PI 圆周率

def pi_01():
    pi, N=0, 100
    func = lambda i: 1/pow(16,i)*(4/(8*i+1)- 2/(8*i+4)-1/(8*i+5)-1/(8*i+6))
    for i in range(N): pi+=func(i)
    print(pi)

import random, time
def pi_02():
    N, k =1000*1000, 0
    start=time.perf_counter()
    for i in range(N):
        x,y = random.random(),random.random()
        dist = pow(x**2+y**2,0.5)
        if dist <= 1.0: k+=1
    pi=4*(k/N)
    print("pi={},run time={:.2f}s".format(pi,time.perf_counter()-start))

# pi = pi * Decimal(12)/Decimal(640320**Decimal(1.5))
def pi_03():
    from decimal import Decimal, getcontext
    getcontext().prec=100
    print(sum(1/Decimal(16)**k * 
                  (Decimal(4)/(8*k+1) - 
                   Decimal(2)/(8*k+4) - 
                   Decimal(1)/(8*k+5) -
                   Decimal(1)/(8*k+6)) for k in range(100)))

if __name__ == "__main__":
    pi_01()
    pi_02()
    pi_03()