Institut d'Électronique et de Télécommunications de Rennes

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Performance evaluation and optimization of fixed-­point systems

Doctorante : Riham NEHMEH.

Directeur de thèse : Daniel MENARD.

Thèse débutée le : 01/04/2012.

The proposed position is conceived in the context of a joint collaboration project between ST Microelectronics and the CAIRN research team at IRISA/INRIA. The aim of the project is to develop a software framework for source-­to-source transformations for conversion of floating-point variables to fixed-­point variables targeting embedded systems. Existing commercial tools use simulation-based approaches. However, using these techniques can be time consuming and hence scale poorly with growing system sizes. Also, the long execution times of the fixed-­point simulation makes it difficult to explore the entire design space before arriving at an optimal fixed-point representation. On the other hand, analytical approaches significantly reduce the optimization time but are limited in their applicability. The aim of this Ph.D is to propose an approach that uses analytical techniques in combination with simulation-­based approaches to accelerate the process of word-­length optimization.

The first step in the fixed-­point conversion corresponds to the determination of the dynamic range or the number of integer bits of all variables. Classical methods based on interval or affine arithmetic can be used for determination of upper and lower bounds. While these approaches guarantee zero overflow, the bounds are often found to be pessimistic. This means, a lot of assigned bits go unused contributing to unnecessary increase in the implementation cost. The word-length optimization is essentially a design trade-­off between the implementation cost and the application performances (quality of service). In numerous practical applications, low overflow probability is acceptable if the performance degradation due to overflow is minimal.

In our previous work [1], a stochastic approach has been used to determine the probability density function (PDF). From this PDF, the number of bits required to code the data with a given probability of overflow is determined. The first objective of this Ph.D is to define an approach to automate the dynamic range evaluation for these stochastic approaches.

The determination of the maximal overflow probability associated with each variable is not straightforward. Thus, the overflow effects on application performance must be evaluated. In this context, the objective is to minimize the integer part word-­length such that the performance degradation due to overflow is lower than the maximum acceptable error. The second objective of this PhD is to define and develop an efficient technique to evaluate the overflow effects on application performance. The modeling of non-­linear effects of overflows with analytical approaches is difficult and simulation based approach has to be used. The challenge is to simulate the application only when overflow occurs. These events are rare in order to preserve application functionality and thus the execution time is limited. This research problem is in the field of performance evaluation by rare event simulation [2].

The third objective is to apply these techniques of rare event simulation to performance evaluation of system containing decision operators. Fixed-­point arithmetic leads to an unavoidable error between the infinite and finite precision values. Quantization error at the input of a decision operator can alter the decision in comparison to decisions in double precision. Analytical methods based on perturbation theory cannot be used to analyze such errors in decision. In a fashion similar to evaluation of the overflow effect, the aim is to use techniques based on simulation only when decision errors occur and to use analytical methods otherwise [3].

These approaches will be tested on digital signal processing applications and on a complete application corresponding to an OFDM modem. The quality of the estimation and the efficiency of the associated tool will be measured for these different examples.

Keywords :

Signal processing, performance evaluation, rare event simulation, fixed-point arithmetic, stochastic approaches, dynamic range evaluation, numerical accuracy, telecommunication applications.

References :

[1] A. Banciu, E. Casseau, D. Ménard, and T. Michel. A Case Study Of The Stochastic Modeling Approach For Range Estimation. In Design and Architectures for Signal and Image Processing, pages 301–308, Edinburgh Royaume-­Uni, 10 2010.

[2] G. Rubino, B. Tuffin, Rare Event Simulation using Monte Carlo Methods, John Wiley & Sons, Ltd, 2009, 9780470745403

[3] K. Parashar, D. Menard, R. Rocher, O. Sentieys, David Novo, and Francky Catthoor. Fast Performance Evaluation of Fixed-­Point Systems with Un-Smooth Operators. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD), San Jose États-­‐Unis, 11 2010.

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