Add tie-breaking exponentiation operators and tests

README.md

@@ -59,6 +59,18 @@ add the package as a dependency. See Swift documentation for details.
 ```swift
 import NumericAnnex
 
+print(2 ** 3)
+// Prints "8".
+
+print(4.0 ** 5.0)
+// Prints "1024.0".
+
+print(Int.cbrt(8))
+// Prints "2".
+
+print(Double.cbrt(27.0))
+// Prints "3.0".
+
 var x: Ratio = 1 / 4
 // Ratio is a type alias for Rational<Int>.
 

Sources/IntegerAlgorithms.swift

@@ -10,10 +10,10 @@ extension BinaryInteger {
   // MARK: Exponentiation
   // ---------------------------------------------------------------------------
 
-  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
-  /// representable value.
-  @_transparent // @_inlineable
-  public static func ** (lhs: Self, rhs: Self) -> Self {
+  // We need to factor out the implementation of `**` so that the tie-breaking
+  // operators implemented in extensions to concrete integer types can call it.
+  @_versioned
+  internal static func _pow(_ lhs: Self, _ rhs: Self) -> Self {
     var x = lhs, n = rhs
     if Self.isSigned && n < 0 {
       x = 1 / x
@@ -34,6 +34,13 @@ extension BinaryInteger {
     return x * y
   }
 
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: Self, rhs: Self) -> Self {
+    return _pow(lhs, rhs)
+  }
+
   /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
   /// to a representable value.
   @_transparent // @_inlineable
@@ -230,3 +237,233 @@ where Self : FixedWidthInteger,
     return (Self(t.high), t.low)
   }
 }
+
+// =============================================================================
+// TIE-BREAKING OPERATORS
+//
+// The following extensions are required so that an expression such as `2 ** 3`
+// is unambiguous as long as `IntegerLiteralType` is one of the standard library
+// types below.
+// =============================================================================
+
+extension Int {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: Int, rhs: Int) -> Int {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout Int, rhs: Int) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension Int8 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: Int8, rhs: Int8) -> Int8 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout Int8, rhs: Int8) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension Int16 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: Int16, rhs: Int16) -> Int16 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout Int16, rhs: Int16) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension Int32 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: Int32, rhs: Int32) -> Int32 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout Int32, rhs: Int32) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension Int64 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: Int64, rhs: Int64) -> Int64 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout Int64, rhs: Int64) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension UInt {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: UInt, rhs: UInt) -> UInt {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout UInt, rhs: UInt) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension UInt8 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: UInt8, rhs: UInt8) -> UInt8 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout UInt8, rhs: UInt8) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension UInt16 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: UInt16, rhs: UInt16) -> UInt16 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout UInt16, rhs: UInt16) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension UInt32 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: UInt32, rhs: UInt32) -> UInt32 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout UInt32, rhs: UInt32) {
+    lhs = lhs ** rhs
+  }
+}
+
+extension UInt64 {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: UInt64, rhs: UInt64) -> UInt64 {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout UInt64, rhs: UInt64) {
+    lhs = lhs ** rhs
+  }
+}
+
+#if false
+extension DoubleWidth {
+  // ---------------------------------------------------------------------------
+  // MARK: Exponentiation
+  // ---------------------------------------------------------------------------
+
+  /// Returns the result of raising `lhs` to the power of `rhs`, rounded to a
+  /// representable value.
+  @_transparent // @_inlineable
+  public static func ** (lhs: DoubleWidth, rhs: DoubleWidth) -> DoubleWidth {
+    return _pow(lhs, rhs)
+  }
+
+  /// Raises `lhs` to the power of `rhs` and stores the result in `lhs`, rounded
+  /// to a representable value.
+  @_transparent // @_inlineable
+  public static func **= (lhs: inout DoubleWidth, rhs: DoubleWidth) {
+    lhs = lhs ** rhs
+  }
+}
+#endif

Tests/LinuxMain.swift

@@ -2,6 +2,7 @@ import XCTest
 @testable import NumericAnnexTests
 
 XCTMain([
+  testCase(DocumentationExampleTests.allTests),
   testCase(ExponentiationTests.allTests),
   testCase(RootExtractionTests.allTests),
   testCase(FactoringTests.allTests),

Tests/NumericAnnexTests/DocumentationExampleTests.swift

@@ -0,0 +1,58 @@
+import XCTest
+/* @testable */ import NumericAnnex
+
+class DocumentationExampleTests : XCTestCase {
+  // It reflects poorly on the project to provide examples that don't compile or
+  // give the wrong result, so test them here:
+  
+  func testReadmeExample() {
+    print(2 ** 3)
+    // Prints "8".
