Under- and Overflow Detection in the Residue Logarithmic Number System
Mark G. Arnold, Ioannis Kouretas, Vassilis Paliouras, John Cowles · 2019
The Residue Number System (RNS) offers fast and cheap carry-free integer arithmetic but has slow and expensive overflow detection. The Logarithmic Number System (LNS) offers fast real multiplication, division and powers with floating-point-like relative precision. The Residue Logarithmic Number System (RLNS) is a combination of the two systems that offers advantages for moderate-precision real applications where a-priori analysis allows under-and overflow to be ignored. An arithmetic hardware generator is essential because of the mathematical obscurity of combining RNS and LNS. Unfortunately, real applications often underflow. We consider options to deal with under-and overflow using the RLNSTool generator as a foundation.