Index: clang/include/clang/AST/ASTContext.h
===================================================================
--- clang/include/clang/AST/ASTContext.h
+++ clang/include/clang/AST/ASTContext.h
@@ -2065,8 +2065,10 @@
   //===--------------------------------------------------------------------===//
 
   /// Return the APFloat 'semantics' for the specified scalar floating
-  /// point type.
-  const llvm::fltSemantics &getFloatTypeSemantics(QualType T) const;
+  /// point type.  Get the semantics from the auxiliary target if one is
+  /// defined and \p PreferAuxTarget.
+  const llvm::fltSemantics &getFloatTypeSemantics(
+      QualType T, bool PreferAuxTarget = false) const;
 
   /// Get the size and alignment of the specified complete type in bits.
   TypeInfo getTypeInfo(const Type *T) const;
Index: clang/include/clang/Basic/DiagnosticSemaKinds.td
===================================================================
--- clang/include/clang/Basic/DiagnosticSemaKinds.td
+++ clang/include/clang/Basic/DiagnosticSemaKinds.td
@@ -8512,6 +8512,8 @@
   "feature, not permitted in C++">;
 def err_type_unsupported : Error<
   "%0 is not supported on this target">;
+def err_type_not_equivalent : Error<
+  "%0 is not equivalent between host and target">;
 def err_nsconsumed_attribute_mismatch : Error<
   "overriding method has mismatched ns_consumed attribute on its"
   " parameter">;
Index: clang/lib/AST/ASTContext.cpp
===================================================================
--- clang/lib/AST/ASTContext.cpp
+++ clang/lib/AST/ASTContext.cpp
@@ -1515,18 +1515,20 @@
 
 /// getFloatTypeSemantics - Return the APFloat 'semantics' for the specified
 /// scalar floating point type.
-const llvm::fltSemantics &ASTContext::getFloatTypeSemantics(QualType T) const {
+const llvm::fltSemantics &ASTContext::getFloatTypeSemantics(
+    QualType T, bool PreferAuxTarget) const {
+  const TargetInfo *Tgt = PreferAuxTarget && AuxTarget ? AuxTarget : Target;
   const auto *BT = T->getAs<BuiltinType>();
   assert(BT && "Not a floating point type!");
   switch (BT->getKind()) {
   default: llvm_unreachable("Not a floating point type!");
   case BuiltinType::Float16:
   case BuiltinType::Half:
-    return Target->getHalfFormat();
-  case BuiltinType::Float:      return Target->getFloatFormat();
-  case BuiltinType::Double:     return Target->getDoubleFormat();
-  case BuiltinType::LongDouble: return Target->getLongDoubleFormat();
-  case BuiltinType::Float128:   return Target->getFloat128Format();
+    return Tgt->getHalfFormat();
+  case BuiltinType::Float:      return Tgt->getFloatFormat();
+  case BuiltinType::Double:     return Tgt->getDoubleFormat();
+  case BuiltinType::LongDouble: return Tgt->getLongDoubleFormat();
+  case BuiltinType::Float128:   return Tgt->getFloat128Format();
   }
 }
 
Index: clang/lib/Sema/SemaOpenMP.cpp
===================================================================
--- clang/lib/Sema/SemaOpenMP.cpp
+++ clang/lib/Sema/SemaOpenMP.cpp
@@ -1588,13 +1588,23 @@
          "OpenMP device compilation mode is expected.");
   QualType Ty = E->getType();
   if ((Ty->isFloat16Type() && !Context.getTargetInfo().hasFloat16Type()) ||
-      ((Ty->isFloat128Type() ||
-        (Ty->isRealFloatingType() && Context.getTypeSize(Ty) == 128)) &&
-       !Context.getTargetInfo().hasFloat128Type()) ||
+      (Ty->isFloat128Type() && !Context.getTargetInfo().hasFloat128Type()) ||
       (Ty->isIntegerType() && Context.getTypeSize(Ty) == 128 &&
        !Context.getTargetInfo().hasInt128Type()))
     targetDiag(E->getExprLoc(), diag::err_type_unsupported)
         << Ty << E->getSourceRange();
+  if (Ty->isRealFloatingType()) {
+    llvm::APFloatBase::Semantics Sem = llvm::APFloatBase::SemanticsToEnum(
+        Context.getFloatTypeSemantics(Ty, /*PreferAuxTarget*/ true));
+    const TargetInfo &TI = Context.getTargetInfo();
+    if ((Ty->isFloat128Type() &&
+         Sem != llvm::APFloatBase::SemanticsToEnum(TI.getFloat128Format())) ||
+        (Ty.getUnqualifiedType() == Context.LongDoubleTy &&
+         Sem != llvm::APFloatBase::SemanticsToEnum(TI.getLongDoubleFormat())))
+      // TODO: Naming the floating point representations would be helpful.
+      targetDiag(E->getExprLoc(), diag::err_type_not_equivalent)
+          << Ty << E->getSourceRange();
+  }
 }
 
