special_functions.hpp File Reference

Implimentations for special functions. More...

#include <iostream>
#include <complex>
#include <cfloat>
#include <cmath>
#include <cstdint>
#include <limits>

Go to the source code of this file.

Namespaces
namespace	special
	Name space for special functions.

Typedefs
template<typename T >
using	complex_type = std::complex< T >
	Type alias for complex types.

Functions
template<typename T >
constexpr complex_type< T >	special::i (static_cast< T >(0), static_cast< T >(1))
	I constant.
template<typename T >
complex_type< T >	special::erfcx (complex_type< T > z)
	Compute erfcx(z) = exp(z^2)*erfz(z)
template<typename T >
T	special::sq (T x)
	x^2
template<typename T >
T	special::w_im_y100 (T x)
	Compute a scaled Dawson integral.
template<typename T >
T	special::isqpi ()
	Define 1.0/sqrt(pi)
template<typename T >
T	special::w_im (T x)
	Compute specal case of w(z) = exp(z^2)*erfz(z).
template<typename T >
T	special::erfcx_y100 (const T y100)
	erfcx(x) = exp(x^2)*erfc(x) function, for real x
template<typename T >
T	special::erfcx (T x)
	erfcx(x) = exp(x^2)*erfc(x) function, for real x
template<typename T >
T	special::sinh_taylor (T x)
	sinh(x)
template<typename T >
T	special::sinc (T x, T sinx)
	sinc(x) = sin(x)/x
template<typename T >
complex_type< T >	special::w (complex_type< T > z)
	Compute w(z) = exp(z^2)*erfz(z).
template<typename T >
complex_type< T >	special::taylor (const complex_type< T > z, const T mRe_z2, const T mIm_z2)
	Taylor series.
template<typename T >
complex_type< T >	special::taylor_erfi (const T x, const T y)
	Taylor erfi series.
template<typename T >
complex_type< T >	special::erf_complex (const complex_type< T > z)
	Compute the error function erf(z)
template<typename T >
complex_type< T >	special::erfi (const complex_type< T > z)
	erfi(z) = -i erf(iz)

Variables
template<typename T >
constexpr T	special::expa2n2 []
	Precomputed table of expa2n2[n-1] = exp(-a2*n*n) for double-precision a2 = 0.26865... in w, below.

Detailed Description

Implimentations for special functions.

Special functions are adapted from http://ab-initio.mit.edu/Faddeeva