How to use the uncertainties.umath function in uncertainties

def exponent_frexp(x):
        return umath.frexp(x)[1]

# to help make it a drop-in replacement for math (even though
        # factorial() does not work on numbers with uncertainties
        # because it is restricted to integers, as for
        # math.factorial()):
        assert umath.factorial(4) == 24

        # Boolean functions:
        assert not umath.isinf(x)

        # Comparison, possibly between an AffineScalarFunc object and a
        # boolean, which makes things more difficult for this code:
        assert umath.isinf(x) == False

        # fsum is special because it does not take a fixed number of
        # variables:
        assert umath.fsum([x, x]).nominal_value == -3

    # The same exceptions should be generated when numbers with uncertainties
    # are used:

    ## !! The Nose testing framework seems to catch an exception when
    ## it is aliased: "exc = OverflowError; ... except exc:..."
    ## surprisingly catches OverflowError. So, tests are written in a
    ## version-specific manner (until the Nose issue is resolved).

    if sys.version_info < (2, 6):

        try:
            math.log(0)
        except OverflowError(err_math):  # "as", for Python 2.6+
            pass
        else:

def test_broadcast_funcs():
    """
    Test of mathematical functions that work with NumPy arrays of
    numbers with uncertainties.
    """

    x = uncertainties.ufloat((0.2, 0.1))
    arr = numpy.array([x, 2*x])
    assert unumpy.cos(arr)[1] == uncertainties.umath.cos(arr[1])

    # Some functions do not bear the same name in the math module and
    # in NumPy (acos instead of arccos, etc.):
    assert unumpy.arccos(arr)[1] == uncertainties.umath.acos(arr[1])
    # The acos() function should not exist in unumpy because it does
    # not exist in numpy:
    assert not hasattr(numpy, 'acos')
    assert not hasattr(unumpy, 'acos')

    # Test of the __all__ variable:
    assert 'acos' not in unumpy.__all__