Generating Test Cases inside Suspicious Intervals for Floating-Point Number Programs∗

Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may dif-fer from the path corresponding to the same computation with real numbers. State-of-the-art tools compute an over-approximation of the error introduced by floating-point oper-ations with respect to the same sequence of operations in an idealized semantics of real numbers. Thus, totally inappropri-ate behaviors of a program may be dreaded but the developer does not know whether these behaviors will actually occur, or not. We introduce here a new constraint-based approach that searches for input values hitting the part of the over-approximation where errors due to floating-point arithmetic would lead to inappropriate behaviors. Preliminary results of experiments on small programs with classical floating-point errors are very encouraging