ChudnovskyPI.py

# Chudnovsky algorithm for Pi
# https://en.wikipedia.org/wiki/Chudnovsky_algorithm
# Juhani Kaukoranta 14.6.2022
from decimal import Decimal, getcontext
import time
def PI(maxK, prec, digits):
    # maxK iterations, prec precision, digits decimals
    getcontext().prec = prec
    K, M, L, X, S = 6, 1, 13591409, 1, 13591409
    for k in range(1, maxK+1):
        M = (K**3 - 16*K) * M // k**3
        L += 545140134
        X *= Decimal(-262537412640768000)
        S += Decimal(M * L) / X
        K += 12
    pi = 426880 * Decimal(10005).sqrt() / S
    pi = Decimal(str(pi)[:digits+2]) # show only decimals
    return pi
digits = int(input("How many decimal digits in Pi "))
maxK = int(digits*0.071)+2 # iterations
prec =digits+8 # internal computing precision
time0 = time.perf_counter()
Pi = PI(maxK,prec,digits)
time1 = time.perf_counter()
print("computing and printing time  ",time1-time0," seconds")