diff --git a/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp b/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
index d347cedb42988..455d1f79d317b 100644
--- a/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
+++ b/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
@@ -718,6 +718,40 @@ ConstraintInfo::getConstraint(CmpInst::Predicate Pred, Value *Op0, Value *Op1,
       Pred != CmpInst::ICMP_SLE && Pred != CmpInst::ICMP_SLT)
     return {};
 
+  // Check if we can eliminate right shifts.
+  auto ShiftOperands = [Pred](Value *&Op0, Value *&Op1) {
+    uint64_t ShAmtC;
+    Value *X;
+    if (!match(Op0, m_Exact(m_Shr(m_Value(X), m_ConstantInt(ShAmtC)))))
+      return false;
+    bool IsLShr = cast<BinaryOperator>(Op0)->getOpcode() == Instruction::LShr;
+    if (IsLShr && ICmpInst::isSigned(Pred))
+      return false;
+    // icmp pred (shr exact X, ShAmtC), (shr exact Y, ShAmtC) --> icmp pred X, Y
+    Value *Y;
+    if (match(Op1, m_Exact(m_Shr(m_Value(Y), m_SpecificInt(ShAmtC)))) &&
+        cast<BinaryOperator>(Op0)->getOpcode() ==
+            cast<BinaryOperator>(Op1)->getOpcode()) {
+      Op0 = X;
+      Op1 = Y;
+      return true;
+    }
+    // icmp pred (shr exact X, ShAmtC), C --> icmp pred X, (C << ShAmtC)
+    const APInt *RHSC;
+    if (!match(Op1, m_APInt(RHSC)))
+      return false;
+    bool Overflow = false;
+    APInt NewC = IsLShr ? RHSC->ushl_ov(ShAmtC, Overflow)
+                        : RHSC->sshl_ov(ShAmtC, Overflow);
+    if (Overflow)
+      return false;
+    Op0 = X;
+    Op1 = ConstantInt::get(Op1->getType(), NewC);
+    return true;
+  };
+  if (!ShiftOperands(Op0, Op1))
+    ShiftOperands(Op1, Op0);
+
   SmallVector<ConditionTy, 4> Preconditions;
   bool IsSigned = ForceSignedSystem || CmpInst::isSigned(Pred);
   auto &Value2Index = getValue2Index(IsSigned);
diff --git a/llvm/test/Transforms/ConstraintElimination/shr-exact.ll b/llvm/test/Transforms/ConstraintElimination/shr-exact.ll
new file mode 100644
index 0000000000000..3a5a900d060f7
--- /dev/null
+++ b/llvm/test/Transforms/ConstraintElimination/shr-exact.ll
@@ -0,0 +1,198 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 6
+; RUN: opt -passes=constraint-elimination -S %s | FileCheck %s
+
+define i1 @precond_icmp_ashr_and_rhsc(i64 %x) {
+; CHECK-LABEL: define i1 @precond_icmp_ashr_and_rhsc(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHR:%.*]] = ashr exact i64 [[X]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i64 [[SHR]], 200
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %shr = ashr exact i64 %x, 3
+  %cond = icmp ult i64 %shr, 200
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i64 %x, 9223372036854775800
+  ret i1 %cmp
+}
+
+define i1 @precond_icmp_ashr_and_ashr(i64 %x, i64 %y) {
+; CHECK-LABEL: define i1 @precond_icmp_ashr_and_ashr(
+; CHECK-SAME: i64 [[X:%.*]], i64 [[Y:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHRX:%.*]] = ashr exact i64 [[X]], 3
+; CHECK-NEXT:    [[SHRY:%.*]] = ashr exact i64 [[Y]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i64 [[SHRX]], [[SHRY]]
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %shrx = ashr exact i64 %x, 3
+  %shry = ashr exact i64 %y, 3
+  %cond = icmp ult i64 %shrx, %shry
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i64 %x, %y
+  ret i1 %cmp
+}
+
+define i1 @precond_icmp_lshr_and_lshr(i64 %x, i64 %y) {
+; CHECK-LABEL: define i1 @precond_icmp_lshr_and_lshr(
+; CHECK-SAME: i64 [[X:%.*]], i64 [[Y:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHRX:%.*]] = lshr exact i64 [[X]], 3
+; CHECK-NEXT:    [[SHRY:%.*]] = lshr exact i64 [[Y]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i64 [[SHRX]], [[SHRY]]
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %shrx = lshr exact i64 %x, 3
+  %shry = lshr exact i64 %y, 3
+  %cond = icmp ult i64 %shrx, %shry
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i64 %x, %y
+  ret i1 %cmp
+}
+
+; Negative tests
+
+define i1 @precond_icmp_lshr_and_rhsc_overflow(i8 %x) {
+; CHECK-LABEL: define i1 @precond_icmp_lshr_and_rhsc_overflow(
+; CHECK-SAME: i8 [[X:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHR:%.*]] = lshr exact i8 [[X]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i8 [[SHR]], 60
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X]], 8
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %shr = lshr exact i8 %x, 3
