/*  sdfcosdv.cpp  by K.Tsuru  */
// function ID 3207     DRADIX, reference
/********************************************************************
SDouble class
trigonometric function cos x for |x| < pi/4 using the divide method
Similar to the method using in Exp(x),x is divided into
    x = a(short number)+b(long but very small)
and uses an addition theorem
  cos(x) = cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b).
*********************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
SDouble CosDiv(const SDouble& x){
    const uint seriesFig = 4u;
    if(x.RdxExp() < -(int)seriesFig) return CosSeries(x);   // |x| << 1.0

    SDouble a, b(x), y;
//Make an approximation by taking out upper seriesFig figures.
// x = a+b, cos(x) = cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b)
    a = b.TakeOutFigures(seriesFig);
    b -= a;
    if( b.Sign(3207) ){
    //It gives a sufficient precision comparing with CosSeries().
        RealSize C;
        C.SetEffFig(x.EffFig() + 2u, C.TEMP_EXTEND);
        a = SinSeries(a);   //a and b have same sign.
        b = SinSeries(b);   //Both series can be rapidly evaluated.
        y = Sqrt((ONE - a*a)*(ONE - b*b)) - a*b;
        C.SetEffFig(0);
    } else y = CosSeries(a);
    return y;
}