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
@@ -128,6 +128,26 @@
   /// NOTE: false does not mean that inverse predicate holds!
   bool icmp(CmpInst::Predicate Pred, const ConstantRange &Other) const;
 
+  /// Return true iff CR1 ult CR2 is equivalent to CR1 slt CR2.
+  /// Does not depend on strictness/direction of the predicate.
+  static bool
+  areInsensitiveToSignednessOfICmpPredicate(const ConstantRange &CR1,
+                                            const ConstantRange &CR2);
+
+  /// Return true iff CR1 ult CR2 is equivalent to CR1 sgt CR2.
+  /// Does not depend on strictness/direction of the predicate.
+  static bool
+  areInsensitiveToSignednessOfSwappedICmpPredicate(const ConstantRange &CR1,
+                                                   const ConstantRange &CR2);
+
+  /// If the comparison between constant ranges this and Other
+  /// is insensitive to the signedness of the comparison predicate,
+  /// return a predicate equivalent to \p Pred, with flipped signedness
+  /// (i.e. unsigned instead of signed or vice versa), and maybe swapped.
+  CmpInst::Predicate
+  getEquivalentPredWithFlippedSignedness(CmpInst::Predicate Pred,
+                                         const ConstantRange &Other) const;
+
   /// Produce the largest range containing all X such that "X BinOp Y" is
   /// guaranteed not to wrap (overflow) for *all* Y in Other. However, there may
   /// be *some* Y in Other for which additional X not contained in the result
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
@@ -147,6 +147,65 @@
   return makeAllowedICmpRegion(Pred, C);
 }
 
+bool ConstantRange::areInsensitiveToSignednessOfICmpPredicate(
+    const ConstantRange &CR1, const ConstantRange &CR2) {
+  if (CR1.isEmptySet() || CR2.isEmptySet())
+    return true;
+
+  if (CR1.isFullSet() || CR2.isFullSet())
+    return false;
+  if (CR1.isWrappedSet() || CR2.isWrappedSet())
+    return false;
+  if (CR1.isSignWrappedSet() || CR2.isSignWrappedSet())
+    return false;
+
+  if (CR1.contains(CR2) || CR2.contains(CR1))
+    return true;
+
+  if (CR1.isAllNonNegative() && CR2.isAllNonNegative())
+    return true;
+
+  if (CR1.isAllNegative() && CR2.isAllNegative())
+    return !CR1.isUpperWrapped() || !CR2.isUpperWrapped();
+
+  return false;
+}
+
+bool ConstantRange::areInsensitiveToSignednessOfSwappedICmpPredicate(
+    const ConstantRange &CR1, const ConstantRange &CR2) {
+  if (CR1.isEmptySet() || CR2.isEmptySet())
+    return true;
+  if (CR1.isFullSet() || CR2.isFullSet())
+    return false;
+
+  bool TrulyEquivalent = true;
+
+  for (auto N1 : {CR1.getUnsignedMin(), CR1.getUnsignedMax(),
+                  CR1.getSignedMin(), CR1.getSignedMax()})
+    for (auto N2 : {CR2.getUnsignedMin(), CR2.getUnsignedMax(),
+                    CR2.getSignedMin(), CR2.getSignedMax()})
+      TrulyEquivalent &= N1.slt(N2) == N1.ugt(N2);
+
+  return TrulyEquivalent;
+}
+
+CmpInst::Predicate ConstantRange::getEquivalentPredWithFlippedSignedness(
+    CmpInst::Predicate Pred, const ConstantRange &Other) const {
+  assert(CmpInst::isIntPredicate(Pred) && CmpInst::isRelational(Pred) &&
+         "Only for relational integer predicates!");
+
+  CmpInst::Predicate FlippedSignednessPred =
+      CmpInst::getFlippedSignednessPredicate(Pred);
+
+  if (areInsensitiveToSignednessOfICmpPredicate(*this, Other))
+    return FlippedSignednessPred;
+
+  if (areInsensitiveToSignednessOfSwappedICmpPredicate(*this, Other))
+    return CmpInst::getSwappedPredicate(FlippedSignednessPred);
+
+  return CmpInst::Predicate::BAD_ICMP_PREDICATE;
+}
+
 bool ConstantRange::getEquivalentICmp(CmpInst::Predicate &Pred,
                                       APInt &RHS) const {
   bool Success = false;
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
@@ -2505,4 +2505,86 @@
       [](const APInt &N) { return ~N; }, PreferSmallest);
 }
 
