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**11 - 13**of**13**### 5-2 Outline

"... Summary The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids divisions and multiplications, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. In this lecture I describe the classical and binary algorithms, and c ..."

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Summary The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids divisions and multiplications, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. In this lecture I describe the classical and binary algorithms, and compare their worst case and average case behaviour. In particular, I correct some small but significant errors in the literature, discuss some recent results of Brigitte Vall'ee, and describe a numerical computation which verifies Vall'ee's conjecture to 44 decimal places.

### Revisiting the Binary Euclidean Algorithm

, 1999

"... Abstract The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids divisions and multiplications, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. I will describe the binary algorithm and consider its average case b ..."

Abstract
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Abstract The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids divisions and multiplications, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. I will describe the binary algorithm and consider its average case behaviour. In particular, I will correct some small but interesting errors in the literature, discuss some recent results of Brigitte Vall'ee, and describe a numerical computation which verifies a conjecture of Vall'ee to 40 decimal places.