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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member functions of Z and reduce number of operations | member functions of Z and reduce number of operations | ||
for minor speed gains. | 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) | inline cmplex logZm1oZp1(const cmplex &Z) | ||
| Line 24: | Line 27: | ||
double y(Z.imag()); | double y(Z.imag()); | ||
double r2=x*x+y*y; | 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 )); | |
| − | |||
| − | |||
| − | |||
| − | return cmplex(0.5*log(1.0-( | ||
| − | |||
} | } | ||
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 ));
}
