diff --git a/llvm/include/llvm/ADT/GenericUniformityImpl.h b/llvm/include/llvm/ADT/GenericUniformityImpl.h
--- a/llvm/include/llvm/ADT/GenericUniformityImpl.h
+++ b/llvm/include/llvm/ADT/GenericUniformityImpl.h
@@ -963,7 +963,14 @@
   LLVM_DEBUG(dbgs() << "taintAndPushPhiNodes in " << Context.print(&JoinBlock)
                     << "\n");
   for (const auto &Phi : JoinBlock.phis()) {
-    if (ContextT::isConstantValuePhi(Phi))
+    // FIXME: The non-undef value is not constant per se; it just happens to be
+    // uniform and may not dominate this PHI. So assuming that the same value
+    // reaches along all incoming edges may itself be undefined behaviour. This
+    // particular interpretation of the undef value was added to
+    // DivergenceAnalysis in the following review:
+    //
+    // https://reviews.llvm.org/D19013
+    if (ContextT::isConstantOrUndefValuePhi(Phi))
       continue;
     if (markDivergent(Phi))
       Worklist.push_back(&Phi);
diff --git a/llvm/include/llvm/CodeGen/MachineSSAContext.h b/llvm/include/llvm/CodeGen/MachineSSAContext.h
--- a/llvm/include/llvm/CodeGen/MachineSSAContext.h
+++ b/llvm/include/llvm/CodeGen/MachineSSAContext.h
@@ -58,7 +58,7 @@
   static void appendBlockTerms(SmallVectorImpl<const MachineInstr *> &terms,
                                const MachineBasicBlock &block);
   MachineBasicBlock *getDefBlock(Register) const;
-  static bool isConstantValuePhi(const MachineInstr &Phi);
+  static bool isConstantOrUndefValuePhi(const MachineInstr &Phi);
 
   Printable print(const MachineBasicBlock *Block) const;
   Printable print(const MachineInstr *Inst) const;
diff --git a/llvm/include/llvm/IR/SSAContext.h b/llvm/include/llvm/IR/SSAContext.h
--- a/llvm/include/llvm/IR/SSAContext.h
+++ b/llvm/include/llvm/IR/SSAContext.h
@@ -63,7 +63,7 @@
                                const BasicBlock &block);
 
   static bool comesBefore(const Instruction *lhs, const Instruction *rhs);
-  static bool isConstantValuePhi(const Instruction &Instr);
+  static bool isConstantOrUndefValuePhi(const Instruction &Instr);
   const BasicBlock *getDefBlock(const Value *value) const;
 
   Printable print(const BasicBlock *Block) const;
diff --git a/llvm/lib/CodeGen/MachineSSAContext.cpp b/llvm/lib/CodeGen/MachineSSAContext.cpp
--- a/llvm/lib/CodeGen/MachineSSAContext.cpp
+++ b/llvm/lib/CodeGen/MachineSSAContext.cpp
@@ -56,7 +56,7 @@
   return RegInfo->getVRegDef(value)->getParent();
 }
 
-bool MachineSSAContext::isConstantValuePhi(const MachineInstr &Phi) {
+bool MachineSSAContext::isConstantOrUndefValuePhi(const MachineInstr &Phi) {
   return Phi.isConstantValuePHI();
 }
 
diff --git a/llvm/lib/IR/SSAContext.cpp b/llvm/lib/IR/SSAContext.cpp
--- a/llvm/lib/IR/SSAContext.cpp
+++ b/llvm/lib/IR/SSAContext.cpp
@@ -75,9 +75,9 @@
   return lhs->comesBefore(rhs);
 }
 
-bool SSAContext::isConstantValuePhi(const Instruction &Instr) {
+bool SSAContext::isConstantOrUndefValuePhi(const Instruction &Instr) {
   if (auto *Phi = dyn_cast<PHINode>(&Instr))
-    return Phi->hasConstantValue();
+    return Phi->hasConstantOrUndefValue();
   return false;
 }
 
diff --git a/llvm/test/Analysis/DivergenceAnalysis/AMDGPU/phi-undef.ll b/llvm/test/Analysis/DivergenceAnalysis/AMDGPU/phi-undef.ll
--- a/llvm/test/Analysis/DivergenceAnalysis/AMDGPU/phi-undef.ll
+++ b/llvm/test/Analysis/DivergenceAnalysis/AMDGPU/phi-undef.ll
@@ -1,15 +1,14 @@
-; RUN: opt -mtriple amdgcn-- -passes='print<divergence>' -disable-output %s 2>&1 | FileCheck %s --check-prefixes=CHECK,LOOPDA
-; RUN: opt -mtriple amdgcn-- -passes='print<uniformity>' -disable-output %s 2>&1 | FileCheck %s --check-prefixes=CHECK,CYCLEDA
+; RUN: opt -mtriple amdgcn-- -passes='print<divergence>' -disable-output %s 2>&1 | FileCheck %s
+; RUN: opt -mtriple amdgcn-- -passes='print<uniformity>' -disable-output %s 2>&1 | FileCheck %s
 
 ; CHECK-LABEL: 'test1':
 ; CHECK: DIVERGENT: i32 %bound
-; CYCLEDA: DIVERGENT: %counter =
-; LOOPDA: {{^  *}} %counter =
-; CHECK-NEXT: DIVERGENT: %break = icmp sge i32 %counter, %bound
-; CYCLEDA: DIVERGENT: %counter.next =
-; CYCLEDA: DIVERGENT: %counter.footer =
-; LOOPDA: {{^  *}}%counter.next =
-; LOOPDA: {{^  *}}%counter.footer =
+; CHECK: {{^  *}} %counter =
+; CHECK: DIVERGENT: %break = icmp sge i32 %counter, %bound
+; CHECK: DIVERGENT: br i1 %break, label %footer, label %body
+; CHECK: {{^  *}}%counter.next =
+; CHECK: {{^  *}}%counter.footer =
+; CHECK: DIVERGENT: br i1 %break, label %end, label %header
 
 ; Note: %counter is not divergent!