diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
index e80ee65abde8..f2740a6ceb41 100644
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -201,9 +201,36 @@ void llvm::ComputeMaskedBits(Value *V, const APInt &Mask,
     ComputeMaskedBits(I->getOperand(1), Mask2, KnownZero, KnownOne, TD,Depth+1);
     ComputeMaskedBits(I->getOperand(0), Mask2, KnownZero2, KnownOne2, TD,
                       Depth+1);
-    assert((KnownZero & KnownOne) == 0 && "Bits known to be one AND zero?"); 
-    assert((KnownZero2 & KnownOne2) == 0 && "Bits known to be one AND zero?"); 
-    
+    assert((KnownZero & KnownOne) == 0 && "Bits known to be one AND zero?");
+    assert((KnownZero2 & KnownOne2) == 0 && "Bits known to be one AND zero?");
+
+    bool isKnownNegative = false;
+    bool isKnownNonNegative = false;
+    // If the multiplication is known not to overflow, compute the sign bit.
+    if (Mask.isNegative() && cast<BinaryOperator>(I)->hasNoSignedWrap()) {
+      Value *Op1 = I->getOperand(1), *Op2 = I->getOperand(0);
+      if (Op1 == Op2) {
+        // The product of a number with itself is non-negative.
+        isKnownNonNegative = true;
+      } else {
+        bool isKnownNonNegative1 = KnownZero.isNegative();
+        bool isKnownNonNegative2 = KnownZero2.isNegative();
+        bool isKnownNegative1 = KnownOne.isNegative();
+        bool isKnownNegative2 = KnownOne2.isNegative();
+        // The product of two numbers with the same sign is non-negative.
+        isKnownNonNegative = (isKnownNegative1 && isKnownNegative2) ||
+          (isKnownNonNegative1 && isKnownNonNegative2);
+        // The product of a negative number and a non-negative number is either
+        // negative or zero.
+        isKnownNegative = (isKnownNegative1 && isKnownNonNegative2 &&
+                           isKnownNonZero(Op2, TD, Depth)) ||
+                          (isKnownNegative2 && isKnownNonNegative1 &&
+                           isKnownNonZero(Op1, TD, Depth));
+        assert(!(isKnownNegative && isKnownNonNegative) &&
+               "Sign bit both zero and one?");
+      }
+    }
+
     // If low bits are zero in either operand, output low known-0 bits.
     // Also compute a conserative estimate for high known-0 bits.
     // More trickiness is possible, but this is sufficient for the
@@ -220,6 +247,12 @@ void llvm::ComputeMaskedBits(Value *V, const APInt &Mask,
     KnownZero = APInt::getLowBitsSet(BitWidth, TrailZ) |
                 APInt::getHighBitsSet(BitWidth, LeadZ);
     KnownZero &= Mask;
+
+    if (isKnownNonNegative)
+      KnownZero.setBit(BitWidth - 1);
+    else if (isKnownNegative)
+      KnownOne.setBit(BitWidth - 1);
+
     return;
   }
   case Instruction::UDiv: {
@@ -767,7 +800,7 @@ bool llvm::isKnownNonZero(Value *V, const TargetData *TD, unsigned Depth) {
   }
 
   // The remaining tests are all recursive, so bail out if we hit the limit.
-  if (Depth++ == MaxDepth)
+  if (Depth++ >= MaxDepth)
     return false;
 
   unsigned BitWidth = getBitWidth(V->getType(), TD);
@@ -851,6 +884,15 @@ bool llvm::isKnownNonZero(Value *V, const TargetData *TD, unsigned Depth) {
     if (YKnownNonNegative && isPowerOfTwo(X, TD, Depth))
       return true;
   }
+  // X * Y.
+  else if (match(V, m_Mul(m_Value(X), m_Value(Y)))) {
+    BinaryOperator *BO = cast<BinaryOperator>(V);
+    // If X and Y are non-zero then so is X * Y as long as the multiplication
+    // does not overflow.
+    if ((BO->hasNoSignedWrap() || BO->hasNoUnsignedWrap()) &&
+        isKnownNonZero(X, TD, Depth) && isKnownNonZero(Y, TD, Depth))
+      return true;
+  }
   // (C ? X : Y) != 0 if X != 0 and Y != 0.
   else if (SelectInst *SI = dyn_cast<SelectInst>(V)) {
     if (isKnownNonZero(SI->getTrueValue(), TD, Depth) &&
diff --git a/llvm/test/Transforms/InstSimplify/compare.ll b/llvm/test/Transforms/InstSimplify/compare.ll
index 2cbd641a7426..3ece11890251 100644
--- a/llvm/test/Transforms/InstSimplify/compare.ll
+++ b/llvm/test/Transforms/InstSimplify/compare.ll
@@ -323,3 +323,34 @@ define i1 @and1(i32 %X) {
   ret i1 %B
 ; CHECK: ret i1 false
 }
+
+define i1 @mul1(i32 %X) {
+; CHECK: @mul1
+; Square of a non-zero number is non-zero if there is no overflow.
+  %Y = or i32 %X, 1
+  %M = mul nuw i32 %Y, %Y
+  %C = icmp eq i32 %M, 0
+  ret i1 %C
+; CHECK: ret i1 false
+}
+
+define i1 @mul2(i32 %X) {
+; CHECK: @mul2
+; Square of a non-zero number is positive if there is no signed overflow.
+  %Y = or i32 %X, 1
+  %M = mul nsw i32 %Y, %Y
+  %C = icmp sgt i32 %M, 0
+  ret i1 %C
+; CHECK: ret i1 true
+}
+
+define i1 @mul3(i32 %X, i32 %Y) {
+; CHECK: @mul3
+; Product of non-negative numbers is non-negative if there is no signed overflow.
+  %XX = mul nsw i32 %X, %X
+  %YY = mul nsw i32 %Y, %Y
+  %M = mul nsw i32 %XX, %YY
+  %C = icmp sge i32 %M, 0
+  ret i1 %C
+; CHECK: ret i1 true
+}