NDLI: Fixed Point Lanczos: Sustaining TFLOP-equivalent Performance in FPGAs for Scientific Computing

Content Provider	IEEE Xplore Digital Library
Author	Jerez, J.L. Constantinides, G.A. Kerrigan, E.C.
Copyright Year	2012
Abstract	We consider the problem of enabling fixed-point implementations of linear algebra kernels to match the strengths of the field-programmable gate array (FPGA). Algorithms for solving linear equations, finding eigen values or finding singular values are typically nonlinear and recursive making the problem of establishing analytical bounds on variable dynamic range non-trivial. Current approaches fail to provide tight bounds for this type of algorithms. We use as a case study one of the most important kernels in scientific computing, the Lanczos iteration, which lies at the heart of well known methods such as conjugate gradient and minimum residual, and we show how we can modify the algorithm to allow us to apply standard linear algebra analysis to prove tight analytical bounds on all variables of the process, regardless of the properties of the original matrix. It is shown that the numerical behaviour of fixed-point implementations of the modified problem can be chosen to be at least as good as a double precision floating point implementation. Using this approach it is possible to get sustained FPGA performance very close to the peak general-purpose graphics processing unit (GPGPU) performance in FPGAs of comparable size when solving a single problem. If there are several independent problems to solve simultaneously it is possible to exceed the peak floating-point performance of a GPGPU, obtaining approximately 1, 2 or 4 TFLOPs for error tolerances of 10-7, 10-5 and 10-3, respectively, in a large Virtex 7 FPGA.
Starting Page	53
Ending Page	60
File Size	309208
Page Count	8
File Format	PDF
ISBN	9781467316057
DOI	10.1109/FCCM.2012.19
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-04-29
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Field programmable gate arrays Accuracy Kernel Eigenvalues and eigenfunctions Linear algebra Dynamic range Symmetric matrices Fixed-point arithmetic Scientific computing High performance computing Iterative algorithms
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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