Optimize some memory allocations from ActorPath.

src/core/Akka.API.Tests/CoreAPISpec.ApproveCore.approved.txt

@@ -483,6 +483,7 @@ namespace Akka.Actor
         public override Akka.Actor.ActorPath Parent { get; }
         public override Akka.Actor.ActorPath Root { get; }
         public override int CompareTo(Akka.Actor.ActorPath other) { }
+        public override int GetHashCode() { }
         public override Akka.Actor.ActorPath WithUid(long uid) { }
     }
     public sealed class CoordinatedShutdown : Akka.Actor.IExtension

src/core/Akka/Actor/ActorPath.cs

@@ -121,7 +121,7 @@ public static bool IsValidPathElement(string s)
             {
                 return false;
             }
-            return !s.StartsWith("$") && Validate(s.ToCharArray(), s.Length);
+            return !s.StartsWith("$") && Validate(s);
         }
 
         private static bool IsValidChar(char c) => (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') ||
@@ -130,8 +130,9 @@ private static bool IsValidChar(char c) => (c >= 'a' && c <= 'z') || (c >= 'A' &
         private static bool IsHexChar(char c) => (c >= 'a' && c <= 'f') || (c >= 'A' && c <= 'F') ||
                                                  (c >= '0' && c <= '9');
 
-        private static bool Validate(IReadOnlyList<char> chars, int len)
+        private static bool Validate(string chars)
         {
+            int len = chars.Length;
             var pos = 0;
             while (pos < len)
             {
@@ -182,8 +183,6 @@ protected ActorPath(ActorPath parentPath, string name, long uid)
         public long Uid { get; }
 
         internal static readonly string[] EmptyElements = { };
-        internal static readonly string[] SystemElements = { "system" };
-        internal static readonly string[] UserElements = { "user" };
 
         /// <summary>
         /// Gets the elements.
@@ -239,7 +238,23 @@ public bool Equals(ActorPath other)
             if (other == null)
                 return false;
 
-            return Address.Equals(other.Address) && Elements.SequenceEqual(other.Elements);
+            if (!Address.Equals(other.Address))
+                return false;
+
+            ActorPath a = this;
+            ActorPath b = other;
+            for (;;)
+            {
+                if (ReferenceEquals(a, b))
+                    return true;
+                else if (a == null || b == null)
+                    return false;
+                else if (a.Name != b.Name)
+                    return false;
+
+                a = a.Parent;
+                b = b.Parent;
+            }
         }
 
         /// <inheritdoc/>
@@ -654,6 +669,19 @@ public override ActorPath WithUid(long uid)
             return new ChildActorPath(_parent, _name, uid);
         }
 
+        /// <inheritdoc/>
+        public override int GetHashCode()
+        {
+            unchecked
+            {
+                var hash = 17;
+                hash = (hash * 23) ^ Address.GetHashCode();
+                for (ActorPath p = this; p != null; p = p.Parent)
+                    hash = (hash * 23) ^ p.Name.GetHashCode();
+                return hash;
+            }
+        }
+
         /// <inheritdoc/>
         public override int CompareTo(ActorPath other)
         {