DOCSLIB.ORG

A Fixed Point Arithmetic Library for Spinnaker

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Fixed Point Arithmetic Library for Spinnaker A fixed point arithmetic library for SpiNNaker A dissertation submitted to the University of Manchester for the degree of Master of Science in the Faculty of Engineering and Physical Sciences -2012- Mircea Moise School of Computer Science Mircea Moise – A fixed point arithmetic library for SpiNNaker Contents Contents .............................................................................................................. 2 List of tables ....................................................................................................... 4 List of figures ...................................................................................................... 5 Abstract ............................................................................................................... 6 Declaration ......................................................................................................... 7 Intellectual property statement .......................................................................... 8 Acknowledgement .............................................................................................. 9 Chapter 1 Introduction ..................................................................................... 10 1.1 Motivation ................................................................................................................. 10 1.2 Aim and Objectives .................................................................................................. 12 1.3 Report Structure ....................................................................................................... 12 Chapter 2 Context ............................................................................................. 14 2.1 SpiNNaker ................................................................................................................. 14 2.2 ARM ........................................................................................................................... 18 2.3 Number representation systems ............................................................................. 20 2.4 Software implementation for fixed point arithmetic ........................................... 21 2.5 Summary .................................................................................................................... 22 Chapter 3 Research Methods ........................................................................... 23 3.1 Project outline ........................................................................................................... 23 3.2 Methodology for assessing algorithms .................................................................. 24 3.3 Tools used .................................................................................................................. 26 3.4 Evaluation strategy ................................................................................................... 27 3.5 Summary .................................................................................................................... 28 Chapter 4 Theoretical Background .................................................................. 29 4.1 Taylor series approximation .................................................................................... 29 4.2 Chebyshev polynomials ........................................................................................... 30 4.3 Newton-Raphson iteration ...................................................................................... 32 4.4 CORDIC algorithms ................................................................................................ 33 2 Mircea Moise – A fixed point arithmetic library for SpiNNaker 4.5 Normalization algorithms ........................................................................................ 35 4.6 Normalization to shorter intervals ......................................................................... 36 4.7 Use of lookup tables................................................................................................. 37 4.8 Summary .................................................................................................................... 38 Chapter 5 Algorithm assessment ...................................................................... 39 5.1 Division ...................................................................................................................... 39 5.2 Square Root ............................................................................................................... 42 5.3 Logarithm .................................................................................................................. 44 5.4 Exponential ............................................................................................................... 47 5.5 Simple trigonometric functions – sine and cosine ............................................... 49 5.6 Summary .................................................................................................................... 54 Chapter 6 Implementation ............................................................................... 55 6.1 Testing approach ...................................................................................................... 55 6.2 Testing framework.................................................................................................... 58 6.3 Libraries overview .................................................................................................... 62 6.4 Basic library ............................................................................................................... 63 6.5 Math library ............................................................................................................... 68 6.6 Debugging library ..................................................................................................... 75 6.7 Summary .................................................................................................................... 77 Chapter 7 Evaluation ........................................................................................ 78 7.1 Evaluation criteria ..................................................................................................... 78 7.2 Software usability ...................................................................................................... 79 7.3 Accuracy ..................................................................................................................... 81 7.4 Efficiency ................................................................................................................... 85 7.5 Summary .................................................................................................................... 90 Chapter 8 Conclusions and future work ........................................................... 91 Appendix A ....................................................................................................... 94 Bibliography ..................................................................................................... 96 Word count: 27 960 3 Mircea Moise – A fixed point arithmetic library for SpiNNaker List of tables Table 1 SpiNNaker machine description .......................................................................... 14 Table 2 Impact of VFP unit on ARM core....................................................................... 20 Table 3 Useful trigonometric formulas ............................................................................. 50 Table 4 Maximum error for Taylor series - sine algorithm ............................................ 51 Table 5 Maximum error for power series - sine algorithm ............................................. 52 Table 6 Maximum error for CORDIC - sine algorithm ................................................. 53 Table 7 Types of validation used ........................................................................................ 57 Table 8 Interpreter – description of methods .................................................................. 61 Table 9 MinUnit description ............................................................................................... 62 Table 10 Libraries description ............................................................................................ 63 Table 11 Names used for functions ................................................................................... 81 Table 12 Division evaluation results - Random case ....................................................... 83 Table 13 Square root evaluation results - Random case ................................................. 84 Table 14 Logarithm evaluation results - Random case ................................................... 84 Table 15 Exponential evaluation results ........................................................................... 85 Table 16 Sin evaluation results ........................................................................................... 85 Table 17 Efficiency results – exponential ......................................................................... 88 Table 18 Efficiency evalutation – logarithm ..................................................................... 88 Table 19 Efficiency evaluation - square root .................................................................... 88 Table 20 Efficiency evaluation - sinus ..............................................................................
