Detecting Errors in Nonlinear Functions for Computer Software

In this research a new approach is proposed to select test data for testing nonlinear functions in computer programs, with only a small additional cost and effort beyond that required for linear functions. This approach is applied to a function used for control flow, such as a predicate inequality or equality constraint, as well as to a function given as an input-output relationship. In this approach, we will obtain test data to detect linear errors in the given nonlinear function. An error-space criterion previously given by Zeil will be utilized. A necessary and sufficient condition for the test data will be specified to guarantee the satisfaction of this criterion. This leads to a simple, practical and efficient method to select test data which satisfies that condition. The advantage of this approach is that the number of test points is about the same as required for comparable linear functions and these test points are very effective in detecting nonlinear errors as well. Our approach shows that, no more than (n + 2) test points are required for the criterion to be satisfied, where n is the number of input variables. A simple extension will be proposed, for the equality case, to detect any error in the nonlinear function; the number of test points required is (n + m + 1), where m is the number of nonlinear terms. The condition that these test points must satisfy will be given. An analysis will also be given to show that the test points chosen according to this simple approach is a very effective subset of a set of test points that can be used to detect any error that could occur in nonlinear functions.