 bool Sema::isOpenMPCapturedByRef(const ValueDecl *D, unsigned Level) const {
Index: clang/test/OpenMP/nvptx_unsupported_type_messages.cpp
===================================================================
--- clang/test/OpenMP/nvptx_unsupported_type_messages.cpp
+++ clang/test/OpenMP/nvptx_unsupported_type_messages.cpp
@@ -1,8 +1,16 @@
 // Test target codegen - host bc file has to be created first.
-// RUN: %clang_cc1 -fopenmp -x c++ -triple x86_64-unknown-linux -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-host.bc
+// RUN: %clang_cc1 -verify=quiet -fopenmp -x c++ -triple x86_64-unknown-linux -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-host.bc
 // RUN: %clang_cc1 -verify -fopenmp -x c++ -triple nvptx64-unknown-unknown -aux-triple x86_64-unknown-linux -fopenmp-targets=nvptx64-nvidia-cuda %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-host.bc -fsyntax-only
-// RUN: %clang_cc1 -fopenmp -x c++ -triple powerpc64le-unknown-linux-gnu -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-host.bc
+// RUN: %clang_cc1 -verify=quiet -fopenmp -x c++ -triple powerpc64le-unknown-linux-gnu -fopenmp-targets=nvptx64-nvidia-cuda -emit-llvm-bc %s -o %t-host.bc
 // RUN: %clang_cc1 -verify -fopenmp -x c++ -triple nvptx64-unknown-unknown -aux-triple powerpc64le-unknown-linux-gnu -fopenmp-targets=nvptx64-nvidia-cuda %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-host.bc -fsyntax-only
+//
+// Make sure this code does compile when the host and target are the same.
+// RUN: %clang_cc1 -verify=quiet -fopenmp -x c++ -triple x86_64-unknown-linux -fopenmp-targets=x86_64-unknown-linux -emit-llvm-bc %s -o %t-host.bc
+// RUN: %clang_cc1 -verify=quiet -fopenmp -x c++ -triple x86_64-unknown-linux -aux-triple x86_64-unknown-linux -fopenmp-targets=x86_64-unknown-linux %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-host.bc -fsyntax-only
+// RUN: %clang_cc1 -verify=quiet -fopenmp -x c++ -triple powerpc64le-unknown-linux-gnu -fopenmp-targets=powerpc64le-unknown-linux-gnu -emit-llvm-bc %s -o %t-host.bc
+// RUN: %clang_cc1 -verify=quiet -fopenmp -x c++ -triple powerpc64le-unknown-linux-gnu -aux-triple powerpc64le-unknown-linux-gnu -fopenmp-targets=powerpc64le-unknown-linux-gnu %s -fopenmp-is-device -fopenmp-host-ir-file-path %t-host.bc -fsyntax-only
+
+// quiet-no-diagnostics
 
 struct T {
   char a;
@@ -16,7 +24,7 @@
 #ifndef _ARCH_PPC
 // expected-error@+4 {{'__float128' is not supported on this target}}
 #else
-// expected-error@+2 {{'long double' is not supported on this target}}
+// expected-error@+2 {{'long double' is not equivalent between host and target}}
 #endif
   T &operator+(T &b) { f += b.a; return *this;}
 };