Load more

Recommended publications
  • Approximate Computing for High Energy-Efficiency in Iot Applications
    THESE DE DOCTORAT DE L'UNIVERSITE DE RENNES 1 COMUE UNIVERSITE BRETAGNE LOIRE ECOLE DOCTORALE N° 601 Mathématiques et Sciences et Technologies de l'Information et de la Communication Spécialité : Informatique Par « Geneviève NDOUR » « Approximate computing for high energy-efficiency in internet-of-things applications » Thèse présentée et soutenue à Grenoble, le 17 juillet 2019 Unités de recherche : CEA LETI Grenoble, IRISA INRIA Lannion Rapporteurs avant soutenance : Florent DE DINECHIN Professeur à l’INSA Lyon, CITI Lionel TORRES Professeur à l’Université de Monpellier, LIRMM Composition du Jury : Président: Olivier SENTIEYS Professeur à l’Université Rennes 1, IRISA INRIA Examinateurs: Alberto BOSIO Professeur à l’Ecole Centrale de Lyon, INL Olivier SENTIEYS Professeur à l’Université Rennes 1, IRISA INRIA Florent DE DINECHIN Professeur à l’INSA Lyon, CITI Lionel TORRES Professeur à l’Université de Monpellier, LIRMM Dir. de thèse: Arnaud TISSERAND Directeur de Recherche CNRS, Lab-STICC Lorient Co-dir. de thèse: Anca MOLNOS Ingénieur de Recherche, CEA LETI Grenoble ACKNOWLEDGEMENT J’adresse mes remerciements à mon directeur de thèse Arnaud TISSERAND et à mon encadrante Anca MOLNOS pour leurs conseils sur toutes les décisions prises pour la réalisation des travaux de recherche et pour mes démarches per- sonnelles. Merci également à Yves DURAND et à Edith BEIGNE pour leur soutien dans l’encadrement de la thèse. Mes remerciements vont aussi aux rapporteurs Lionel TORRES et Florent DE DINECHIN pour la relecture de la thèse et à tous les membres du jury qui ont accepté d’évaluer mon travail. Je remercie également Tiago TREVISAN-JOST pour l’implémentation du sim- ulateur RISC-V et les collègues du DACLE/LISAN pour l’estimation du modèle d’énergie.
    [Show full text]
  • Downloaded from the Gitlab Repository [63]
    sensors Article RcdMathLib: An Open Source Software Library for Computing on Resource-Limited Devices Zakaria Kasmi 1 , Abdelmoumen Norrdine 2,* , Jochen Schiller 1 , Mesut Güne¸s 3 and Christoph Motzko 2 1 Freie Universität Berlin, Department of Mathematics and Computer Science, Takustraße 9, 14195 Berlin, Germany; [email protected] (Z.K.); [email protected] (J.S.) 2 Technische Universität Darmstadt, Institut für Baubetrieb, El-Lissitzky-Straße 1, 64287 Darmstadt, Germany; [email protected] 3 Otto-von-Guericke University, Faculty of Computer Science, Universitätsplatz 2, 39106 Magdeburg, Germany; [email protected] * Correspondence: [email protected] Abstract: We developped an open source library called RcdMathLib for solving multivariate linear and nonlinear systems. RcdMathLib supports on-the-fly computing on low-cost and resource- constrained devices, e.g., microcontrollers. The decentralized processing is a step towards ubiquitous computing enabling the implementation of Internet of Things (IoT) applications. RcdMathLib is modular- and layer-based, whereby different modules allow for algebraic operations such as vector and matrix operations or decompositions. RcdMathLib also comprises a utilities-module providing sorting and filtering algorithms as well as methods generating random variables. It enables solving linear and nonlinear equations based on efficient decomposition approaches such as the Singular Value Decomposition (SVD) algorithm. The open source library also provides optimization methods such as Gauss–Newton and Levenberg–Marquardt algorithms for solving problems of regression smoothing and curve fitting. Furthermore, a positioning module permits computing positions of Citation: Kasmi, Z.; Norrdine, A.; IoT devices using algorithms for instance trilateration. This module also enables the optimization of Schiller, J.; Güne¸s,M.; Motzko, C.
    [Show full text]
  • Anomaly Detection in Networked Embedded Sensor Systems
    Anomaly detection in networked embedded sensor systems Citation for published version (APA): Bosman, H. H. W. J. (2016). Anomaly detection in networked embedded sensor systems. Technische Universiteit Eindhoven. Document status and date: Published: 12/09/2016 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim.
    [Show full text]
  • Design and Implementation of Power Management Strategies for Long Range Radio Module with Energy Harvesting Philip-Dylan Gléonec
    Design and implementation of power management strategies for long range radio module with energy harvesting Philip-Dylan Gléonec To cite this version: Philip-Dylan Gléonec. Design and implementation of power management strategies for long range radio module with energy harvesting. Hardware Architecture [cs.AR]. Université Rennes 1, 2019. English. NNT : 2019REN1S017. tel-02281759 HAL Id: tel-02281759 https://tel.archives-ouvertes.fr/tel-02281759 Submitted on 9 Sep 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THESE DE DOCTORAT DE L'UNIVERSITE DE RENNES 1 COMUE UNIVERSITE BRETAGNE LOIRE ECOLE DOCTORALE N° 601 Mathématiques et Sciences et Technologies de l'Information et de la Communication Spécialité : Télécommunications Par Philip-Dylan GLEONEC Design and implementation of power management strategies for long range radio modules with energy harvesting Thèse présentée et soutenue à Rennes, le 08/02/2018 Unité de recherche : IRISA -- UMR6074 | Equipe GRANIT Rapporteurs avant soutenance : Alain Pégatoquet Maître de Conférences – HDR, Université de Nice-Sophia Antipolis Hervé Barthélémy Professeur d’Université, Université de Toulon-Var Composition du Jury : Président : Laurent Clavier Professeur d’Université, Institut Mines-Télécom Examinateurs : Jeremy Ardouin CTO, Wi6labs Jean-François Diouris Professeur d’Université, Université de Nantes Sylvie Kerouedan Maître de Conférences – HDR, IMT Atlantique Dir.
