Chudnovsky_Pi.py

# Chudnovsky algorithm for Pi
from decimal import Decimal as Dec, getcontext as gc
import time
def PI(maxK=70, prec=1008, disp=1007): # parameter defaults chosen to gain 1000+ digits within a few seconds
    gc().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 *= -262537412640768000
        S += Dec(M * L) / X
        K += 12
    pi = 426880 * Dec(10005).sqrt() / S
    pi = Dec(str(pi)[:disp]) # drop few digits of precision for accuracy
    print("PI(maxK={} iterations, gc().prec={}, disp={} digits) =\n{}".format(maxK, prec, disp, pi))
    return pi
time0 = time.perf_counter()
Pi = PI()
time1 = time.perf_counter()
print("computing and printing time ",time1-time0)
print("\nFor greater precision and more digits (takes a few extra seconds) - Try")
print("Pi = PI(317,4501,4500)")
print("Pi = PI(353,5022,5020)")