diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -1228,6 +1228,24 @@
         match(Op0, m_NUWShl(m_Specific(Op1), m_Value())))))
     return Constant::getNullValue(Op0->getType());
 
+  // (X << S1) % (X << S2)
+  // (S1 >= S2) ? -> 0 : -> (X << S1)
+  Value *ShiftX;
+  ConstantInt *S1, *S2;
+  if (match(Op0, m_Shl(m_Value(ShiftX), m_ConstantInt(S1))) &&
+      match(Op1, m_Shl(m_Deferred(ShiftX), m_ConstantInt(S2)))) {
+    auto Shl0 = cast<OverflowingBinaryOperator>(Op0);
+    if (S1 >= S2 &&
+        ((Opcode == Instruction::SRem && Q.IIQ.hasNoSignedWrap(Shl0)) ||
+         (Opcode == Instruction::URem && Q.IIQ.hasNoUnsignedWrap(Shl0))))
+      return Constant::getNullValue(Shl0->getType());
+
+    auto Shl1 = cast<OverflowingBinaryOperator>(Op1);
+    if ((Opcode == Instruction::SRem && Q.IIQ.hasNoSignedWrap(Shl1)) ||
+        (Opcode == Instruction::URem && Q.IIQ.hasNoUnsignedWrap(Shl1)))
+      return Op0;
+  }
+
   // If the operation is with the result of a select instruction, check whether
   // operating on either branch of the select always yields the same value.
   if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
diff --git a/llvm/test/Transforms/InstSimplify/rem.ll b/llvm/test/Transforms/InstSimplify/rem.ll
--- a/llvm/test/Transforms/InstSimplify/rem.ll
+++ b/llvm/test/Transforms/InstSimplify/rem.ll
@@ -488,3 +488,129 @@
   %mod = urem i8 %mul, %y
   ret i8 %mod
 }
+
+define i8 @urem_shl(i8 %x){
+; CHECK-LABEL: @urem_shl(
+; CHECK-NEXT:    ret i8 0
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nuw i8 %x, 2
+  %1 = urem i8 %x2, %x1
+  ret i8 %1
+}
+
+define i8 @urem_shl_2(i8 %x){
+; CHECK-LABEL: @urem_shl_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    ret i8 [[X1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nuw i8 %x, 2
+  %1 = urem i8 %x1, %x2
+  ret i8 %1
+}
+
+define i8 @srem_shl(i8 %x){
+; CHECK-LABEL: @srem_shl(
+; CHECK-NEXT:    ret i8 0
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nsw i8 %x, 2
+  %1 = srem i8 %x2, %x1
+  ret i8 %1
+}
+
+define i8 @srem_shl_2(i8 %x){
+; CHECK-LABEL: @srem_shl_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    ret i8 [[X1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nsw i8 %x, 2
+  %1 = srem i8 %x1, %x2
+  ret i8 %1
+}
+
+; Cannot simplify to ret 0 when larger shift is missing nuw with urem
+define i8 @neg_urem_shl_no_nuw(i8 %x){
+; CHECK-LABEL: @neg_urem_shl_no_nuw(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = urem i8 [[X2]], [[X1]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = urem i8 %x2, %x1
+  ret i8 %1
+}
+
+; Cannot simplify to ret %x1 when larger shift is missing nuw with urem
+define i8 @neg_urem_shl_no_nuw_2(i8 %x){
+; CHECK-LABEL: @neg_urem_shl_no_nuw_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = urem i8 [[X1]], [[X2]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = urem i8 %x1, %x2
+  ret i8 %1
+}
+
+; Cannot simplify to ret 0 when larger shift is missing nuw with urem; ignore nsw
+define i8 @neg_urem_shl_no_nuw_3(i8 %x){
+; CHECK-LABEL: @neg_urem_shl_no_nuw_3(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl nsw i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = urem i8 [[X2]], [[X1]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nsw i8 %x, 2
+  %1 = urem i8 %x2, %x1
+  ret i8 %1
+}
+
+; Cannot simplify to ret 0 when larger shift is missing nsw with srem
+define i8 @neg_srem_shl_no_nsw(i8 %x){
+; CHECK-LABEL: @neg_srem_shl_no_nsw(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = srem i8 [[X2]], [[X1]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = srem i8 %x2, %x1
+  ret i8 %1
+}
+
+; Cannot simplify to ret %x1 when larger shift is missing nsw with srem
+define i8 @neg_srem_shl_no_nsw_2(i8 %x){
+; CHECK-LABEL: @neg_srem_shl_no_nsw_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = srem i8 [[X1]], [[X2]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = srem i8 %x1, %x2
+  ret i8 %1
+}
+
+; Cannot simplify to ret 0 when larger shift is missing nsw with srem; ignore nuw
+define i8 @neg_srem_shl_no_nsw_3(i8 %x){
+; CHECK-LABEL: @neg_srem_shl_no_nsw_3(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl nuw i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = srem i8 [[X2]], [[X1]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nuw i8 %x, 2
+  %1 = srem i8 %x2, %x1
+  ret i8 %1
+}