Generating test cases inside suspicious intervals for floating-point number programs

Abstract

International audiencePrograms 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. * This work was partially supported by ANR VACSIM (ANR-11-INSE-0004), ANR AEOLUS (ANR-10-SEGI-0013), and OSEO ISI PAJERO projects

Floating-point symbolic execution: A case study in N-version programming

“…[4], [8], [22], [23], [39]), and various methods have been proposed for verifying floating-point properties through abstract interpretation [35], [36], [65], decision procedures [16], [40], [50], [81], [82], theorem proving [9], [10], and combinations of techniques [13], [14], [62], [63]. Recent work has also focused on estimating bounds on round-off error in floating-point computation [26], [55], [73].…”