from math import *


def halveringsmetoden(f, a, b, N, epsilon):
    i = 0
    m = (a + b)/2.0
    abserr = (b-a)/2.0
    while i <= N and abserr > epsilon*abs(m):
        if f(m) == 0:
            a = m
            b = m
        if f(a)*f(m) < 0:
            b = m
        else:
            a = m
        i = i + 1
        #print "i: %2d, |m - c|: %e" %( i, abs(m - sqrt(2)))
        m = (a + b)/2.0
        abserr = (b-a)/2.0
    return m

f = lambda x: x*x - 2.0
a = 1
b = 2
epsilon = 1e-10
N = 60;


halveringsmetoden(f, a, b, N, epsilon)