/*  sdfatant.cpp  by K.Tsuru  */
// function ID = 3602   DARDIX
/**************************************************
SDouble class
inverse trigonometric function arctan x
using an addition theorem
    arctan(x) = arctan(y) + arctan{(x-y)/(1+x*y)}.
For the algorithm see Asin().It is faster than AtanA(x)
a little.The the conditions |x| << 1.0 and |x| >> 1.0
are not checked.They are done in Atan().
**************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static void AtanTApproX(const SDouble& x, SDouble& approX){
    SDouble y;
    y = Tan(approX); // fastest function TanBS() is used version 2.21. See "snmath.h"
    y = (x - y)/(1.0 + x*y);
    approX += AtanSeries(y, approX.RdxExp());
}
SDouble AtanT(const SDouble& x){
    RealSize C;
    SDouble r;
// Oct 19, 2000 Change here.
    // exclude "const" since 2.191 for the error of bcc55 E2015
    uint ef = x.EffFig(), fig = (ef >= 2048u) ? 125u : 25u;
    double dblX = doubleD(x);
//An intermediate step is inserted.
    C.SetEffFig(min(fig, ef));
    r = atan(dblX);
    AtanTApproX(x, r);
    C.SetEffFig(0);

    if( x.EffFig() > fig ) AtanTApproX(x, r); //full precision
    return r;
}