FAST MULTIPLICATION IN RESIDUE NUMBER SYSTEMS USING INTERVAL LOGARITHMIC CHARACTERISTIC

Modular Multiplication and Base Extensions in Residue Number Systems

We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery’s method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an effect corresponding to a redundant high-radix implementation is achieved, due to the carry-free nature of residue arithmetic. The actual computation in the multiplication takes place in co...

The Interval Logarithmic Number System

This paper introduces the Interval Logarithmic Number System (ILNS), in which the Logarithmic Number System (LNS) is used as the underlying number system for interval arithmetic. The basic operations in ILNS are introduced and an efficient method for performing ILNS addition and subtraction is presented. The paper compares ILNS to Interval Floating Point (IFP) for a few sample applications. For...

Semi-Logarithmic Number Systems

We present a new class of number systems, called Semi-Logarithmic Number Systems, that constitute a family of various compromises between floating-point and logarithmic number systems. We propose arithmetic algorithms for the Semi-Logarithmic Number Systems, and we compare these number systems to the classical floating-point or logarithmic number systems. performed using tables for the function...

High Speed Convolution Using Residue Number Systems

This thesis investigates architectures for high speed signal convolution using residue number system techniques. The focus is on VLSI implementations, a choice that gives two parameters by which judge different architectures: speed and hardware size. Although the focus is on the standard residue number system, the same concepts can be directly applied to quadratic residue number system architec...

Fast Multiplication of Interval Matrices (Interval Version of Strassen's Algorithm)