Re: Request For Comments: Verrou, a Valgrind tool for floating-point debugging (Ivo Raisr)
Ivo Raisr wrote (I've deleted chunks)
> I also wonder if random rounding leads to tremendous understatement or
> overstatement of a rounding problem. I can imagine the former, since
> random choices might tend to cancel each other out. I could also imagine
> the latter, since interval arithmetic (most pessimistic rounding) was
> rather incapable of judging the numerical stability of conventional
> algorithms. I'm more inclined to bet on the former.
It's hard to know without experimenting. But I think I disagree. Consider the
classical [Davenport,J.H. & Fischer,H.-C., Manipulation of Expressions. In
Improving Floating-Point Programming (ed. P.J.L. Wallis), Wiley, 1990, pp. 149-167.]
x*(1-x) with x \in [0,1], where interval arithmetic returns [0,1], while truth is [0,1/4].
This system should return [0,1/4+\epsilon].
I also note that a very similar technique returned good results on classic cases:
Parker,D.S.,Pierce,B. & Eggert,P.R.,
Monte Carlo Arithmetic: How to Gamble with Floating Point and Win.
Computing in Science & Engineering 2(2003) 4 pp. 58-68.
More generally, there is no single magic bullet for numerical analysis, but
MCA has generally been hampered by lack of tools, so a valgrind integration
Seems useful. I'd like to play with it.
Fulbright CyberSecurity Scholar (at New York University)
Hebron & Medlock Professor of Information Technology, University of Bath
National Teaching Fellow 2014
OpenMath Content Dictionary Editor
Director of Studies EPSRC Doctoral Taught Course Centre for HPC
Chair, IMU Committee on Electronic Information and Communication
Vice-President and Academy Trustee, British Computer Society