Implementation of floating point MAC using Residue Number System

摘要

This paper presents the design and implementation of 16-bit floating point RNS Multiply and Accumulate (MAC) unit. Residue Number System (RNS) gained popularity in the implementation of fast arithmetic and fault-tolerant computing applications. Its attractive properties such as parallelism and carry free computation have speed up the arithmetic computations. Floating Point can be represented as M×B^E where M is Mantissa, E is the Exponent and B is the Base. The MAC unit consists of three units - Floating-point multiplier, Conversion unit and an Accumulator. The floating-point multiplier makes use of Brickell's Algorithm, the conversion unit makes use of a parallel conversion for the forward conversion and the Chinese Remainder Theorem for reverse conversion and the accumulator includes an adder unit which can make use of any of the conventional adders that depends on the moduli of the RNS being used. The input takes form of half-precision format where there is 1-bit for sign, 5-bits for exponent and 10-bits for mantissa. The design is coded in Verilog HDL and the synthesis is done using Cadence RTL Compiler.