diff --git a/stdlib/public/core/BridgeObjectiveC.swift b/stdlib/public/core/BridgeObjectiveC.swift
index 2b0694534c6..1a4e1fbaf13 100644
--- a/stdlib/public/core/BridgeObjectiveC.swift
+++ b/stdlib/public/core/BridgeObjectiveC.swift
@@ -469,6 +469,14 @@ public struct AutoreleasingUnsafeMutablePointer<Pointee /* TODO : class */>
     guard let unwrapped = from else { return nil }
     self.init(unwrapped)
   }
+
+  @_transparent
+  public static func == (
+    lhs: AutoreleasingUnsafeMutablePointer,
+    rhs: AutoreleasingUnsafeMutablePointer
+  ) -> Bool {
+    return Bool(Builtin.cmp_eq_RawPointer(lhs._rawValue, rhs._rawValue))
+  }
 }
 
 extension UnsafeMutableRawPointer {
@@ -523,14 +531,6 @@ extension AutoreleasingUnsafeMutablePointer : CustomDebugStringConvertible {
   }
 }
 
-@_transparent
-public func == <Pointee>(
-  lhs: AutoreleasingUnsafeMutablePointer<Pointee>,
-  rhs: AutoreleasingUnsafeMutablePointer<Pointee>
-) -> Bool {
-  return Bool(Builtin.cmp_eq_RawPointer(lhs._rawValue, rhs._rawValue))
-}
-
 @_fixed_layout
 @_versioned
 internal struct _CocoaFastEnumerationStackBuf {
diff --git a/stdlib/public/core/DropWhile.swift.gyb b/stdlib/public/core/DropWhile.swift.gyb
index 9d009e86623..477c62932de 100644
--- a/stdlib/public/core/DropWhile.swift.gyb
+++ b/stdlib/public/core/DropWhile.swift.gyb
@@ -103,20 +103,18 @@ extension LazySequenceProtocol {
 public struct LazyDropWhileIndex<Base : Collection> : Comparable {
   /// The position corresponding to `self` in the underlying collection.
   public let base: Base.Index
-}
 
-public func == <Base>(
-  lhs: LazyDropWhileIndex<Base>,
-  rhs: LazyDropWhileIndex<Base>
-) -> Bool {
-  return lhs.base == rhs.base
-}
+  public static func == (
+    lhs: LazyDropWhileIndex, rhs: LazyDropWhileIndex
+  ) -> Bool {
+    return lhs.base == rhs.base
+  }
 
-public func < <Base>(
-  lhs: LazyDropWhileIndex<Base>,
-  rhs: LazyDropWhileIndex<Base>
-) -> Bool {
-  return lhs.base < rhs.base
+  public static func < (
+    lhs: LazyDropWhileIndex, rhs: LazyDropWhileIndex
+  ) -> Bool {
+    return lhs.base < rhs.base
+  }
 }
 
 % for Traversal in ['Forward', 'Bidirectional']:
diff --git a/stdlib/public/core/FloatingPoint.swift.gyb b/stdlib/public/core/FloatingPoint.swift.gyb
index 9d1215b938e..426220b57b5 100644
--- a/stdlib/public/core/FloatingPoint.swift.gyb
+++ b/stdlib/public/core/FloatingPoint.swift.gyb
@@ -1424,12 +1424,12 @@ public enum FloatingPointRoundingRule {
   case awayFromZero
 }
 
-@_transparent
-public func == <T : FloatingPoint>(lhs: T, rhs: T) -> Bool {
-  return lhs.isEqual(to: rhs)
-}
-
 extension FloatingPoint {
+  @_transparent
+  public static func == (lhs: Self, rhs: Self) -> Bool {
+    return lhs.isEqual(to: rhs)
+  }
+
   @_transparent
   public static func < (lhs: Self, rhs: Self) -> Bool {
     return lhs.isLess(than: rhs)
diff --git a/stdlib/public/core/ManagedBuffer.swift b/stdlib/public/core/ManagedBuffer.swift
index 110e64e39bb..25b8b45d20a 100644
--- a/stdlib/public/core/ManagedBuffer.swift
+++ b/stdlib/public/core/ManagedBuffer.swift
@@ -427,17 +427,16 @@ public struct ManagedBufferPointer<Header, Element> : Equatable {
       _headerOffset + MemoryLayout<Header>.size,
       toAlignment: MemoryLayout<Element>.alignment)
   }
+  
+  public static func == (
+    lhs: ManagedBufferPointer, rhs: ManagedBufferPointer
+  ) -> Bool {
+    return lhs._address == rhs._address
+  }
 
