15.2.1 Testing the bisection algorithm

Let's examine automated testing for the bisection algorithm. With this algorithm, a zero of a real-valued function is found. It is described in Exercise 4 in Section 7.10: Exercises. An implementation of the algorithm can have the following form:

def bisect(f, a, b, tol=1.e-8):
    """
    Implementation of the bisection algorithm 
    f real valued function
    a,b interval boundaries (float) with the property 
    f(a) * f(b) <= 0
    tol tolerance (float)
    """
    if f(a) * f(b)> 0:
        raise ValueError("Incorrect initial interval [a, b]") 
    for i in range(100):
        c = (a + b) / 2.
        if f(a) * f(c) <= 0:
            b = c
        else:
            a = c
        if abs(a - b) < tol:
            return (a + b) / 2
    raise Exception('No root found within the given tolerance {tol}')

We assume this to be stored in a file named bisection...