Fix invalid canonicalizedTransform for quaternions with negative real

Author: markuswntr

Sources/QuaternionModule/Quaternion.swift

@@ -286,8 +286,8 @@ extension Quaternion {
   /// For normal quaternion instances with a RealType conforming to
   /// BinaryFloatingPoint (the common case) and a non-negative real component,
   /// the result is simply this value unmodified. For instances with a negative
-  /// real component, the result is a quaternion with a positive real component
-  /// of equal magnitude and an unmodified imaginary compontent (-r, x, y, z).
+  /// real component, the result is this quaternion negated -(r, x, y, z); so
+  /// the real component is always positive.
   /// For zeros, the result has the representation (+0, +0, +0, +0). For
   /// infinite values, the result has the representation (+inf, +0, +0, +0).
   ///
@@ -299,11 +299,9 @@ extension Quaternion {
   /// - `.canonicalized`
   @_transparent
   public var canonicalizedTransform: Self {
-    var canonical = canonicalized
+    let canonical = canonicalized
     if canonical.real.sign == .plus { return canonical }
-    // Clear the signbit of real even for -0
-    canonical.real.negate()
-    return canonical
+    return -canonical
   }
 }
 

Tests/QuaternionTests/PropertyTests.swift

@@ -104,28 +104,28 @@ final class PropertyTests: XCTestCase {
     // that rotations in *R³* of `q` and `-q` will hash to same value.
     let pairs: [(lhs: Quaternion<T>, rhs: Quaternion<T>)] = [
       (
-        Quaternion<T>(real:  .pi, imaginary:  .pi,  .pi,  .pi),
-        Quaternion<T>(real: -.pi, imaginary:  .pi,  .pi,  .pi)
+        Quaternion<T>(real: -.pi, imaginary:  .pi,  .pi,  .pi),
+        Quaternion<T>(real:  .pi, imaginary: -.pi, -.pi, -.pi)
       ), (
         Quaternion<T>(real:  .pi, imaginary: -.pi,  .pi,  .pi),
-        Quaternion<T>(real: -.pi, imaginary: -.pi,  .pi,  .pi)
+        Quaternion<T>(real: -.pi, imaginary:  .pi, -.pi, -.pi)
       ), (
         Quaternion<T>(real:  .pi, imaginary:  .pi, -.pi,  .pi),
-        Quaternion<T>(real: -.pi, imaginary:  .pi, -.pi,  .pi)
+        Quaternion<T>(real: -.pi, imaginary: -.pi,  .pi, -.pi)
       ), (
         Quaternion<T>(real:  .pi, imaginary:  .pi,  .pi, -.pi),
-        Quaternion<T>(real: -.pi, imaginary:  .pi,  .pi, -.pi)
-      ), (
-        Quaternion<T>(real:  .pi, imaginary: -.pi, -.pi,  .pi),
         Quaternion<T>(real: -.pi, imaginary: -.pi, -.pi,  .pi)
       ), (
-        Quaternion<T>(real:  .pi, imaginary: -.pi,  .pi, -.pi),
-        Quaternion<T>(real: -.pi, imaginary: -.pi,  .pi, -.pi)
+        Quaternion<T>(real: -.pi, imaginary: -.pi,  .pi,  .pi),
+        Quaternion<T>(real:  .pi, imaginary:  .pi, -.pi, -.pi)
+      ), (
+        Quaternion<T>(real:  .pi, imaginary: -.pi, -.pi,  .pi),
+        Quaternion<T>(real: -.pi, imaginary:  .pi,  .pi, -.pi)
       ), (
         Quaternion<T>(real:  .pi, imaginary:  .pi, -.pi, -.pi),
-        Quaternion<T>(real: -.pi, imaginary:  .pi, -.pi, -.pi)
+        Quaternion<T>(real: -.pi, imaginary: -.pi,  .pi,  .pi)
       ), (
-        Quaternion<T>(real:  .pi, imaginary: -.pi, -.pi, -.pi),
+        Quaternion<T>(real:  .pi, imaginary:  .pi,  .pi,  .pi),
         Quaternion<T>(real: -.pi, imaginary: -.pi, -.pi, -.pi)
       )
     ]