+  %cond = icmp ult i8 %shr, 60
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i8 %x, 8
+  ret i1 %cmp
+}
+
+
+define i1 @precond_icmp_lshr_unknown_shamt_and_rhsc(i8 %x, i8 %shamt) {
+; CHECK-LABEL: define i1 @precond_icmp_lshr_unknown_shamt_and_rhsc(
+; CHECK-SAME: i8 [[X:%.*]], i8 [[SHAMT:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHR:%.*]] = lshr exact i8 [[X]], [[SHAMT]]
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i8 [[SHR]], 8
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X]], 8
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %shr = lshr exact i8 %x, %shamt
+  %cond = icmp ult i8 %shr, 8
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i8 %x, 8
+  ret i1 %cmp
+}
+
+define i1 @precond_icmp_ashr_and_rhsc_overflow(i8 %x) {
+; CHECK-LABEL: define i1 @precond_icmp_ashr_and_rhsc_overflow(
+; CHECK-SAME: i8 [[X:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHR:%.*]] = ashr exact i8 [[X]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i8 [[SHR]], 60
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X]], 8
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %shr = ashr exact i8 %x, 3
+  %cond = icmp ult i8 %shr, 60
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i8 %x, 8
+  ret i1 %cmp
+}
+
+define i1 @precond_icmp_ashr_and_lshr(i64 %x, i64 %y) {
+; CHECK-LABEL: define i1 @precond_icmp_ashr_and_lshr(
+; CHECK-SAME: i64 [[X:%.*]], i64 [[Y:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHRX:%.*]] = ashr exact i64 [[X]], 3
+; CHECK-NEXT:    [[SHRY:%.*]] = lshr exact i64 [[Y]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i64 [[SHRX]], [[SHRY]]
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i64 [[X]], [[Y]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %shrx = ashr exact i64 %x, 3
+  %shry = lshr exact i64 %y, 3
+  %cond = icmp ult i64 %shrx, %shry
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i64 %x, %y
+  ret i1 %cmp
+}
+
+define i1 @precond_icmp_ashr_and_ashr_mismatched_shamt(i64 %x, i64 %y) {
+; CHECK-LABEL: define i1 @precond_icmp_ashr_and_ashr_mismatched_shamt(
+; CHECK-SAME: i64 [[X:%.*]], i64 [[Y:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHRX:%.*]] = ashr exact i64 [[X]], 3
+; CHECK-NEXT:    [[SHRY:%.*]] = ashr exact i64 [[Y]], 4
+; CHECK-NEXT:    [[COND:%.*]] = icmp ult i64 [[SHRX]], [[SHRY]]
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i64 [[X]], [[Y]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %shrx = ashr exact i64 %x, 3
+  %shry = ashr exact i64 %y, 4
+  %cond = icmp ult i64 %shrx, %shry
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp eq i64 %x, %y
+  ret i1 %cmp
+}
+
+; LShr doesn't preserve the sign of the value, so we cannot perform
+; the transformation for signed comparisons.
+define i1 @precond_icmp_lshr_and_lshr_signed_pred(i64 %x, i64 %y) {
+; CHECK-LABEL: define i1 @precond_icmp_lshr_and_lshr_signed_pred(
+; CHECK-SAME: i64 [[X:%.*]], i64 [[Y:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[SHRX:%.*]] = lshr exact i64 [[X]], 3
+; CHECK-NEXT:    [[SHRY:%.*]] = lshr exact i64 [[Y]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp slt i64 [[SHRX]], [[SHRY]]
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i64 [[X]], [[Y]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %shrx = lshr exact i64 %x, 3
+  %shry = lshr exact i64 %y, 3
+  %cond = icmp slt i64 %shrx, %shry
+  call void @llvm.assume(i1 %cond)
+  %cmp = icmp slt i64 %x, %y
+  ret i1 %cmp
+}
+
+; Regression: After converting (ashr X, 3) u> 4 to X u> 32, we should still
+; be able to use the original condition to simplify icmp with ashr.
+define i1 @precond_icmp_ashr_and_constant_regression(i64 %x) {
+; CHECK-LABEL: define i1 @precond_icmp_ashr_and_constant_regression(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[ASHR:%.*]] = ashr exact i64 [[X]], 3
+; CHECK-NEXT:    [[COND:%.*]] = icmp ugt i64 [[ASHR]], 4
+; CHECK-NEXT:    call void @llvm.assume(i1 [[COND]])
+; CHECK-NEXT:    [[ADD:%.*]] = add nsw i64 [[ASHR]], -1
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i64 [[ADD]], 0
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+entry:
+  %ashr = ashr exact i64 %x, 3
+  %cond = icmp ugt i64 %ashr, 4
+  call void @llvm.assume(i1 %cond)
+  %add = add nsw i64 %ashr, -1
+  %cmp = icmp eq i64 %add, 0
+  ret i1 %cmp
+}