/*  sdfatanh.cpp  by K.Tsuru  */
// function ID 3311     DRADIX
/*************************************************************************
SDouble class
inverse hyperbolic artanh x(area tanh) defined by
    artanh x = (1/2)*log( (1+x)/(1-x) ) (|x|<1.0)
When |x| is very near to 1.0 a large error causes
in this case series expansion
    atanh(x) = (1/2)*log( (1+x)/(1-x) ) = x + x^3/3+x^5/5 + ...
must be used. See AtanhSeries(x)
*************************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static const char* const func = "Atanh";
#define usesAtanhSeriesInAtanh 0
// for test. =1(use) 76.5sec(very slow), =0(no use) 13.4sec when 10,000 eff figs 
SDouble Atanh(const SDouble& x){
    if(x.Sign(3311) == 0) return 0.0;
#if usesAtanhSeriesInAtanh
    if(x.NetRdxExp() < 0) return AtanhSeries(x);    // |x| <1/DRADIX
    uint fig = x.Last() - x.First() + 1u;
    if(fig <= 4){   // short and small
        double xd = fabs(doubleD(x, 0));
        if(xd < 0.15) return AtanhSeries(x);    // |x| < 0.15
   }
#endif
    SDouble X(Dabs(x)), r; // X > 0
    r = ONE - X;
    if(r.Sign(3311) <= 0 || r.IsMLT(ONE)) x.SetError(x.DOMAIN_ERR, func, 3311); // x >= 1.0
    // here r > 0
    r = (ONE + X)/r; // > 0
    r = Log(r);
    r = DsDiv(r, 2);

    return x.Sign(3311) > 0 ? r : -r;
}