Binary GCD Algorithm: A Faster Alternative to Standard Euclidean Algorithm
By
tosh
A baker's-dozen of insight crammed into one ring.
Summary
The article explains the binary GCD algorithm, a faster variant of the Euclidean algorithm for computing greatest common divisors. It covers the mathematical foundations, implementation details, and performance optimizations that make it approximately twice as fast as the standard C++ library implementation. The content includes mathematical formulas, algorithmic analysis, and practical programming considerations for efficient computation.
Key quotes
· 4 pulledIn this section, we will derive a variant of gcd that is ~2x faster than the one in the C++ standard library.
Euclid's algorithm solves the problem of finding the greatest common divisor (GCD) of two integer numbers $a$ and $b$, which is defined as the largest such number $g$ that divides both $a$ and $b$.
The binary GCD algorithm uses bitwise operations and properties of even/odd numbers to compute GCD more efficiently than the standard Euclidean algorithm.
This optimization makes the algorithm particularly effective for modern processors that handle bitwise operations efficiently.
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