A Parameterized Floating-Point Formalizaton in HOL Light

We present a new, open-source formalization of fixed and floating-point numbers for arbitrary radix and precision that is now part of the HOL Light distribution [10]. We prove correctness and error bounds for the four different rounding modes, and formalize a subset of the IEEE 754 [1] standard by gluing together a set of fixed-point and floating-point numbers to represent the subnormals and normals. In our floating-point proofs, we treat phases of floating-point numbers as copies of fixed-point numbers of varying precision so that we can reuse fixed-point rounding theorems.