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// serega.cin is the numerical C++ implementation of functions 
// Serega function and ArcSerega.
/*  //headers recommended: 
using namespace std;
#include <complex>
// #include"ado.cin"
#include "conto.cin" 
#define DO(x,y) for(x=0;x<y;x++)
#define DB double
#define z_type complex<double>
#define Re(x) (x.real())
#define Im(x) (x.imag())
// Warining: non-holomorphic functions below!
z_type Serega(z_type z){ DB x,y, p,q, r,s,c; int n;  x=Re(z); y=Im(z);  
r=exp(y); s=sin(x); c=cos(x); p=x-r*s; q=y+r*c; return z_type(p,q);  }
z_type ArcSerega(z_type z){  DB x,y ,X,Y,X0,Y0, r,s,c, rc,rs, dX, dY; int n;
X0=Re(z); Y0=Im(z); r=exp(Y0-1.); s=sin(X0); c=cos(X0); rc=r*c; rs=r*s; 
DO(n,8) { r=exp(y - exp(-.5*n));  s=sin(x); x=X0+r*s; y=Y0-r*cos(x); if(y>0){ x-=s*(1.+y); y=0.;} }
DO(n,32){ r=exp(y - exp(-.5*(2.*n+8.))); c=cos(x); s=sin(x); rc=r*c; rs=r*s;
 X=x-rs; dX=X-X0; 
 Y=y+rc; dY=Y-Y0;  DB d=1.-r*r; d*=1.01;
 x-= ( (1+rc)*dX + rs *dY )/d;
 y-= ( rs  *dX +(1-rc)*dY )/d;  if(y>0){ return z_type(99., 99.);}  //99 is errorcode; feel free to change it to anything more suitable.
return z_type(x,y);



Serega function, ArcSerega, C++ Cateogry:Navier–Stokes