This is an automatically generated file.

Part 1

Part 2

def test_tiny_differences():
    """"With no gradual underflow, look for x != z but x-z = 0.
    This function is called after cases 1, 2, and 3 of underflow
    triage, where case 4 captures gradual underflow. The idea is
    to show how the nonzero differences between tiny numbers are
    not representable in the arithmetic.

    Usually, base_tiny == underflow_threshold but if it's smaller,
    then r * underflow_threshold is the geometric mean of the two.
    In the typical non-gradual-underflow cases when tiny_x and
    underflow_threshold differ by  a factor of 1 or H, the else
    clause below is taken.

    Basic 5000-5080
    """

Part 3

    print("")
    try:
        r = sqrt(base_tiny / underflow_threshold)
    except ZeroDivisionError:
        print("base_tiny / underflow_threshold failed!")
        r = H + H  # fall through to else case below
    if r <= H:
        z = r * underflow_threshold
        x = z * (ONE + r * H * (ONE + H))
    else:
        z = underflow_threshold
        x = z * (ONE + H * H * (ONE + H))

Part 4

    if (x != z) and (x - z == ZERO):
        bad_cond(err_flaw, "")
        print("x = {:0.17e}\n\tis not equal to z = {:0.17e} ."
              .format(x, z))
        w = x - z
        print("yet x - z yields {:0.17e} .".format(w))
        print("    Should this NOT signal Underflow, ")
        print("this is a SERIOUS DEFECT\nthat causes ")
        print("confusion when innocent statements like");
        print("    if (x == z)  ...  else")
        print("  ... (f(x) - f(z)) / (x - z) ...")
        print("encounter Division by ZERO although actually")
        try:
            print("x / z = 1 + {:g} .".format((x / z - ONE_HALF) - ONE_HALF))
        except ZeroDivisionError:
            print("x / z fails!")
    return

Part 5