Use Swift Numerics for elementary functions instead of Darwin/Glibc/etc (apple#28)

Also lets us use root instead of exp(log(x)/k), which is more accurate in some cases (but mainly is just nicer to read).

The downside is that this introduces a dependency for Algorithms, where previously it had none. I think that Numerics is an OK thing to depend on (especially for these functions, which are available from 0.0.1), but it _is_ a _massive increase_ in the number of dependencies that the package has, and we should give that some thought.

Author: stephentyrone

Package.swift

@@ -20,11 +20,14 @@ let package = Package(
             targets: ["Algorithms"]),
     ],
     dependencies: [
+        .package(url: "https://github.com/apple/swift-numerics", from: "0.0.1"),
     ],
     targets: [
         .target(
             name: "Algorithms",
-            dependencies: []),
+            dependencies: [
+              .product(name: "RealModule", package: "swift-numerics"),
+            ]),
         .testTarget(
             name: "SwiftAlgorithmsTests",
             dependencies: ["Algorithms"]),

Sources/Algorithms/RandomSample.swift

@@ -9,17 +9,9 @@
 //
 //===----------------------------------------------------------------------===//
 
-// For log(_:) and exp(_:)
-#if canImport(Glibc)
+// For log(_:) and root(_:_:)
 @_implementationOnly
-import Glibc
-#elseif canImport(ucrt)
-@_implementationOnly
-import ucrt
-#elseif canImport(Darwin)
-@_implementationOnly
-import Darwin
-#endif
+import RealModule
 
 //===----------------------------------------------------------------------===//
 // randomStableSample(count:)
@@ -90,15 +82,15 @@ extension Collection {
 // https://dl.acm.org/doi/pdf/10.1145/198429.198435
 
 fileprivate func nextW<G: RandomNumberGenerator>(
-  k: Double, using rng: inout G
+  k: Int, using rng: inout G
 ) -> Double {
-  exp(log(Double.random(in: 0..<1, using: &rng)) / k)
+  Double.root(.random(in: 0..<1, using: &rng), k)
 }
 
 fileprivate func nextOffset<G: RandomNumberGenerator>(
   w: Double, using rng: inout G
 ) -> Int {
-  Int(log(Double.random(in: 0..<1, using: &rng)) / log(1 - w))
+  Int(Double.log(.random(in: 0..<1, using: &rng)) / .log(1 - w))
 }
 
 extension Collection {
@@ -129,11 +121,10 @@ extension Collection {
       result.append(self[i])
       formIndex(after: &i)
     }
-        
-    let dk = Double(k)
+    
     while i < endIndex {
       // Calculate the next value of w.
-      w *= nextW(k: dk, using: &rng)
+      w *= nextW(k: k, using: &rng)
 
       // Find index of the next element to swap into the reservoir.
       let offset = nextOffset(w: w, using: &rng)
@@ -198,10 +189,9 @@ extension Sequence {
       result.append(el)
     }
 
-    let dk = Double(k)
     while true {
       // Calculate the next value of w.
-      w *= nextW(k: dk, using: &rng)
+      w *= nextW(k: k, using: &rng)
 
       // Find the offset of the next element to swap into the reservoir.
       var offset = nextOffset(w: w, using: &rng) + 1