Paper Info
Title
Formal Verification of Programs Computing the Floating-Point Average.
Abstract
The most well-known feature of floating-point arithmetic is the limited precision, which creates round-off errors and inaccuracies. Another important issue is the limited range, which creates underflow and overflow, even if this topic is dismissed most of the time. This article shows a very simple example: the average of two floating-point numbers. As we want to take exceptional behaviors into account, we cannot use the naive formula (x+y)/2. Based on hints given by Sterbenz, we first write an accurate program and formally prove its properties. An interesting fact is that Sterbenz did not give this program, but only specified it. We prove this specification and include a new property: a precise certified error bound. We also present and formally prove a new algorithm that computes the correct rounding of the average of two floating-point numbers. It is more accurate than the previous one and is correct whatever the inputs.
Year
Venue
Field
2015
ICFEM
Arithmetic underflow,Floating point,Computer science,Theoretical computer science,Rounding,Proof assistant,Formal verification,Formal proof
DocType
Citations 
PageRank 
Conference
0
0.34
References 
Authors
6
1
Name
Order
Citations
PageRank
Sylvie Boldo129226.85