Custom Floating Point Arithmetic For Integer Processors
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Custom Floating Point Arithmetic For Integer Processors
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Author : Jingyan Jourdan
language : en
Publisher:
Release Date : 2012
Custom Floating Point Arithmetic For Integer Processors written by Jingyan Jourdan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Media processing applications typically involve numerical blocks that exhibit regular floating-point computation patterns. For processors whose architecture supports only integer arithmetic, these patterns can be profitably turned into custom operators, coming in addition to the five basic ones (+, -, X, / and √), but achieving better performance by treating more operations. This thesis addresses the design of such custom operators as well as the techniques developed in the compiler to select them in application codes. We have designed optimized implementations for a set of custom operators which includes squaring, scaling, adding two nonnegative terms, fused multiply-add, fused square-add (x*x+z, with z>=0), two-dimensional dot products (DP2), sums of two squares, as well as simultaneous addition/subtraction and sine/cosine. With novel algorithms targeting high instruction-level parallelism and detailed here for squaring, scaling, DP2, and sin/cos, we achieve speedups of up to 4.2x for individual custom operators even when subnormal numbers are fully supported. Furthermore, we introduce the optimizations developed in the ST231 C/C++ compiler for selecting such operators. Most of the selections are achieved at high level, using syntactic criteria. However, for fused square-add, we also enhance the framework of integer range analysis to support floating-point variables in order to prove the required positivity condition z>= 0. Finally, we provide quantitative evidence of the benefits to support this selection of custom operations: on DSP kernels and benchmarks, our approach allows us to be up to 1.59x faster compared to the sole usage of basic ones.
Handbook Of Floating Point Arithmetic
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Author : Jean-Michel Muller
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-11
Handbook Of Floating Point Arithmetic written by Jean-Michel Muller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-11 with Mathematics categories.
Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.
Implementation Of Binary Floating Point Arithmetic On Embedded Integer Processors
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Author : Guillaume Revy
language : en
Publisher:
Release Date : 2009
Implementation Of Binary Floating Point Arithmetic On Embedded Integer Processors written by Guillaume Revy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Today some embedded systems still do not integrate their own floating-point unit, for area, cost, or energy consumption constraints. However, this kind of architectures is widely used in application domains highly demanding on floating-point calculations (multimedia, audio and video, or telecommunications). To compensate this lack of floating-point hardware, floating-point arithmetic has to be emulated efficiently through a software implementation. This thesis addresses the design and implementation of an efficient software support for IEEE 754 floating-point arithmetic on embedded integer processors. More specifically, it proposes new algorithms and tools for the efficient generation of fast and certified programs, allowing in particular to obtain C codes of very low latency for polynomial evaluation in fixed-point arithmetic. Compared to fully hand-written implementations, these tools allow to significantly reduce the development time of floating-point operators. The first part of the thesis deals with the design of optimized algorithms for some binary floating-point operators, and gives details on their software implementation for the binary32 floating-point format and for some embedded VLIW integer processors like those of the STMicroelectronics ST200 family. In particular, we propose here a uniform approach for correctly-rounded roots and their reciprocals, and an extension to division. Our approach, which relies on the evaluation of a single bivariate polynomial, allows higher ILP-exposure than previous methods and turns out to be particularly efficient in practice. This work allowed us to produce a fully revised version of the FLIP library, leading to significant gains compared to the previous version. The second part of the thesis presents a methodology for automatically and efficiently generating fast and certified C codes for the evaluation of bivariate polynomials in fixed-point arithmetic. In particular, it consists of some heuristics for computing highly parallel, low-latency evaluation schemes, as well as some techniques to check if those schemes remain efficient on a real target, and accurate enough to ensure correct rounding of the underlying operator implementations. This approach has been implemented in the software tool CGPE (Code Generation for Polynomial Evaluation). We have used our tool to quickly generate and certify significant parts of the codes of FLIP.
