diff --git a/llvm/include/llvm/IR/ConstantRange.h b/llvm/include/llvm/IR/ConstantRange.h
--- a/llvm/include/llvm/IR/ConstantRange.h
+++ b/llvm/include/llvm/IR/ConstantRange.h
@@ -434,6 +434,12 @@
   /// Perform a signed saturating subtraction of two constant ranges.
   ConstantRange ssub_sat(const ConstantRange &Other) const;
 
+  /// Perform an unsigned saturating multiplication of two constant ranges.
+  ConstantRange umul_sat(const ConstantRange &Other) const;
+
+  /// Perform a signed saturating multiplication of two constant ranges.
+  ConstantRange smul_sat(const ConstantRange &Other) const;
+
   /// Perform an unsigned saturating left shift of this constant range by a
   /// value in \p Other.
   ConstantRange ushl_sat(const ConstantRange &Other) const;
diff --git a/llvm/lib/IR/ConstantRange.cpp b/llvm/lib/IR/ConstantRange.cpp
--- a/llvm/lib/IR/ConstantRange.cpp
+++ b/llvm/lib/IR/ConstantRange.cpp
@@ -1333,6 +1333,41 @@
   return getNonEmpty(std::move(NewL), std::move(NewU));
 }
 
+ConstantRange ConstantRange::umul_sat(const ConstantRange &Other) const {
+  if (isEmptySet() || Other.isEmptySet())
+    return getEmpty();
+
+  APInt NewL = getUnsignedMin().umul_sat(Other.getUnsignedMin());
+  APInt NewU = getUnsignedMax().umul_sat(Other.getUnsignedMax()) + 1;
+  return getNonEmpty(std::move(NewL), std::move(NewU));
+}
+
+ConstantRange ConstantRange::smul_sat(const ConstantRange &Other) const {
+  if (isEmptySet() || Other.isEmptySet())
+    return getEmpty();
+
+  // 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*2, 3*-2, 3*2) = -6.
+  // Similarly for the upper bound, swapping min for max.
+
+  APInt this_min = getSignedMin().sext(getBitWidth() * 2);
+  APInt this_max = getSignedMax().sext(getBitWidth() * 2);
+  APInt Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
+  APInt 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); };
+
+  // Note that we wanted to perform signed saturating multiplication,
+  // so since we performed plain multiplication in twice the bitwidth,
+  // we need to perform signed saturating truncation.
+  return getNonEmpty(std::min(L, Compare).truncSSat(getBitWidth()),
+                     std::max(L, Compare).truncSSat(getBitWidth()) + 1);
+}
+
 ConstantRange ConstantRange::ushl_sat(const ConstantRange &Other) const {
   if (isEmptySet() || Other.isEmptySet())
     return getEmpty();
diff --git a/llvm/unittests/IR/ConstantRangeTest.cpp b/llvm/unittests/IR/ConstantRangeTest.cpp
--- a/llvm/unittests/IR/ConstantRangeTest.cpp
+++ b/llvm/unittests/IR/ConstantRangeTest.cpp
@@ -2217,6 +2217,14 @@
       });
 }
 
+TEST_F(ConstantRangeTest, UMulSat) {
+  TestUnsignedBinOpExhaustive(
+      [](const ConstantRange &CR1, const ConstantRange &CR2) {
+        return CR1.umul_sat(CR2);
+      },
+      [](const APInt &N1, const APInt &N2) { return N1.umul_sat(N2); });
+}
+
 TEST_F(ConstantRangeTest, UShlSat) {
   TestUnsignedBinOpExhaustive(
       [](const ConstantRange &CR1, const ConstantRange &CR2) {
@@ -2245,6 +2253,14 @@
       });
 }
 
+TEST_F(ConstantRangeTest, SMulSat) {
+  TestSignedBinOpExhaustive(
+      [](const ConstantRange &CR1, const ConstantRange &CR2) {
+        return CR1.smul_sat(CR2);
+      },
+      [](const APInt &N1, const APInt &N2) { return N1.smul_sat(N2); });
+}
+
 TEST_F(ConstantRangeTest, SShlSat) {
   TestSignedBinOpExhaustive(
       [](const ConstantRange &CR1, const ConstantRange &CR2) {