# Simulation of Approximate Computing Applied to Numerical Methods**Team:** 48
**School:** La Cueva High
**Area of Science:** Computer Science
**Interim:** Problem Definition:
While computers are constantly becoming more powerful, they are limited by increasing energy consumption requirements. They consume large amounts of power in order to perform exact calculations, but this precision isn’t always necessary. Approximate computers balance power efficiency with small inaccuracies to optimize power usage. So far, they have been used with success in video and image processing, where inaccuracy is invisible to the human eye and therefore not problematic. On the other hand, use of inaccurate computing hasn’t been significantly investigated in the literature for application to scientific computations because error would harm the results. However, in an iterative solution method, it may be possible for error to be tolerated without compromising the results.
The goal of this project is to simulate and evaluate the use of an approximate processor for numerical calculations. The simulated inexact processor will run in conjunction with global operations on a traditional processor to take advantage of the inaccurate processor efficiency without compromising results. The numerical method used to test this computer model is an iterative matrix solver. This problem is an ideal test because it is highly parallelizable and widely applicable to the solution of systems of equations that arise in physical models.
Problem Solution:
Three models of iterative solvers with approximate processors are implemented. The first is the solver itself with very small amounts of error introduced in the results of certain operations. This model shows the effect of error on the upper level of the solver. The second model is of the approximate processor itself. It converts numbers to binary and performs basic operations while introducing bit errors in a way similar to an actual approximate processor. This low level model of the inexact processor is then implemented into the iterative solver. To find the optimal setup, then, the approximate processor methods will be tested to discover where they save costs without compromising results. The final model is the most complex and accurate representation. A main processor, representative of a traditional, accurate CPU, controls data flow between multiple inaccurate processors, and calls the steps in each iteration of the solver. The inaccurate processors each model a low-power chip on which some calculations could be done accurately even while others are done allowing some error.
Progress to Date:
To date, each of the three models has been constructed and the first two have been tested. Experiments on the most basic model, of error at the highest level of the solver calculations, have shown where error is most tolerable and that the solver converges, albeit with increased iterations, when error less than a certain threshold is introduced; this threshold depends on where the error is introduced. The second model has shown that the same frequency of error in the calculations used to model the inexact processor binary operations has a larger net effect.
Expected Results:
The expected results will show how to optimally build a computer system combining precise and imprecise processors in order to consume less power without compromising numerical results. Data will be collected on the amount of error tolerated and the trade-off between error and efficiency, based on the increase in iterations required to converge on a solution. With this data, the model can be improved and, in conjunction with power consumption data, indicate potential power savings of a computer that incorporates inaccurate processors.
Works Cited:
Bates, Joseph. "Processing with Compact Arithmetic Processing Element" Patent PCT/US2010/038769. 15 June 2010.
Bates, Joseph. "Computing 10,000X More Efficiently." MIT Media Lab. Singular Computing LLC, n.d. Web. 6 Dec. 2012.
"Conjugate Gradient Method." Iowa State Computer Science. Iowa State, 6 Nov. 2007. Web. 6 Dec. 2012.
"Computing Experts Unveil Superefficient Inexact Chip." Rice University News & Media. N.p., 17 May 2012. Web. 06 Dec. 2012.
Lingamneni, Avinash. "Energy Parsimonious Circuit Design through Probabilistic Pruning." NTU-Rice Institute for Sustainable and Applied Infodynamics, 2011. Web. 6 Dec. 2012.
**Team Members:**
Alexandra Porter
**Sponsoring Teacher:** Samuel Smith
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