Fix the edge-case handling of Complex.pow(.zero, <int>)

Author: stephentyrone

Sources/ComplexModule/Complex+ElementaryFunctions.swift

@@ -420,7 +420,9 @@ extension Complex: ElementaryFunctions {
 
   @inlinable
   public static func pow(_ z: Complex, _ n: Int) -> Complex {
-    if z.isZero { return .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

@@ -399,6 +399,18 @@ 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)
+	}
+	
+	func testPowN<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
+		XCTAssertEqual(Complex<T>.pow(.zero, -1), .infinity)
+		XCTAssertEqual(Complex<T>.pow(.zero,  0), .one)
+		XCTAssertEqual(Complex<T>.pow(.zero, +1), .zero)
+	}
 
   func testFloat() {
     testExp(Float.self)
@@ -411,6 +423,8 @@ final class ElementaryFunctionTests: XCTestCase {
     testAcosh(Float.self)
     testAsinh(Float.self)
     testAtanh(Float.self)
+		testPowR(Float.self)
+		testPowN(Float.self)
   }
 
   func testDouble() {
@@ -424,6 +438,8 @@ final class ElementaryFunctionTests: XCTestCase {
     testAcosh(Double.self)
     testAsinh(Double.self)
     testAtanh(Double.self)
+		testPowR(Double.self)
+		testPowN(Double.self)
   }
 
   #if (arch(i386) || arch(x86_64)) && !os(Windows) && !os(Android)
@@ -438,6 +454,8 @@ final class ElementaryFunctionTests: XCTestCase {
     testAcosh(Float80.self)
     testAsinh(Float80.self)
     testAtanh(Float80.self)
+		testPowR(Float80.self)
+		testPowN(Float80.self)
   }
   #endif
 }