diff --git a/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp b/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
index 9a743b95a2a6..fc5ee2359a76 100644
--- a/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
+++ b/llvm/lib/Transforms/Scalar/ConstraintElimination.cpp
@@ -1223,6 +1223,16 @@ void State::addInfoFor(BasicBlock &BB) {
       break;
     }
 
+    // Add facts from unsigned division and remainder.
+    //   urem x, n: result < n  and  result <= x
+    //   udiv x, n: result <= x
+    if (auto *BO = dyn_cast<BinaryOperator>(&I)) {
+      if ((BO->getOpcode() == Instruction::URem ||
+           BO->getOpcode() == Instruction::UDiv) &&
+          isGuaranteedNotToBePoison(BO))
+        WorkList.push_back(FactOrCheck::getInstFact(DT.getNode(&BB), BO));
+    }
+
     GuaranteedToExecute &= isGuaranteedToTransferExecutionToSuccessor(&I);
   }
 
@@ -2000,6 +2010,21 @@ static bool eliminateConstraints(Function &F, DominatorTree &DT, LoopInfo &LI,
         continue;
       }
 
+      if (auto *BO = dyn_cast<BinaryOperator>(CB.Inst)) {
+        if (BO->getOpcode() == Instruction::URem) {
+          // urem x, n: result < n (remainder is always less than divisor)
+          AddFact(CmpInst::ICMP_ULT, BO, BO->getOperand(1));
+          // urem x, n: result <= x (remainder is at most the dividend)
+          AddFact(CmpInst::ICMP_ULE, BO, BO->getOperand(0));
+          continue;
+        }
+        if (BO->getOpcode() == Instruction::UDiv) {
+          // udiv x, n: result <= x (quotient is at most the dividend)
+          AddFact(CmpInst::ICMP_ULE, BO, BO->getOperand(0));
+          continue;
+        }
+      }
+
       auto &DL = F.getDataLayout();
       auto AddFactsAboutIndices = [&](Value *Ptr, Type *AccessType) {
         CmpPredicate Pred;
diff --git a/llvm/test/Transforms/ConstraintElimination/urem-udiv.ll b/llvm/test/Transforms/ConstraintElimination/urem-udiv.ll
new file mode 100644
index 000000000000..c9c326032661
--- /dev/null
+++ b/llvm/test/Transforms/ConstraintElimination/urem-udiv.ll
@@ -0,0 +1,361 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 4
+; RUN: opt -passes=constraint-elimination -S %s | FileCheck %s
+
+; n < m  /\  r = urem x, n  ==>  r < n < m  ==>  r < m
+define i1 @urem_ult_divisor_bound(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @urem_ult_divisor_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    ret i1 true
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ult i32 %n, %m
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = urem i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ult i32 %r, %m
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; n <= m  /\  r = urem x, n  ==>  r < n <= m  ==>  r ule m
+define i1 @urem_ule_divisor_bound(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @urem_ule_divisor_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[N]], [[M]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    ret i1 true
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ule i32 %n, %m
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = urem i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ule i32 %r, %m
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; x <= limit  /\  r = urem x, n  ==>  r <= x <= limit
+define i1 @urem_ule_dividend_bound(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
+; CHECK-LABEL: define i1 @urem_ule_dividend_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    ret i1 true
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ule i32 %x, %limit
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = urem i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ule i32 %r, %limit
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; x <= limit  /\  q = udiv x, n  ==>  q <= x <= limit
+define i1 @udiv_ule_dividend_bound(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
+; CHECK-LABEL: define i1 @udiv_ule_dividend_bound(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[Q:%.*]] = udiv i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    ret i1 true
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ule i32 %x, %limit
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %q = udiv i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ule i32 %q, %limit
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; n < m  /\  m < k  /\  r = urem x, n  ==>  r < n < m < k  ==>  r < k
+define i1 @urem_chain_three_hops(i32 noundef %x, i32 noundef %n, i32 noundef %m, i32 noundef %k) {
+; CHECK-LABEL: define i1 @urem_chain_three_hops(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]], i32 noundef [[K:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[C1:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT:    br i1 [[C1]], label [[BB1:%.*]], label [[OUT:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    [[C2:%.*]] = icmp ult i32 [[M]], [[K]]
