/*  sdfdsins.cpp  by K.Tsuru  */
// function ID 3210   DRADIX
/****************************************************
SDouble class
It provides the function sin x by series   |x| < 1.0.
*****************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static const char* func = "SinSeries";
SDouble SinSeries(const SDouble& x){
//  if(x.Sign(3210) == 0 ) return 0.0;//It does not check x==0 or not.

    SDouble sum(x), xsq(x*x), delta;
    ulong n = 4, den, mt = x.SlOpMaxValue();
// check |x| < 1.0.
    if(x.NetRdxExp() > 1) sum.SetError(sum.OUT_OF_RANGE, func, 3210);
    sum.FixedPoint(x.RdxExp());
    delta = DsDiv(x*xsq, 6);    //(x^3)/6
    sum -= delta;

    while(delta.Sign(3210)){// n(n+1) < x.SlOpMaxValue()
        den = n*(n+1);  //The value of "den" does not discontinuously exceed ULONG_MAX.
        if(den >= mt) break;
        delta *= xsq;
        delta = DsDiv(delta, den);
        if(n & 2) sum -= delta;
        else      sum += delta;
        n += 2;
    }
    while(delta.Sign(3210)){// n(n+1) >= x.SlOpMaxValue();
        if(n >= mt){
            sum.SetError(sum.NOT_CONVERGE, func, -3210);        break;
        }
        delta *= xsq;
        delta = DsDiv(delta, n);
        delta = DsDiv(delta, n+1);
        if(n & 2) sum -= delta;
        else      sum += delta;
        n += 2;
    }
    sum.PointFree();
    sum.Reform(3210);
    sum.upToTerm = n/2;
    return sum;
}