BigInt

Package.swift

@@ -3,7 +3,7 @@
 //
 // This source file is part of the Swift Numerics open source project
 //
-// Copyright (c) 2019 Apple Inc. and the Swift Numerics project authors
+// Copyright (c) 2019-2020 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
@@ -15,20 +15,24 @@ import PackageDescription
 let package = Package(
   name: "swift-numerics",
   products: [
+    .library(name: "BigIntModule", targets: ["BigIntModule"]),
     .library(name: "ComplexModule", targets: ["ComplexModule"]),
     .library(name: "Numerics", targets: ["Numerics"]),
     .library(name: "RealModule", targets: ["RealModule"]),
   ],
   dependencies: [
+    .package(url: "https://github.com/attaswift/BigInt.git", from: "3.0.0")
   ],
   targets: [
+    .target(name: "BigIntModule", dependencies: []),
     .target(name: "ComplexModule", dependencies: ["RealModule"]),
-    .target(name: "Numerics", dependencies: ["ComplexModule", "RealModule"]),
+    .target(name: "Numerics", dependencies: ["BigIntModule", "ComplexModule", "RealModule"]),
     .target(name: "RealModule", dependencies: ["_NumericsShims"]),
 
     .target(name: "_NumericsShims", dependencies: []),
     .target(name: "_TestSupport", dependencies: ["Numerics"]),
 
+    .testTarget(name: "BigIntTests", dependencies: ["_TestSupport", "BigInt"]),
     .testTarget(name: "ComplexTests", dependencies: ["_TestSupport"]),
     .testTarget(name: "RealTests", dependencies: ["_TestSupport"]),
   ]

Sources/BigIntModule/BigInt.Words.swift

@@ -0,0 +1,85 @@
+//===--- BigInt.Words.swift -----------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift Numerics open source project
+//
+// Copyright (c) 2020 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 BigInt {
+  /// The words of an arbitrarily large signed integer.
+  ///
+  /// For a negative value, words are of the two’s complement representation.
+  @frozen
+  public struct Words {
+    /// The arbitrarily large signed integer.
+    @usableFromInline
+    internal var _value: BigInt
+
+    /// Creates a `BigInt.Words` from the given arbitrarily large signed
+    /// integer.
+    ///
+    /// - Parameter value: The arbitrarily large signed integer.
+    @inlinable
+    internal init(_ value: BigInt) {
+      _value = value
+    }
+  }
+}
+
+extension BigInt.Words: RandomAccessCollection {
+  @inlinable
+  public var count: Int {
+    guard !_value._isZero else { return 1 }
+    let temporary = _value._exponent + _value._significand.count
+    let lastIndex = _value._significand.count &- 1
+    let highWord = _value._significand[lastIndex]
+    guard Int(bitPattern: highWord) < 0 else { return temporary }
+    // If the leading bit is set, then--
+    //
+    // For a positive value:
+    // We need to add at least one leading zero bit (and therefore one
+    // additional word) for a signed representation.
+    if _value._combination > 0 { return temporary + 1 }
+    // For a negative value:
+    // The two's complement of a magnitude has the same bit width as that of
+    // the magnitude itself if and only if the magnitude is a power of two.
+    // Otherwise, we need one additional bit (and therefore one additional
+    // word) to fit the two's complement.
+    //
+    // (Note that `(x & (x &- 1)) == 0` is a method of determining if `x` is
+    // a power of two.)
+    return lastIndex == 0 && (highWord & (highWord &- 1)) == 0
+      ? temporary
+      : temporary + 1
+  }
+
+  @inlinable
+  public var startIndex: Int { 0 }
+
+  @inlinable
+  public var endIndex: Int { count }
+
+  @inlinable
+  public func index(before i: Int) -> Int { i - 1 }
+
+  @inlinable
+  public func index(after i: Int) -> Int { i + 1 }
+
+  @inlinable
+  public subscript(position: Int) -> UInt {
+    precondition(position >= 0, "Index out of bounds")
+    guard position >= _value._exponent else { return 0 }
+    let idx = position &- _value._exponent
+    guard idx < _value._significand.count else {
+      return _value._combination < 0 ? UInt.max : 0
+    }
+    let word = _value._significand[idx]
+    return _value._combination < 0
+      ? idx == 0 ? ~word &+ 1 : ~word
+      : word
+  }
+}