/*  scfcsin.cpp  by K.Tsuru  */
// function ID = 9113
/*****************************************
SComplex class
It returns sin(z).
Let z = x+iy,
sin(z) = sin(x)*cosh(y)+i*cos(x)sinh(y)
 = (i/2)*[exp(-iz)- exp(iz)]
*****************************************/
#ifndef SN_H
#include "sn.h"
#endif

#define UseMultI 0

SComplex Csin(const SComplex& z){
#if 0 // 16.1 sec
    SDouble rr, ri, sh;
    sh = Sinh(z.Imag());
    rr = Sin(z.Real())*Sqrt(1.0+sh*sh);
    ri = Cos(z.Real())*sh;

    return SComplex(rr, ri);

#elif UseMultI // 15.9 sec
    SComplex eiz = Cexp(MultI(z)), r;
    r = 1.0/eiz - eiz;
    r.MultI();
    return r.CsDiv(2L); // faster than r/2
#else // 15.8 sec
    SComplex eiz = Cexp(IU*z), r;
    r = 1.0/eiz - eiz;
    r *= IU; // faster than r = r*I
    return r.CsDiv(2L); // faster than r/2
#endif
}