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Habib Mehrez - One of the best experts on this subject based on the ideXlab platform.
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Arithmetic Data path Optimization using Borrow-Save Representation
2008Co-Authors: Sophie Belloeil, Roselyne Chotin-avot, Habib MehrezAbstract:Considering the performance increase provided by redundant operators such as adders and multipliers, it appears interesting to generalize the use of those operators in high computational digital circuit design. Using redundant Arithmetic in conjunction with Classical Arithmetic is nevertheless a complex task. Optimization CAD tools which automate its use become therefore very helpful. However the existing approaches are restricted in using only the Carry-Save representation. In this paper we propose to overcome this limitation with an exploration of the possible optimizations of using the Borrow-Save representation also. To illustrate this, the optimizations of a Distance Computation Unit (DCU) and a Discrete Cosine Transform (DCT) operators are presented.
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ISVLSI - Arithmetic Data Path Optimization Using Borrow-Save Representation
2008 IEEE Computer Society Annual Symposium on VLSI, 2008Co-Authors: Sophie Belloeil, Roselyne Chotin-avot, Habib MehrezAbstract:Considering the performance increase provided by redundant operators such as adders and multipliers, it appears interesting to generalize the use of those operators in high computational digital circuit design. Using redundant Arithmetic in conjunction with Classical Arithmetic is nevertheless a complex task. Optimization CAD tools which automate its use become therefore very helpful. However the existing approaches are restricted in using only the Carry-Save representation. In this paper we propose to overcome this limitation with an exploration of the possible optimizations of using the Borrow-Save representation also. To illustrate this, the optimizations of a Distance Computation Unit (DCU) and a Discrete Cosine Transform (DCT) operators are presented.
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A fast and low-power distance computation unit dedicated to neural networks, based on redundant Arithmetic
2001Co-Authors: Y. Dumonteix, Y. Bajot, Habib MehrezAbstract:This paper presents the design of a fast and low power consumption distance computation unit : /spl Sigma//sub i/(A/sub i/-B/sub i/)/sup 2/. It is dedicated to the digital RBF neural network implementation. The proposed architecture is composed of two parts. The first computes the distance (A/sub i/-B/sub i/)/sup 2/, and the second performs the sum of these distances. It is based on an efficient squarer in redundant Arithmetic. Thank to this operator, the distance measure circuits developed offer better performances than those based on Classical Arithmetic. The average gain is equal to 11% in delay and 18% in power consumption.
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ISCAS (4) - A fast and low-power distance computation unit dedicated to neural networks, based on redundant Arithmetic
ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 1Co-Authors: Y. Dumonteix, Y. Bajot, Habib MehrezAbstract:This paper presents the design of a fast and low power consumption distance computation unit : /spl Sigma//sub i/(A/sub i/-B/sub i/)/sup 2/. It is dedicated to the digital RBF neural network implementation. The proposed architecture is composed of two parts. The first computes the distance (A/sub i/-B/sub i/)/sup 2/, and the second performs the sum of these distances. It is based on an efficient squarer in redundant Arithmetic. Thank to this operator, the distance measure circuits developed offer better performances than those based on Classical Arithmetic. The average gain is equal to 11% in delay and 18% in power consumption.
Manqun Zhang - One of the best experts on this subject based on the ideXlab platform.
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Novel Design for Reversible Arithmetic Logic Unit
International Journal of Theoretical Physics, 2014Co-Authors: Rigui Zhou, Manqun ZhangAbstract:Reversible logic circuits are of high interests to calculate with minimum energy consumption having applications in low-power CMOS design, optical computing and nanotechnology, especially in quantum computer. Quantum computer requires quantum Arithmetic. A new design of a reversible Arithmetic logic unit (reversible ALU) for quantum Arithmetic has been proposed in this article. As we known, ALU is an important part of central processing unit (CPU) as the execution unit. So this article provides explicit construction of reversible ALU effecting basic Arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the Classical Arithmetic and logic operation in a reversible integrated system. This article provides a new more powerful ALU which contains more functions and it will make contribute to the realization of reversible Programmable Logic Device (RPLD) in future using reversible ALU.
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Reversible Arithmetic logic unit
arXiv: Hardware Architecture, 2011Co-Authors: Rigui Zhou, Yang Shi, Manqun ZhangAbstract:Quantum computer requires quantum Arithmetic. The sophisticated design of a reversible Arithmetic logic unit (reversible ALU) for quantum Arithmetic has been investigated in this letter. We provide explicit construction of reversible ALU effecting basic Arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the Classical Arithmetic and logic operation in a reversible integrated system. This letter provides actual evidence to prove the possibility of the realization of reversible Programmable Logic Device (RPLD) using reversible ALU.
