deLorimier, Michael (2006) Floating-point sparse matrix-vector multiply for FPGAs. Master's thesis, California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05132005-144347
Large, high density FPGAs with high local distributed memory bandwidth surpass the peak floating-point performance of high-end, general-purpose processors. Microprocessors do not deliver near their peak floating-point performance on efficient algorithms that use the Sparse Matrix-Vector Multiply (SMVM) kernel. In fact, microprocessors rarely achieve 33% of their peak floating-point performance when computing SMVM. We develop and analyze a scalable SMVM implementation on modern FPGAs and show that it can sustain high throughput, near peak, floating-point performance. Our implementation consists of logic design as well as scheduling and data placement techniques. For benchmark matrices from the Matrix Market Suite we project 1.5 double precision Gflops/FPGA for a single VirtexII-6000-4 and 12 double precision Gflops for 16 Virtex IIs (750 Mflops/FPGA). We also analyze the asymptotic efficiency of our architecture as parallelism scales using a constant rent-parameter matrix model. This demonstrates that our data placement techniques provide an asymptotic scaling benefit.
While FPGA performance is attractive, higher performance is possible if we re-balance the hardware resources in FPGAs with embedded memories. We show that sacrificing half the logic area for memory area rarely degrades performance and improves performance for large matrices, by up to 5 times. We also 0 the performance effect of adding custom floating-point using a simple area model to preserve total chip area. Sacrificing logic for memory and custom floating-point units increases single FPGA performance to 5 double precision Gflops.
|Item Type:||Thesis (Master's thesis)|
|Subject Keywords:||Floating Point; FPGA; Reconfigurable Architecture; Sparse Matrix|
|Degree Grantor:||California Institute of Technology|
|Division:||Engineering and Applied Science|
|Major Option:||Computer Science|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||5 June 2005|
|Author Email:||mdel (AT) cs.caltech.edu|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||13 May 2005|
|Last Modified:||26 Dec 2012 02:41|
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