Solving constraints on the invisible bits of the intermediate result for floating-point verification

Abstract

Test generation for datapath floating-point verification involves targeting intricate corner cases, which can often be solved only through complex constraint solving. In the process of calculating the result, we use an intermediate result whose significand comprises a finite number of bits and a sticky bit that is 0 if and only if the intermediate result is exact. We refer to all the bits beyond those represented in the final result as the invisible bits. We deal with corner cases that can only be defined via constraints on the intermediate result. Our work investigates the following problem: given a floating-point operation, and constraints on the invisible bits and the sticky bit, find two inputs for the operation that yield an intermediate result compatible with the constraints. The paper supplies a deterministic solution for addition and subtraction, and probabilistic solutions for multiplication and division. It also discusses the application of these algorithms to the verification of floating-point implementations.