Index: include/llvm/IR/ConstantRange.h
===================================================================
--- include/llvm/IR/ConstantRange.h
+++ include/llvm/IR/ConstantRange.h
@@ -208,8 +208,7 @@
   ConstantRange sub(const ConstantRange &Other) const;
 
   /// Return a new range representing the possible values resulting
-  /// from a multiplication of a value in this range and a value in \p Other.
-  /// TODO: This isn't fully implemented yet.
+  /// from a multiplication of a value in this range and a value in \p Other.
   ConstantRange multiply(const ConstantRange &Other) const;
 
   /// Return a new range representing the possible values resulting
Index: lib/IR/ConstantRange.cpp
===================================================================
--- lib/IR/ConstantRange.cpp
+++ lib/IR/ConstantRange.cpp
@@ -587,6 +587,13 @@
   if (isEmptySet() || Other.isEmptySet())
     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
 
+  // Multiplication is signedness-independent. However different ranges can be
+  // obtained depending on how the input ranges are treated. These different
+  // ranges are all conservatively correct, but one might be better than the
+  // other. We calculate two ranges; one treating the inputs as unsigned
+  // and the other signed, then return the smallest of these ranges.
+
+  // Unsigned range first.
   APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
   APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
   APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
@@ -594,7 +601,26 @@
 
   ConstantRange Result_zext = ConstantRange(this_min * Other_min,
                                             this_max * Other_max + 1);
-  return Result_zext.truncate(getBitWidth());
+  ConstantRange UR = Result_zext.truncate(getBitWidth());
+
+  // Now the signed range. Because we could be dealing with negative numbers
+  // here, the lower bound is the smallest of the cartesian product of the
+  // lower and upper ranges; for example:
+  //   [-1,4) * [-2,3) = min(-1*-2, -1*3, 4*-2, 4*3) = -8.
+  // Similarly for the upper bound, swapping min for max.
+
+  this_min = getSignedMin().sext(getBitWidth() * 2);
+  this_max = getSignedMax().sext(getBitWidth() * 2);
+  Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
+  Other_max = Other.getSignedMax().sext(getBitWidth() * 2);
+  
+  auto L = {this_min * Other_min, this_min * Other_max,
+            this_max * Other_min, this_max * Other_max};
+  auto Compare = [](const APInt &A, const APInt &B) { return A.slt(B); };
+  ConstantRange Result_sext(std::min(L, Compare), std::max(L, Compare) + 1);
+  ConstantRange SR = Result_sext.truncate(getBitWidth());
+
+  return UR.getSetSize().ult(SR.getSetSize()) ? UR : SR;
 }
 
 ConstantRange
Index: unittests/IR/ConstantRangeTest.cpp
===================================================================
--- unittests/IR/ConstantRangeTest.cpp
+++ unittests/IR/ConstantRangeTest.cpp
@@ -400,6 +400,13 @@
   EXPECT_EQ(ConstantRange(APInt(4, 1), APInt(4, 6)).multiply(
                 ConstantRange(APInt(4, 6), APInt(4, 2))),
             ConstantRange(4, /*isFullSet=*/true));
+
+  EXPECT_EQ(ConstantRange(APInt(8, 254), APInt(8, 0)).multiply(
+              ConstantRange(APInt(8, 252), APInt(8, 4))),
+            ConstantRange(APInt(8, 250), APInt(8, 9)));
+  EXPECT_EQ(ConstantRange(APInt(8, 254), APInt(8, 255)).multiply(
+              ConstantRange(APInt(8, 2), APInt(8, 4))),
+            ConstantRange(APInt(8, 250), APInt(8, 253)));
 }
 
 TEST_F(ConstantRangeTest, UMax) {