ChudnovskyPI.py

# Chudnovsky algorithm for Pi
# Juhani Kaukoranta 14.8.2023
# https://en.wikipedia.org/wiki/Chudnovsky_algorithm
from decimal import Decimal as Dec,getcontext as gc
import time
def PI(digits): # digits=piin desimaalien haluttu määrä
    maxK = int(digits*0.071+2) # max numbers of iterations
    gc().prec = digits+8
    K, M, L, X, S = 6, 1, 13591409, 1, 13591409
    for k in range(1, maxK):
        M = (K**3 - 16*K) * M // k**3
        L += 545140134
        X *= -262537412640768000
        S += Dec(M * L) / X
        K += 12
    pi = 426880 * Dec(10005).sqrt() / S
    pi = Dec(str(pi)[:digits+2]) # drop few digits of precision for accuracy
    print(pi)