pi

import time


N = 200000


## arctan(1/n)をTaylor展開で求める
def arctan(p, n):
    x = p//n
    nn = n*n
    c = 1
    s = x
    k = 1
    while x > 0:
        x //= nn
        k += 2
        c = -c
        s += c*(x//k)
    return s

## 円周率を求める
## 整数部分「3」も含む仮数表現の長整数で返します
def pi_mantissa(digit, redund=10):
    p = 10**digit
    q = 10**redund
    p *= q
    pi = 4*(12*arctan(p,18)+8*arctan(p,57)-5*arctan(p,239))
    pi //= q
    return pi

start_time = time.time()
result = pi_mantissa(N)
end_time = time.time()
print(result)

print("実行時間 = {0:.3f} 秒".format(end_time - start_time))