Provably correct posit arithmetic with fixed-point big integer

Abstract

Floating-point number format is used extensively in many applications, especially scientific software. The applications rely on efficient hardware floating-point support to perform arithmetic operations. With the advent of multicore CPUs and massively parallel GPUs, the memory bandwidth of a computer system is increasingly limited for each of the compute cores. The limited memory bandwidth is a serious bottleneck to the system performance. The posit number format [12] is a promising approach to improve the accuracy of the arithmetic operations with more efficient use of bit storage, hence, reducing memory contention. However, robust and reliable software implementations of posit arithmetic libraries in C/C++ or Python are not readily available. In this paper, we seek to develop provably correct posit arithmetic based on fixed-point big integers. A robust and reliable implementation can then serve as a reference for other hardware-optimized implementations, as a test bed for applications to experiment with different posit bit configurations, and to analyze the relative errors of using smaller bit sizes in the posit numbers compared to using the native 32-bit or 64-bit floating-point numbers.