1. A method for finding zeros of a function, f, within an interval, X, using the interval version of Newton's method, wherein f′ is the derivative of the function f, the method comprising: receiving a representation of the interval X, the representation including a first floating-point number, a, representing the left endpoint of X, and a second floating-point number, b, representing the right endpoint of X; performing an interval Newton step on X, wherein the point of expansion is the midpoint, x, of the interval X, and wherein performing the interval Newton step involves evaluating f(x) to produce an interval result f I (x); and if f I (x) contains zero, evaluating f I (a) to produce an interval result f I (a), evaluating f(b) to produce an interval result f I (b), evaluating a termination condition for the processing of the current interval X, wherein the termination condition is TRUE if a number of conditions are satisfied, including if f I (a) contains zero and if f I (b) contains zero, and if the termination condition is TRUE, terminating the processing of the current interval X, and recording X as a final bound.