using static System.Math;
using static System.Console;
class main{
const double inf=double.PositiveInfinity;
public static bool approx
(double x, double y, double acc=1e-6, double eps=1e-6){
        if(Abs(x-y)<acc)return true;
        if(Abs(x-y)<eps*(Abs(x)+Abs(y))/2)return true;
        return false;
}
static int Main(){

int ncalls=0,ierr=0;
double q,exact,acc,eps;
System.Func<double,double> f;

acc=1e-5; eps=0; exact = -4;
WriteLine($"o8av: ∫_0^1 Log(x)/Sqrt(x)dx={exact}, acc={acc} eps={eps}");
f = delegate(double x){ ncalls++; return Log(x)/Sqrt(x);};
ncalls=0; q=quad.o8av(f,0,1,acc,eps);
WriteLine($"result = {q}, result/exact={q/exact} ncalls={ncalls}");
if(approx(q,exact,acc,eps))WriteLine("test passed\n");
else {ierr++;WriteLine("test failed\n");}

acc=1e-6; eps=0; exact = Sqrt(PI);
WriteLine($"o8av: testing ∫_-∞^∞ exp(-x^2)dx={exact},acc={acc},eps={eps}");
f = delegate(double x){ ncalls++; return Exp(-x*x);};
ncalls=0; q=quad.o8av(f,-inf,inf,acc,eps);
WriteLine($"result = {q}, result/exact={q/exact} ncalls={ncalls}");
if(approx(q,exact,acc,eps))WriteLine("test passed\n");
else {ierr++;WriteLine("test failed\n");}

acc=1e-6; eps=0; exact = Sqrt(PI)/2;
WriteLine($"o8av: testing ∫_0^∞ exp(-x^2)dx={exact},acc={acc},eps={eps}");
f = delegate(double x){ ncalls++; return Exp(-x*x);};
ncalls=0; q=quad.o8av(f,0,inf,acc,eps);
WriteLine($"result = {q}, result/exact={q/exact} ncalls={ncalls}");
if(approx(q,exact,acc,eps))WriteLine("test passed\n");
else {ierr++;WriteLine("test failed\n");}

acc=1e-6; eps=0; exact = 2;
WriteLine($"o8av: testing ∫_0^1 ln(1/x)^2 dx={exact},acc={acc},eps={eps}");
f = delegate(double x){ ncalls++; return Pow(Log(1/x),2); };
ncalls=0; q=quad.o8av(f,0,1,acc,eps);
WriteLine($"result = {q}, result/exact={q/exact} ncalls={ncalls}");
if(approx(q,exact,acc,eps))WriteLine("test passed\n");
else {ierr++;WriteLine("test failed\n");}

acc=1e-6; eps=0; exact = 6;
WriteLine($"o8av: testing ∫_0^1 ln(1/x)^3 dx={exact},acc={acc},eps={eps}");
f = delegate(double x){ ncalls++; return Pow(Log(1/x),3); };
ncalls=0; q=quad.o8av(f,0,1,acc,eps);
WriteLine($"result = {q}, result/exact={q/exact} ncalls={ncalls}");
if(approx(q,exact,acc,eps))WriteLine("test passed\n");
else {ierr++;WriteLine("test failed\n");}

acc=1e-6; eps=0; exact = Sqrt(PI)/2;
WriteLine($"o8av: testing ∫_0^1 ln(1/x)^0.5 dx={exact},acc={acc},eps={eps}");
f = delegate(double x){ ncalls++; return Sqrt(Log(1/x)); };
ncalls=0; q=quad.o8av(f,0,1,acc,eps);
WriteLine($"result = {q}, result/exact={q/exact} ncalls={ncalls}");
if(approx(q,exact,acc,eps))WriteLine("test passed\n");
else {ierr++;WriteLine("test failed\n");}

WriteLine($"failed tests: {ierr}");
return ierr;
}
}