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import time
def calculate_next_square_root(number, square_root):
next_square_root = ((number / square_root) + square_root) / 2
return next_square_root
def calculate_square_root(number, digits, add):
square_root = 1 * (10 ** (digits + add))
next_square_root = calculate_next_square_root(number=number, square_root=square_root)
while (next_square_root != square_root):
square_root = next_square_root
next_square_root = calculate_next_square_root(number=number, square_root=square_root)
return square_root
def calculate_next_pi(a, b, t, digits, add):
next_pi = ((10 ** (digits + add)) * ((a + b) ** 2)) / (4 * t)
return next_pi
digits = int(input('How many digits of pi? '))
add = digits
a = 10 ** (digits + add)
b = calculate_square_root(number=(10 ** ((digits + add) * 2)) / 2, digits=digits, add=add)
t = (10 ** ((digits + add) * 2)) / 4
p = 1
pi = -1
n = 0
next_pi = calculate_next_pi(a=a, b=b, t=t, digits=digits, add=add)
while True:
try:
while (next_pi != pi):
pi = next_pi
next_a = (a + b) / 2
next_b = calculate_square_root(number=a * b, digits=digits, add=add)
next_t = t - (p * ((a - next_a) ** 2))
next_p = 2 * p
a = next_a
b = next_b
t = next_t
p = next_p
next_pi = calculate_next_pi(a=a, b=b, t=t, digits=digits, add=add)
n += 1
pi /= (10 ** add)
pi = [int(i) for i in str(pi)]
except KeyboardInterrupt:
print ('\n',pi)
quit()
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