    [Show full text]
  • Approximate Computing for High Energy-Efficiency in Iot Applications
    Approximate computing for high energy-efficiency in IoT applications Geneviève Ndour To cite this version: Geneviève Ndour. Approximate computing for high energy-efficiency in IoT applications. Other [cs.OH]. Université Rennes 1, 2019. English. NNT : 2019REN1S033. tel-02292988v2 HAL Id: tel-02292988 https://tel.archives-ouvertes.fr/tel-02292988v2 Submitted on 22 Nov 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THESE DE DOCTORAT DE L'UNIVERSITE DE RENNES 1 COMUE UNIVERSITE BRETAGNE LOIRE ECOLE DOCTORALE N° 601 Mathématiques et Sciences et Technologies de l'Information et de la Communication Spécialité : Informatique Par « Geneviève NDOUR » « Approximate computing for high energy-efficiency in internet-of-things applications » Thèse présentée et soutenue à Grenoble, le 17 juillet 2019 Unités de recherche : CEA LETI Grenoble, IRISA INRIA Lannion Rapporteurs avant soutenance : Florent DE DINECHIN Professeur à l’INSA Lyon, CITI Lionel TORRES Professeur à l’Université de Monpellier, LIRMM Composition du Jury : Président: Olivier SENTIEYS Professeur à l’Université Rennes 1, IRISA INRIA Examinateurs: Alberto BOSIO Professeur à l’Ecole Centrale de Lyon, INL Olivier SENTIEYS Professeur à l’Université Rennes 1, IRISA INRIA Florent DE DINECHIN Professeur à l’INSA Lyon, CITI Lionel TORRES Professeur à l’Université de Monpellier, LIRMM Dir.
    [Show full text]
  • An Open-Source Tool for Classification Models in Resource-Constrained Hardware 3
    IEEE SENSORS JOURNAL, VOL. XX, NO. XX, XXXX 2021 1 An Open-Source Tool for Classification Models in Resource-Constrained Hardware Lucas Tsutsui da Silva, Vinicius M. A. Souza, and Gustavo E. A. P. A. Batista Abstract— Applications that need to sense, measure, and gather real-time information from the environment frequently face three main restrictions: power consumption, cost, and lack of infras- tructure. Most of the challenges imposed by these limitations can be better addressed by embedding Machine Learning (ML) classifiers in the hardware that senses the environment, creating smart sensors able to interpret the low-level data stream. However, for this approach to be cost-effective, we need highly efficient classifiers suitable to execute in unresourceful hardware, such as low-power microcontrollers. In this paper, we present an open-source tool named EmbML – Embedded Machine Learning that implements a pipeline to develop classifiers for resource-constrained hardware. We describe its implementation details and provide a comprehensive analysis of its classifiers considering accuracy, classification time, and memory usage. Moreover, we compare the performance of its classifiers with classifiers produced by related tools to demonstrate that our tool provides a diverse set of classification algorithms that are both compact and accurate. Finally, we validate EmbML classifiers in a practical application of a smart sensor and trap for disease vector mosquitoes. Index Terms— Classification, edge computing, machine learning, smart sensors I. INTRODUCTION the cloud. Therefore, these smart sensors are more power- PPLICATIONS that need to sense, measure, and gather efficient since they eliminate the need for communicating all real-time information from the environment frequently the raw data.
    [Show full text]
  • An SMT Theory of Fixed-Point Arithmetic⋆
    An SMT Theory of Fixed-Point Arithmetic? Marek Baranowski1, Shaobo He1, Mathias Lechner2, Thanh Son Nguyen1, and Zvonimir Rakamari¢1 1 School of Computing, University of Utah Salt Lake City, UT, USA {baranows,shaobo,thanhson,zvonimir}@cs.utah.edu 2 IST Austria Klosterneuburg, Austria [email protected] Abstract. Fixed-point arithmetic is a popular alternative to oating- point arithmetic on embedded systems. Existing work on the verication of xed-point programs relies on custom formalizations of xed-point arithmetic, which makes it hard to compare the described techniques or reuse the implementations. In this paper, we address this issue by proposing and formalizing an SMT theory of xed-point arithmetic. We present an intuitive yet comprehensive syntax of the xed-point theory, and provide formal semantics for it based on rational arithmetic. We also describe two decision procedures for this theory: one based on the theory of bit-vectors and the other on the theory of reals. We implement the two decision procedures, and evaluate our implementations using exist- ing mature SMT solvers on a benchmark suite we created. Finally, we perform a case study of using the theory we propose to verify properties of quantized neural networks. Keywords: SMT · Fixed-Point Arithmetic · Decision Procedure. 1 Introduction Algorithms based on real arithmetic have become prevalent. For example, the mathematical models in machine learning algorithms operate on real numbers. Similarly, signal processing algorithms often implemented on embedded systems (e.g., fast Fourier transform) are almost always dened over real numbers. How- ever, real arithmetic is not implementable on computer systems due to its un- limited precision.
