def clog2(num: int) ->int:
    """Return the ceiling log base two of an integer :math:`\\ge 1`.

    This function tells you the minimum dimension of a Boolean space with at
    least N points.

    For example, here are the values of ``clog2(N)`` for :math:`1 \\le N < 18`:

    >>> [clog2(n) for n in range(1, 18)]
    [0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5]

    This function is undefined for non-positive integers:

    >>> clog2(0)
    Traceback (most recent call last):
        ...
    ValueError: expected num >= 1
    """
    if num < 1:
        raise ValueError('expected num >= 1')
    accum, shifter = 0, 1
    while num > shifter:
        shifter <<= 1
        accum += 1
    return accum
