diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -2046,32 +2046,27 @@
   case Instruction::Trunc:
     return OrZero && isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q);
   case Instruction::Shl:
-    if (OrZero || Q.IIQ.hasNoUnsignedWrap(I) || Q.IIQ.hasNoSignedWrap(I))
-      return isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q);
-    return false;
   case Instruction::LShr:
-    if (OrZero || Q.IIQ.isExact(cast<BinaryOperator>(I)))
-      return isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q);
-    return false;
+    return isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q) &&
+           (OrZero || isKnownNonZero(I, Depth, Q));
   case Instruction::UDiv:
     if (Q.IIQ.isExact(cast<BinaryOperator>(I)))
       return isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q);
     return false;
   case Instruction::Mul:
-    return OrZero &&
-           isKnownToBeAPowerOfTwo(I->getOperand(1), OrZero, Depth, Q) &&
-           isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q);
+    return isKnownToBeAPowerOfTwo(I->getOperand(1), OrZero, Depth, Q) &&
+           isKnownToBeAPowerOfTwo(I->getOperand(0), OrZero, Depth, Q) &&
+           (OrZero || isKnownNonZero(I, Depth, Q));
   case Instruction::And:
-    if (OrZero) {
-      // A power of two and'd with anything is a power of two or zero.
-      if (isKnownToBeAPowerOfTwo(I->getOperand(0), /*OrZero*/ true, Depth, Q) ||
-          isKnownToBeAPowerOfTwo(I->getOperand(1), /*OrZero*/ true, Depth, Q))
-        return true;
-      // X & (-X) is always a power of two or zero.
-      if (match(I->getOperand(0), m_Neg(m_Specific(I->getOperand(1)))) ||
-          match(I->getOperand(1), m_Neg(m_Specific(I->getOperand(0)))))
-        return true;
-    }
+    // A power of two and'd with anything is a power of two or zero.
+    if (OrZero &&
+        (isKnownToBeAPowerOfTwo(I->getOperand(0), /*OrZero*/ true, Depth, Q) ||
+         isKnownToBeAPowerOfTwo(I->getOperand(1), /*OrZero*/ true, Depth, Q)))
+      return true;
+    // X & (-X) is always a power of two or zero.
+    if (match(I->getOperand(0), m_Neg(m_Specific(I->getOperand(1)))) ||
+        match(I->getOperand(1), m_Neg(m_Specific(I->getOperand(0)))))
+      return OrZero || isKnownNonZero(I->getOperand(0), Depth, Q);
     return false;
   case Instruction::Add: {
     // Adding a power-of-two or zero to the same power-of-two or zero yields
diff --git a/llvm/test/Analysis/ValueTracking/known-power-of-two.ll b/llvm/test/Analysis/ValueTracking/known-power-of-two.ll
--- a/llvm/test/Analysis/ValueTracking/known-power-of-two.ll
+++ b/llvm/test/Analysis/ValueTracking/known-power-of-two.ll
@@ -383,7 +383,7 @@
 ; CHECK-NEXT:    [[ZP2:%.*]] = shl i16 2, [[ZSMALL]]
 ; CHECK-NEXT:    [[XX:%.*]] = mul nuw nsw i16 [[XP2]], [[ZP2]]
 ; CHECK-NEXT:    [[AND:%.*]] = and i16 [[XX]], [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i16 [[AND]], [[XX]]
+; CHECK-NEXT:    [[R:%.*]] = icmp ne i16 [[AND]], 0
 ; CHECK-NEXT:    ret i1 [[R]]
 ;
   %xsmall = and i16 %x, 3
@@ -449,7 +449,7 @@
 ; CHECK-NEXT:    [[XSMALL:%.*]] = and i16 [[X]], 7
 ; CHECK-NEXT:    [[XX:%.*]] = shl i16 4, [[XSMALL]]
 ; CHECK-NEXT:    [[AND:%.*]] = and i16 [[XX]], [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i16 [[AND]], [[XX]]
+; CHECK-NEXT:    [[R:%.*]] = icmp ne i16 [[AND]], 0
 ; CHECK-NEXT:    ret i1 [[R]]
 ;
   %xsmall = and i16 %x, 7
@@ -500,7 +500,7 @@
 ; CHECK-NEXT:    [[XSMALL:%.*]] = and i16 [[X]], 7
 ; CHECK-NEXT:    [[XX:%.*]] = lshr i16 512, [[XSMALL]]
 ; CHECK-NEXT:    [[AND:%.*]] = and i16 [[XX]], [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i16 [[AND]], [[XX]]
+; CHECK-NEXT:    [[R:%.*]] = icmp ne i16 [[AND]], 0
 ; CHECK-NEXT:    ret i1 [[R]]
 ;
   %xsmall = and i16 %x, 7
@@ -550,9 +550,9 @@
 ; CHECK-SAME: (i16 [[X:%.*]], i16 [[Y:%.*]]) {
 ; CHECK-NEXT:    [[XNZ:%.*]] = or i16 [[X]], 4
 ; CHECK-NEXT:    [[X_NEG:%.*]] = sub nsw i16 0, [[XNZ]]
-; CHECK-NEXT:    [[XX:%.*]] = and i16 [[XNZ]], [[X_NEG]]
-; CHECK-NEXT:    [[AND:%.*]] = and i16 [[XX]], [[Y]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i16 [[AND]], [[XX]]
+; CHECK-NEXT:    [[TMP1:%.*]] = and i16 [[X_NEG]], [[Y]]
+; CHECK-NEXT:    [[AND:%.*]] = and i16 [[TMP1]], [[XNZ]]
+; CHECK-NEXT:    [[R:%.*]] = icmp ne i16 [[AND]], 0
 ; CHECK-NEXT:    ret i1 [[R]]
 ;
   %xnz = or i16 %x, 4
diff --git a/llvm/test/Transforms/InstSimplify/ctpop-pow2.ll b/llvm/test/Transforms/InstSimplify/ctpop-pow2.ll
--- a/llvm/test/Transforms/InstSimplify/ctpop-pow2.ll
+++ b/llvm/test/Transforms/InstSimplify/ctpop-pow2.ll
@@ -41,10 +41,7 @@
 
