This is an automatically generated file.

Part 1

Part 2

def test_sqrt_monotonicity():
    """Test for monotonicity around the radix B."""
    i = - 1
    x = B_MINUS_ULP
    y = B
    z = B + B * ULP_OF_ONE_PLUS  # B plus 1 ulp
    not_monot = False
    monot = False

Part 3

    while not (not_monot or monot):
        i = i + 1
        # CASE: y = B
        x = sqrt(x)
        q = sqrt(y)
        z = sqrt(z)
        if x > q or q > z:
            not_monot = True

Part 4

        else:
            q = floor(q + ONE_HALF)
            # B = q*q only if radix B is 16 or 4
            if (i <= 0) and (B != q * q):
                monot = True  # exit early unless B is 16 or 4

Part 5

            elif i <= 0:
                # CASE: y = sqrt(B), if B = 4, 16 or other square
                y = q
                x = y - ULP_OF_ONE_PLUS
                z = y + ULP_OF_ONE_PLUS

Part 6

            elif i == 1:
                # CASE: 7 = 1/sqrt(B), if B = 4, 16, or other square
                y = y * ONE_OVER_B
                x = y - ULP_OF_ONE_MINUS
                z = y + ULP_OF_ONE_MINUS
            else:
                # Have survived three cases
                monot = True

Part 7

    if monot:
        print("sqrt has passed a test for Monotonicity.")
    else:
        bad_cond(err_defect, "")
        print("sqrt(x) is non-monotonic for x near {:0.7e} .".format(y))

Part 8