LogZp1oZm1
From aemwiki
- 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. -------------------------------------------------------------------------------*/ inline cmplex logZm1oZp1(const cmplex &Z) { double x(Z.real()); double y(Z.imag()); double r2=x*x+y*y; double den(r2+x+x+1.0); double add=0.0; if ((r2)<1.0){ add=-PI; if (y>=0.0){add=PI;} } return cmplex(0.5*log(1.0-4.0*x/den), add+atan( (y+y) /(r2-1.0) )); }