By Michael Butler, Sylvain Conchon, Fatiha Zaïdi
This booklet constitutes the refereed court cases of the seventeenth overseas convention on Formal Engineering equipment, ICFEM 2015, held in Paris, France, in November 2015. The 27 revised complete papers provided have been conscientiously reviewed and chosen from eighty two submissions. The papers disguise quite a lot of subject matters within the quarter of formal equipment and software program engineering and are dedicated to advancing the cutting-edge of utilising formal tools in perform. They concentration specifically on combos of conceptual and methodological points with their formal origin and power support.
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Additional info for Formal Methods and Software Engineering: 17th International Conference on Formal Engineering Methods, ICFEM 2015, Paris, France, November 3-5, 2015, Proceedings
00 Proofs of behavior are quite simple as they are calls to the previously studied average1 and average2 functions. The diﬃcult part, as expected, is overﬂow. 30 S. Boldo It is handled automatically by Gappa, except the proof that x + y does not overﬂow, provided that |x| < C ≤ 2970 . More precisely, even if y is the biggest ﬂoating-point number, if |x| < 2970 , then x ⊕ y will not overﬂow as it will round to y. 6 Conclusion and Perspectives The initial goal was to prove a program computing the average without overﬂow.
The fact that average1(x, y) is between min(x, y) and max(x, y) is slightly more diﬃcult as rounding is involved. The implies = 0 implies average1(x, y) = 0 and that 2Ei ≤ x+y facts that x+y 2 2 average1(x, y) = 0 are also quite simple from basic ﬂoating-point properties of the rounding. The rounding error here is very small as it is equivalent to only one rounding: average1(x, y) − x+y 1 ≤ ulp 2 2 x+y 2 . Formal Veriﬁcation of Programs Computing the Floating-Point Average 23 An interesting point is the fact that this algorithm requires x and y to be of diﬀerent signs in order to not overﬂow.
It means we want to have the tightest precondition, in order to cover all cases that do not fail. And this requires additional work. Unfortunately, programs are often not carefully written with overﬂow in mind. There are overﬂowing examples in an overwhelming proportion of them. Our work is therefore either to give precise conditions for them to work correctly, or to rewrite them. Acknowledgments. The author is indebted to a referee of a previous version of this work, who rightfully pitied the fact that no program existed for a correctly-rounded average and pointed out the previously dismissed average2 function.