find_radix_from_big_2_to_nth()

This function's argument is the result from find_big_2_to_nth(). The low-order digit in big is in the B's place, that is the 2's place in binary, the 10's place in decimal, and so on.

def find_radix_from_big_2_to_nth(big):
    """The radix is marked by a change in the 'tens' place.

    Args:
        big: smallest value satisfying |((big + 1) - big) - 1| >= 1

    Returns:
        radix, which may not be integral in log arithmetic
    """

The loop simply adds the values $1$, $2$, $4$, $8$, ... in sequence until b exceeds big. In binary, this will happen on the first or second step, but the result is the same.

In decimal, the low order digit will change when y is 8 or 16, depending on whether the arithmetic is rounded or chopped.

The digits x and z depend on the decimal precision, but the algorithm applies, regardless.

    y = ONE
    while True:
        b = big + y
        y = y + y
        b = b - big
        if b != ZERO: break
    return b