Merge pull request #236 from stephentyrone/further-complex-pow-tweaks

Further improvement to Complex.pow(_:Self,_:Self) edge cases.

Author: stephentyrone

Sources/ComplexModule/Complex+ElementaryFunctions.swift

@@ -413,16 +413,21 @@ extension Complex: ElementaryFunctions {
   }
 
   // MARK: - pow-like functions
+  /// `exp(w*log(z))`
+  ///
+  /// Edge cases for this function are defined according to the defining
+  /// expression exp(w log(z)), except that we define pow(0, w) to be 0
+  /// instead of infinity when w is in the (strict) right half-plane, so that
+  /// we agree with RealType.pow on the positive real line.
   @inlinable
   public static func pow(_ z: Complex, _ w: Complex) -> Complex {
+    if z.isZero { return w.real > 0 ? zero : infinity }
     return exp(w * log(z))
   }
 
   @inlinable
   public static func pow(_ z: Complex, _ n: Int) -> Complex {
-    if z.isZero {
-      return n < 0 ? .infinity : n == 0 ? .one : .zero
-    }
+    if z.isZero { return n < 0 ? infinity : n == 0 ? one : zero }
     // TODO: this implementation is not quite correct, because n may be
     // rounded in conversion to RealType. This only effects very extreme
     // cases, so we'll leave it alone for now.

Tests/ComplexTests/ElementaryFunctionTests.swift

@@ -403,7 +403,7 @@ final class ElementaryFunctionTests: XCTestCase {
   func testPowR<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
     XCTAssertEqual(Complex<T>.pow(.zero, -.one),  .infinity)
     XCTAssertEqual(Complex<T>.pow(.zero,  .zero), .infinity)
-    XCTAssertEqual(Complex<T>.pow(.zero, +.one),  .infinity)
+    XCTAssertEqual(Complex<T>.pow(.zero, +.one),  .zero)
   }
 
   func testPowN<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {