Floating Point Error For A Reversible Function
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by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission. Abstract Floating-point floating point number example arithmetic is considered an esoteric subject by many people. This is
Floating Point Rounding Error
rather surprising because floating-point is ubiquitous in computer systems. Almost every language has a floating-point datatype; computers floating point calculator from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond
Floating Point Python
to floating-point exceptions such as overflow. This paper presents a tutorial on those aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with numerous examples of how computer builders can better support floating point arithmetic examples floating-point. Categories and Subject Descriptors: (Primary) C.0 [Computer Systems Organization]: General -- instruction set design; D.3.4 [Programming Languages]: Processors -- compilers, optimization; G.1.0 [Numerical Analysis]: General -- computer arithmetic, error analysis, numerical algorithms (Secondary) D.2.1 [Software Engineering]: Requirements/Specifications -- languages; D.3.4 Programming Languages]: Formal Definitions and Theory -- semantics; D.4.1 Operating Systems]: Process Management -- synchronization. General Terms: Algorithms, Design, Languages Additional Key Words and Phrases: Denormalized number, exception, floating-point, floating-point standard, gradual underflow, guard digit, NaN, overflow, relative error, rounding error, rounding mode, ulp, underflow. Introduction Builders of computer systems often need information about floating-point arithmetic. There are, however, remarkably few sources of detailed information about it. One of the few books on the subject, Floating-Point Computation by Pat Sterbenz, is long out of print. This paper is a tutorial on those aspects of floating-point arithmetic (floating-point hereafter) that have a direct connection to systems building. It consists of three loosely connected parts. The first section, Rounding Error, discusses the implications of using different rounding strategies for the
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Floating Point Numbers Explained
Join the Stack Overflow Community Stack Overflow is a community of 4.7 million programmers, just like you, helping each other. Join them; it only takes floating point representation a minute: Sign up Floating point inaccuracy examples up vote 29 down vote favorite 46 How do you explain floating point inaccuracy to fresh programmers and laymen who still think computers are infinitely wise and accurate? Do you have a https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html favourite example or anecdote which seems to get the idea across much better than an precise, but dry, explanation? How is this taught in Computer Science classes? floating-point floating-accuracy share edited Apr 24 '10 at 22:34 community wiki 4 revs, 3 users 57%David Rutten locked by Bill the Lizard May 6 '13 at 12:41 This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence http://stackoverflow.com/questions/2100490/floating-point-inaccuracy-examples that you can ask similar questions here. This question and its answers are frozen and cannot be changed. More info: help center. Take a look into this article: What Every Computer Scientist Should Know About Floating-Point Arithmetic –Rubens Farias Jan 20 '10 at 10:17 1 You can comprove this with this simple javascript:alert(0.1*0.1*10); –user216441 Apr 24 '10 at 23:07 comments disabled on deleted / locked posts / reviews| 7 Answers 7 active oldest votes up vote 26 down vote accepted There are basically two major pitfalls people stumble in with floating-point numbers. The problem of scale. Each FP number has an exponent which determines the overall “scale” of the number so you can represent either really small values or really larges ones, though the number of digits you can devote for that is limited. Adding two numbers of different scale will sometimes result in the smaller one being “eaten” since there is no way to fit it into the larger scale. PS> $a = 1; $b = 0.0000000000000000000000001 PS> Write-Host a=$a b=$b a=1 b=1E-25 PS> $a + $b 1 As an analogy for this case you could picture a large swimming pool and a teaspoon of water. Both are of very different sizes, but individually you can easily grasp how much they roughly are. Pouring the teaspoon into the swimming pool, however, will leave you still with roughly a swimming pool full of water. (If the people learning th
