The Residue Logarithmic Number System: Theory and Implementation

— The Residue Logarithmic Number System (RLNS) represents real values as quantized logarithms which, in turn, are represented using the Residue Number System (RNS). Compared to the conventional Logarithmic Number System (LNS) in which quantized logarithms are represented as binary integers, RLNS offers faster multiplication and division times. RLNS and LNS use a table lookup involving all bits for addition. The width, dynamic range, precision and na¨ıve table size of RLNS (with careful moduli selection) is as good as those for conventional LNS. Conventional LNS can be more efficient than na¨ıve addition lookup. First, commutativity allows interchanging arguments. Second, the addition function is often essentially zero, and does not have to be tabulated. In binary, comparing arguments for commutativity and essential zero is easy during initial steps subsequent table lookup depends upon. In residue, comparisons are slow. Although RLNS inherently demands comparison, this paper show...

• Type: Conference
• Year: 2005
• Where: ARITH
• Authors: Mark G. Arnold
• Keywords: Applied Computing, ARITH 2005, Conventional Lns, Logarithmic Number System, Table Lookup