Abstract

The residue number system (RNS) provides two main advantages to arithmetic computation: high dynamic range problems are subdivided into several independent modules of reduced dynamic range; and the arithmetic operations of addition, subtraction, and multiplication are performed in parallel with no carries between residue digits. Thus a high-accuracy multiplication can be divided into several medium-accuracy multiplications which can all be performed in parallel. Traditionally, m × m position-coded RNS look-up tables (LUTs) exhibit a spatial complexity (defined as the number of active elements) of m² for each modulus m, yielding a quadratic system complexity of $\Sigma m_i^2$, where the summation is over all the residue digits and m, is the particular modulus.

© 1988 Optical Society of America