/*  scftanbs.cpp  by K.Tsuru  */
// function ID = 9123  since ver.2.18
/*****************************************
SComplex class
It returns tan(z) using binary splitting method.
Let z = x+iy,
tan(z) = {sin(2*x)+i*sinh(2*y)}/{cos(2*x)+cosh(2*y)}.
*****************************************/
#ifndef SN_H
#include "sn.h"
#endif
SComplex CtanBS(const SComplex& z){
    SDouble c2, s2, ch2, sh2;
    CosSinBS(2 * z.Real(), c2, s2); // c2 = cos(2x), s2 = sin(2x)
    SDouble e, r;
    int ys = z.Imag().Sign(9122);

    if(ys > 0) {    // y > 0
        e = ExpBS(2 * z.Imag());    // = exp(2y)
        r = 1/e;
        ch2 = DDiv2(e + r);     // = cosh(2y)
        sh2 = ch2 - r;          // = sinh(2y)
    } else if(ys == 0) {    // y = 0
        ch2 = 1;    sh2 = 0.0;
    } else {    // y < 0
        e = ExpBS(-2 * z.Imag());   // = exp(-2y)
        r = 1/e;
        ch2 = DDiv2(e + r);     // = cosh(-2y)
        sh2 = ch2 - e;          // = -sinh(-2y)
    }

    SDouble r_den, rr, ri;
    r_den = 1.0/(c2 + ch2);

    rr = s2 * r_den;
    ri = sh2 * r_den;

    return SComplex(rr, ri);
}