#include <stdio.h>
#include <math.h>

#define N1 4
// The four-point Newton-Cotes formula
//double w1[N1]={0.25,0.75,0.75,0.25};
//double x1[N1]={-1,-1.0/3,1.0/3,1};
// The four-point Gauss formula
double x1[N1]={
  -0.86113631159405257523,-0.33998104358485626480, 
   0.33998104358485626480, 0.86113631159405257523};
double w1[N1]={
   0.34785484513745385736, 0.65214515486254614264, 
   0.65214515486254614264, 0.34785484513745385736};

//double w1[N1]={0.25,0.75,0.75,0.25};
//double x1[N1]={-1,-1.0/3,1.0/3,1};
#define N2 5
// The five-point Newton-Cotes formula
//double w2[N2]={7.0/45,32.0/45,4.0/15,
//             32.0/45,7.0/45};
//double x2[N2]={-1,-0.5,0,0.5,1};

#define N2 5
// The five-point Gauss formula
double w2[N2]={.23692688505618908753, .47862867049936646802, 
 .56888888888888888891, .47862867049936646802,
 .23692688505618908753};
double x2[N2]={-.90617984593866399279,
   -.53846931010568309104, 0,
   .53846931010568309104, .90617984593866399279};
double g(double x){
//    return 1/(1+x*x);
//    return sqrt(x);
    return sin(1/x);
}
double quad1(double a,double delta){
    double s=0.0;
    for(int k=0;k<N1;k++){
        s+=w1[k]*g((x1[k]+1)*delta/2+a);
    }
    return s*delta/2;
}
double quad2(double a,double delta){
    double s=0.0;
    for(int k=0;k<N2;k++){
        s+=w2[k]*g((x2[k]+1)*delta/2+a);
    }
    return s*delta/2;
}
double ncquad(int m,double a,double b){
    double s=0.0,delta=(b-a)/m;
    for(int j=0;j<m;j++){
        s+=quad1(a+j*delta,delta);
    }
    return s;
}
double aquad(double epsilon,double a,double b){
    double A1=quad1(a,b-a);
    double A2=quad2(a,b-a);
    if(fabs(A1-A2)<epsilon) return A2;
    double c=(a+b)/2;
//    printf("recursing for [%g,%g] and [%g %g]\n",
//        a,c,c,b);
    A1=aquad(epsilon/2,a,c);
    A2=aquad(epsilon/2,c,b);
    return A1+A2;
}
int main(){
    int m=1;
    for(int i=0;i<20;i++){        
        m*=2;
        double y=aquad(1.0/m,1e-8,1/M_PI);
//        double err=fabs(y-atan(3));
//        double err=fabs(y-2.0/3*(pow(3,3.0/2)-1));
//        printf("%g %21.14e %g\n",1.0/m,y,err);
        printf("%g %21.14e\n",1.0/m,y);
    }
    return 0;
}