The Mixed Binary Euclid Algorithm

We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and we prove that its bit-time complexity is still O ( n 2 ) for two n-bit integers in the worst case. Our preliminar experiments show a potential spee...

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Vydané v:Electronic notes in discrete mathematics Ročník 35; s. 169 - 176
Hlavný autor: Sedjelmaci, Sidi Mohamed
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.12.2009
Predmet:
Algorithms
Greatest common divisor (GCD)
Parallel Complexity
Greatest common divisor (GCD)
Algorithms
Parallel Complexity
ISSN:1571-0653, 1571-0653
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Shrnutí:We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and we prove that its bit-time complexity is still O ( n 2 ) for two n-bit integers in the worst case. Our preliminar experiments show a potential speedup for small integers. A parallel version matches the best presently known time complexity, namely O ( n / log n ) time with O ( n 1 + ϵ ) processors, for any constant ϵ > 0 .
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2009.11.029