This is an automatically generated file.

Part 1

Part 2

def num_theory_sqrt_test(x, D, y, z2):
    """Test utility."""

Part 3

    test = 0
    if x - B >= z2 - B and x - z2 <= BIG_B_NTH - z2:
        test = 1
        if ultra_verbose:
            print("\t\tnum_theory_sqrt_test x = {:.6f} D = {:.6f}".format(x, D))
        X2 = sqrt(x * D)
        if ultra_verbose:
            print("\t\t       X2 = {:.6f} = sqrt( {:.6f} )"
                  .format(X2, x * D))
        y2 = (X2 - z2) - (y - z2)
        X2 = X8 / (y - ONE_HALF)
        X2 = X2 - ONE_HALF * X2 * X2

Part 4

        down_err = (y2 + ONE_HALF) + (ONE_HALF - X2)
        up_err = y2 - X2
        if ultra_verbose:
            print("\t\t       y2 = {:.5e} X2 = {:.5e}".format(y2, X2))
            print("\t\t       dn = {:.5e} up = {:.5e}"
                  .format(down_err, up_err))
        update_sqrt_errors(down_err, up_err)
        if ultra_verbose:
            print("\tnew X2 = {:.17e} y2 = {:.17e}".format(X2, y2))
    elif verbose:
        print("\thasty exit from num_theory_sqrt_test()")
    return test

Part 5