VCFloat is a tool for Coq proofs about floating-point round-off error, as well as a Coq library useful for other reasoning about floating-point computations.
in floating-point with a fixed number of mantissa bits,
the result of
x*5.7 cannot always be represented exactly
in the same number of bits, ditto the result of the addition
so some low-order bits must be thrown away—there is round-off error.
VCFloat can calculate and prove an error theorem, bounding the difference
between the floating-point calculation and the exact value one would have
gotten in the infinite-precision reals.
VCFloat 2 is rebuilt and maintained by Andrew W. Appel and Ariel E. Kellison. VCFloat 1.0 was built by Tahina Ramananandro, Paul Mountcastle, Benoit Meister, and Richard Lethin.
Install via opam. The package name is
coq-vcfloat (opam publication is in progress).
VCFloat is an open-source project; the repository and license is at [https://github.com/VeriNum/vcfloat].
VCFloat Reference Manual, by Andrew W. Appel and Ariel E. Kellison
VCFloat2: Floating-point error analysis in Coq, preliminary draft 2022, by Appel and Kellison.
A unified Coq framework for verifying C programs with floating-point computations, by Tahina Ramananandro, Paul Mountcastle, Benoit Meister, and Richard Lethin, in Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP’16), pages 15–26, 2016.