A Double-Digit Lehmer-Euclid Algorithm for Finding the GCD of Long Integers

The use of pairs of double digits in the Lehmer-Euclid multiprecision GCD algorithm halves the number of long multiplications, but a straightforward implementation of this idea does not give the desired speed-up. We show how to overcome the practical difficulties by using an enhanced condition for exiting the partial cosequence computation. Also, additional speed-up is achieved by approximative GCD computation. The combined effect of these improvements is an experimentally measured speed-up by a factor of 2 for operands with 100 32-bit words.