Compact RNS Conversion for Lower Bit-Width Storage
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Solution Overview
Problem
The conversion between binary number system (BNS) and residual number system (RNS) representations leads to excessive storage overhead and memory bandwidth issues due to the need for at least n+1 bits in RNS to represent an n-bit BNS value, causing inefficiencies in hardware resources and energy consumption.
Innovation Solution
A compact residual number system (CRNS) is introduced, allowing conversion of n+1-bit RNS representations to n-bit CRNS representations using a bijection mapping, where the truncated bit is either copied or recoded based on its value, reducing storage consumption and power usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If RNS representation is used to represent n-bit BNS values, then the dynamic range and representation capability are improved, but the storage overhead and memory bandwidth requirements increase due to requiring at least n+1 bits
Solution Approach 1:
The patent changes the parameter of bit width from n+1 bits to n bits by introducing a compact RNS representation. This is achieved by modifying the modulus set and applying a mapping function that compresses the RNS representation to use only n bits while maintaining the ability to represent all 2^n values, thus reducing storage overhead without sacrificing representation capability
Solution Approach 2:
The patent creates a bijection mapping between n-bit CRNS representations and n-bit BNS values. This mapping allows direct representation of BNS values in CRNS format without requiring additional bits, effectively copying the efficiency of BNS storage while maintaining RNS computational advantages
2Productivity
If conversion between BNS and RNS representations is performed, then the ability to utilize RNS computational advantages is improved, but the power consumption and hardware resources increase
Solution Approach 1:
The patent extracts the essential computational advantages of RNS (parallelism, no carry propagation) while removing the overhead of n+1 bit representation. By taking only the necessary n bits and creating a compact representation that maintains RNS properties, the system achieves computational efficiency without the additional power consumption associated with wider bit representations
Solution Approach 2:
The patent changes the representation parameter from n+1 bits to n bits, which directly reduces power consumption while maintaining the ability to perform RNS operations. The compact representation reduces the number of transistors and memory cells required, leading to lower dynamic power consumption during conversions and operations
3Reliability
If n+1-bit RNS representations are stored instead of n-bit representations, then the representation of all 2^n BNS values is ensured, but the storage consumption and memory bandwidth overhead increase
Solution Approach 1:
The patent applies a parameter change by transforming the representation from n+1 bits to n bits through a compact encoding scheme. This is achieved by selecting a specific modulus set and applying a bijective mapping function that ensures all 2^n values can be uniquely represented in n bits, thereby maintaining representation accuracy while reducing storage consumption by one bit per value
Data Source
AI summary
Embodiments of the present application provide a method and a device for converting representations of values between RNS and CRNS. The present application can be used in any product to which RNS is applied. A compact RNS (called CRNS) is proposed by the present application, and a bijection between RNS representations and CRNS representations is created. The bijection maps between (n+1)-bit RNS representations and n-bit CRNS representations by using a logic function. The bijection maps only 2n values corresponding to an n-bit BNS value in a dynamic range [0, 2n−1].