Handbook Of Floating Point Arithmetic
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Author : Jean-Michel Muller
language : en
Publisher: Birkhäuser
Release Date : 2018-05-02
Handbook Of Floating Point Arithmetic written by Jean-Michel Muller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-02 with Mathematics categories.
Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.
Embedded Dsp Processor Design
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Author : Dake Liu
language : en
Publisher: Morgan Kaufmann
Release Date : 2008-05-30
Embedded Dsp Processor Design written by Dake Liu and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-30 with Computers categories.
This book provides design methods for Digital Signal Processors and Application Specific Instruction set Processors, based on the author's extensive, industrial design experience. Top-down and bottom-up design methodologies are presented, providing valuable guidance for both students and practicing design engineers. Coverage includes design of internal-external data types, application specific instruction sets, micro architectures, including designs for datapath and control path, as well as memory sub systems. Integration and verification of a DSP-ASIP processor are discussed and reinforced with extensive examples. Instruction set design for application specific processors based on fast application profiling Micro architecture design methodology Micro architecture design details based on real examples Extendable architecture design protocols Design for efficient memory sub systems (minimizing on chip memory and cost) Real example designs based on extensive, industrial experiences
Handbook Of Floating Point Arithmetic
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Author :
language : en
Publisher:
Release Date : 2010
Handbook Of Floating Point Arithmetic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computer arithmetic categories.
Flip A Floating Point Library For Integer Processors
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Author : Saurabh-Kumar Raina
language : en
Publisher:
Release Date : 2006
Flip A Floating Point Library For Integer Processors written by Saurabh-Kumar Raina and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Computer Arithmetic And Formal Proofs
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Author : Sylvie Boldo
language : en
Publisher: Elsevier
Release Date : 2017-11-17
Computer Arithmetic And Formal Proofs written by Sylvie Boldo and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Computers categories.
Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical use Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic Includes real analysis and a case study about numerical analysis
Integer Emulation Of Floating Point Arithmetic
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Author : Jeffrey L. Baker
language : en
Publisher:
Release Date : 1982
Integer Emulation Of Floating Point Arithmetic written by Jeffrey L. Baker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Floating-point arithmetic categories.
Computer Arithmetic
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Author : Earl E Swartzlander
language : en
Publisher: World Scientific
Release Date : 2015-02-12
Computer Arithmetic written by Earl E Swartzlander and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-12 with Mathematics categories.
Computer Arithmetic Volume III is a compilation of key papers in computer arithmetic on floating-point arithmetic and design. The intent is to show progress, evolution, and novelty in the area of floating-point arithmetic. This field has made extraordinary progress since the initial software routines on mainframe computers have evolved into hardware implementations in processors spanning a wide range of performance. Nevertheless, these papers pave the way to the understanding of modern day processors design where computer arithmetic are supported by floating-point units. The goal of Volume III is to collect the defining document for floating-point arithmetic and many of the key papers on the implementation of both binary and decimal floating-point arithmetic into a single volume. Although fewer than forty papers are included, their reference lists will direct the interested reader to other excellent work that could not be included here. Volume III is specifically oriented to the needs of designers and users of both general-purpose computers and special-purpose digital processors. The book should also be useful to systems engineers, computer architects, and logic designers. It is also intended to serve as a primary text for a course on floating-point arithmetic, as well as a supplementary text for courses in digital arithmetic and high-speed signal processing. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewFloating-Point AdditionFloating-Point MultiplicationRoundingFused Multiply AddFloating-Point DivisionElementary FunctionsDecimal Floating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:The papers that are included cover the key concepts needed to develop efficient (fast, small and low-power) floating-point processing unitsThe papers include presentations by the initial developers in their own words to better explain the basic techniquesIncludes five papers on decimal floating-point arithmetic, which has been added to the IEEE standardKeywords:Floating-Point Addition;Floating-Point Multiplication;Floating-Point Division;Decimal Floating-Point Arithmetic