Combining Testing and Static Analysis to Overflow and Roundoff Error Detection

This paper proposes a technique for automaticdetection of overflow and roundoff errors, causedby the floating-point number to fixed-point number conversion. First, a new range representation, “extended affine interval”, is proposed to overapproximate overflow and roundoff errors. Second, the overflow and roundoff error analysis problem is encoded as a weighted model checking, which is implemented as a static analyzer CANA. Last, we propose a new testing refinement loop, called “counterexample-guided narrowing”, by combining the static analysis and testing. They arecomposed and implemented in a prototype tool, CANAT, in which analysis results are used not only for possible roundoff error detection, but also for finding dominant error factors in input parameters. To avoid widening, currently we focus on programs with bounded loops and arrays with fixed length, which typically appear in encoder/decoder reference algorithms. Experimental results on small programs show that the extended affine interval is much more precise than classical interval, andthe counterexample-guided narrowing approach outperforms the random testing technique.リサーチレポート（北陸先端科学技術大学院大学情報科学研究科