Analytical Fixed-Point Accuracy Evaluation in Linear Time-Invariant Systems

Ménard, Daniel; Rocher, Romuald; Sentieys, Olivier

doi:10.1109/tcsi.2008.923279

Cited by 58 publications

(40 citation statements)

References 18 publications

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“…This is discussed at length in [14] and is omitted here for the lack of space. The technique for identification of all paths involving the preprocessing step is discussed in [7]. The generalization of the same is described in [6].…”

Section: A Sns Modelmentioning

confidence: 99%

Accelerated Performance Evaluation of Fixed-Point Systems With Un-Smooth Operations

Parashar

Ménard

Sentieys

2014

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-The problem of accuracy evaluation is one of the most time consuming tasks during the fixed-point refinement process. Analytical techniques based on perturbation theory have been proposed in order to overcome the need for long fixed-point simulation. However, these techniques are not applicable in the presence of certain operations classified as un-smooth operations. In such circumstances, fixed-point simulation should be used. In this paper, an algorithm detailing the hybrid technique which makes use of an analytical accuracy evaluation technique used to accelerate fixed-point simulation is presented. This technique is applicable to signal processing systems with both feed-forward and feedback interconnect topology between its operations. The acceleration obtained as a result of applications of the proposed technique is consistent with fixed-point simulation, while reducing the time taken for fixed-point simulation by several orders of magnitude.

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Section: A Sns Modelmentioning

confidence: 99%

Accelerated Performance Evaluation of Fixed-Point Systems With Un-Smooth Operations

Parashar

Ménard

Sentieys

2014

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…3) Approaches Based on System Characteristics: The approaches presented in [11], [25] provide an approximation of the mathematical expression of the output quantization noise power in the case of Linear and Time Invariant (LTI) systems. The principle of [25] is based on the system transfer functions and the expressions of the coefficients Ki and Li are…”

Section: ) Simulation-based Computationmentioning

confidence: 99%

“…The principle of [25] is based on the system transfer functions and the expressions of the coefficients Ki and Li are…”

Section: ) Simulation-based Computationmentioning

confidence: 99%

Analytical Approach for Numerical Accuracy Estimation of Fixed-Point Systems Based on Smooth Operations

Rocher

Ménard²,

Scalart³

et al. 2012

IEEE Trans. Circuits Syst. I

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Abstract-In embedded systems using fixed-point arithmetic, converting applications into fixed-point representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixed-point system, which is accurate and valid for all systems formulated with smooth operations (e.g. additions, subtractions, multiplications and divisions). The mathematical expression of the system output noise power is determined using matrices to obtain more compact expressions. The proposed approach is based on the determination of the timevarying impulse-response of the system. To speedup computation of the expressions, the impulse response is modelled using a linear prediction approach. The approach is illustrated in the general case of time-varying recursive systems by the Least Mean Square (LMS) algorithm example. Experiments on various and representative applications show the fixedpoint accuracy estimation quality of the proposed approach. Moreover, the approach using the linear-prediction approximation is very fast even for recursive systems. A significant speed-up compared to the best known accuracy evaluation approaches is measured even for the most complex benchmarks.

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“…We note that the work by Constantinides et al [14], [47] and Menard et al [48] have avoided these problems by restricting the problem domain to linear time invariant systems, these are systems that consist only of additions, subtractions and constant coefficient multi-plications. In this problem domain, it is possible to analytically calculate the optimum number of bits using LTI theory, and then optimise the individual word-lengths to minimise the area and satisfy a design criterion, such as signal to noise ratio, using heuristics or integer linear programming.…”

Section: Introductionmentioning

confidence: 99%

A Scalable Precision Analysis Framework

Boland

Constantinides

2013

IEEE Trans. Multimedia

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Abstract-In embedded computing, typically some form of silicon area or power budget restricts the potential performance achievable. For algorithms with limited dynamic range, custom hardware accelerators manage to extract significant additional performance for such a budget via mapping operations in the algorithm to fixed-point. However, for complex applications requiring floating-point computation, the potential performance improvement over software is reduced. Nonetheless, custom hardware can still customise the precision of floating-point operators, unlike software which is restricted to IEEE standard single or double precision, to increase the overall performance at the cost of increasing the error observed in the final computational result. Unfortunately, because it is difficult to determine if this error increase is tolerable, this task is rarely performed.We present a new analytical technique to calculate bounds on the range or relative error of output variables, enabling custom hardware accelerators to be tolerant of floating point errors by design. In contrast to existing tools that perform this task, our approach scales to larger examples and obtains tighter bounds, within a smaller execution time. Furthermore, it allows a user to trade the quality of bounds with execution time of the procedure, making it suitable for both small and large-scale algorithms.

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Analytical Fixed-Point Accuracy Evaluation in Linear Time-Invariant Systems

Abstract: International audienc

Cited by 58 publications

References 18 publications

Accelerated Performance Evaluation of Fixed-Point Systems With Un-Smooth Operations

Accelerated Performance Evaluation of Fixed-Point Systems With Un-Smooth Operations

Analytical Approach for Numerical Accuracy Estimation of Fixed-Point Systems Based on Smooth Operations

A Scalable Precision Analysis Framework

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