/*  sdfatnhs.cpp  by K.Tsuru  */
// function ID 3312     DRADIX
/*********************************************************
SDouble class
inverse hyperbolic function atanh(x) by series expansion
   atanh(x) = 0.5*log{(1+x)/(1-x)} = x + x^3/3+x^5/5 + ...
 x can be negative and |x| < 1.0.
***********************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static const char* func= "AtanhSeries";
SDouble AtanhSeries(const SDouble& x){
//  if(x.SNSign() == 0) return x; do not check x == 0
    SDouble x1(x), x2(x*x), result(x), delta;
    if(x.NetRdxExp() > 0) x.SetError(x.DOMAIN_ERR, func, 3312); // |x| > 1.0
    x1.FixedPoint(x.RdxExp());

    ulong k = 3uL, mt = x.SlOpMaxValue();

    do{
        x1 *= x2;
        delta = DsDiv(x1, k);
        result += delta;
        if( (k += 2) >= mt ){
            result.SetError(result.NOT_CONVERGE, func, -3312);
            break;
        }
    } while(delta.Sign(3312));

    x.upToTerm = (k+1uL)/2uL;
    x1.PointFree();     //Must use the object which called FixedPoint().
    result.Reform(3312);
    return result;
}