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))