{d}\phi\). More...
 
constexpr callable_ellint_rj_ eve::ellint_rj = {}
 Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{J}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle(t+p)^{-1}[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\). More...