   internal var _nativeBuffer: Builtin.NativeObject
 }
 
-public func == <Header, Element>(
-  lhs: ManagedBufferPointer<Header, Element>,
-  rhs: ManagedBufferPointer<Header, Element>
-) -> Bool {
-  return lhs._address == rhs._address
-}
-
 // FIXME: when our calling convention changes to pass self at +0,
 // inout should be dropped from the arguments to these functions.
 // FIXME(docs): isKnownUniquelyReferenced should check weak/unowned counts too, 
diff --git a/stdlib/public/core/PrefixWhile.swift.gyb b/stdlib/public/core/PrefixWhile.swift.gyb
index ca234d31624..14166c9f94a 100644
--- a/stdlib/public/core/PrefixWhile.swift.gyb
+++ b/stdlib/public/core/PrefixWhile.swift.gyb
@@ -111,33 +111,31 @@ public struct LazyPrefixWhileIndex<Base : Collection> : Comparable {
   internal init(endOf: Base) {
     self._value = .pastEnd
   }
-}
 
-public func == <Base>(
-  lhs: LazyPrefixWhileIndex<Base>,
-  rhs: LazyPrefixWhileIndex<Base>
-) -> Bool {
-  switch (lhs._value, rhs._value) {
-  case let (.index(l), .index(r)):
-    return l == r
-  case (.pastEnd, .pastEnd):
-    return true
-  default:
-    return false
+  public static func == (
+    lhs: LazyPrefixWhileIndex, rhs: LazyPrefixWhileIndex
+  ) -> Bool {
+    switch (lhs._value, rhs._value) {
+    case let (.index(l), .index(r)):
+      return l == r
+    case (.pastEnd, .pastEnd):
+      return true
+    default:
+      return false
+    }
   }
-}
 
-public func < <Base>(
-  lhs: LazyPrefixWhileIndex<Base>,
-  rhs: LazyPrefixWhileIndex<Base>
-) -> Bool {
-  switch (lhs._value, rhs._value) {
-  case let (.index(l), .index(r)):
-    return l < r
-  case (.index, .pastEnd):
-    return true
-  default:
-    return false
+  public static func < (
+    lhs: LazyPrefixWhileIndex, rhs: LazyPrefixWhileIndex
+  ) -> Bool {
+    switch (lhs._value, rhs._value) {
+    case let (.index(l), .index(r)):
+      return l < r
+    case (.index, .pastEnd):
+      return true
+    default:
+      return false
+    }
   }
 }
 
diff --git a/stdlib/public/core/Stride.swift.gyb b/stdlib/public/core/Stride.swift.gyb
index 7576e7d1e29..27a51256ceb 100644
--- a/stdlib/public/core/Stride.swift.gyb
+++ b/stdlib/public/core/Stride.swift.gyb
@@ -55,15 +55,16 @@ public protocol ${Self} : ${Conformance} {
 
 % end
 
-/// Compare two `Strideable`s.
-@_inlineable
-public func < <T : Strideable>(x: T, y: T) -> Bool {
-  return x.distance(to: y) > 0
-}
+extension Strideable {
+  @_inlineable
+  public static func < (x: Self, y: Self) -> Bool {
+    return x.distance(to: y) > 0
+  }
 
-@_inlineable
-public func == <T : Strideable>(x: T, y: T) -> Bool {
-  return x.distance(to: y) == 0
+  @_inlineable
+  public static func == (x: Self, y: Self) -> Bool {
+    return x.distance(to: y) == 0
+  }
 }
 
 //===----------------------------------------------------------------------===//