Formal Methods Applied to a Floating-Point Number System

This report presents a formalisation of the IEEE standard for binary floating-point arithmetic in the set-theoretic specification language Z. The formal specification is refined into four sequential components which unpack the operands, perform the arithmetic, pack and round the result. This refinement follows proven rules and so demonstrates a mathematically rigorous method of program development. In the course of the proofs useful internal representations of floating-point numbers are specified. The procedures which are presented here form the basis for the floating-point unit of the inmos IMS T800 transputer.