AMPS: Approximating Procedures for Speed
Abstract
The thesis describes an automated system, AutoHiPA (history-based piecewise approximation), that is developed to reduce the setup cost of the proposed HiPA scheme and enhance its ease of use. The system consists of a static analyzer, a profiler, a code generator, an auto-tuner, and a driver. It automatically identifies candidate functions, replaces them with their approximate counterparts, selects scheme variants and their parameters, and tunes them across runs to find the most efficient approximation for a given application. This thesis makes the following specific contributions. 1. A novel function approximation scheme is introduced and explored, called history-based piecewise approximation (HiPA). This scheme divides the input range of a function into a number of regions, based on the function invocation history, and performs lower-order polynomial approximation in these regions. The initial approach uses polynomials in single variables. HiPA is an efficient software-only scheme that comes in two variants, non-uniform and uniform; their realizations and characteristics are described. The evaluation of 90 mathematical and scientific functions from the GNU Scientific Library (GSL) [10] shows that HiPA is able to improve the performance of 90% of all functions. For 80% of the functions, the normalized RMS error in the approximated result is very small (0.04 on average) with 7.5x average speedup. For another 10% of the functions, the error is 0.4 with an average speedup of 5x. The evaluation of five real applications demonstrates the feasibility, practicality, and effectiveness of the HiPA scheme. On average, the speedup for these applications is 2.9x with 0.25% error. 2. AutoHiPA, an automated function approximation system consisting of a static analyzer, a profiler, a code generator, an auto-tuner, and a driver. AutoHiPA automatically identifies and replaces candidate functions with their approximate counterparts, selects scheme variants and their parameters and tunes them across runs to find the best approximation. 3. HiPA++, an advanced history-based piecewise approximation scheme that supports dynamic online training and provides error control knobs. It introduces and employs a novel customized hash-based data structure; it may be of use for other applications. The scheme also harnesses idle cores in a multicore system to expedite and improve function approximation. It is capable of speculatively training and monitoring quality. The evaluation of HiPA++ shows that the scheme is able to improve approximation leveraging dynamic online training from HiPA's 71.4% to 99.7% for an application from financial domain. For a physics application with high training overhead, it reports an increase of 2.2x in application speedup compared to HiPA's 1.5x, by leveraging available parallelism. (Abstract shortened by ProQuest.)
Degree
Ph.D.
Advisors
Eigenmann, Purdue University.
Subject Area
Computer Engineering|Electrical engineering
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