Computer Floating Point Error
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by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing
Computer Floating Point Accuracy
Machinery, Inc., reprinted by permission. Abstract Floating-point arithmetic is considered floating point rounding error an esoteric subject by many people. This is rather surprising because floating-point is ubiquitous in floating point relative error computer systems. Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile
Invalid Floating Point Operation Error
floating-point algorithms from time to time; and virtually every operating system must respond 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
Floating Point Overflow Error
a discussion of the IEEE floating-point standard, and concludes with numerous examples of how computer builders can better support 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
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Floating Point Error Matlab
developers or posting ads with us Stack Overflow Questions Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the floating point error calculator Stack Overflow Community Stack Overflow is a community of 4.7 million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up Floating point inaccuracy examples up vote https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html 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 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 http://stackoverflow.com/questions/2100490/floating-point-inaccuracy-examples 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 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
asked for help on https://support.microsoft.com/en-us/kb/42980 some forum and got pointed to a long article with lots of formulas that floating point didn’t seem to help with your problem. Well, this site is here to: Explain concisely why you get that unexpected result Tell you how to deal with floating point error this problem If you’re interested, provide in-depth explanations of why floating-point numbers have to work like that and what other problems can arise You should look at the Basic Answers first - but don’t stop there! © Published at floating-point-gui.de under the Creative Commons Attribution License (BY) The Floating-Point Guide Home Basic Answers References xkcd Number Formats Binary Fractions Floating-Point Exact Types On Using Integers Errors Rounding Comparison Propagation Languagecheat sheets C# Java JavaScript Perl PHP Python Ruby SQL
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