Create GCD.swift

Binary GCD algorithm

Author: NevinBR

Sources/IntegerUtilities/GCD.swift

@@ -0,0 +1,44 @@
+//===--- GCD.swift --------------------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift Numerics open source project
+//
+// Copyright (c) 2021 Apple Inc. and the Swift Numerics project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+//
+//===----------------------------------------------------------------------===//
+
+extension BinaryInteger {
+  
+  /// The greatest common divisor of `a` and `b`.
+  ///
+  /// If both inputs are zero, the result is zero.
+  @inlinable
+  public static func gcd(_ a: Self, _ b: Self) -> Self {
+    var x = a.magnitude
+    var y = b.magnitude
+    
+    if x == 0 { return Self(y) }
+    if y == 0 { return Self(x) }
+    
+    let xtz = x.trailingZeroBitCount
+    let ytz = y.trailingZeroBitCount
+    
+    x >>= xtz
+    y >>= ytz
+    
+    // The binary GCD algorithm
+    //
+    // At the top of the loop both x and y are odd. Each pass removes at least
+    // one low-order bit from the larger of the two, so the number of iterations
+    // is bounded by the sum of the bit-widths of the inputs.
+    while x != 0 {
+      if x < y { swap(&x, &y) }
+      x -= y
+      x >>= x.trailingZeroBitCount
+    }
+    
+    return Self(y << min(xtz, ytz))
+  }
+}