struct Adapt {
	Doub TOL,toler;
	static const Doub alpha,beta,x1,x2,x3,x[12];
	bool terminate,out_of_tolerance;
	Adapt(Doub tol);
	template <class T>
	Doub integrate(T &func, const Doub a, const Doub b);
	template <class T>
	Doub adaptlob(T &func, const Doub a, const Doub b, const Doub fa,
		const Doub fb, const Doub is);
};

Adapt::Adapt(Doub tol) : TOL(tol),terminate(true),out_of_tolerance(false)
{
	const Doub EPS=numeric_limits<Doub>::epsilon();
	if (TOL < 10.0*EPS)
		TOL=10.0*EPS;
}

template <class T>
Doub Adapt::integrate(T &func, const Doub a, const Doub b)
{
	Doub m,h,fa,fb,i1,i2,is,erri1,erri2,r,y[13];
	m=0.5*(a+b);
	h=0.5*(b-a);
	fa=y[0]=func(a);
	fb=y[12]=func(b);
	for (Int i=1;i<12;i++)
		y[i]=func(m+x[i]*h);
	i2=(h/6.0)*(y[0]+y[12]+5.0*(y[4]+y[8]));
	i1=(h/1470.0)*(77.0*(y[0]+y[12])+432.0*(y[2]+y[10])+
		625.0*(y[4]+y[8])+672.0*y[6]);
	is=h*(0.0158271919734802*(y[0]+y[12])+0.0942738402188500*
		(y[1]+y[11])+0.155071987336585*(y[2]+y[10])+
		0.188821573960182*(y[3]+y[9])+0.199773405226859*
		(y[4]+y[8])+0.224926465333340*(y[5]+y[7])+
		0.242611071901408*y[6]);
	erri1=abs(i1-is);
	erri2=abs(i2-is);
	r=(erri2 != 0.0) ? erri1/erri2 : 1.0;
	toler=(r > 0.0 && r < 1.0) ? TOL/r : TOL;
	if (is == 0.0)
		is=b-a;
	is=abs(is);
	return adaptlob(func,a,b,fa,fb,is);
}

template <class T>
Doub Adapt::adaptlob(T &func, const Doub a, const Doub b, const Doub fa,
		const Doub fb, const Doub is)
{
	Doub m,h,mll,ml,mr,mrr,fmll,fml,fm,fmrr,fmr,i1,i2;
	m=0.5*(a+b);
	h=0.5*(b-a);
	mll=m-alpha*h;
	ml=m-beta*h;
	mr=m+beta*h;
	mrr=m+alpha*h;
	fmll=func(mll);
	fml=func(ml);
	fm=func(m);
	fmr=func(mr);
	fmrr=func(mrr);
	i2=h/6.0*(fa+fb+5.0*(fml+fmr));
	i1=h/1470.0*(77.0*(fa+fb)+432.0*(fmll+fmrr)+625.0*(fml+fmr)+672.0*fm);
	if (abs(i1-i2) <= toler*is || mll <= a || b <= mrr) {
		if ((mll <= a || b <= mrr) && terminate) {
			out_of_tolerance=true;
			terminate=false;
		}
		return i1;
	}
	else
		return adaptlob(func,a,mll,fa,fmll,is)+
			adaptlob(func,mll,ml,fmll,fml,is)+
			adaptlob(func,ml,m,fml,fm,is)+
			adaptlob(func,m,mr,fm,fmr,is)+
			adaptlob(func,mr,mrr,fmr,fmrr,is)+
			adaptlob(func,mrr,b,fmrr,fb,is);
}
const Doub Adapt::alpha=sqrt(2.0/3.0);
const Doub Adapt::beta=1.0/sqrt(5.0);
const Doub Adapt::x1=0.942882415695480;
const Doub Adapt::x2=0.641853342345781;
const Doub Adapt::x3=0.236383199662150;
const Doub Adapt::x[12]={0,-x1,-alpha,-x2,-beta,-x3,0.0,x3,beta,x2,alpha,x1};