Solving Constraints on the Intermediate Result of Decimal Floating-Point Operations

The draft revision of the IEEE Standard for Floating-Point Arithmetic (IEEE P754) includes a definition for dec-imal floating-point (FP) in addition to the widely used bi-nary FP specification. The decimal standard raises new concerns with regard to the verification of hardware- and software-based designs. The verification process normally emphasizes intricate cor-ner cases and uncommon events. The decimal format intro-duces several new classes of such events in addition to those characteristic of binary FP. Our work addresses the following problem: Given a dec-imal floating-point operation, a constraint on the interme-diate result, and a constraint on the representation selected for the result, find random inputs for the operation that yield an intermediate result compatible with these specifications. The paper supplies efficient analytic solutions for addi-tion and for some cases of multiplication and division. We provide probabilistic algorithms for the remaining cases. These algorithms prove to be efficient in the actual imple-mentation.