    [Show full text]
  • Energy-Efficient Embedded Machine Learning Algorithms for Smart Sensing Systems
    UNIVERSITY OF GENOVA Polytechnic School Doctoral Program in Science and Technology for Electronic and Telecommunication Engineering (XXXII cycle) Energy-efficient embedded machine learning algorithms for smart sensing systems Mario Osta Supervisor: Prof. M. Valle A thesis submitted for the degree of Doctor of Philosophy February 2020 i ACKNOWLEDGMENTS This Ph.D. journey is a combined effort of several individuals, including the scholars, family members who supported me, and friends who were always accessible through this journey. First and foremost, I would like to express my gratitude to my marvelous thesis supervisor Prof. Maurizio Valle whose support, guidance during these three years has made this thesis possible. He gave me opportunities to improve my work through my learning path. I am very grateful to my colleague Dr. Ali Ibrahim for his encouragement and extensive support through my Ph.D. journey. His evaluation and suggestions were essential to solving various bottlenecks in my research work innovatively. He influenced me to work hard and persist in my determination. During my Ph.D., I had the opportunity to work at the Swiss Federal Institue of Technology in Zurich (ETH) as a visiting researcher. I am grateful to my internship mentor for making this research work successful. I would like to thank my friends and lab mates at the COSMIC lab for the lively discussion and unforgettable adventures. I am also grateful to all my friends at the ETH IIS lab in Zurich. Last but not least, I would also like to thank my parents, my sister, and my brother, for their advice and support throughout my life.
    [Show full text]
  • Open Source Software License for HP Laserjet and HP Scanjet Printers
    Open-Source Software License Agreements for HP LaserJet and ScanJet Printers Table of Contents Introduction................................................................................................................................................... 6 AFL-2 .............................................................................................................................................................. 6 Apache log4net ............................................................................................................................................ 9 cURL ............................................................................................................................................................. 13 Cyrus SASL .............................................................................................................................................. 14 DotNetZip .................................................................................................................................................... 15 expat ............................................................................................................................................................ 16 GNU Licenses .............................................................................................................................................. 17 GNU GENERAL PUBLIC LICENSE .......................................................................................................... 17 GPLv2 .....................................................................................................................................................
    [Show full text]
  • Coap) [Shelby Et Al., 2014] (An Application-Layer Protocol Allowing Low-Power Devices to Appear As Web Servers)
    NNT : 2016SACLX090 Thèse de doctorat de l’Université Paris-Saclay préparée à Ecole Polytechnique École doctorale n∘580 Sciences et technologies de l’information et de la communication Spécialité de doctorat: Informatique par M. Oliver Hahm Enabling Energy Efficient Smart Object Networking at Internet-Scale Experimental Tools, Software Platform, and Information-Centric Networking Protocols Thèse présentée et soutenue à Berlin, le 01 décembre 2016. Composition du Jury : M. Jochen H. Schiller Professeur (Président du jury) Freie Universität Berlin M. Carsten Bormann Professeur (Rapporteur) Universität Bremen M. Dirk Kutscher Docteur (Rapporteur) Huawei German Research Center M. Anis Laouiti Maître de conférences (Examinateur) Telecom SudParis M. Emmanuel Baccelli Professeur (Directeur de thèse) INRIA This dissertation is the result of a long, exciting, sometimes cumbersome, often surpris- ing journey. It is dedicated to my grandmother Erna who inspired and motivated me to begin this journey. It is also dedicated to my parents, Doris and Dieter, whose love and un- conditional support made this journey possible. And finally, it is dedicated to Judith who was my solace and light in the darkest nights during this journey. ii Acknowledgments During my journey towards this dissertation, I was incredibly lucky to meet many supporting and inspiring people. I would not have been able to finish this journey without the help of all of them. First and foremost, I would like to thank Emmanuel Baccelli who supported and helped me in many ways. His guidance, expertise, and experience, but also his kindness were invaluable for me. I am also very grateful to my reviewers, Carsten Bormann and Dirk Kutscher who were willing to read and examine this manuscript.
