Error sensitive applications in high-performance computing are unable to benefit from existing approximatecomputing strategies that are not developed with guaranteed error bounds . Using qdot for the dot products in CG can result in amajority of components being perforated or quantized to half precision withoutincreasing the iteration count required for convergence to the same solution as CG using a double precision dot product . In this paper, we propose a general framework for designing error-bounded strategies and apply it to the dot product kernel todevelop qdot . We perform a theoretical analysis that yields adeterministic bound on the relative approximation error introduced by qdot. In particular, using qdot, we demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks — Conjugate Gradient (CG) and the Powermethod. In this article, we also provide an analysis to illustrate the tightness of the derived errorbound and to demonstrate qdot’s effectiveness ofqdot” on a simulated data set. In fact, usingqdot for CG can .

Author(s) : James Diffenderfer, Daniel Osei-Kuffuor, Harshitha Menon

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Keywords : qdot - dot - cg - error - product -

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