Floating-point Error Distributive Law
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addition commutative and associative?UpdateCancelAnswer Wiki3 Answers Tikhon Jelvis, studied and did research on programming languagesWritten 141w ago · Upvoted by Justin Rising, MSE in CS and Arjun Narayan, Ph.D student in computer scienceFloating point addition is not associative. floating point calculator This is actually surprisingly easy to demonstrate:Prelude> let r₁ = (0.1 + 0.2) + 0.3; floating point arithmetic r₂ = 0.1 + (0.2 + 0.3) Prelude> r₁ 0.6000000000000001 Prelude> r₂ 0.6 Prelude> r₁ - r₂ 1.1102230246251565e-16 However, addition is floating point arithmetic examples commutative. I don't know how to prove this off-hand, but I remember reading it in the past, and it's confirmed on Wikipedia :).As an aside, floating-point multiplication is not distributive over addition. Prelude> 100 * (0.1 floating point addition + 0.2) 30.000000000000004 Prelude> 100 * 0.1 + 100 * 0.2 30.0 Actually, floating point numbers violate pretty much every property you care about. Floating-point equality isn't even reflexive, for example! Prelude> nan NaN Prelude> nan == nan False (It is symmetric and transitive though, so that's something. I guess.)If you care about nice numerical properties (but not about performance), you can look at using some other numeric representation like arbitrary-precision
Floating Point Mantissa
rational numbers or even constructive real numbers. Admittedly, Haskell is the only language I've see where people ever use either of these: rational numbers come in the standard library (in the Prelude as Rational) and constructive reals as part of the numbers package (Data.Number.CReal).4.2k Views · View UpvotesRelated QuestionsMore Answers BelowIn IEEE floating point, are 1*x and x bitwise identical even for nan?Why doesn't compiler optimize x*2 to x << 1, if x is a float?What is a floating point?How does floating point division work?CPUs: How much slower is floating point arithmetic than integer arithmetic? Sameer Gupta, Ken'ani // int (*a) (int)Written 140w agoIt is not associative:[math](10^{-3}+1)-1 \sim 0[/math][math]10^{-3}+(1-1)=10^{-3}[/math]To be precise, >>> (pow(10,-3)+1)-1 0.0009999999999998899 >>> pow(10,-3)+(1-1) 0.001 >>> 1.2k Views · View Upvotes George Gonzalez, Software and hardware guruWritten 141w agoDepends on the floating-point format, the rounding mode and rules, the magnitude of the numbers, and how picky you are.For example, if you have a very large number, adding two small numbers to it will have no effect. But if you first add the two wall numbers, they may have enough significant bits overlapping the big number to make them actually add up.So if you're picky, down to the very last bit, then probably not. There will always be a few bits l
programming languages, see operator associativity. "Associative" and "non-associative" redirect here. For associative and non-associative learning, see Learning §Types. This article needs additional citations for verification. Please help improve
Floating Point Operations
this article by adding citations to reliable sources. Unsourced material may be associative and distributive law in floating point arithmetic challenged and removed. (June 2009) (Learn how and when to remove this template message) Transformation rules Propositional calculus machine epsilon Rules of inference Modus ponens/ Modus tollens Biconditional introduction/ elimination Conjunction introduction/ elimination Disjunction introduction/ elimination Disjunctive/ Hypothetical syllogism Constructive/ Destructive dilemma Absorption Modus ponendo tollens Rules of replacement Associativity https://www.quora.com/Is-floating-point-addition-commutative-and-associative Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology Negation introduction Predicate logic Universal generalization/ instantiation Existential generalization/ instantiation v t e In mathematics, the associative property[1] is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences https://en.wikipedia.org/wiki/Associative_property in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is, rearranging the parentheses in such an expression will not change its value. Consider the following equations: ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) = 9 {\displaystyle (2+3)+4=2+(3+4)=9\,} 2 × ( 3 × 4 ) = ( 2 × 3 ) × 4 = 24. {\displaystyle 2\times (3\times 4)=(2\times 3)\times 4=24.} Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations". Associativity is not to be confused with commutativity, which addresses whether or not the order of two operands changes the result. For example, the order doesn't matter in the multiplication of real numbers, that is, a × b = b × a, so we s
is experimenting with adspdfFloating Point Arithmetic5 PagesFloating Point ArithmeticUploaded floating point byGobinda Das AdhikaryViewsconnect to downloadGetpdfREAD PAPERFloating Point ArithmeticDownloadFloating Point ArithmeticUploaded byGobinda Das AdhikaryLoading PreviewSorry, preview is currently unavailable. You floating point arithmetic can download the paper by clicking the button above.GET pdf ×CloseLog InLog InwithFacebookLog InwithGoogleorEmail:Password:Remember me on this computerorreset passwordEnter the email address you signed up with and we'll email you a reset link.Need an account?Click here to sign up Job BoardAboutPressBlogPeoplePapersTermsPrivacyCopyrightWe're Hiring!Help Center Find new research papers in:PhysicsChemistryBiologyHealth SciencesEcologyEarth SciencesCognitive ScienceMathematicsComputer Science Academia © 2016
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