Merge pull request #189 from NevinBR/patch-6

GCD function for BinaryInteger

Author: stephentyrone

Sources/IntegerUtilities/GCD.swift

@@ -0,0 +1,49 @@
+//===--- 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
+//
+//===----------------------------------------------------------------------===//
+
+/// The greatest common divisor of `a` and `b`.
+///
+/// If both inputs are zero, the result is zero. If one input is zero, the
+/// result is the absolute value of the other input.
+///
+/// The result must be representable within its type. In particular, the gcd
+/// of a signed, fixed-width integer type's minimum with itself (or zero)
+/// cannot be represented, and results in a trap.
+///
+///     gcd(Int.min, Int.min)   // Overflow error
+///     gcd(Int.min, 0)         // Overflow error
+///
+/// [wiki]: https://en.wikipedia.org/wiki/Greatest_common_divisor
+@inlinable
+public func gcd<T: BinaryInteger>(_ a: T, _ b: T) -> T {
+  var x = a.magnitude
+  var y = b.magnitude
+  
+  if y == 0 { return T(x) }
+  
+  let xtz = x.trailingZeroBitCount
+  let ytz = y.trailingZeroBitCount
+  
+  y >>= ytz
+  
+  // The binary GCD algorithm
+  //
+  // After the right-shift in 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 {
+    x >>= x.trailingZeroBitCount
+    if x < y { swap(&x, &y) }
+    x -= y
+  }
+  
+  return T(y << min(xtz, ytz))
+}

Tests/IntegerUtilitiesTests/GCDTests.swift

@@ -0,0 +1,44 @@
+//===--- GCDTests.swift ---------------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift.org open source project
+//
+// Copyright (c) 2021 Apple Inc. and the Swift project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+//
+//===----------------------------------------------------------------------===//
+
+import IntegerUtilities
+import XCTest
+
+final class IntegerUtilitiesGCDTests: XCTestCase {
+  func testGCDInt() {
+    XCTAssertEqual(gcd(0, 0), 0)
+    XCTAssertEqual(gcd(0, 1), 1)
+    XCTAssertEqual(gcd(1, 0), 1)
+    XCTAssertEqual(gcd(0, -1), 1)
+    XCTAssertEqual(gcd(1, 1), 1)
+    XCTAssertEqual(gcd(1, 2), 1)
+    XCTAssertEqual(gcd(2, 2), 2)
+    XCTAssertEqual(gcd(4, 2), 2)
+    XCTAssertEqual(gcd(6, 8), 2)
+    XCTAssertEqual(gcd(77, 91), 7)
+    XCTAssertEqual(gcd(24, -36), 12)
+    XCTAssertEqual(gcd(-24, -36), 12)
+    XCTAssertEqual(gcd(51, 34), 17)
+    XCTAssertEqual(gcd(64, 96), 32)
+    XCTAssertEqual(gcd(-64, 96), 32)
+    XCTAssertEqual(gcd(4*7*19, 27*25), 1)
+    XCTAssertEqual(gcd(16*315, 11*315), 315)
+    XCTAssertEqual(gcd(97*67*53*27*8, 83*67*53*9*32), 67*53*9*8)
+    XCTAssertEqual(gcd(Int.min, 2), 2)
+    
+    // TODO: Enable these when version compatibility allows.
+    //
+    // XCTExpectFailure{ gcd(0, Int.min) }
+    // XCTExpectFailure{ gcd(Int.min, 0) }
+    // XCTExpectFailure{ gcd(Int.min, Int.min) }
+  }
+}