Frédéric Jacquemin - One of the best experts on this subject based on the ideXlab platform.
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On the meaning of the chosen set‐averaging method within Eshelby‐Kröner self‐consistent scale transition model: the geometric mean versus the Classical Arithmetic average
ZAMM - Journal of Applied Mathematics and Mechanics Zeitschrift für Angewandte Mathematik und Mechanik, 2011Co-Authors: Sylvain Fréour, Emmanuel Lacoste, Jamal Fajoui, Frédéric JacqueminAbstract:Scale-transition models, such as Eshelby-Kroner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. In the present work, the fundamental formalism historically introduced by Kroner is, for the first time, considered from the point of view of both the geometric and the Arithmetic set averages methods. It is demonstrated in this paper that the polarization tensors describing the relations existing between the local and the macroscopic mechanical states do have a strong physical meaning when expressed using the geometric average, instead of the Classical Arithmetic mean.
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On the meaning of the chosen set-averaging method within Eshelby-Kröner self-consistent scale transition model: the geometric mean versus the Classical Arithmetic average
Journal of Applied Mathematics and Mechanics Zeitschrift für Angewandte Mathematik und Mechanik, 2011Co-Authors: Sylvain Fréour, Emmanuel Lacoste, Jamal Fajoui, Frédéric JacqueminAbstract:Scale-transition models, such as Eshelby-Kröner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. In the present work, the fundamental formalism historically introduced by Kröner is, for the first time, considered from the point of view of both the geometric and the Arithmetic set averages methods. It is demonstrated in this paper that the polarization tensors describing the relations existing between the local and the macroscopic mechanical states do have a strong physical meaning when expressed using the geometric average, instead of the Classical Arithmetic mean.
Etienne Miquey - One of the best experts on this subject based on the ideXlab platform.
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A constructive proof of dependent choice in Classical Arithmetic via memoization.
arXiv: Logic in Computer Science, 2019Co-Authors: Etienne MiqueyAbstract:In a recent paper, Herbelin developed dPA${^\omega}$, a calculus in which constructive proofs for the axioms of countable and dependent choices could be derived via the memoization of choice functions. However, the property of normalization (and therefore the one of soundness) was only conjectured. The difficulty for the proof of normalization is due to the simultaneous presence of dependent types (for the constructive part of the choice), of control operators (for Classical logic), of coinductive objects (to encode functions of type ${\mathbb{N} \to A}$ into streams (${a_0},{a_1},...$)) and of lazy evaluation with sharing (for memoizing these coinductive objects). Elaborating on previous works, we introduce in this paper a variant of dPA${^\omega}$ presented as a sequent calculus. On the one hand, we take advantage of a variant of Krivine Classical realizability that we developed to prove the normalization of Classical call-by-need. On the other hand, we benefit from dL${_{\hat{tp}}}$, a Classical sequent calculus with dependent types in which type safety is ensured by using delimited continuations together with a syntactic restriction. By combining the techniques developed in these papers, we manage to define a realizability interpretation a la Krivine of our calculus that allows us to prove normalization and soundness. This paper goes over the whole process, starting from Herbelin's calculus dPA${^\omega}$ until our introduction of its sequent calculus counterpart dLPA${^\omega}$.
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a sequent calculus with dependent types for Classical Arithmetic
Logic in Computer Science, 2018Co-Authors: Etienne MiqueyAbstract:In a recent paper [11], Herbelin developed dPAω, a calculus in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of it components. However, the property of normalization (and therefore the one of soundness) was only conjectured. The difficulty for the proof of normalization is due to the simultaneous presence of dependent types (for the constructive part of the choice), of control operators (for Classical logic), of coinductive objects (to encode functions of type N→A into streams (a0, a1, ...)) and of lazy evaluation with sharing (for these coinductive objects). Elaborating on previous works, we introduce in this paper a variant of dPAω presented as a sequent calculus. On the one hand, we take advantage of a variant of Krivine Classical realizability that we developed to prove the normalization of Classical call-by-need [20]. On the other hand, we benefit from dLtp, a Classical sequent calculus with dependent types in which type safety is ensured by using delimited continuations together with a syntactic restriction [19]. By combining the techniques developed in these papers, we manage to define a realizability interpretation a la Krivine of our calculus that allows us to prove normalization and soundness.
