diff --git a/llvm/include/llvm/Support/KnownBits.h b/llvm/include/llvm/Support/KnownBits.h
--- a/llvm/include/llvm/Support/KnownBits.h
+++ b/llvm/include/llvm/Support/KnownBits.h
@@ -304,7 +304,8 @@
                                     KnownBits RHS);
 
   /// Compute known bits resulting from multiplying LHS and RHS.
-  static KnownBits mul(const KnownBits &LHS, const KnownBits &RHS);
+  static KnownBits mul(const KnownBits &LHS, const KnownBits &RHS,
+                       bool SelfMultiply = false);
 
   /// Compute known bits from sign-extended multiply-hi.
   static KnownBits mulhs(const KnownBits &LHS, const KnownBits &RHS);
diff --git a/llvm/lib/Support/KnownBits.cpp b/llvm/lib/Support/KnownBits.cpp
--- a/llvm/lib/Support/KnownBits.cpp
+++ b/llvm/lib/Support/KnownBits.cpp
@@ -412,10 +412,13 @@
   return KnownAbs;
 }
 
-KnownBits KnownBits::mul(const KnownBits &LHS, const KnownBits &RHS) {
+KnownBits KnownBits::mul(const KnownBits &LHS, const KnownBits &RHS,
+                         bool SelfMultiply) {
   unsigned BitWidth = LHS.getBitWidth();
   assert(BitWidth == RHS.getBitWidth() && !LHS.hasConflict() &&
          !RHS.hasConflict() && "Operand mismatch");
+  assert((!SelfMultiply || (LHS.One == RHS.One && LHS.Zero == RHS.Zero)) &&
+         "Self multiplication knownbits mismatch");
 
   // Compute a conservative estimate for high known-0 bits.
   unsigned LeadZ =
@@ -489,6 +492,14 @@
   Res.Zero.setHighBits(LeadZ);
   Res.Zero |= (~BottomKnown).getLoBits(ResultBitsKnown);
   Res.One = BottomKnown.getLoBits(ResultBitsKnown);
+
+  // If we're self-multiplying then bit[1] is guaranteed to be zero.
+  if (SelfMultiply && BitWidth > 1) {
+    assert(Res.One[1] == 0 &&
+           "Self-multiplication failed Quadratic Reciprocity!");
+    Res.Zero.setBit(1);
+  }
+
   return Res;
 }
 
diff --git a/llvm/unittests/Support/KnownBitsTest.cpp b/llvm/unittests/Support/KnownBitsTest.cpp
--- a/llvm/unittests/Support/KnownBitsTest.cpp
+++ b/llvm/unittests/Support/KnownBitsTest.cpp
@@ -267,6 +267,23 @@
       EXPECT_TRUE(ComputedAShr.One.isSubsetOf(KnownAShr.One));
     });
   });
+
+  // Also test 'unary' binary cases where the same argument is repeated.
+  ForeachKnownBits(Bits, [&](const KnownBits &Known) {
+    KnownBits KnownMul(Bits);
+    KnownMul.Zero.setAllBits();
+    KnownMul.One.setAllBits();
+
+    ForeachNumInKnownBits(Known, [&](const APInt &N) {
+      APInt Res = N * N;
+      KnownMul.One &= Res;
+      KnownMul.Zero &= ~Res;
+    });
+
+    KnownBits ComputedMul = KnownBits::mul(Known, Known, /*SelfMultiply*/ true);
+    EXPECT_TRUE(ComputedMul.Zero.isSubsetOf(KnownMul.Zero));
+    EXPECT_TRUE(ComputedMul.One.isSubsetOf(KnownMul.One));
+  });
 }
 
 TEST(KnownBitsTest, UnaryExhaustive) {