Delphi Spin Edit With Real Support' title='Delphi Spin Edit With Real Support' />Join the NASDAQ Community today and get free, instant access to portfolios, stock ratings, realtime alerts, and more Join Today.Modulo operation Wikipedia.Quotient red and remainder green functions using different algorithms.In computing, the modulo operation finds the remainder after division of one number by another sometimes called modulus.Given two positive numbers, a the dividend and n the divisor, a modulo n abbreviated as a mod n is the remainder of the Euclidean division of a by n.For example, the expression 5 mod 2 would evaluate to 1 because 5 divided by 2 leaves a quotient of 2 and a remainder of 1, while 9 mod 3 would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0 there is nothing to subtract from 9 after multiplying 3 times 3.Note that doing the division with a calculator will not show the result referred to here by this operation the quotient will be expressed as a decimal fraction.Although typically performed with a and n both being integers, many computing systems allow other types of numeric operands.The range of numbers for an integer modulo of n is 0 to n 1.See modular arithmetic for an older and related convention applied in number theory.When either a or n is negative, the naive definition breaks down and programming languages differ in how these values are defined.Remainder calculation for the modulo operationeditInteger modulo operators in various programming languages.Language. Operator.Result has same sign as.ABAPMODPositive always.Startups news from the, including the latest news, articles, quotes, blog posts, photos, video and more.Delphi Spin Edit With Real Support' title='Delphi Spin Edit With Real Support' />A Wikibookian believes this page should be split into smaller pages with a narrower subtopic.You can help by splitting this big page into smaller ones.Please make. Action.ScriptDividend. Adamod.Divisorrem. Dividend.ALGOL 6. Positive always.AMPLmod. Dividend.APL1Divisor. Apple.Scriptmod. Dividend.Auto. LISPrem d nRemainder.AWKDividend. BASICMod.UndefinedbashDividendbcDividend.C ISO 1. 99. 0Implementation defineddiv.Dividend. C ISO 1.Implementation defined1div.Dividend. C ISO 1.Dividend2C ISO 2.Dividend. CDividend.ClarionDividend. Clojuremod.Divisorrem. Dividend.COBOL2FUNCTION MODDivisor.Coffee. ScriptDividendDivisor3Cold.Fusion, MODDividend.Common Lispmod. Divisorrem.Dividend. Construct 2DDividend4DartPositive alwaysremainderDividend.EiffelDividend. 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PerlDivisor5PHPDividend.PIC BASIC ProDividend.PLImod. Divisor ANSI PLIPower.ShellDividend. Progressmodulo.Dividend. Prolog ISO 1.Divisorrem. Dividend.Pure. Basic,Modx,yDividend.PythonDivisormath.Dividend. Racketremainder.Dividend. Real. Basic.MODDividend. RDivisor.RexxDividend. RPGREMDividend.Ruby, moduloDivisorremainderDividend.RustDividend. ScalaDividend.Schememodulo. Divisorremainder.Dividend. Scheme R6.RSmod. Positive always5mod.Nearest to zero5Seed.Divisorrem. Dividend.Sense. Talkmodulo.Divisorrem. Dividend.SmalltalkDivisorrem Dividend.SpinDivisor. SQL SQL 1.Dividend. SQL SQL 2.Dividend. Standard MLmod.Divisor. Int. rem.Dividend. Statamodx,yPositive always.SwiftDividend. TclDivisor.TorqueDividend. Turingmod.Divisor. Verilog 2.Dividend. VHDLmod.Divisorrem. Dividend.Vim. LDividend. Visual Basic.Mod. Dividendx. 86 assembly.IDIVDividend. XBaseDividend.ModDivisor. Z3 theorem proverdiv, mod. Adobe Reader Text To Speech Downloadable Wav . Positive always. In mathematics, the result of the modulo operation is the remainder of the Euclidean division.However, other conventions are possible.Computers and calculators have various ways of storing and representing numbers thus their definition of the modulo operation depends on the programming language or the underlying hardware.In nearly all computing systems, the quotientq and the remainder r of a divided by n satisfyqZanqrrlt ndisplaystyle beginalignedq, in mathbb Z a, nqrr, lt nendaligned1However, this still leaves a sign ambiguity if the remainder is nonzero two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur.Usually, in number theory, the positive remainder is always chosen, but programming languages choose depending on the language and the signs of a or n.Standard Pascal and ALGOL 6.C9. 0, leave it to the implementation when either of n or a is negative.See the table for details.As described by Leijen,Boute argues that Euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by Knuth, is also a good definition.Despite its widespread use, truncated division is shown to be inferior to the other definitions.Daan Leijen, Division and Modulus for Computer Scientists9Common pitfallseditWhen the result of a modulo operation has the sign of the dividend, it can lead to surprising mistakes.For example, to test if an integer is odd, one might be inclined to test if the remainder by 2 is equal to 1 boolisoddintnreturnn21 But in a language where modulo has the sign of the dividend, that is incorrect, because when n the dividend is negative and odd, n mod 2 returns 1, and the function returns false.One correct alternative is to test that it is not 0 because remainder 0 is the same regardless of the signs boolisoddintnreturnn20 Or, by understanding in the first place that for any odd number, the modulo remainder may be either 1 or 1 boolisoddintnreturnn21n2 1 NotationeditThis section is about the binary mod operation.For the mod m notation, see congruence relation.Some calculators have a mod function button, and many programming languages have a similar function, expressed as moda, n, for example.Some also support expressions that use, mod, or Mod as a modulo or remainder operator, such asa nora mod nor equivalent, for environments lacking a mod function note that int inherently produces the truncated value of ana n intanPerformance issueseditModulo operations might be implemented such that a division with a remainder is calculated each time.For special cases, on some hardware, faster alternatives exist.For example, the modulo of powers of 2 can alternatively be expressed as a bitwise AND operation x 2n x 2n 1Examples assuming x is a positive integer x 2 x 1x 4 x 3x 8 x 7.In devices and software that implement bitwise operations more efficiently than modulo, these alternative forms can result in faster calculations.Optimizingcompilers may recognize expressions of the form expression constant where constant is a power of two and automatically implement them as expression constant 1.This can allow writing clearer code without compromising performance.This optimization is not possible for languages in which the result of the modulo operation has the sign of the dividend including C, unless the dividend is of an unsigned integer type.This is because, if the dividend is negative, the modulo will be negative, whereas expression constant 1 will always be positive.EquivalencieseditSome modulo operations can be factored or expanded similar to other mathematical operations.This may be useful in cryptography proofs, such as the DiffieHellman key exchange.Identity. a mod n a mod n mod n 0.Distributive. a b mod n a mod n b mod n mod n.Division definition ab mod n a mod nb1 mod n mod n, when the right hand side is defined that is when b and n are coprime.Undefined otherwise.Inverse multiplication ab mod nb1 mod n mod n a mod n.See alsoeditReferenceseditISOIEC 1.Programming languages C.
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