Index: lib/Target/NVPTX/NVPTXAssignValidGlobalNames.cpp
===================================================================
--- lib/Target/NVPTX/NVPTXAssignValidGlobalNames.cpp
+++ lib/Target/NVPTX/NVPTXAssignValidGlobalNames.cpp
@@ -37,6 +37,8 @@
 
   /// \brief Clean up the name to remove symbols invalid in PTX.
   std::string cleanUpName(StringRef Name);
+  /// \brief Set a clean name, ensuring collisions are avoided.
+  void generateCleanName(Value &V);
 };
 }
 
@@ -53,17 +55,33 @@
   for (GlobalVariable &GV : M.globals()) {
     // We are only allowed to rename local symbols.
     if (GV.hasLocalLinkage()) {
-      // setName doesn't do extra work if the name does not change.
-      // Note: this does not create collisions - if setName is asked to set the
-      // name to something that already exists, it adds a proper postfix to
-      // avoid collisions.
-      GV.setName(cleanUpName(GV.getName()));
+      generateCleanName(GV);
+    }
+  }
+
+  // Clean function symbols.
+  for (auto &FN : M.functions()) {
+    if (FN.hasLocalLinkage()) {
+      generateCleanName(FN);
     }
   }
 
   return true;
 }
 
+void NVPTXAssignValidGlobalNames::generateCleanName(Value &V) {
+  while (1) {
+    std::string ValidName = cleanUpName(V.getName());
+    // setName doesn't do extra work if the name does not change.
+    // Collisions are avoided by adding a suffix (which may yet be unclean in
+    // PTX).
+    V.setName(ValidName);
+    // If there are no collisions return, otherwise clean up the new name.
+    if (V.getName().equals(ValidName))
+      return;
+  }
+}
+
 std::string NVPTXAssignValidGlobalNames::cleanUpName(StringRef Name) {
   std::string ValidName;
   raw_string_ostream ValidNameStream(ValidName);
Index: test/CodeGen/NVPTX/symbol-naming.ll
===================================================================
--- test/CodeGen/NVPTX/symbol-naming.ll
+++ test/CodeGen/NVPTX/symbol-naming.ll
@@ -3,14 +3,15 @@
 
 ; Verify that the NVPTX target removes invalid symbol names prior to emitting
 ; PTX.
+; A symbol is invalid in PTX if it contains a '.' or a '@'.
 
 ; PTX32-NOT: .str
 ; PTX64-NOT: .str
 
-; PTX32-DAG: _$_str.1
+; PTX32-DAG: _$_str_$_1
 ; PTX32-DAG: _$_str
 
-; PTX64-DAG: _$_str.1
+; PTX64-DAG: _$_str_$_1
 ; PTX64-DAG: _$_str
 
 target datalayout = "e-i64:64-v16:16-v32:32-n16:32:64"
@@ -28,4 +29,15 @@
   ret void
 }
 
+; PTX32-NOT: omp_outlined.1
+; PTX64-NOT: omp_outlined.1
+; PTX32-DAG: omp_outlined_$_1_$_2_$_3
+; PTX64-DAG: omp_outlined_$_1_$_2_$_3
+define internal void @omp_outlined.1() {
+  ret void
+}
+
+declare void @omp_outlined_$_1()
+declare void @omp_outlined_$_1_$_2()
+
 declare i32 @printf(i8*, ...)