Index: lib/Analysis/InstructionSimplify.cpp
===================================================================
--- lib/Analysis/InstructionSimplify.cpp
+++ lib/Analysis/InstructionSimplify.cpp
@@ -1040,6 +1040,13 @@
        match(Op0, m_URem(m_Value(), m_Specific(Op1)))))
     return Op0;
 
+  // (X << Y) % X -> 0
+  if ((Opcode == Instruction::SRem &&
+       match(Op0, m_NSWShl(m_Specific(Op1), m_Value()))) ||
+      (Opcode == Instruction::URem &&
+       match(Op0, m_NUWShl(m_Specific(Op1), m_Value()))))
+    return Constant::getNullValue(Op0->getType());
+
   // 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))
Index: test/Transforms/InstSimplify/rem.ll
===================================================================
--- test/Transforms/InstSimplify/rem.ll
+++ test/Transforms/InstSimplify/rem.ll
@@ -189,9 +189,7 @@
 
 define i32 @rem5(i32 %x, i32 %y) {
 ; CHECK-LABEL: @rem5(
-; CHECK-NEXT:    [[SHL:%.*]] = shl nsw i32 [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[MOD:%.*]] = srem i32 [[SHL]], [[X]]
-; CHECK-NEXT:    ret i32 [[MOD]]
+; CHECK-NEXT:    ret i32 0
 ;
   %shl = shl nsw i32 %x, %y
   %mod = srem i32 %shl, %x
@@ -200,9 +198,7 @@
 
 define <2 x i32> @rem6(<2 x i32> %x, <2 x i32> %y) {
 ; CHECK-LABEL: @rem6(
-; CHECK-NEXT:    [[SHL:%.*]] = shl nsw <2 x i32> [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[MOD:%.*]] = srem <2 x i32> [[SHL]], [[X]]
-; CHECK-NEXT:    ret <2 x i32> [[MOD]]
+; CHECK-NEXT:    ret <2 x i32> zeroinitializer
 ;
   %shl = shl nsw <2 x i32> %x, %y
   %mod = srem <2 x i32> %shl, %x
@@ -224,9 +220,7 @@
 
 define i32 @rem8(i32 %x, i32 %y) {
 ; CHECK-LABEL: @rem8(
-; CHECK-NEXT:    [[SHL:%.*]] = shl nuw i32 [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[MOD:%.*]] = urem i32 [[SHL]], [[X]]
-; CHECK-NEXT:    ret i32 [[MOD]]
+; CHECK-NEXT:    ret i32 0
 ;
   %shl = shl nuw i32 %x, %y
   %mod = urem i32 %shl, %x
@@ -235,9 +229,7 @@
 
 define <2 x i32> @rem9(<2 x i32> %x, <2 x i32> %y) {
 ; CHECK-LABEL: @rem9(
-; CHECK-NEXT:    [[SHL:%.*]] = shl nuw <2 x i32> [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[MOD:%.*]] = urem <2 x i32> [[SHL]], [[X]]
-; CHECK-NEXT:    ret <2 x i32> [[MOD]]
+; CHECK-NEXT:    ret <2 x i32> zeroinitializer
 ;
   %shl = shl nuw <2 x i32> %x, %y
   %mod = urem <2 x i32> %shl, %x