-}  // anonymous namespace
+template <typename T>
+void testConstantRangeICmpPredEquivalence(ICmpInst::Predicate SrcPred, T Func) {
+  unsigned Bits = 4;
+  EnumerateTwoConstantRanges(Bits, [&](const ConstantRange &CR1,
+                                       const ConstantRange &CR2) {
+    ICmpInst::Predicate TgtPred;
+    bool ExpectedEquivalent;
+    std::tie(TgtPred, ExpectedEquivalent) = Func(CR1, CR2, SrcPred);
+    if (TgtPred == CmpInst::Predicate::BAD_ICMP_PREDICATE)
+      return;
+    bool TrulyEquivalent = true;
+    ForeachNumInConstantRange(CR1, [&](const APInt &N1) {
+      if (!TrulyEquivalent)
+        return;
+      ForeachNumInConstantRange(CR2, [&](const APInt &N2) {
+        if (!TrulyEquivalent)
+          return;
+        TrulyEquivalent &= ICmpInst::compare(N1, N2, SrcPred) ==
+                           ICmpInst::compare(N1, N2, TgtPred);
+      });
+    });
+    ASSERT_EQ(TrulyEquivalent, ExpectedEquivalent);
+  });
+}
+
+TEST_F(ConstantRangeTest, areInsensitiveToSignednessOfICmpPredicate) {
+  for (auto Pred : seq((unsigned)ICmpInst::Predicate::FIRST_ICMP_PREDICATE,
+                       ICmpInst::Predicate::LAST_ICMP_PREDICATE + 1)) {
+    if (ICmpInst::isEquality((ICmpInst::Predicate)Pred))
+      continue;
+    ICmpInst::Predicate FlippedSignednessPred =
+        ICmpInst::getFlippedSignednessPredicate((ICmpInst::Predicate)Pred);
+    testConstantRangeICmpPredEquivalence(
+        (ICmpInst::Predicate)Pred,
+        [FlippedSignednessPred](const ConstantRange &CR1,
+                                const ConstantRange &CR2,
+                                ICmpInst::Predicate SrcPred) {
+          return std::make_pair(
+              FlippedSignednessPred,
+              ConstantRange::areInsensitiveToSignednessOfICmpPredicate(CR1,
+                                                                       CR2));
+        });
+  }
+}
+
+TEST_F(ConstantRangeTest, areInsensitiveToSignednessOfSwappedICmpPredicate) {
+  for (auto Pred : seq((unsigned)ICmpInst::Predicate::FIRST_ICMP_PREDICATE,
+                       ICmpInst::Predicate::LAST_ICMP_PREDICATE + 1)) {
+    if (ICmpInst::isEquality((ICmpInst::Predicate)Pred))
+      continue;
+    ICmpInst::Predicate FlippedSignednessPred =
+        ICmpInst::getFlippedSignednessPredicate((ICmpInst::Predicate)Pred);
+    ICmpInst::Predicate SwappedFlippedSignednessPred =
+        ICmpInst::getSwappedPredicate(FlippedSignednessPred);
+    testConstantRangeICmpPredEquivalence(
+        (ICmpInst::Predicate)Pred,
+        [SwappedFlippedSignednessPred](const ConstantRange &CR1,
+                                       const ConstantRange &CR2,
+                                       ICmpInst::Predicate SrcPred) {
+          return std::make_pair(
+              SwappedFlippedSignednessPred,
+              ConstantRange::areInsensitiveToSignednessOfSwappedICmpPredicate(
+                  CR1, CR2));
+        });
+  }
+}
+
+TEST_F(ConstantRangeTest, getEquivalentPredWithFlippedSignedness) {
+  for (auto Pred : seq((unsigned)ICmpInst::Predicate::FIRST_ICMP_PREDICATE,
+                       ICmpInst::Predicate::LAST_ICMP_PREDICATE + 1)) {
+    if (ICmpInst::isEquality((ICmpInst::Predicate)Pred))
+      continue;
+    testConstantRangeICmpPredEquivalence(
+        (ICmpInst::Predicate)Pred,
+        [](const ConstantRange &CR1, const ConstantRange &CR2,
+           ICmpInst::Predicate SrcPred) {
+          return std::make_pair(
+              CR1.getEquivalentPredWithFlippedSignedness(SrcPred, CR2), true);
+        });
+  }
+}
+
+} // anonymous namespace