Happy Pi Day!

[Albert Chan]

Hi, DM48

A better PI spigot is with continued fraction:

PI = 4/(1+1/(3+2^2/(5+3^2/(7+4^2/(9+5^2/(11 ...

This keep integers *much* smaller ⇒ code run faster.
see ABC Programmer's Handbook, Pi example (*)

Below Python code produce 7656 pi digits, in 6 sec on my laptop.
To produce same output, your code (adjusted to range(33080)) take 31 sec.
(It take about 2 sec to print digits, speed ratio ≈ 29/4 ≈ 7)

Code:

p, q = 1, 3
a, b, a1, b1 = 4, 1, 12, 4
for i in range(10000):
    p, q = p+q, q+2        # next convergent
    a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1
    while 1:
        d = a//b
        r = a1 - d*b1      # break if a//b != a1//b1
        if r < 0 or r >= b1: break
        print d,           # common digits
        a, a1 = 10*(a-d*b), 10*r

(*) Python is descendant of ABC, both developed by Guido van Rossum