Difference between revisions of "LogZp1oZm1"
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Analytophile (talk | contribs) (revised summary of speedup, changed y=0 to y>=0 for consistency with c++ complex library) |
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; Purpose: Calculates <math>\ln\left(\frac{Z-1}{Z+1}\right)</math> | ; Purpose: Calculates <math>\ln\left(\frac{Z-1}{Z+1}\right)</math> | ||
| − | ; Author: James R. Craig | + | ; Author: James R. Craig, Ph. Le Grand |
#include <math.h> | #include <math.h> | ||
| Line 12: | Line 12: | ||
logZm1oZp1 | logZm1oZp1 | ||
optimized version of log ((Z-1.0)/(Z+1.0)): | 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 | Author: James R. Craig | ||
Modified 2007 12 06 by Ph. Le Grand: | Modified 2007 12 06 by Ph. Le Grand: | ||
| Line 28: | Line 28: | ||
if ((r2)<1.0){ | if ((r2)<1.0){ | ||
add=-PI; | add=-PI; | ||
| − | if (y>0.0){add=PI;} | + | if (y>=0.0){add=PI;} |
} | } | ||
return cmplex(0.5*log(1.0-((x*(den-2)+den-r2-1.0)/(0.25*den*den))), | return cmplex(0.5*log(1.0-((x*(den-2)+den-r2-1.0)/(0.25*den*den))), | ||
add+atan( (y+y) /(den-x-x-2.0) )); | add+atan( (y+y) /(den-x-x-2.0) )); | ||
} | } | ||
Revision as of 08:51, 7 December 2007
- 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.
-------------------------------------------------------------------------------*/
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-((x*(den-2)+den-r2-1.0)/(0.25*den*den))),
add+atan( (y+y) /(den-x-x-2.0) ));
}
