Difference between revisions of "LogZp1oZm1"
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#include <math.h> | #include <math.h> | ||
#include <complex> | #include <complex> | ||
| − | typedef complex<double> cmplex; | + | typedef std::complex<double> cmplex; |
const double PI=3.141592653589793238462643; // pi | const double PI=3.141592653589793238462643; // pi | ||
/******************************************************************************* | /******************************************************************************* | ||
| Line 14: | Line 14: | ||
1.1% of the cost of a direct call- 2 orders of magnitude speedup! | 1.1% of the cost of a direct call- 2 orders of magnitude speedup! | ||
Author: James R. Craig | 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) | inline cmplex logZm1oZp1(const cmplex &Z) | ||
| − | { | + | { |
| − | double | + | 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; | double add=0.0; | ||
| − | if (( | + | if ((r2)<1.0){ |
add=-PI; | add=-PI; | ||
| − | if ( | + | if (y>0.0){add=PI;} |
} | } | ||
| − | return cmplex(0.5*log(1.0-(( | + | return cmplex(0.5*log(1.0-((x*(den-2)+den-r2-1.0)/(0.25*den*den))), |
| − | add+atan( ( | + | add+atan( (y+y) /(den-x-x-2.0) )); |
} | } | ||
Revision as of 17:34, 6 December 2007
- Language
- c++
- Purpose
- Calculates <math>\ln\left(\frac{Z-1}{Z+1}\right)</math>
- Author
- James R. Craig
#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)):
1.1% of the cost of a direct call- 2 orders 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) ));
}
