Abstract
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 [John Harrison. HOL Light: A tutorial introduction. In Formal Methods in Computer-Aided Design, pages 265–269. Springer, 1996]. We prove correctness and error bounds for the four different rounding modes, and formalize a subset of the IEEE 754 [IEEE standard for floating point arithmetic. IEEE Std. 754-2008, 2008] 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.
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