Efficient Approximate Wordlength Optimization

Fiore, P.D.

doi:10.1109/tc.2008.87

Cited by 14 publications

(15 citation statements)

References 31 publications

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“…Finding feasible operating points is chosen. Two points (7,7,4) and (7,7,5) exist in the vicinity corresponding to this quantization noise-power.…”

Section: Noise Power Input Bits (66) Input Bits(77) Input Bits(88)mentioning

confidence: 94%

“…In [7], an approximate but an analytical framework for optimizing word-lengths are presented. The approach here is to trace a Pareto-optimal trade-off curve and hence be able to specify bounds on the achievable minimum system cost.…”

Section: Background and Previous Workmentioning

confidence: 99%

“…With the input constraints applied, it is clear that the trade-off point must lie on the vertical line corresponding to the input constraints(7,7). After translation, the cost of the operation is C constraint .…”

mentioning

confidence: 99%

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A polynomial time algorithm for solving the word-length optimization problem

Parashar

Ménard

Sentieys

2013

2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Trading off accuracy to the system costs is popularly addressed as the word-length optimization (WLO) problem. Owing to its NP-hard nature, this problem is solved using combinatorial heuristics. In this paper, a novel approach is taken by relaxing the integer constraints on the optimization variables and obtain an alternate noise-budgeting problem. This approach uses the quantization noise power introduced into the system due to fixed-point word-lengths as optimization variables instead of using the actual integer valued fixed-point wordlengths. The noise-budgeting problem is proved to be convex in the rounding mode quantization case and can therefore be solved using analytical convex optimization solvers. An algorithm with linear time complexity is provided in order to realize the actual fixed-point word-lengths from the noise budgets obtained by solving the convex noise-budgeting problem.

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“…Finding feasible operating points is chosen. Two points (7,7,4) and (7,7,5) exist in the vicinity corresponding to this quantization noise-power.…”

Section: Noise Power Input Bits (66) Input Bits(77) Input Bits(88)mentioning

confidence: 94%

Section: Background and Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

A polynomial time algorithm for solving the word-length optimization problem

Parashar

Ménard

Sentieys

2013

2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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“…Approaches based on hybrid techniques [31], [10], [17] have been proposed to compute the coefficients Ki and Lij of (3) from a set of simulations. In [31], these Ne × (Ne + 1) coefficients are obtained by solving a linear system in which Ki and Lij are the variables.…”

Section: ) Simulation-based Computationmentioning

confidence: 99%

“…At least Ne × (Ne + 1) fixed-point simulations are required to solve the system of linear equations. A similar approach to [31] is used in [17] to obtain the coefficients by simulation.…”

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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Resource optimization for emulation of behavioral models of mixed signal circuits on FPGA: a case study of DC–DC buck converter

Bhattacharya

Kumar

Biswas

2017

Circuit Theory & Apps

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Summary This paper presents a semi‐automated word‐length optimization framework to reduce field‐programmable gate array (FPGA) resource utilization for FPGA‐based pre‐silicon test emulation of analog and mixed signal circuits while achieving the desired accuracy and overcoming long optimization time. Although high‐level behavioral models exist for modeling analog and mixed signal circuits, these comprise many complex differential equations which cannot be realized implicitly using Boolean logic (which is the basic functional block of an FPGA) on an FPGA. So, a more convenient way is explored to map analog circuits into digital domain by converting them into fixed‐point architectures because of its advantage of manipulating data with lower word‐length. To address the loss of accuracy due to finite word‐length effects and limited reconfigurable resources, word‐lengths are optimized under the constraint of given performance metrics. The proposed technique built in MATLAB/Simulink environment with Xilinx System Generator support is illustrated with the help of a case study of a peak‐current‐mode‐controlled buck‐type switching converter implemented on Xilinx Virtex™‐5 FPGA. To illustrate the applicability of this environment for pre‐silicon test development, well‐accepted fault models are emulated with the help of non‐ideal model of a buck converter. The emulation results are seen to be close to that of a post‐fabricated power converter in the presence of faults. Experimental results show that FPGA resource utilization can be reduced significantly while achieving the desired performance accuracy under the constraint of multiple error metrics. Copyright © 2017 John Wiley & Sons, Ltd.

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Efficient Approximate Wordlength Optimization

Cited by 14 publications

References 31 publications

A polynomial time algorithm for solving the word-length optimization problem

A polynomial time algorithm for solving the word-length optimization problem

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

Resource optimization for emulation of behavioral models of mixed signal circuits on FPGA: a case study of DC–DC buck converter

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