/*  sdfdcoss.cpp  by K.Tsuru  */
// function ID 3209     DRADIX
/***********************************************************
 cos(x) by series for |x| < pi/4
 if first != 0 calculate the value cos(x) , else cos(x) - 1.
************************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static const char* func = "CosSeries";
SDouble CosSeries(const SDouble& x, int first){
    SDouble sum, xsq, delta;
    ulong n = 3, den, mt = x.SlOpMaxValue();

    if(x.NetRdxExp() > 1) sum.SetError(sum.DOMAIN_ERR, func, 3209);
    xsq = x*x;
    delta = DsDiv(xsq, 2);

    if(first){
        sum = 1.0;  sum.FixedPoint(0);
        sum -= delta;
    } else {
        sum = -delta;
        sum.FixedPoint(sum.RdxExp());
    }

    while(delta.Sign(3209)){// n(n+1) < x.SlOpMaxValue()
        den = n*(n+1);
        if(den >= mt) break;
        delta *= xsq;
        delta = DsDiv(delta, den);
        if(n & 2) sum += delta;
        else      sum -= delta;
        n += 2;
    }

    while(delta.Sign(3209)){// n(n+1) >= x.SlOpMaxValue()
        if(n >= mt){
            sum.SetError(sum.NOT_CONVERGE, func, -3209);
            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(3209);
    sum.upToTerm = n/2;
    return sum;
}