from GoogleSign inHidden fieldsBooksbooks.google.com - Over the past four decades microprocessors have come to be a vital and inseparable part of the modern world, becoming the digital brain https://books.google.com/books?id=UHWMWNgyERoC&pg=PA50&lpg=PA50&dq=floating+point+error+for+a+reversible+function&source=bl&ots=YwSU7HPaf0&sig=7IrUoKPt6R-D75zYOUrmYLz8FDA&hl=en&sa=X&ved=0ahUKEwiEm4DfjdfPAhWCgFQKHbJSDzoQ of numerous electronic devices and gadgets that make today's lifestyle https://books.google.com/books?id=Lq_MBQAAQBAJ&pg=PA215&lpg=PA215&dq=floating+point+error+for+a+reversible+function&source=bl&ots=UQ4O35-hoi&sig=irpLymFs-KVaqxsHttr349Sm9ME&hl=en&sa=X&ved=0ahUKEwiEm4DfjdfPAhWCgFQKHbJSDz possible. Processors are capable of performing computation at astonishingly high speeds and are...https://books.google.com/books/about/An_Effective_Verification_Solution_for_M.html?id=UHWMWNgyERoC&utm_source=gb-gplus-shareAn Effective Verification Solution for Modern MicroprocessorsMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableProQuestFind in a libraryAll sellers»Get Textbooks on Google PlayRent and save from the world's floating point largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »An Effective Verification Solution for Modern MicroprocessorsProQuest, 2008 - 155 pages 0 Reviewshttps://books.google.com/books/about/An_Effective_Verification_Solution_for_M.html?id=UHWMWNgyERoCOver the past four decades microprocessors have come to be a vital and inseparable part of the modern world, becoming floating point number the digital brain of numerous electronic devices and gadgets that make today's lifestyle possible. Processors are capable of performing computation at astonishingly high speeds and are extremely integrated, occupying only a few square centimeters of silicon die. However, this computational power comes at a price: the task of verifying a modern microprocessor and guaranteeing correctness of its operation is increasingly challenging, even for most established processor vendors. Always attempting to deliver higher performance to end-users, processor manufacturers are forced to design progressively more complex circuits and employ immense verification teams to eliminate critical design bugs in a timely manner. Unfortunately, too often size doesn't seem to matter in verification, as schedules continue to slip and microprocessors find their way to the marketplace with design errors. Preview this book » What people are saying-Write a reviewWe haven't found any reviews in the usual places.Selected page
from GoogleSign inHidden fieldsBooksbooks.google.com - Few books comprehensively cover the software and programming aspects of reversible computing. Filling this gap, Introduction to Reversible Computing offers an expanded view of the field that includes the traditional energy-motivated hardware viewpoint as well as the emerging application-motivated software...https://books.google.com/books/about/Introduction_to_Reversible_Computing.html?id=Lq_MBQAAQBAJ&utm_source=gb-gplus-shareIntroduction to Reversible ComputingMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableCRC PressAmazon.comBarnes&Noble.comBooks-A-MillionIndieBoundAll sellers»Get Textbooks on Google PlayRent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »Introduction to Reversible ComputingKalyan S. PerumallaCRC Press, Sep 10, 2013 - Computers - 325 pages 0 Reviewshttps://books.google.com/books/about/Introduction_to_Reversible_Computing.html?id=Lq_MBQAAQBAJFew books comprehensively cover the software and programming aspects of reversible computing. Filling this gap, Introduction to Reversible Computing offers an expanded view of the field that includes the traditional energy-motivated hardware viewpoint as well as the emerging application-motivated software approach. Collecting scattered knowledge into one coherent account, the book provides a compendium of both classical and recently developed results on reversible computing. It explores up-and-coming theories, techniques, and tools for the application of reversible computing—the logical next step in the evolution of computing systems. The book covers theory, hardware and software aspects, fundamental limits, complexity analyses, practical algorithms, compilers, efficiency improvement techniques, and application areas. The topics span several areas of computer science, including high-performance computing, parallel/distributed systems, computational theory, compilers, power-aware computing, and supercomputing. The book presents sufficient material for newcomers to easily get started. It provides citations to original articles on seminal results so that readers can consult the corresponding publications in the literature. Po