/*  sdfacos.cpp  by K.Tsuru  */
// function ID 3101  DRADIX
/****************************************************************
SDouble class
 arccos x
If |x| is very close to one, the formura
  arccos x = arcsin(sqrt((1-x)*(1+x))
is used.
When x = 1.0 - 10^(-100), test whether a full precision can be
obtained or not.
****************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
SDouble Acos(const SDouble& x){
    if(x.Sign(3101) == 0) return MPi2();// x = 0, pi/2
    if(x.IsOne()){  // |x| = 1
        if(x.Sign() < 0) return Pi();   // x = -1
        return 0.0; // x = 1
    }

    SDouble r;
    bool nearlyOne = false;  // 1-|x| << 1.0  ?

    if(x.Sign() > 0) r = ONE - x;   // must be r = 1.0 - |x| >= 0
    else             r = ONE + x;

    if(r.NetRdxExp() < -1) nearlyOne = true;// |r| < 10^(-2*DFIGURES) = 1e-8
    if(r.Sign() < 0) x.SetError(x.DOMAIN_ERR, "Acos",3101); // |x|>1

    if(nearlyOne){  // by a formula arccos x = arcsin sqrt(1-x*x)
        if(x.Sign() > 0) r *= (ONE + x);
        else             r *= (ONE - x);
        SDouble x1 = Sqrt(r);   // r = 1-x^2, x1 < 1e-4
        r = Asin(x1);           // r > 0 and 0 < x1 << 1.0
        if(x.Sign() < 0) r = Pi() - r;  // arccos x = pi - arccos(-x)
    } else r = MPi2() - Asin(x);        // pi/2 - arcsin x
    return r;
}