Up to now, we have only used functional tests. A functional test checks whether the functionality is correct. For the bisection algorithm, this algorithm actually finds a zero when there is one. In that simple example, it is not really clear what a unit test is. Although, it might seem slightly contrived, it is still possible to make a unit test for the bisection algorithm. It will demonstrate how unit testing often leads to more compartmentalized implementation.

So, in the bisection method, we would like to check, for instance, that at each step the interval is chosen correctly. How to do that? Note that it is absolutely impossible with the current implementation, because the algorithm is hidden inside the function. One possible remedy is to run only one step of the bisection algorithm. Since all the steps are similar, we might argue that we have tested all the possible steps. We also need to be able to inspect the current bounds a and b at the current step of the algorithm. So we have to add the number of steps to be run as a parameter and change the return interface of the function. We will do that as shown:

def bisect(f,a,b,n=100):
  ...
  for iteration in range(n):
    ...
  return a,b

Note that we have to change the existing unit tests in order to accommodate for that change. We may now add a unit test as shown:

def test_midpoint(self):
  a,b = bisect(identity,-2.,1.,1)
  self.assertAlmostEqual(a,-0.5)
  self.assertAlmostEqual(b,1.)