HDU1724 Ellipse(数值积分)

补一下一些小盲区，譬如simpson这种数值积分的方法虽然一直知道，但是从未实现过，做一道例题存一个模板。

#pragma warning(disable:4996)
#include<iostream>
#include<cstring>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
using namespace std;

double a, b, l, r;

double sqr(double x){
	return x*x;
}

double f(double x){
	return b / a*sqrt(sqr(a) - sqr(x));
}

double simpson(double l, double r)
{
	return (f(l) + 4 * f((l + r) / 2) + f(r))*(r - l) / 6;
}

double simpson(double l, double r, double all, double eps){
	double m = (l + r) / 2;
	double L = simpson(l, m), R = simpson(m, r);
	if (fabs(L + R - all) <= 15 * eps) return L + R + (L + R - all) / 15;
	return simpson(l, m, L, eps / 2.0) + simpson(m, r, R, eps / 2.0);
}

double simpson(double l, double r, double eps){
	return simpson(l, r, simpson(l, r), eps);
}

int main()
{
	int T; cin >> T;
	while (T--){
		cin >> a >> b >> l >> r;
		printf("%.3lf\n", 2*simpson(l, r, 1e-4));
	}
	return 0;
}