/*  scfccos.cpp  by K.Tsuru  */
// function ID = 9112
/*****************************************
SComplex class
It returns cos(z).
Let z = x+iy,
cos(z) = cos(x)*cosh(y)-i*sin(x)sinh(y)
 =(1/2){cos(x)[e^y + e^(-y)]+i*sin(x)[e^(-y) - e^y]
 = [exp(iz)+ exp(-iz)]/2
*****************************************/
#ifndef SN_H
#include "sn.h"
#endif
#define UseMultIccos 0
#define UseCSBSccos 1
SComplex Ccos(const SComplex& z){ // z = x+iy
#if UseCSBSccos //  16.14 sec
    SDouble c, s, ch, sh, rp, ip;
    CosSinBS(Re(z), c, s); // c = cos(x), s = sin(x);
    Hyperbolic(Im(z), ch, sh); // ch = cosh(y) sh = sinh(y)
    rp = c*ch;  ip= -s*sh;

    return SComplex(rp, ip);
/*
    SDouble rr = Cos(z.Real())*Cosh(z.Imag());
    SDouble ri = Sin(z.Real())*Sinh(z.Imag());
    ri.ChangeSign();    // ri = -ri
    return SComplex(rr, ri);
*/
#elif UseMultIccos // 15.9 sec
    SComplex eiz = Cexp(MultI(z)), r;
    r = eiz + 1.0/eiz;
    return r.CsDiv(2L); // faster than r/2
#else  // 15.94 sec
    SComplex eiz = Cexp(I*z), r;
    r = eiz + 1.0/eiz;
    return r.CsDiv(2L); // faster than r/2
#endif
}