diff --git a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -911,6 +911,26 @@
                                CxtI.getName() + ".simplified");
 }
 
+/// Fold (icmp eq ctpop(X) 1) | (icmp eq X 0) into (icmp ult ctpop(X) 2) and
+/// fold (icmp ne ctpop(X) 1) & (icmp ne X 0) into (icmp uge ctpop(X) 2).
+static Value *foldIsPowerOf2OrZero(ICmpInst *Cmp0, ICmpInst *Cmp1, bool IsAnd,
+                                   InstCombiner::BuilderTy &Builder) {
+  CmpInst::Predicate Pred0, Pred1;
+  Value *X;
+  if (!match(Cmp0, m_ICmp(Pred0, m_Intrinsic<Intrinsic::ctpop>(m_Value(X)),
+                          m_SpecificInt(1))) ||
+      !match(Cmp1, m_ICmp(Pred1, m_Specific(X), m_ZeroInt())))
+    return nullptr;
+
+  Value *CtPop = Cmp0->getOperand(0);
+  if (IsAnd && Pred0 == ICmpInst::ICMP_NE && Pred1 == ICmpInst::ICMP_NE)
+    return Builder.CreateICmpUGE(CtPop, ConstantInt::get(CtPop->getType(), 2));
+  if (!IsAnd && Pred0 == ICmpInst::ICMP_EQ && Pred1 == ICmpInst::ICMP_EQ)
+    return Builder.CreateICmpULT(CtPop, ConstantInt::get(CtPop->getType(), 2));
+
+  return nullptr;
+}
+
 /// Reduce a pair of compares that check if a value has exactly 1 bit set.
 static Value *foldIsPowerOf2(ICmpInst *Cmp0, ICmpInst *Cmp1, bool JoinedByAnd,
                              InstCombiner::BuilderTy &Builder) {
@@ -1237,6 +1257,11 @@
   if (Value *V = foldAndOrOfICmpsWithConstEq(RHS, LHS, And, Builder, Q))
     return V;
 
+  if (Value *V = foldIsPowerOf2OrZero(LHS, RHS, /*IsAnd=*/true, Builder))
+    return V;
+  if (Value *V = foldIsPowerOf2OrZero(RHS, LHS, /*IsAnd=*/true, Builder))
+    return V;
+
   // E.g. (icmp sge x, 0) & (icmp slt x, n) --> icmp ult x, n
   if (Value *V = simplifyRangeCheck(LHS, RHS, /*Inverted=*/false))
     return V;
@@ -2595,6 +2620,11 @@
   if (Value *V = foldAndOrOfICmpsWithConstEq(RHS, LHS, Or, Builder, Q))
     return V;
 
