Automatic generation and verification of test-stable floating-point code

Abstract

Test instability in a floating-point program occurs when the control flow of the program diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by the presence of roundoff errors that affect the evaluation of arithmetic expressions occurring in conditional statements. Unstable tests may lead to significant errors in safety-critical applications that depend on numerical computations. Writing programs that take into consideration test instability is a difficult task that requires expertise on finite precision computations and rounding errors. This paper presents a toolchain to automatically generate and verify a provably correct test-stable floating-point program from a functional specification in real arithmetic. The input is a real-valued program written in the Prototype Verification System (PVS) specification language and the output is a transformed floating-point C program annotated with ANSI/ISO C Specification Language (ACSL) contracts. These contracts relate the floating-point program to its functional specification in real arithmetic. The transformed program detects if unstable tests may occur and, in these cases, issues a warning and terminate. An approach that combines the Frama-C analyzer, the PRECiSA round-off error estimator, and PVS is proposed to automatically verify that the generated program code is correct in the sense that, if the program terminates without a warning, it follows the same computational path as its real-valued functional specification.