diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
index c55c40c88bc84..753fb9ab5692d 100644
--- a/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
@@ -1847,6 +1847,33 @@ Instruction *InstCombinerImpl::visitCallInst(CallInst &CI) {
         return CastInst::Create(Instruction::ZExt, NarrowMaxMin, II->getType());
       }
     }
+    // If C is not 0:
+    //   umax(nuw_shl(x, C), x + 1) -> x == 0 ? 1 : nuw_shl(x, C)
+    // If C is not 0 or 1:
+    //   umax(nuw_mul(x, C), x + 1) -> x == 0 ? 1 : nuw_mul(x, C)
+    auto foldMaxMulShift = [&](Value *A, Value *B) -> Instruction * {
+      const APInt *C;
+      Value *X;
+      if (!match(A, m_NUWShl(m_Value(X), m_APInt(C))) &&
+          !(match(A, m_NUWMul(m_Value(X), m_APInt(C))) && !C->isOne()))
+        return nullptr;
+      if (C->isZero())
+        return nullptr;
+      if (!match(B, m_OneUse(m_Add(m_Specific(X), m_One()))))
+        return nullptr;
+
+      Value *Cmp = Builder.CreateICmpEQ(X, ConstantInt::get(X->getType(), 0));
+      Value *NewSelect =
+          Builder.CreateSelect(Cmp, ConstantInt::get(X->getType(), 1), A);
+      return replaceInstUsesWith(*II, NewSelect);
+    };
+
+    if (IID == Intrinsic::umax) {
+      if (Instruction *I = foldMaxMulShift(I0, I1))
+        return I;
+      if (Instruction *I = foldMaxMulShift(I1, I0))
+        return I;
+    }
     // If both operands of unsigned min/max are sign-extended, it is still ok
     // to narrow the operation.
     [[fallthrough]];
diff --git a/llvm/test/Transforms/InstCombine/add-shl-mul-umax.ll b/llvm/test/Transforms/InstCombine/add-shl-mul-umax.ll
new file mode 100644
index 0000000000000..a219503456432
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/add-shl-mul-umax.ll
@@ -0,0 +1,353 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 5
+
+; RUN: opt -S -passes=instcombine < %s | FileCheck %s
+
+; When C0 is neither 0 nor 1:
+;   umax(nuw_mul(x, C0), x + 1) is optimized to:
+;   x == 0 ? 1 : nuw_mul(x, C0)
+; When C0 is not 0:
+;   umax(nuw_shl(x, C0), x + 1) is optimized to:
+;   x == 0 ? 1 : nuw_shl(x, C0)
+
+; Positive Test Cases for `shl`
+
+define i64 @test_shl_by_2(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_by_2(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[TMP2:%.*]] = shl nuw i64 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[TMP2]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw i64 %x, 2
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_shl_by_5(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_by_5(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[TMP2:%.*]] = shl nuw i64 [[X]], 5
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[TMP2]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw i64 %x, 5
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_shl_with_nsw(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_with_nsw(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[SHL:%.*]] = shl nuw nsw i64 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[SHL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw nsw i64 %x, 2
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define <2 x i64> @test_shl_vector_by_2(<2 x i64> %x) {
+; CHECK-LABEL: define <2 x i64> @test_shl_vector_by_2(
+; CHECK-SAME: <2 x i64> [[X:%.*]]) {
+; CHECK-NEXT:    [[SHL:%.*]] = shl nuw <2 x i64> [[X]], splat (i64 2)
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq <2 x i64> [[X]], zeroinitializer
+; CHECK-NEXT:    [[MAX:%.*]] = select <2 x i1> [[TMP1]], <2 x i64> splat (i64 1), <2 x i64> [[SHL]]
+; CHECK-NEXT:    ret <2 x i64> [[MAX]]
+;
+  %x1 = add <2 x i64> %x, <i64 1, i64 1>
+  %shl = shl nuw <2 x i64> %x, <i64 2, i64 2>
+  %max = call <2 x i64> @llvm.umax.v2i64(<2 x i64> %shl, <2 x i64> %x1)
+  ret <2 x i64> %max
+}
+
+; Commuted Test Cases for `shl`
+
+define i64 @test_shl_umax_commuted(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_umax_commuted(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[SHL:%.*]] = shl nuw i64 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[SHL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw i64 %x, 2
+  %max = call i64 @llvm.umax.i64(i64 %x1, i64 %shl)
+  ret i64 %max
+}
+
+; Negative Test Cases for `shl`
+
+define i64 @test_shl_by_zero(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_by_zero(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[X]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw i64 %x, 0
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_shl_add_by_2(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_add_by_2(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 2
+; CHECK-NEXT:    [[SHL:%.*]] = shl nuw i64 [[X]], 2
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[SHL]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 2
+  %shl = shl nuw i64 %x, 2
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_shl_without_nuw(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_without_nuw(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    [[SHL:%.*]] = shl i64 [[X]], 2
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[SHL]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl i64 %x, 2
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_shl_umin(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_umin(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    [[SHL:%.*]] = shl nuw i64 [[X]], 2
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umin.i64(i64 [[SHL]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw i64 %x, 2
