@stdlib/math-base-special-gcd/lib/binary_gcd.js

Compute the greatest common divisor (gcd).

/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

/**
* Computes the greatest common divisor (gcd) using the binary GCD algorithm.
*
* ## References
*
* -   Stein, Josef. 1967. "Computational problems associated with Racah algebra." _Journal of Computational Physics_ 1 (3): 397–405. doi:[10.1016/0021-9991(67)90047-2][@stein:1967].
*
* [@stein:1967]: https://doi.org/10.1016/0021-9991(67)90047-2
*
* @private
* @param {integer} a - integer
* @param {integer} b - integer
* @returns {integer} greatest common divisor
*
* @example
* var v = gcd( 1.2676506002282294e+30, 9007199254740992 );
* // returns 9007199254740992
*/
function gcd( a, b ) {
	var k = 1;
	var t;

	// Simple cases:
	if ( a === 0 ) {
		return b;
	}
	if ( b === 0 ) {
		return a;
	}
	// Reduce `a` and/or `b` to odd numbers and keep track of the greatest power of 2 dividing both `a` and `b`...
	while ( a%2 === 0 && b%2 === 0 ) {
		a /= 2; // right shift
		b /= 2; // right shift
		k *= 2; // left shift
	}
	// Reduce `a` to an odd number...
	while ( a%2 === 0 ) {
		a /= 2; // right shift
	}
	// Henceforth, `a` is always odd...
	while ( b ) {
		// Remove all factors of 2 in `b`, as they are not common...
		while ( b%2 === 0 ) {
			b /= 2; // right shift
		}
		// `a` and `b` are both odd. Swap values such that `b` is the larger of the two values, and then set `b` to the difference (which is even)...
		if ( a > b ) {
			t = b;
			b = a;
			a = t;
		}
		b -= a; // b=0 iff b=a
	}
	// Restore common factors of 2...
	return k * a;
}


// EXPORTS //

module.exports = gcd;