+  if (Value *V = foldIsPowerOf2OrZero(LHS, RHS, /*IsAnd=*/false, Builder))
+    return V;
+  if (Value *V = foldIsPowerOf2OrZero(RHS, LHS, /*IsAnd=*/false, Builder))
+    return V;
+
   // E.g. (icmp slt x, 0) | (icmp sgt x, n) --> icmp ugt x, n
   if (Value *V = simplifyRangeCheck(LHS, RHS, /*Inverted=*/true))
     return V;
diff --git a/llvm/test/Transforms/InstCombine/icmp-or.ll b/llvm/test/Transforms/InstCombine/icmp-or.ll
--- a/llvm/test/Transforms/InstCombine/icmp-or.ll
+++ b/llvm/test/Transforms/InstCombine/icmp-or.ll
@@ -363,3 +363,131 @@
   %r = icmp sgt i8 %or, -1
   ret i1 %r
 }
+
+declare i32 @llvm.ctpop.i32(i32)
+
+; (icmp eq ctpop(X) 1) | (icmp eq X 0) --> icmp ult ctpop(X) 2
+
+define i1 @ctpop_or_eq_to_ctpop(i32 %0) {
+; CHECK-LABEL: @ctpop_or_eq_to_ctpop(
+; CHECK-NEXT:    [[TMP2:%.*]] = call i32 @llvm.ctpop.i32(i32 [[TMP0:%.*]]), !range [[RNG0:![0-9]+]]
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp ult i32 [[TMP2]], 2
+; CHECK-NEXT:    ret i1 [[TMP3]]
+;
+  %2 = call i32 @llvm.ctpop.i32(i32 %0)
+  %3 = icmp eq i32 %2, 1
+  %4 = icmp eq i32 %0, 0
+  %5 = or i1 %4, %3
+  ret i1 %5
+}
+
+; negative test - wrong constants
+
+define i1 @not_ctpop_or_eq_to_ctpop(i32 %0) {
+; CHECK-LABEL: @not_ctpop_or_eq_to_ctpop(
+; CHECK-NEXT:    [[TMP2:%.*]] = call i32 @llvm.ctpop.i32(i32 [[TMP0:%.*]]), !range [[RNG0]]
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp eq i32 [[TMP2]], 2
+; CHECK-NEXT:    [[TMP4:%.*]] = icmp eq i32 [[TMP0]], 0
+; CHECK-NEXT:    [[TMP5:%.*]] = or i1 [[TMP4]], [[TMP3]]
+; CHECK-NEXT:    ret i1 [[TMP5]]
+;
+  %2 = call i32 @llvm.ctpop.i32(i32 %0)
+  %3 = icmp eq i32 %2, 2
+  %4 = icmp eq i32 %0, 0
+  %5 = or i1 %4, %3
+  ret i1 %5
+}
+
+declare <2 x i32> @llvm.ctpop.v2i32(<2 x i32>)
+
+define <2 x i1> @ctpop_or_eq_to_ctpop_vec(<2 x i32> %0) {
+; CHECK-LABEL: @ctpop_or_eq_to_ctpop_vec(
+; CHECK-NEXT:    [[TMP2:%.*]] = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> [[TMP0:%.*]])
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp ult <2 x i32> [[TMP2]], <i32 2, i32 2>
+; CHECK-NEXT:    ret <2 x i1> [[TMP3]]
+;
+  %2 = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> %0)
+  %3 = icmp eq <2 x i32> %2, <i32 1, i32 1>
+  %4 = icmp eq <2 x i32> %0, <i32 0, i32 0>
+  %5 = or <2 x i1> %4, %3
+  ret <2 x i1> %5
+}
+
+; negative test - wrong constants
+
+define <2 x i1> @not_ctpop_or_eq_to_ctpop_vec(<2 x i32> %0) {
+; CHECK-LABEL: @not_ctpop_or_eq_to_ctpop_vec(
+; CHECK-NEXT:    [[TMP2:%.*]] = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> [[TMP0:%.*]])
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp eq <2 x i32> [[TMP2]], <i32 2, i32 2>
+; CHECK-NEXT:    [[TMP4:%.*]] = icmp eq <2 x i32> [[TMP0]], zeroinitializer
+; CHECK-NEXT:    [[TMP5:%.*]] = or <2 x i1> [[TMP4]], [[TMP3]]
+; CHECK-NEXT:    ret <2 x i1> [[TMP5]]
+;
+  %2 = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> %0)
+  %3 = icmp eq <2 x i32> %2, <i32 2, i32 2>
+  %4 = icmp eq <2 x i32> %0, <i32 0, i32 0>
+  %5 = or <2 x i1> %4, %3
+  ret <2 x i1> %5
+}
+
+; (icmp ne ctpop(X) 1) & (icmp ne X 0) --> icmp uge ctpop(X) 2
+
+define i1 @ctpop_and_ne_to_ctpop(i32 %0) {
+; CHECK-LABEL: @ctpop_and_ne_to_ctpop(
+; CHECK-NEXT:    [[TMP2:%.*]] = call i32 @llvm.ctpop.i32(i32 [[TMP0:%.*]]), !range [[RNG0]]
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp ugt i32 [[TMP2]], 1
+; CHECK-NEXT:    ret i1 [[TMP3]]
+;
+  %2 = call i32 @llvm.ctpop.i32(i32 %0)
+  %3 = icmp ne i32 %2, 1
+  %4 = icmp ne i32 %0, 0
+  %5 = and i1 %4, %3
+  ret i1 %5
+}
+
+; negative test - wrong constants
+
+define i1 @not_ctpop_and_ne_to_ctpop(i32 %0) {
+; CHECK-LABEL: @not_ctpop_and_ne_to_ctpop(
+; CHECK-NEXT:    [[TMP2:%.*]] = call i32 @llvm.ctpop.i32(i32 [[TMP0:%.*]]), !range [[RNG0]]
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp ne i32 [[TMP2]], 2
+; CHECK-NEXT:    [[TMP4:%.*]] = icmp ne i32 [[TMP0]], 0
+; CHECK-NEXT:    [[TMP5:%.*]] = and i1 [[TMP4]], [[TMP3]]
+; CHECK-NEXT:    ret i1 [[TMP5]]
+;
+  %2 = call i32 @llvm.ctpop.i32(i32 %0)
+  %3 = icmp ne i32 %2, 2
+  %4 = icmp ne i32 %0, 0
+  %5 = and i1 %4, %3
+  ret i1 %5
+}
+
+define <2 x i1> @ctpop_and_ne_to_ctpop_vec(<2 x i32> %0) {
+; CHECK-LABEL: @ctpop_and_ne_to_ctpop_vec(
+; CHECK-NEXT:    [[TMP2:%.*]] = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> [[TMP0:%.*]])
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp ugt <2 x i32> [[TMP2]], <i32 1, i32 1>
+; CHECK-NEXT:    ret <2 x i1> [[TMP3]]
+;
+  %2 = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> %0)
+  %3 = icmp ne <2 x i32> %2, <i32 1, i32 1>
+  %4 = icmp ne <2 x i32> %0, <i32 0, i32 0>
+  %5 = and <2 x i1> %4, %3
+  ret <2 x i1> %5
+}
+
+; negative test - wrong constants
+
+define <2 x i1> @not_ctpop_and_ne_to_ctpop_vec(<2 x i32> %0) {
+; CHECK-LABEL: @not_ctpop_and_ne_to_ctpop_vec(
+; CHECK-NEXT:    [[TMP2:%.*]] = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> [[TMP0:%.*]])
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp ne <2 x i32> [[TMP2]], <i32 2, i32 2>
+; CHECK-NEXT:    [[TMP4:%.*]] = icmp ne <2 x i32> [[TMP0]], zeroinitializer
+; CHECK-NEXT:    [[TMP5:%.*]] = and <2 x i1> [[TMP4]], [[TMP3]]
+; CHECK-NEXT:    ret <2 x i1> [[TMP5]]
+;
+  %2 = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> %0)
+  %3 = icmp ne <2 x i32> %2, <i32 2, i32 2>
+  %4 = icmp ne <2 x i32> %0, <i32 0, i32 0>
+  %5 = and <2 x i1> %4, %3
+  ret <2 x i1> %5
+}
diff --git a/llvm/test/Transforms/InstCombine/ispow2.ll b/llvm/test/Transforms/InstCombine/ispow2.ll
--- a/llvm/test/Transforms/InstCombine/ispow2.ll
+++ b/llvm/test/Transforms/InstCombine/ispow2.ll
@@ -535,15 +535,11 @@
   ret i1 %r
 }
 
