python之圆周率

 #!/usr/bin/env python
 #-*- coding:utf-8 -*-
 ############################
 #File Name: pi.py
 #Author: frank
 #Mail: frank0903@aliyun.com
 #Created Time:2018-04-29 15:46:50
 ############################

 import random
 import time

 #spigot algorithms 计算圆周率
 #圆周率近似公式计算
 #pi = 0.0
 #N = 1000
 #
 #for k in range(N):
 #    pi += 1/pow(16, k) * (4/(8*k+1) - 2/(8*k+4) - 1/(8*k+5) - 1/(8*k+6))
 #
 #print(pi);

 #蒙特卡罗方法计算圆周率
 #思想:用概率的方法得到圆的面积S,然后用圆的面积除以半径的平方得到PI的值,即PI=S/(R*R)
 #设,正方形的长为a,内切圆的半径为r,将正方形分为4等分,坐标原点在圆心;
 #以第一象限的4分之一正方形/内切圆为对象,设投掷的总次数为N,投掷在圆内的次数为m(m<=N)
 #PI = 4 * (m/N)

 #程序中设定r=1
 #投掷点在圆内的条件是: 点(x,y)到圆心的距离小于等于r，则认为投掷在圆内;即，(x*x+y*y)的平方根 <= 1

 pi = 0.0
 #1,000,000,000 十亿 599.390809s
 #1,000,000 百万 0.6s
 #10,000,000 千万  6.05s
 #100,000,000 一亿  59.98s
 N = 1000000000
 r = 1.0
 m = 0

 time_start = time.perf_counter()
 for i in range(N):
     x = random.random()
     y = random.random()
     if (pow((x**2 + y**2), 0.5) <= r):
     ¦   m += 1;

 pi = 4*m/N
 print("圆周率是:{:f},m={:d}".format(pi,m))
 print("计算耗时:{:f}s".format(time.perf_counter()-time_start))