Index: lib/Analysis/InstructionSimplify.cpp
===================================================================
--- lib/Analysis/InstructionSimplify.cpp
+++ lib/Analysis/InstructionSimplify.cpp
@@ -4066,20 +4066,13 @@
   unsigned MaskNumElts = Mask->getType()->getVectorNumElements();
   unsigned InVecNumElts = InVecTy->getVectorNumElements();
 
-  auto *Op0Const = dyn_cast<Constant>(Op0);
-  auto *Op1Const = dyn_cast<Constant>(Op1);
-
-  // If all operands are constant, constant fold the shuffle.
-  if (Op0Const && Op1Const)
-    return ConstantFoldShuffleVectorInstruction(Op0Const, Op1Const, Mask);
-
   SmallVector<int, 32> Indices;
   ShuffleVectorInst::getShuffleMask(Mask, Indices);
   assert(MaskNumElts == Indices.size() &&
          "Size of Indices not same as number of mask elements?");
 
-  // If only one of the operands is constant, constant fold the shuffle if the
-  // mask does not select elements from the variable operand.
+  // Canonicalization: If mask does not select elements from an input vector,
+  // replace that input vector with undef.
   bool MaskSelects0 = false, MaskSelects1 = false;
   for (unsigned i = 0; i != MaskNumElts; ++i) {
     if (Indices[i] == -1)
@@ -4089,23 +4082,41 @@
     else
       MaskSelects1 = true;
   }
-  if (!MaskSelects0 && Op1Const)
-    return ConstantFoldShuffleVectorInstruction(UndefValue::get(InVecTy),
-                                                Op1Const, Mask);
-  if (!MaskSelects1 && Op0Const)
-    return ConstantFoldShuffleVectorInstruction(Op0Const,
-                                                UndefValue::get(InVecTy), Mask);
+  if (!MaskSelects0)
+    Op0 = UndefValue::get(InVecTy);
+  if (!MaskSelects1)
+    Op1 = UndefValue::get(InVecTy);
+
+  auto *Op0Const = dyn_cast<Constant>(Op0);
+  auto *Op1Const = dyn_cast<Constant>(Op1);
+
+  // If all operands are constant, constant fold the shuffle.
+  if (Op0Const && Op1Const)
+    return ConstantFoldShuffleVectorInstruction(Op0Const, Op1Const, Mask);
+
+  // Canonicalization: if only one input vector is constant, it shall be the
+  // second one.
+  if (Op0Const && !Op1Const) {
+    std::swap(Op0, Op1);
+    for (int &Idx : Indices) {
+      if (Idx == -1)
+        continue;
+      Idx = Idx < (int)InVecNumElts ? Idx + InVecNumElts : Idx - InVecNumElts;
+      assert(Idx >= 0 && Idx < (int)InVecNumElts * 2 &&
+             "shufflevector mask index out of range");
+    }
+    Mask = ConstantDataVector::get(
+        Mask->getContext(),
+        makeArrayRef(reinterpret_cast<uint32_t *>(Indices.data()),
+                     MaskNumElts));
+  }
 
   // A shuffle of a splat is always the splat itself. Legal if the shuffle's
   // value type is same as the input vectors' type.
   if (auto *OpShuf = dyn_cast<ShuffleVectorInst>(Op0))
-    if (!MaskSelects1 && RetTy == InVecTy &&
+    if (isa<UndefValue>(Op1) && RetTy == InVecTy &&
         OpShuf->getMask()->getSplatValue())
       return Op0;
-  if (auto *OpShuf = dyn_cast<ShuffleVectorInst>(Op1))
-    if (!MaskSelects0 && RetTy == InVecTy &&
-        OpShuf->getMask()->getSplatValue())
-      return Op1;
 
   // Don't fold a shuffle with undef mask elements. This may get folded in a
   // better way using demanded bits or other analysis.
Index: test/Transforms/InstSimplify/shufflevector.ll
===================================================================
--- test/Transforms/InstSimplify/shufflevector.ll
+++ test/Transforms/InstSimplify/shufflevector.ll
@@ -233,3 +233,17 @@
   ret <8 x i64> %s7
 }
 
+; This case covers internal canonicalization of shuffles with one constant input vector.
+
+;FIXME: Another issue exposed here, this whole function could be simplified to:
+;         ret <2 x float> zeroinitializer
+define <2 x float> @PR32872(<2 x float> %x) {
+; CHECK-LABEL: @PR32872(
+; CHECK-NEXT:    [[TMP1:%.*]] = shufflevector <2 x float> [[X:%.*]], <2 x float> zeroinitializer, <4 x i32> <i32 2, i32 2, i32 0, i32 1>
+; CHECK-NEXT:    [[TMP4:%.*]] = shufflevector <4 x float> zeroinitializer, <4 x float> [[TMP1]], <2 x i32> <i32 4, i32 5>
+; CHECK-NEXT:    ret <2 x float> [[TMP4]]
+;
+  %tmp1 = shufflevector <2 x float> %x, <2 x float> zeroinitializer, <4 x i32> <i32 2, i32 2, i32 0, i32 1>
+  %tmp4 = shufflevector <4 x float> zeroinitializer, <4 x float> %tmp1, <2 x i32> <i32 4, i32 5>
+  ret <2 x float> %tmp4
+}