Floating Point versus Fixed point Tradeoffs in FPGA Implementations of QR Decomposition Algorithm

Abstract

A wide variety of digital communication systems are encountered with high computational tasks. QR decomposition is one of such algorithms that can be implemented on FPGAs as a solution to large complex matrix inversion problems. A flexible vector processing architecture for the fixed and floating point implementations of the QR decomposition is presented. The design is implemented on the StratixIV device with 230K logic elements and verified with the SignalTap II built-in logic analyzer. Throughputs of 2.4M and 2.11M decompositions per second with maximum clock frequency of 340 MHz and 360 MHz are achieved for 4×4 matrices with the fixed and floating point designs respectively. The FPGA resource utilizations of the two data type implementations are also compared for different matrix sizes for the StratixIV and Arria10 devices.

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