/*  scfctanh.cpp  by K.Tsuru  */
// function ID = 9111
/*********************************************************
SComplex class
It returns tanh(z) = {exp(2*z)-1}/{exp(2*z)+1}.
Let z = x+i*y,
tanh(x+i*y) = {sinh(2*x)+i*sin(2*y)}/{cosh(2*x)+cos(2*y)}.
**********************************************************/
#ifndef SN_H
#include "sn.h"
#endif
#define Usectanh 0
#define Useez2ctanh 0

SComplex Ctanh(const SComplex& z)
{
    if(z.IsZero()) return 0.0;
 #if Usectanh // 31.8 sec
    SComplex z2 = 2*z;
    SDouble den = Cosh(z2.Real())+Cos(z2.Imag());
    SDouble rr =Sinh(z2.Real()), ri = Sin(z2.Imag());

    den = 1.0/den;
    rr *= den;  ri *= den;
    return SComplex(rr, ri);

 #elif Useez2ctanh // 16.15 sec
    SComplex e2z = Cexp(2.0*z), r = (e2z - 1.0)/(e2z + 1.0);

    return r;

 #else // 15.9 sec
    SDouble ch2x, sh2x, c2y, s2y, x2(2*Re(z)), y2(2*Im(z));

    Hyperbolic(x2, ch2x, sh2x); // ch2x = cosh(2x) sh2x = sinh(2x)
    CosSinBS(y2, c2y, s2y);     // c2y = cos(2y), s2y = sin(2y);

    SDouble dr = 1.0/(ch2x + c2y), rr = sh2x * dr, ri = s2y * dr;

    return SComplex(rr, ri);
 #endif
}