+; CHECK-NEXT:    br i1 [[C2]], label [[BB2:%.*]], label [[OUT]]
+; CHECK:       bb2:
+; CHECK-NEXT:    ret i1 true
+; CHECK:       out:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %c1 = icmp ult i32 %n, %m
+  br i1 %c1, label %bb1, label %out
+
+bb1:
+  %r = urem i32 %x, %n
+  %c2 = icmp ult i32 %m, %k
+  br i1 %c2, label %bb2, label %out
+
+bb2:
+  %v = icmp ult i32 %r, %k
+  ret i1 %v
+
+out:
+  ret i1 false
+}
+
+define i1 @udiv_urem_combined(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
+; CHECK-LABEL: define i1 @udiv_urem_combined(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ult i32 [[N]], [[LIMIT]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT:    [[AND:%.*]] = and i1 [[CMP1]], [[CMP2]]
+; CHECK-NEXT:    br i1 [[AND]], label [[THEN:%.*]], label [[ELSE:%.*]]
+; CHECK:       then:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    [[Q:%.*]] = udiv i32 [[X]], [[N]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 true, true
+; CHECK-NEXT:    ret i1 [[RES]]
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+  %cmp1 = icmp ult i32 %n, %limit
+  %cmp2 = icmp ule i32 %x, %limit
+  %and = and i1 %cmp1, %cmp2
+  br i1 %and, label %then, label %else
+
+then:
+  %r = urem i32 %x, %n
+  %q = udiv i32 %x, %n
+  %cmp3 = icmp ule i32 %r, %limit
+  %cmp4 = icmp ule i32 %q, %limit
+  %res = and i1 %cmp3, %cmp4
+  ret i1 %res
+
+else:
+  ret i1 false
+}
+
+define i1 @urem_i64(i64 noundef %x, i64 noundef %n, i64 noundef %m) {
+; CHECK-LABEL: define i1 @urem_i64(
+; CHECK-SAME: i64 noundef [[X:%.*]], i64 noundef [[N:%.*]], i64 noundef [[M:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i64 [[N]], [[M]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = urem i64 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    ret i1 true
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ult i64 %n, %m
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = urem i64 %x, %n
+  br label %check
+
+check:
+  %v = icmp ult i64 %r, %m
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; Without noundef, isGuaranteedNotToBePoison may fail; don't add facts.
+define i1 @neg_urem_no_noundef(i32 %x, i32 %n, i32 %m) {
+; CHECK-LABEL: define i1 @neg_urem_no_noundef(
+; CHECK-SAME: i32 [[X:%.*]], i32 [[N:%.*]], i32 [[M:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT:    ret i1 [[V]]
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ult i32 %n, %m
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = urem i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ult i32 %r, %m
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+define i1 @neg_udiv_no_noundef(i32 %x, i32 %n, i32 %limit) {
+; CHECK-LABEL: define i1 @neg_udiv_no_noundef(
+; CHECK-SAME: i32 [[X:%.*]], i32 [[N:%.*]], i32 [[LIMIT:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[Q:%.*]] = udiv i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    [[V:%.*]] = icmp ule i32 [[Q]], [[LIMIT]]
+; CHECK-NEXT:    ret i1 [[V]]
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ule i32 %x, %limit
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %q = udiv i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ule i32 %q, %limit
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; srem/sdiv are NOT handled.
+define i1 @neg_srem_not_handled(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @neg_srem_not_handled(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = srem i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT:    ret i1 [[V]]
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ult i32 %n, %m
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = srem i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ult i32 %r, %m
+  ret i1 %v
+
+else:
+  ret i1 false
+}
+
+; No dominating constraint relating n to m; can't simplify.
+define i1 @neg_no_dominating_fact(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @neg_no_dominating_fact(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT:    ret i1 [[V]]
+;
+  %r = urem i32 %x, %n
+  %v = icmp ult i32 %r, %m
+  ret i1 %v
+}
+
+; Wrong direction: m < n, r < n, but r < m is NOT implied.
+define i1 @neg_wrong_direction(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
+; CHECK-LABEL: define i1 @neg_wrong_direction(
+; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[M]], [[N]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
+; CHECK:       mid:
+; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
+; CHECK-NEXT:    br label [[CHECK:%.*]]
+; CHECK:       check:
+; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
+; CHECK-NEXT:    ret i1 [[V]]
+; CHECK:       else:
+; CHECK-NEXT:    ret i1 false
+;
+entry:
+  %cmp = icmp ult i32 %m, %n
+  br i1 %cmp, label %mid, label %else
+
+mid:
+  %r = urem i32 %x, %n
+  br label %check
+
+check:
+  %v = icmp ult i32 %r, %m
+  ret i1 %v
+
+else:
+  ret i1 false
+}