+  %max = call i64 @llvm.umin.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+; Multi-use Test Cases for `shl`
+declare void @use(i64)
+
+define i64 @test_shl_multi_use_add(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_multi_use_add(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    call void @use(i64 [[X1]])
+; CHECK-NEXT:    [[TMP2:%.*]] = shl nuw i64 [[X]], 3
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[TMP2]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  call void @use(i64 %x1)
+  %shl = shl nuw i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_shl_multi_use_shl(i64 %x) {
+; CHECK-LABEL: define i64 @test_shl_multi_use_shl(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[SHL:%.*]] = shl nuw i64 [[X]], 2
+; CHECK-NEXT:    call void @use(i64 [[SHL]])
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[SHL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %shl = shl nuw i64 %x, 2
+  call void @use(i64 %shl)
+  %max = call i64 @llvm.umax.i64(i64 %shl, i64 %x1)
+  ret i64 %max
+}
+
+; Positive Test Cases for `mul`
+
+define i64 @test_mul_by_3(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_by_3(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i64 [[X]], 3
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[MUL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_by_5(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_by_5(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i64 [[X]], 5
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[MUL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 5
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_with_nsw(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_with_nsw(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw nsw i64 [[X]], 3
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[MUL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw nsw i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define <2 x i64> @test_mul_vector_by_3(<2 x i64> %x) {
+; CHECK-LABEL: define <2 x i64> @test_mul_vector_by_3(
+; CHECK-SAME: <2 x i64> [[X:%.*]]) {
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw <2 x i64> [[X]], splat (i64 3)
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq <2 x i64> [[X]], zeroinitializer
+; CHECK-NEXT:    [[MAX:%.*]] = select <2 x i1> [[TMP1]], <2 x i64> splat (i64 1), <2 x i64> [[MUL]]
+; CHECK-NEXT:    ret <2 x i64> [[MAX]]
+;
+  %x1 = add <2 x i64> %x, <i64 1, i64 1>
+  %mul = mul nuw <2 x i64> %x, <i64 3, i64 3>
+  %max = call <2 x i64> @llvm.umax.v2i64(<2 x i64> %mul, <2 x i64> %x1)
+  ret <2 x i64> %max
+}
+
+; Commuted Test Cases for `mul`
+
+define i64 @test_mul_max_commuted(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_max_commuted(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i64 [[X]], 3
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[MUL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %x1, i64 %mul)
+  ret i64 %max
+}
+
+; Negative Test Cases for `mul`
+
+define i64 @test_mul_by_zero(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_by_zero(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    ret i64 [[X1]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 0
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_by_1(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_by_1(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[X]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 1
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_add_by_2(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_add_by_2(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 2
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i64 [[X]], 3
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[MUL]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 2
+  %mul = mul nuw i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_without_nuw(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_without_nuw(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    [[MUL:%.*]] = mul i64 [[X]], 3
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[MUL]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_umin(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_umin(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i64 [[X]], 3
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umin.i64(i64 [[MUL]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 3
+  %max = call i64 @llvm.umin.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+; Multi-use Test Cases for `mul`
+
+define i64 @test_mul_multi_use_add(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_multi_use_add(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[X1:%.*]] = add i64 [[X]], 1
+; CHECK-NEXT:    call void @use(i64 [[X1]])
+; CHECK-NEXT:    [[TMP2:%.*]] = mul nuw i64 [[X]], 3
+; CHECK-NEXT:    [[MAX:%.*]] = call i64 @llvm.umax.i64(i64 [[TMP2]], i64 [[X1]])
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  call void @use(i64 %x1)
+  %mul = mul nuw i64 %x, 3
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}
+
+define i64 @test_mul_multi_use_mul(i64 %x) {
+; CHECK-LABEL: define i64 @test_mul_multi_use_mul(
+; CHECK-SAME: i64 [[X:%.*]]) {
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i64 [[X]], 3
+; CHECK-NEXT:    call void @use(i64 [[MUL]])
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp eq i64 [[X]], 0
+; CHECK-NEXT:    [[MAX:%.*]] = select i1 [[TMP1]], i64 1, i64 [[MUL]]
+; CHECK-NEXT:    ret i64 [[MAX]]
+;
+  %x1 = add i64 %x, 1
+  %mul = mul nuw i64 %x, 3
+  call void @use(i64 %mul)
+  %max = call i64 @llvm.umax.i64(i64 %mul, i64 %x1)
+  ret i64 %max
+}