I. Demand analysis

Enter the number of digits you want to calculate to the decimal point, and calculate the value of Pi Pi.

Second, the algorithm: MCA Youth formula

π/4=4arctan1/5-arctan1/239

The formula was discovered in 1706 by John Mathews, a professor of British astronomy. He used the formula to calculate the 100-digit pi. The MCA youth formula can get a decimal precision of 1.4 bits per calculation. Because it's calculated by multiplying and dividend are not long integers, it can be easily programmed on a computer.

Three, the Python language to write a request for PI to any bit of the program is as follows:

#-*-Coding:utf-8-*-
__future__ Import Division
################### #导入时间模块
import Time
####### ####### #计算当前时间
time1=time.time ()
############### #算法根据马青公式计算圆周率 #################### number
= Int (raw_ Input (' Please enter the number of digits you want to calculate to the decimal point N: ')
# 10 more digits to prevent the effect of the mantissa trade-off
number1 = number+10
# After the decimal point number1
b = 10**number1
# 4/5 First
x1 = B*4//5
# to find 1/239 of the first
x2 = b// -239
# Find the first big item He
= X1+x2
#设置下面循环的终点, That is, the total number of n items
*= 2
#循环初值 = 3, the last value 2n, step =2 for
i in Xrange (3,number,2):
# to find each containing 1/5 items and symbols
x1//= -25< c23/># for each item and symbol containing 1/239
x2//= -57121
# Find two and
x = (x1+x2)//I
# seek the sum of he
+ x
# to find pi
pai = He*4
#舍掉后十位
pai//= 10**10
############ output pi pi value
paistring=str (PAI)
result=paistring[0]+ Str ('. ') +paistring[1:len (paistring)]
print result
time2=time.time ()
print U ' total time consuming: ' + str (time2-time1) + ' s '

Run Result:

"D:\Program Files\python27\python.exe" d:/pycharmprojects/learn2017/pi.py Enter the number of digits you want to compute to the decimal point n:20 3.14159265358979323846 total time consuming: 3.55100011826s Process finished with exit code 0 "D:\Program Files\pyth
On27\python.exe "d:/pycharmprojects/learn2017/pi.py Please enter the number of digits you want to calculate after the decimal point n:50 3.14159265358979323846264338327950288419716939937510 Total time consuming: 2.67100000381s Process finished with exit code 0