-; Negative test - wrong predicate (but this could reduce).
-
-define i1 @isnot_pow2_ctpop_wrong_pred1(i32 %x) {
-; CHECK-LABEL: @isnot_pow2_ctpop_wrong_pred1(
+define i1 @is_pow2_or_zero(i32 %x) {
+; CHECK-LABEL: @is_pow2_or_zero(
 ; CHECK-NEXT:    [[T0:%.*]] = tail call i32 @llvm.ctpop.i32(i32 [[X:%.*]]), !range [[RNG0]]
-; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i32 [[T0]], 1
-; CHECK-NEXT:    [[ISZERO:%.*]] = icmp eq i32 [[X]], 0
-; CHECK-NEXT:    [[R:%.*]] = or i1 [[ISZERO]], [[CMP]]
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ult i32 [[T0]], 2
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %t0 = tail call i32 @llvm.ctpop.i32(i32 %x)
   %cmp = icmp eq i32 %t0, 1
@@ -552,13 +548,11 @@
   ret i1 %r
 }
 
-define i1 @isnot_pow2_ctpop_wrong_pred1_logical(i32 %x) {
-; CHECK-LABEL: @isnot_pow2_ctpop_wrong_pred1_logical(
+define i1 @is_pow2_or_zero_logical(i32 %x) {
+; CHECK-LABEL: @is_pow2_or_zero_logical(
 ; CHECK-NEXT:    [[T0:%.*]] = tail call i32 @llvm.ctpop.i32(i32 [[X:%.*]]), !range [[RNG0]]
-; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i32 [[T0]], 1
-; CHECK-NEXT:    [[ISZERO:%.*]] = icmp eq i32 [[X]], 0
-; CHECK-NEXT:    [[R:%.*]] = or i1 [[ISZERO]], [[CMP]]
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ult i32 [[T0]], 2
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %t0 = tail call i32 @llvm.ctpop.i32(i32 %x)
   %cmp = icmp eq i32 %t0, 1