π calculation using a Machin-like arctangent formula

#!/usr/bin/python3
from decimal import Decimal, getcontext
import sys
digits = int(sys.argv[1]) if len(sys.argv) > 1 else 50
getcontext().prec = digits + 5  # a few extra digits to avoid rounding errors

def arctan(x):
    """Compute arctan(1/x) using the Taylor series."""
    x = Decimal(x)
    x2 = x * x
    term = Decimal(1) / x
    total = term
    n = 1
    sign = -1
    while True:
        term = term / x2
        delta = term / (2 * n + 1)
        if delta == 0:
            break
        total += sign * delta
        sign *= -1
        n += 1
    return total

pi = 16 * arctan(5) - 4 * arctan(239)
pi = +pi  # unary plus applies current context precision
print(f"Pi to {digits} digits:\n{str(pi)[:digits+2]}")