+    XCTAssertEqual("\(2 ** 3)", "8")
+
+    print(4.0 ** 5.0)
+    // Prints "1024.0".
+    XCTAssertEqual("\(4.0 ** 5.0)", "1024.0")
+
+    print(Int.cbrt(8))
+    // Prints "2".
+    XCTAssertEqual("\(Int.cbrt(8))", "2")
+
+    print(Double.cbrt(27.0))
+    // Prints "3.0".
+    XCTAssertEqual("\(Double.cbrt(27.0))", "3.0")
+
+    var x: Ratio = 1 / 4
+    // Ratio is a type alias for Rational<Int>.
+
+    print(x.reciprocal())
+    // Prints "4".
+    XCTAssertEqual("\(x.reciprocal())", "4")
+
+    x *= 8
+    print(x + x)
+    // Prints "4".
+    XCTAssertEqual("\(x + x)", "4")
+
+    x = Ratio(Float.phi) // Golden ratio.
+    print(x)
+    // Prints "13573053/8388608".
+    XCTAssertEqual("\(x)", "13573053/8388608")
+
+    var z: Complex64 = 42 * .i
+    // Complex64 is a type alias for Complex<Float>.
+
+    print(Complex.sqrt(z))
+    // Prints "4.58258 + 4.58258i".
+    XCTAssertEqual("\(Complex.sqrt(z))", "4.58258 + 4.58258i")
+
+    z = .pi + .i * .log(2 - .sqrt(3))
+    print(Complex.cos(z).real)
+    // Prints "-2.0".
+    XCTAssertEqual("\(Complex.cos(z).real)", "-2.0")
+  }
+
+  static var allTests = [
+    ("testReadmeExample", testReadmeExample),
+  ]
+}

Tests/NumericAnnexTests/ExponentiationTests.swift

@@ -27,8 +27,47 @@ class ExponentiationTests : XCTestCase {
     }
   }
 
+  func testConcreteIntegerTypePow() {
+    XCTAssertEqual((2 as Int) ** 3, 8 as Int)
+    XCTAssertEqual((2 as Int8) ** 3, 8 as Int8)
+    XCTAssertEqual((2 as Int16) ** 3, 8 as Int16)
+    XCTAssertEqual((2 as Int32) ** 3, 8 as Int32)
+    XCTAssertEqual((2 as Int64) ** 3, 8 as Int64)
+
+    do { var x = 2 as Int; x **= 3; XCTAssertEqual(x, 8 as Int) }
+    do { var x = 2 as Int8; x **= 3; XCTAssertEqual(x, 8 as Int8) }
+    do { var x = 2 as Int16; x **= 3; XCTAssertEqual(x, 8 as Int16) }
+    do { var x = 2 as Int32; x **= 3; XCTAssertEqual(x, 8 as Int32) }
+    do { var x = 2 as Int64; x **= 3; XCTAssertEqual(x, 8 as Int64) }
+
+    XCTAssertEqual((2 as UInt) ** 3, 8 as UInt)
+    XCTAssertEqual((2 as UInt8) ** 3, 8 as UInt8)
+    XCTAssertEqual((2 as UInt16) ** 3, 8 as UInt16)
+    XCTAssertEqual((2 as UInt32) ** 3, 8 as UInt32)
+    XCTAssertEqual((2 as UInt64) ** 3, 8 as UInt64)
+
+    do { var x = 2 as UInt; x **= 3; XCTAssertEqual(x, 8 as UInt) }
+    do { var x = 2 as UInt8; x **= 3; XCTAssertEqual(x, 8 as UInt8) }
+    do { var x = 2 as UInt16; x **= 3; XCTAssertEqual(x, 8 as UInt16) }
+    do { var x = 2 as UInt32; x **= 3; XCTAssertEqual(x, 8 as UInt32) }
+    do { var x = 2 as UInt64; x **= 3; XCTAssertEqual(x, 8 as UInt64) }
+  }
+
+  func testGenericIntegerTypePow() {
+    func _testPow<
+      T : BinaryInteger
+    >(_: T.Type = T.self, lhs: T, rhs: T, expected: T) {
+      XCTAssertEqual(lhs ** rhs, expected)
+      do { var x = lhs; x **= rhs; XCTAssertEqual(x, expected) }
+    }
+    _testPow(lhs: 2 as Int, rhs: 3, expected: 8)
+    _testPow(lhs: 2 as UInt, rhs: 3, expected: 8)
+  }
+
   static var allTests = [
     ("testIntPow", testIntPow),
     ("testUIntPow", testUIntPow),
+    ("testConcreteIntegerTypePow", testConcreteIntegerTypePow),
+    ("testGenericIntegerTypePow", testGenericIntegerTypePow),
   ]
 }