hdu 1724 Ellipse simpson积分

/*

hdu 1724 Ellipse simpson积分



求椭圆的部分面积

simpson积分法 http://zh.wikipedia.org/zh-tw/%E8%BE%9B%E6%99%AE%E6%A3%AE%E7%A7%AF%E5%88%86%E6%B3%95

*/

#include<stdio.h>

#include<math.h>

const double eps=1e-8;

inline double jue(double a)

{

	return a>0?a:-a;

}

int dbcmp(double a)

{

	if(a>eps)return 1;

	if(a<(-eps)) return -1;

	return 0;

}

template<typename T>

inline T sqr(T d){return d*d;}

double a,b;

inline double func(double x)

{

	return 2*b*sqrt(1-sqr(x)/sqr(a));

}

double simpson(double l,double r)

{

	return (func(l)+func(r)+4*func((l+r)/2))/6*(r-l);

}

double work(double l,double r)

{

	double mid=(l+r)/2;

	double ans=simpson(l,r);

	if(dbcmp(ans-simpson(l,mid)-simpson(mid,r))==0)

	{

		return ans;

	}else

	{

		return work(l,mid)+work(mid,r);

	}

}

int main()

{

	int n;

	double l,r;

	scanf("%d",&n);

	while(n--)

	{

		scanf("%lf%lf%lf%lf",&a,&b,&l,&r);

		double ret=work(l,r);

		printf("%.3f\n",ret);

	}

	return 0;

}