// ellip_acdf()
//
// complex elliptic inverse cd() function (Jacobian elliptic
// arc cosine)
//
// _w : vector in the complex u-plane
// _k : elliptic modulus (0 <= _k < 1)
// _n : number of Landen iterations (typically 5-6)
float complex ellip_acdf(float complex _w,
float _k,
unsigned int _n)
{
float v[_n];
landenf(_k,_n,v);
float v1;
float complex w = _w;
unsigned int i;
for (i=0; i<_n; i++) {
v1 = (i==0) ? _k : v[i-1];
w = w / (1 + liquid_csqrtf(1 - w*w*v1*v1)) * 2.0 / (1+v[i]);
//printf(" w[%3u] = %12.8f + j*%12.8f\n", i, crealf(w), cimagf(w));
}
float complex u = liquid_cacosf(w) * 2.0 / M_PI;
//printf(" u = %12.8f + j*%12.8f\n", crealf(u), cimagf(u));
#if 0
float K, Kp;
ellipkf(_k, _n, &K, &Kp);
float R = Kp / K;
#endif
return u;
}
// complex arcsin
float complex liquid_casinf(float complex _z)
{
return 0.5f*M_PI - liquid_cacosf(_z);
}
