/*  sdfsindv.cpp  by K.Tsuru  */
// function ID 3208  DRADIX
/****************************************************************
SDouble class
sin x for |x| < pi/4
The divide method is used similar to that used in Exp(x).
x is divided into the sum
  x = a(short number)+b(long but very small number)
and the addition theorem
  sin(a+b) = cos(a)*sin(b) + sin(a)*cos(b)
is used.Combining with SinRN (x/(R^N) method) it becomes slower.
****************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
SDouble SinDiv(const SDouble& x){
    // seriesFig : The change of this value refering the number of effective figures
    //yields the same speed or slower.
    const uint seriesFig = 4u;
    if(x.RdxExp() < -(int)seriesFig) return SinSeries(x);   // |x| << 1.0

    SDouble a, b(x), y;
//It takes out upper 'seriesFig' figures.
// x = a+b, sin(x) = sin(a+b) = cos(a)*sin(b) + sin(a)*cos(b)
    if(x.Sign() < 0) b.ChangeSign();    // b = |x|
    a = b.TakeOutFigures(seriesFig);
    b -= a;
    if( b.Sign(3208) ){
//Comparing 'SinSeries' an enough precision can be obtained.
        RealSize C;
        C.SetEffFig(x.EffFig() -seriesFig); //It can reduce the number of effective figures.
        b = SinSeries(b);
        C.SetEffFig(0);
        C.SetEffFig(x.EffFig() + 2u, C.TEMP_EXTEND);
        a = CosSeries(a);
        y = a*b + Sqrt((ONE - a*a)*(ONE - b*b));
        C.SetEffFig(0);
        y.Reform(3208);
    } else y = SinSeries(a);    // b = 0 for short x.
    if(x.Sign() < 0) y.ChangeSign();
    return y;
}