Binary GCD Algorithm vs. Euclid's Algorithm on modern computers?

The answer is of course "it depends". It depends on hardware, compiler, specific implementation, whatever I forgot. On machines with slow division, binary GCD tends to outperform the Euclidean algorithm.

I benchmarked it a couple of years ago on a Pentium4 in C, Java and a few other languages, overall in that benchmark, binary gcd with a 256-element lookup table beat the Euclidean algorithm by a factor of between 1.6 and nearly 3. Euclidean came closer when instead of immediately dividing, first a few rounds of subtraction were performed. I don't remember the figures, but binary still was considerably faster If the machine has fast division, things may be different, since the Euclidean algorithm needs fewer operations.

If the difference of cost between division and subtraction/shifts is small enough, binary will be slower. Which one is better in your circumstances, you have to find out by benchmarking yourself.

The answer is of course "it depends". It depends on hardware, compiler, specific implementation, whatever I forgot. On machines with slow division, binary GCD tends to outperform the Euclidean algorithm.

I benchmarked it a couple of years ago on a Pentium4 in C, Java and a few other languages, overall in that benchmark, binary gcd with a 256-element lookup table beat the Euclidean algorithm by a factor of between 1.6 and nearly 3. Euclidean came closer when instead of immediately dividing, first a few rounds of subtraction were performed. I don't remember the figures, but binary still was considerably faster.

If the machine has fast division, things may be different, since the Euclidean algorithm needs fewer operations. If the difference of cost between division and subtraction/shifts is small enough, binary will be slower. Which one is better in your circumstances, you have to find out by benchmarking yourself.

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