diff --git a/lib/Analysis/InstructionSimplify.cpp b/lib/Analysis/InstructionSimplify.cpp
index 982dacb..c23abb7 100644
--- a/lib/Analysis/InstructionSimplify.cpp
+++ b/lib/Analysis/InstructionSimplify.cpp
@@ -1434,6 +1434,9 @@
         return ConstantInt::getTrue(CI->getContext());
       break;
     }
+
+    // TODO: integer div and rem with constant RHS all produce values in a
+    // constant range. We should check whether the comparison is a tautology.
   }
 
   // Compare of cast, for example (zext X) != 0 -> X != 0
@@ -1644,6 +1647,21 @@
     }
   }
 
+  if (LBO && match(LBO, m_URem(m_Value(), m_Specific(RHS)))) {
+    switch (Pred) {
+    default:
+      break;
+    case ICmpInst::ICMP_EQ:
+    case ICmpInst::ICMP_UGT:
+    case ICmpInst::ICMP_UGE:
+      return ConstantInt::getFalse(RHS->getContext());
+    case ICmpInst::ICMP_NE:
+    case ICmpInst::ICMP_ULT:
+    case ICmpInst::ICMP_ULE:
+      return ConstantInt::getTrue(RHS->getContext());
+    }
+  }
+
   // If the comparison is with the result of a select instruction, check whether
   // comparing with either branch of the select always yields the same value.
   if (isa<SelectInst>(LHS) || isa<SelectInst>(RHS))
diff --git a/test/Transforms/InstSimplify/compare.ll b/test/Transforms/InstSimplify/compare.ll
index 250e44c..f392d3a 100644
--- a/test/Transforms/InstSimplify/compare.ll
+++ b/test/Transforms/InstSimplify/compare.ll
@@ -187,3 +187,19 @@
   ret i1 %c
 ; CHECK: ret i1 %cond
 }
+
+define i1 @urem1(i32 %X, i32 %Y) {
+; CHECK: @urem1
+  %A = urem i32 %X, %Y
+  %B = icmp ult i32 %A, %Y
+  ret i1 %B
+; CHECK: ret i1 true
+}
+
+define i1 @urem2(i32 %X, i32 %Y) {
+; CHECK: @urem2
+  %A = urem i32 %X, %Y
+  %B = icmp eq i32 %A, %Y
+  ret i1 %B
+; CHECK ret i1 false
+}