/*  sdfacosh.cpp  by K.Tsuru  */
// function ID 3309 DRADIX
/********************************************
 inverse hyperbolic (area cosh)
 arcosh(x) for x >= 1.0     ... not arccosh
Definition
 arcosh(x) = [+|-]log(x + sqrt(x*x - 1) )
For 0 < x - 1.0 << 1.0 a formura
 arcosh x = 2*artanh(sqrt( (x-1)/(x+1) ))
is used.
Return a positive value.
**********************************************/
#ifndef SN_H
#include "sn.h"
#endif
SDouble Acosh(const SDouble& x){
    SDouble  r;
    SDouble dev1 = x - ONE;

    if(dev1.Sign(3309) < 0) x.SetError(x.DOMAIN_ERR, "Acosh",3309); //x < 1
// x >= 1
    if(dev1.Sign() == 0){   // x = 1
        r.SetZero();    return r;
    }
// x > 1
    int dev1exp = dev1.NetRdxExp();
    if(dev1exp < -1){   // x - 1.0 < DRADIX^(-2)
    // arcosh x = 2*artanh(sqrt( (x-1)/(x+1) ))
        r = (x+ONE)/dev1;   // (x+1)/(x-1)
        r = RecSqrt(r);     // r < 1/DRADIX
        r = AtanhSeries(r);
        r = DsMult(r, 2);
    } else{
        r = x + Sqrt(dev1*(x + ONE));   // r = x+Sqrt(x*x -1)
        r = Log(r);
    }
    return r;
}