"""
Simple implentation of the bisection method.
The function takes a tolerance as argument in addition
to the function f and the interval bounds a and b, 
and returns the approximate solution x and the
number of iterations used. 
"""


def bisection(f, a, b, eps):
    fa = f(a)
    if fa * f(b) > 0:
        return None, 0
        # Alternativ: raise ValueError(
        # f'Ingen fortegnsskifte i [{a:g},{b:g}]')
    i = 0 # iterasjonsteller
    
    while b - a > eps:
        i += 1
        m = (a + b)/2.0
        fm = f(m)
        if fa * fm <= 0:
            b = m # roten er i venstre halvdel av [a,b]
        else:
            a = m # roten er i høyre halvdel av [a,b]
            fa = fm
    return m, i


#solve the linear equation 2x - 3 = 0
print(bisection(f=lambda x: 2 * x - 3, a=0, b=10, eps=1E-5))