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Enhancing the implementation of mathematical formulas for fixedpoint and floatingpoint arithmetics
 In First International Workshop on Numerical Abstractions for Software Verification, NSV’08
, 2008
"... In general, the computations carried out on machines are approximative because of the finite representation of numbers. Then an obvious question is how to estimate the quality of a certain implementation of a formula and how to enhance it. For example, one may wish to measure the absolute or relativ ..."
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Cited by 12 (6 self)
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In general, the computations carried out on machines are approximative because of the finite representation of numbers. Then an obvious question is how to estimate the quality of a certain implementation of a formula and how to enhance it. For example, one may wish to measure the absolute or relative precision of the
Program transformation for numerical precision
 In PEPM ’09: Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation
, 2009
"... This article introduces a new program transformation in order to enhance the numerical accuracy of floatingpoint computations. We consider that a program would return an exact result if the computations were carried out using real numbers. In practice, roundoff errors due to the finite representat ..."
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This article introduces a new program transformation in order to enhance the numerical accuracy of floatingpoint computations. We consider that a program would return an exact result if the computations were carried out using real numbers. In practice, roundoff errors due to the finite representation of values arise during the execution. These errors are closely related to the way formulas are evaluated. Indeed, mathematically equivalent formulas, obtained using laws like associativity, distributivity, etc., may lead to very different numerical results in the computer arithmetic. We propose a semanticsbased transformation in order to optimize the numerical accuracy of programs. This transformation is expressed in the abstract interpretation framework and it aims at rewriting pieces of numerical codes in order to obtain results closer to what the computer would output if it used the exact arithmetic.
Dynamic Precision Scaling for Low Power WCDMA Receiver
 in "Proc. of the IEEE International Symposium on Circuits and Systems, ISCAS 2009
, 2009
"... Abstract — One of the most important applications of Digital Signal Processing (DSP) is wireless communication. This kind of application requires low power implementation of DSP, which generally uses fixedpoint arithmetic. The fixedpoint architectures should be developed to maintain the energy co ..."
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Abstract — One of the most important applications of Digital Signal Processing (DSP) is wireless communication. This kind of application requires low power implementation of DSP, which generally uses fixedpoint arithmetic. The fixedpoint architectures should be developed to maintain the energy consumption power at a reasonable level. In this paper, an approach which adapts the fixedpoint specification according to the input receiver SignaltoNoise Ratio (SNR) is proposed. To underline our approach interest, the rake receiver of a WCDMA receiver is examined. Results show about 25 % – 40 % energy savings with our dynamic precision approach. I.
Synthesis of Arithmetic Expressions for the FixedPoint Arithmetic: The Sardana Approach 1
, 2012
"... Abstract—Sardana is a tool which optimizes the arithmetic expressions present in source codes. The optimization is done by synthesizing automatically new mathematically equal expressions, given ranges of values for the variables. In previous work, Sardana has been used to optimize the numerical accu ..."
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Abstract—Sardana is a tool which optimizes the arithmetic expressions present in source codes. The optimization is done by synthesizing automatically new mathematically equal expressions, given ranges of values for the variables. In previous work, Sardana has been used to optimize the numerical accuracy of floatingpoint expressions, by minimizing the worst roundoff error on the result of the evaluation. In this article, we show how our tool can be used to synthesize arithmetic expressions optimized for the fixedpoint arithmetic. In this context, Sardana minimizes the number of bits required to represent without overflow the integer parts of the fixedpoint numbers possibly occurring at any stage of the evaluation of an expression. We present experimental results showing how our tool optimizes the implementation of digital filters commonly used in image processing.
Accuracy evaluation of fixedpoint based LMS algorithm
, 2010
"... The implementation of adaptive filters with fixedpoint arithmetic requires computation quality evaluation. The accuracy may be determined by computing the global quantization noise power at the system output. In this paper, a new model for evaluating analytically the global noise power in LMSbase ..."
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The implementation of adaptive filters with fixedpoint arithmetic requires computation quality evaluation. The accuracy may be determined by computing the global quantization noise power at the system output. In this paper, a new model for evaluating analytically the global noise power in LMSbased algorithms is presented. Thus, the model is developed for LMS and NLMS algorithms. The accuracy of our model is analyzed by simulations.
doi:10.1155/2010/171027 Research Article SQNR Estimation of FixedPoint DSP Algorithms
"... Copyright © 2010 Gabriel Caffarena et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A fast and accurate quantization noise esti ..."
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Copyright © 2010 Gabriel Caffarena et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A fast and accurate quantization noise estimator aiming at fixedpoint implementations of Digital Signal Processing (DSP) algorithms is presented. The estimator enables significant reduction in the computation time required to perform complex wordlength optimizations. The proposed estimator is based on the use of Affine Arithmetic (AA) and it is presented in two versions: (i) a general version suitable for differentiable nonlinear algorithms, and Linear TimeInvariant (LTI) algorithms with and without feedbacks; and (ii) an LTI optimized version. The process relies on the parameterization of the statistical properties of the noise at the output of fixedpoint algorithms. Once the output noise is parameterized (i.e., related to the fixedpoint formats of the algorithm signals), a fast estimation can be applied throughout the wordlength optimization process using as a precision metric the SignaltoQuantization Noise Ratio (SQNR). The estimator is tested using different LTI filters and transforms, as well as a subset of nonlinear operations, such as vector operations, adaptive filters, and a channel equalizer. Fixedpoint optimization times are boosted by three orders of magnitude while keeping the average estimation error down to 4%. 1.
doi:10.1155/2008/242584 Research Article Accuracy Constraint Determination in FixedPoint System Design
"... Most of digital signal processing applications are specified and designed with floatingpoint arithmetic but are finally implemented using fixedpoint architectures. Thus, the design flow requires a floatingpoint to fixedpoint conversion stage which optimizes the implementation cost under execution ..."
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Most of digital signal processing applications are specified and designed with floatingpoint arithmetic but are finally implemented using fixedpoint architectures. Thus, the design flow requires a floatingpoint to fixedpoint conversion stage which optimizes the implementation cost under execution time and accuracy constraints. This accuracy constraint is linked to the application performances and the determination of this constraint is one of the key issues of the conversion process. In this paper, a method is proposed to determine the accuracy constraint from the application performance. The fixedpoint system is modeled with an infinite precision version of the system and a single noise source located at the system output. Then, an iterative approach for optimizing the fixedpoint specification under the application performance constraint is defined and detailed. Finally the efficiency of our approach is demonstrated by experiments on an MP3 encoder. Copyright © 2008 D. Menard et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Team R2D2 Reconfigurable and Retargetable Digital Devices
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2.2.2.
"... c t i v it y e p o r t 2007 Table of contents 1. Team.................................................................................... 1 ..."
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c t i v it y e p o r t 2007 Table of contents 1. Team.................................................................................... 1