K-Cluster RNS Lookup Tables With Reduced Memory for Arithmetic
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Solution Overview
Problem
The Residue Number System (RNS) requires large memory capacity for lookup tables, which is a drawback in memory-centric neural computing due to the memory size being dependent on the square of each modulus and the number of bits, leading to excessive memory requirements compared to logic gate design.
Innovation Solution
A k-cluster residue number system is introduced, which generates reduced-size addition and subtraction look-up tables with 2mi cells and multiplication look-up tables with S=(mi^2-14) cells, utilizing a processor and memory to perform operations efficiently by transforming traditional two-dimensional tables into one-dimensional linear arrays and mirroring properties to reduce memory size.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional lookup tables are used for RNS operations, then arithmetic operations can be performed in parallel, but the memory size becomes excessively large (dependent on the square of each modulus and number of bits)
Solution Approach 1:
The patent divides the traditional two-dimensional lookup table into multiple one-dimensional lookup tables, each storing only a specific column of the original table. This segmentation reduces the memory size from O(m²) to O(m) while maintaining parallel computation capability through coordinated access to multiple segmented tables
Solution Approach 2:
The patent transforms the two-dimensional lookup table structure into one-dimensional lookup tables by adding a new dimension - the column index. Instead of storing all values in a single 2D table, the system uses multiple 1D tables indexed by column position, effectively redistributing the data storage across multiple dimensions to reduce individual table size
2Ease of operation
If lookup tables are used for all arithmetic operations, then computation is simplified, but the memory requirement becomes too large compared to logic gate design
Solution Approach 1:
The patent applies lookup tables partially - only for specific operations (addition and multiplication) where they provide significant benefit, while using conventional logic gates for other operations. This partial application maintains ease of operation for critical paths while avoiding excessive memory usage across all operations
Solution Approach 2:
The patent changes the parameters of the lookup table implementation by reducing the table size from complete 2D tables to smaller 1D tables, and by changing the data representation to use only necessary columns. This parameter optimization maintains operational simplicity while dramatically reducing memory capacity requirements
Data Source
AI summary
A k-cluster residue number system has a processor and a memory. The processor is used to generate an addition and subtraction look-up table and a multiplication look-up table based on periodic behaviors of the modulo to compress the sizes of the addition and subtraction look-up table and the multiplication look-up table. The addition and subtraction look-up table has 2mi cells for recording values from zero to (mi−1) in an ascending order twice, wherein mi is a coprime integer of a modular set of the k-cluster residue number system. The multiplication look-up table has S cells, whereS=(mi2-14).