This paper provides an approach to test nonlinear functions in computer programs, whether this function is used for control flow, such as a predicate inequality or equality constraint, or is given as an input-output relationship. This approach will obtain test data to detect linear errors in the given nonlinear function. An error-space criterion previously given by Zeil will be utilized, and a necessary and sufficient condition for the test data will be specified to guarantee the satisfaction of this criterion. This leads to a simple and efficient method to select test data which satisfies that condition; only (n+2) tests are required, where n is the number of input variables. An analysis will be given to show that this simple approach can be very effective in detecting nonlinear errors as well.

Domain testing attempts to find errors in the numeric expressions affecting the flow of control through a program. Intuitively, domain testing provides a systematic form of boundary value testing for the conditional statements within a program. Several forms of domain testing have been proposed, all dealing with the detection of linear errors in linear functions. Perturbation analysis has been previously developed as a measure of the volume of faults, from within a selected space of possible faults, left undetected by a test set. It is adapted here to errors and error spaces. The adapted form is used to show that the different forms of domain testing are closer in error detection ability than had been supposed. They may all be considered effective for finding linear errors in linear predicate functions. A simple extension is proposed, which allows them to detect linear errors in nonlinear predicate functions using only a single additional test point.