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GCD test information


In compiler theory, a greatest common divisor test (GCD test) is the test used in study of loop optimization and loop dependence analysis to test the dependency between loop statements.

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GCD test

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greatest common divisor test (GCD test) is the test used in study of loop optimization and loop dependence analysis to test the dependency between loop...

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AKS primality test

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(1 < gcd(a,n) < n for some a ≤ r), output composite. For (a = r; a > 1; a--) { If ((gcd = GCD[a,n]) > 1 && gcd < n), Return[Composite] } gcd = {GCD(29,31)=1...

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Pocklington primality test

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that i is a divisor for j; and gcd is the greatest common divisor. Note: Equation (1) is simply a Fermat primality test. If we find any value of a, not...

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Extended Euclidean algorithm

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common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that a x + b y = gcd ( a , b ) . {\displaystyle...

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Fermat primality test

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for which all values of a {\displaystyle a} with gcd ⁡ ( a , n ) = 1 {\displaystyle \operatorname {gcd} (a,n)=1} are Fermat liars. For these numbers, repeated...

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Polynomial greatest common divisor

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their GCD. gcd ( p , q ) = gcd ( q , p ) . {\displaystyle \gcd(p,q)=\gcd(q,p).} gcd ( p , q ) = gcd ( q , p + r q ) {\displaystyle \gcd(p,q)=\gcd(q,p+rq)}...

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Greatest common divisor

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divisor of x and y is denoted gcd ( x , y ) {\displaystyle \gcd(x,y)} . For example, the GCD of 8 and 12 is 4, that is, gcd(8, 12) = 4. In the name "greatest...

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Binary GCD algorithm

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binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor (GCD) of...

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Banerjee test

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statements must be executed in order of their (potential) true dependence. GCD test Randy Allen and Ken Kennedy. Optimizing Compilers for Modern Architectures:...

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Euclidean algorithm

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algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without...

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Coprime integers

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algorithm in base n > 1: gcd ( n a − 1 , n b − 1 ) = n gcd ( a , b ) − 1. {\displaystyle \gcd \left(n^{a}-1,n^{b}-1\right)=n^{\gcd(a,b)}-1.} A set of integers...

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Elliptic curve primality

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{p}}+1\right)^{2}\leq \left({\sqrt[{4}]{N}}+1\right)^{2}<q} and thus gcd ( q , m p ) = 1 {\displaystyle \gcd(q,m_{p})=1} and there exists an integer u with the property...

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RDNA 3

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lower yields. RDNA 3 uses two types of chiplets: the Graphics Compute Die (GCD) and Memory Cache Dies (MCDs). On Ryzen and Epyc processors, AMD used its...

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Global Credit Data

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Global Credit Data (GCD) (formerly named PECDC or the Pan-European Credit Data Consortium) was formed in December 2004 as a credit data pooling initiative...

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JavaScript

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prototype.gcd. // Note that this leads to a wrong result if the LCMCalculator object members "a" or "b" are altered afterwards.) // Also, 'gcd' === "gcd", this['gcd']...

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Factorization of polynomials over finite fields

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Factors with deg(u) > d do if gcd(g, u) ≠ 1 and gcd(g, u) ≠ u, then Factors:= Factors ∖ { u } ∪ { ( gcd ( g , u ) , u / gcd ( g , u ) ) } {\displaystyle...

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Radeon RX 7000 series

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graphics card to be based on a chiplet design TSMC N5 for Graphics Compute Die (GCD) TSMC N6 for Memory Cache Die (MCD) Up to 24 GB of GDDR6 video memory Doubled...

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Associative property

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common multiple functions act associatively. gcd ⁡ ( gcd ⁡ ( x , y ) , z ) = gcd ⁡ ( x , gcd ⁡ ( y , z ) ) = gcd ⁡ ( x , y , z )   lcm ⁡ ( lcm ⁡ ( x , y )...

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Jacobi symbol

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n ) = { 0 if  gcd ( a , n ) ≠ 1 , ± 1 if  gcd ( a , n ) = 1. {\displaystyle \left({\frac {a}{n}}\right)={\begin{cases}0&{\text{if }}\gcd(a,n)\neq 1,\\\pm...

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Lucas pseudoprime

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Provided GCD(n, Q) = 1 then testing for congruence (4) is equivalent to augmenting our Lucas test with a "base Q" Solovay–Strassen primality test. Additional...

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