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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| Vydáno v: | Electronic notes in discrete mathematics Ročník 35; s. 169 - 176 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.12.2009
|
| Témata: | |
| ISSN: | 1571-0653, 1571-0653 |
| On-line přístup: | Získat plný text |
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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 |