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A sequent calculus with dependent types for Classical Arithmetic
2018Co-Authors: Etienne MiqueyAbstract:In a recent paper, Herbelin developed a calculus dPA$^\omega$ in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of it components. However, the property of normalization (and therefore the one of soundness) was only conjectured. The difficulty for the proof of normalization is due to the simultaneous presence of dependent dependent types (for the constructive part of the choice), of control operators (for Classical logic), of coinductive objects (to encode functions of type $\mathbb{N} \to A$ into streams $(a_0,a_1,\ldots)$) and of lazy evaluation with sharing (for these coinductive objects).Building on previous works, we introduce in this paper a variant of dPA$^\omega$ presented as a sequent calculus. On the one hand, we take advantage of a variant of Krivine Classical realizability we developed to prove the normalization of Classical call-by-need. On the other hand, we benefit of dL, a Classical sequent calculus with dependent types in which type safety is ensured using delimited continuations together with a syntactic restriction. By combining the techniques developed in these papers, we manage to define a realizability interpretation à la Krivine of our calculus that allows us to prove normalization and soundness.
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LICS - A sequent calculus with dependent types for Classical Arithmetic
Proceedings of the 33rd Annual ACM IEEE Symposium on Logic in Computer Science, 2018Co-Authors: Etienne MiqueyAbstract:In a recent paper [11], Herbelin developed dPAω, a calculus in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of it components. However, the property of normalization (and therefore the one of soundness) was only conjectured. The difficulty for the proof of normalization is due to the simultaneous presence of dependent types (for the constructive part of the choice), of control operators (for Classical logic), of coinductive objects (to encode functions of type N→A into streams (a0, a1, ...)) and of lazy evaluation with sharing (for these coinductive objects). Elaborating on previous works, we introduce in this paper a variant of dPAω presented as a sequent calculus. On the one hand, we take advantage of a variant of Krivine Classical realizability that we developed to prove the normalization of Classical call-by-need [20]. On the other hand, we benefit from dLtp, a Classical sequent calculus with dependent types in which type safety is ensured by using delimited continuations together with a syntactic restriction [19]. By combining the techniques developed in these papers, we manage to define a realizability interpretation a la Krivine of our calculus that allows us to prove normalization and soundness.
Mozammel H. A. Khan - One of the best experts on this subject based on the ideXlab platform.
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Classical Arithmetic logic unit embedded on reversible quantum circuit
Computer and Information Technology, 2012Co-Authors: Mozammel H. A. KhanAbstract:Reversible circuit dissipates less heat than irreversible circuit. A promising use of reversible circuit may be embedding of reversible circuits in irreversible general purpose computers to allow low-power design. In this paper, we embed an n-bit Classical ALU on reversible circuit, which can perform addition, subtraction, EXOR, EXNOR, AND, NAND, OR, NOR, and NOT operations on n-bit data. The quantum realization of our n-bit ALU requires 27n — 10 primitive quantum gates with quantum circuit width of 4n + 5. The known reversible n-bit ALU capable of performing only mod 2n addition, subtraction, negative subtraction, EXOR, and no-operation requires 22n — 10 primitive quantum gates with quantum circuit width of 2n + 5. With a marginal increase of quantum primitive gate count and nearly doubling the quantum circuit width, our ALU implements a larger set of operation needed for general purpose computing.
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Classical Arithmetic logic unit embedded on reversible/quantum circuit
2012 15th International Conference on Computer and Information Technology (ICCIT), 2012Co-Authors: Mozammel H. A. KhanAbstract:Reversible circuit dissipates less heat than irreversible circuit. A promising use of reversible circuit may be embedding of reversible circuits in irreversible general purpose computers to allow low-power design. In this paper, we embed an n-bit Classical ALU on reversible circuit, which can perform addition, subtraction, EXOR, EXNOR, AND, NAND, OR, NOR, and NOT operations on n-bit data. The quantum realization of our n-bit ALU requires 27n — 10 primitive quantum gates with quantum circuit width of 4n + 5. The known reversible n-bit ALU capable of performing only mod 2n addition, subtraction, negative subtraction, EXOR, and no-operation requires 22n — 10 primitive quantum gates with quantum circuit width of 2n + 5. With a marginal increase of quantum primitive gate count and nearly doubling the quantum circuit width, our ALU implements a larger set of operation needed for general purpose computing.