LogZp1oZm1

Language

c++

Purpose

Calculates <math>\ln\left(\frac{Z-1}{Z+1}\right)</math>

Author

James R. Craig

#include <math.h>
#include <complex>
typedef complex<double> cmplex;
const double PI=3.141592653589793238462643; // pi 
/*******************************************************************************
logZm1oZp1
optimized version of log ((Z-1.0)/(Z+1.0)): 
1.1% of the cost of a direct call- 2 orders of magnitude speedup!
Author: James R. Craig
-------------------------------------------------------------------------------*/
inline cmplex logZm1oZp1(const cmplex &Z)
{ 													 
	double den(Z.real()*Z.real()+Z.imag()*Z.imag()+Z.real()+Z.real()+1.0);
	double add=0.0; 
	if ((Z.real()*Z.real()+Z.imag()*Z.imag())<1.0){
		add=-PI;
		if (Z.imag()>0.0){add=PI;}
	}
	return cmplex(0.5*log(1.0-((Z.real()*(den-Z.real()-2)+den-Z.imag()*Z.imag()-1.0)/(0.25*den*den))),
		      add+atan( (Z.imag()+Z.imag()) /(den-Z.real()-Z.real()-2.0) ));   
}