/*  sdfatans.cpp  by K.Tsuru  */
// function ID = 3603  DARDIX
/***************************************************************
SDouble class
inverse trigonometric function arctan x using series expansion
    arctan x = x - x^3/3 + x^5/5 -.... (|x|<1.0).
Please use for a very small value |x|.
See AsinSeries() for the meaning of "fe".
Not default argument.
*****************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static const char* func = "AtanSeries";
SDouble AtanSeries(const SDouble& x, int fe){
    if(x.NetRdxExp() > 0) x.SetError(x.OUT_OF_RANGE, func, 3603); // |x| > 1.0

    SDouble sum(x), xn(x), xsq(x*x), delta;
    ulong n = 1uL, mt = sum.SlOpMaxValue();
    sum.FixedPoint(fe);

    do{
        xn *= xsq;
        n += 2uL;
        if(n > mt){
            sum.SetError(sum.NOT_CONVERGE, func, -3603);
            break;
        }
        delta = DsDiv(xn, n);
        if(n & 2uL) sum -= delta; // n = 3, 7, 11, ...
        else        sum += delta; // n = 5, 9, 13
    } while(delta.Sign(3603));

    sum.PointFree();
    sum.Reform(3603);
    sum.upToTerm = (n+1uL)/2uL;

    return sum;
}