Merge pull request #31 from mastermatt/master

Added a recursive binary implementation of the greatest common divisor.

algorithms/math/gcd.js

@@ -43,4 +43,64 @@ var gcdDivisionBased = function (a, b) {
   return a;
 };
 
+/**
+ * Binary GCD algorithm (Stein's Algorithm)
+ *
+ * @link https://en.wikipedia.org/wiki/Binary_GCD_algorithm
+ * This is basically a js version of the c implementation on Wikipedia
+ *
+ * @param Number
+ * @param Number
+ *
+ * @return Number
+ */
+var gcdBinaryIterative = function (a, b) {
+
+  // GCD(0,b) == b; GCD(a,0) == a, GCD(0,0) == 0
+  if (a === 0) {
+    return b;
+  }
+
+  if (b === 0) {
+    return a;
+  }
+
+  // Let shift = log(K), where K is the greatest power of 2 dividing both a and b
+  for (var shift = 0; ((a | b) & 1) == 0; ++shift) {
+    a >>= 1;
+    b >>= 1;
+  }
+
+  // Remove all factors of 2 in a -- they are not common
+  // Note: a is not zero, so while will terminate
+  while ((a & 1) === 0) {
+    a >>= 1;
+  }
+
+  var tmp;
+
+  // From here on, a is always odd
+  do {
+    // Remove all factors of 2 in b -- they are not common
+    // Note: b is not zero, so while will terminate
+    while ((b & 1) === 0) {
+      b >>= 1;
+    }
+
+    // Now a and b are both odd. Swap if necessary so a <= b,
+    // then set b = b - a (which is even).
+    if (a > b) {
+      tmp = b;
+      b = a;
+      a = tmp;
+    }
+
+    b -= a;  // Here b >= a
+  } while (b !== 0);
+
+  // restore common factors of 2
+  return a << shift;
+};
+
+gcdDivisionBased.binary = gcdBinaryIterative;
 module.exports = gcdDivisionBased;

test/algorithms/math/gcd.js

@@ -37,6 +37,20 @@ describe('GCD', function () {
     assert.equal(gcd(7, 5), 1);
     assert.equal(gcd(35, 49), 7);
   });
+
+  it('should calculate the correct GCD between two numbers using the binary method', function () {
+    var gcdb = gcd.binary;
+    assert.equal(gcdb(1, 0), 1);
+    assert.equal(gcdb(2, 2), 2);
+    assert.equal(gcdb(2, 4), 2);
+    assert.equal(gcdb(4, 2), 2);
+    assert.equal(gcdb(5, 2), 1);
+    assert.equal(gcdb(10, 100), 10);
+    assert.equal(gcdb(10000000, 2), 2);
+    assert.equal(gcdb(7, 49), 7);
+    assert.equal(gcdb(7, 5), 1);
+    assert.equal(gcdb(35, 49), 7);
+  });
 });