Computational Bit-width Allocation for Operations in Vector Calculus

Automated bit-width allocation is a key step required for the design of hardware accelerators. The use of computational methods based on SAT-Modulo Theory to the problem of finite-precision bit-width allocation has recently been shown to overcome challenges faced by the known-art, particularly in the scientific computing domain. However, many such real-life applications are specified in terms of vectors and matrices and they are rendered infeasible by expansion into scalar equations. This paper proposes a framework to include operations from vector calculus and thus it enables tackling applications of practically relevant complexity.