计算圆周率π的C++实现（任意精度）

$\pi$的计算公式

代码

#include 
#include 
#include 

double compute_pi(int N) //计算pi函数
{
	double dx = 1.0 / N;
	double pi = 0;
	for (int i = 1; i < N; ++i)
	{
		pi += 2 * sqrt(1 - i * dx*i*dx); // 积分函数
	}
	pi += 1;
	pi *= 2 * dx;
	return pi;
}

int main()
{
	std::cout << "Please input a number: ";
	int N = 0;
	std::cin >> N;
	double pi = compute_pi(N);
	std::cout.setf(std::ios::scientific);
	std::cout << "The computing value of π is " << std::setprecision(10)<<pi << '\n';
	std::cout << "The computing error is " << std::setprecision(10) << abs(pi - M_PI) << '\n';

	std::cout << "Please input a tolerance: ";
	double dtol = 0;
	std::cin >> dtol; // 输入误差精度，例如 0.000001
	int M = (int)sqrt(dtol) / dtol; // 以 √dtol / dtol 作为初始的 N 的估计值，记为M
	pi = compute_pi(M);
	while (abs(pi - M_PI) > dtol)  // 若计算误差大于输入的容忍误差，则递增M
	{
		M += (int)1/sqrt(dtol); // 递增的步进为 1 / √dtol，此处可根据程序运行快慢进行调整
		pi = compute_pi(M); // 再次计算π值
	}
	std::cout << "The computing error is " << std::setprecision(10) << abs(pi - M_PI) << '\n';
	std::cout << "The number of intervals is " << M << '\n';
}

结果