Difference between revisions of "LogZp1oZm1"

Latest revision as of 14:56, 12 January 2008

Language

c++

Purpose

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

Author

James R. Craig, Ph. Le Grand

#include <math.h>
#include <complex>
typedef std::complex<double> cmplex;
const double PI=3.141592653589793238462643; // pi 
/*******************************************************************************
logZm1oZp1
optimized version of log ((Z-1.0)/(Z+1.0)): 
~13% of the cost of a direct call- 1 order of magnitude speedup!
Author: James R. Craig
Modified 2007 12 06 by Ph. Le Grand:
    Added local variables x,y,r2 to reduce number of calls to 
    member functions of Z and reduce number of operations 
    for minor speed gains.
Modified 2008 01 11 by Ph. Le Grand:
    Reduced some operations for minor speed gains,
    used atan2, for speed and reduction of logic.
-------------------------------------------------------------------------------*/
inline cmplex logZm1oZp1(const cmplex &Z)
{ 	
	double x(Z.real());
	double y(Z.imag());	
	double r2=x*x+y*y;								 

	return cmplex(0.5*log(1.0-4.0*x/(r2+x+x+1.0)),
		      atan2( y+y, r2-1.0 ));   
}