/*  sdfasinh.cpp  by K.Tsuru  */
// function ID 3310     DRADIX
/***************************************************************
SDouble class
inverse hyperbolic function arsinh(x)(area sinh)
[Definition]
    r = sqrt(x*x+1)
    x > 0 : arsinh(x)= log(r + x)
    x < 0 : arsinh(x)= -log(r - x)
If |x| is much less than one,the addition x to r(very close to one)
causes a loss of trailing digits.Then a formula
    arsinh x = artanh( x/sqrt(x^2+1) )
is used.The series is used to evaluate "artanh".
****************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
SDouble Asinh(const SDouble& x){
    if(x.Sign(3310) == 0) return 0.0;
    SDouble r, y, one(1.0);

    if(x.NetRdxExp() < 0){ // |x| < 1/DRADIX
        r = x*RecSqrt(x*x+one); // r = x/sqrt(x*x+1)
        y = AtanhSeries(r);     // Asinh(x) = Atanh( x/sqrt(x*x+1) )
    } else {
        r = Sqrt(x*x+one);
        if(x.Sign() > 0) r = r + x;
        else             r = r - x;
        y = Log(r);
        if(x.Sign() < 0) y.ChangeSign();    // r = -r;
    }
    return y;
}