    [Show full text]
  • Universid Ade De Sã O Pa
    Evaluating classification models for resource-constrained hardware Lucas Tsutsui da Silva Dissertação de Mestrado do Programa de Pós-Graduação em Ciências de Computação e Matemática Computacional (PPG-CCMC) UNIVERSIDADE DE SÃO PAULO DE SÃO UNIVERSIDADE Instituto de Ciências Matemáticas e de Computação Instituto Matemáticas de Ciências SERVIÇO DE PÓS-GRADUAÇÃO DO ICMC-USP Data de Depósito: Assinatura: ______________________ Lucas Tsutsui da Silva Evaluating classification models for resource-constrained hardware Dissertation submitted to the Institute of Mathematics and Computer Sciences – ICMC-USP – in accordance with the requirements of the Computer and Mathematical Sciences Graduate Program, for the degree of Master in Science. FINAL VERSION Concentration Area: Computer Science and Computational Mathematics Advisor: Prof. Dr. Gustavo Enrique de Almeida Prado Alves Batista USP – São Carlos November 2020 Ficha catalográfica elaborada pela Biblioteca Prof. Achille Bassi e Seção Técnica de Informática, ICMC/USP, com os dados inseridos pelo(a) autor(a) da Silva, Lucas Tsutsui d111e Evaluating classification models for resource- constrained hardware / Lucas Tsutsui da Silva; orientador Gustavo Enrique de Almeida Prado Alves Batista. -- São Carlos, 2020. 141 p. Dissertação (Mestrado - Programa de Pós-Graduação em Ciências de Computação e Matemática Computacional) -- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 2020. 1. Machine learning. 2. Classification. 3. Embedded classifier. 4. WEKA. 5. scikit-learn. I. Batista,
    [Show full text]
  • A Method for Energy-Efficient Sampling of Analog to Digital
    1 A Method for Energy-Efficient Sampling of Analog to Digital Converters Neil Klingensmith, Member, IEEE, Suman Banerjee, Member, IEEE, F Abstract—We present PANDA, a data acquisition technique for energy- manufacturers, and it represents a large and growing por- constrained sensor nodes that reduces the energy per operation re- tion of microcontroller sales. quired to sample and preprocess analog sensor data. PANDA takes To extend the battery life of sensor nodes, we seek to advantage of the energy consumption patterns of commodity micro- reduce the energy per operation of sampling and prepro- controllers by sampling input signals in short bursts followed by long cessing our input sensor data. To do so, we put the CPU periods of inactivity. This approach reduces the overhead of repetitively transitioning the CPU and analog components in and out of low-power and analog components into sleep mode for as much time sleep states. This nonuniformly-spaced input data is then fed to a as our application will allow. nonuniform FFT algorithm that computes the frequency spectrum. We However, sleeping the analog components between sam- show that the spectrum computed with the nonuniform FFT is very close ple acquisitions poses a problem for real time systems to the spectrum that would be computed from uniformly sampled data because the process of putting each component to sleep preprocessed with a conventional FFT. The output of the nonuniform and waking it up consumes a significant amount of time FFT can be filtered or postprocessed with conventional frequency do- and energy. We have found that for many microcontrollers, main analysis techniques, and a uniformly resampled output can be waking the ADC from sleep mode takes roughly the same constructed with the conventional inverse FFT.
    [Show full text]