Whenever we base some decision on a comparison of numerical values, we must con- sider the impurity of those values. Thus, if a decision depends on whether v = 0, we instead test if |v | ≤ τ , where τ is some small value called a tolerance. More generally, for a particular comparison of the form v = V , we define two tolerances: absolute and relative, denoted τa and τr , respectively. Then, we test if
|