 define i8 @ctpop_x_nz_and_negx(i8 %x) {
 ; CHECK-LABEL: @ctpop_x_nz_and_negx(
-; CHECK-NEXT:    [[X1:%.*]] = or i8 [[X:%.*]], 1
-; CHECK-NEXT:    [[V0:%.*]] = sub i8 0, [[X1]]
-; CHECK-NEXT:    [[V1:%.*]] = and i8 [[X1]], [[V0]]
-; CHECK-NEXT:    ret i8 [[V1]]
+; CHECK-NEXT:    ret i8 1
 ;
   %x1 = or i8 %x, 1
   %v0 = sub i8 0, %x1
@@ -78,10 +75,7 @@
 
 define i32 @ctpop_2_shl_nz(i32 %x) {
 ; CHECK-LABEL: @ctpop_2_shl_nz(
-; CHECK-NEXT:    [[XA30:%.*]] = and i32 30, [[X:%.*]]
-; CHECK-NEXT:    [[V:%.*]] = shl i32 2, [[XA30]]
-; CHECK-NEXT:    [[CNT:%.*]] = call i32 @llvm.ctpop.i32(i32 [[V]])
-; CHECK-NEXT:    ret i32 [[CNT]]
+; CHECK-NEXT:    ret i32 1
 ;
   %xa30 = and i32 30, %x
   %v = shl i32 2, %xa30
@@ -179,10 +173,7 @@
 
 define <2 x i32> @ctpop_shl2_1_vec_nz(<2 x i32> %x) {
 ; CHECK-LABEL: @ctpop_shl2_1_vec_nz(
-; CHECK-NEXT:    [[AND:%.*]] = and <2 x i32> [[X:%.*]], <i32 15, i32 15>
-; CHECK-NEXT:    [[SHL:%.*]] = shl <2 x i32> <i32 2, i32 1>, [[AND]]
-; CHECK-NEXT:    [[CNT:%.*]] = call <2 x i32> @llvm.ctpop.v2i32(<2 x i32> [[SHL]])
-; CHECK-NEXT:    ret <2 x i32> [[CNT]]
+; CHECK-NEXT:    ret <2 x i32> <i32 1, i32 1>
 ;
   %and = and <2 x i32> %x, <i32 15 ,i32 15>
   %shl = shl <2 x i32> <i32 2 ,i32 1>, %and