This is an automatically generated file.

Part 1

Part 2

def is_gradual_underflow_IEEE(t):
    """Test gradual underflow for IEEE compatibility.

    Args:
        t - tiniest nonzero number discovered

    Returns:
        boolean reply to question

    Basic 5150
    """

Part 3

    print("Underflow is gradual; it incurs Absolute Error =")
    print("(roundoff in underflow_threshold) < min_positive.")
    # Test for IEEE rounding at the very bottom of the range.
    # The test looks for a double rounding, first to a
    # higher precision, then the target. The computation is just
    # under half an ulp, but an extra rounding will push it to a
    # half-way case that will round up.

Part 4

    # y = t/C * (3/2 + u)
    # x = 1/C * (1 + u)
    # y/x = t * (3/2 + u) * (1 - u + u**2 - ...)
    #     = t * (1 + 1/2 - u/2 + u**2/2 - ...)
    #     = t, barely rounding down
    y = t * ONE_OVER_C
    y = y * (ONE_AND_HALF + ULP_OF_ONE_PLUS)
    x = ONE_OVER_C * (ONE + ULP_OF_ONE_PLUS)
    y = y / x
    return (y == t)

Part 5