diff --git a/llvm/lib/Transforms/Utils/LoopUnrollPeel.cpp b/llvm/lib/Transforms/Utils/LoopUnrollPeel.cpp
--- a/llvm/lib/Transforms/Utils/LoopUnrollPeel.cpp
+++ b/llvm/lib/Transforms/Utils/LoopUnrollPeel.cpp
@@ -215,11 +215,10 @@
     // consider AddRecs of the loop we are trying to peel and avoid
     // non-monotonic predicates, as we will not be able to simplify the loop
     // body.
-    // FIXME: For the non-monotonic predicates ICMP_EQ and ICMP_NE we can
-    //        simplify the loop, if we peel 1 additional iteration, if there
-    //        is no wrapping.
+    if (!LeftAR->isAffine() || LeftAR->getLoop() != &L)
+      continue;
     bool Increasing;
-    if (!LeftAR->isAffine() || LeftAR->getLoop() != &L ||
+    if (!(ICmpInst::isEquality(Pred) && LeftAR->hasNoSelfWrap()) &&
         !SE.isMonotonicPredicate(LeftAR, Pred, Increasing))
       continue;
     (void)Increasing;
diff --git a/llvm/test/Transforms/LoopUnroll/peel-loop-conditions.ll b/llvm/test/Transforms/LoopUnroll/peel-loop-conditions.ll
--- a/llvm/test/Transforms/LoopUnroll/peel-loop-conditions.ll
+++ b/llvm/test/Transforms/LoopUnroll/peel-loop-conditions.ll
@@ -526,18 +526,62 @@
 ;        i != 3 becomes false
 ; CHECK-LABEL: @test7(
 ; CHECK-NEXT:  for.body.lr.ph:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_BEGIN:%.*]]
+; CHECK:       for.body.peel.begin:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL:%.*]]
+; CHECK:       for.body.peel:
+; CHECK-NEXT:    [[CMP1_PEEL:%.*]] = icmp ne i32 0, 3
+; CHECK-NEXT:    br i1 [[CMP1_PEEL]], label [[IF_THEN_PEEL:%.*]], label [[FOR_INC_PEEL:%.*]]
+; CHECK:       if.then.peel:
+; CHECK-NEXT:    call void @f1()
+; CHECK-NEXT:    br label [[FOR_INC_PEEL]]
+; CHECK:       for.inc.peel:
+; CHECK-NEXT:    [[INC_PEEL:%.*]] = add nsw i32 0, 1
+; CHECK-NEXT:    [[CMP_PEEL:%.*]] = icmp slt i32 [[INC_PEEL]], [[K:%.*]]
+; CHECK-NEXT:    br i1 [[CMP_PEEL]], label [[FOR_BODY_PEEL_NEXT:%.*]], label [[FOR_END:%.*]]
+; CHECK:       for.body.peel.next:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL2:%.*]]
+; CHECK:       for.body.peel2:
+; CHECK-NEXT:    [[CMP1_PEEL3:%.*]] = icmp ne i32 [[INC_PEEL]], 3
+; CHECK-NEXT:    br i1 [[CMP1_PEEL3]], label [[IF_THEN_PEEL4:%.*]], label [[FOR_INC_PEEL5:%.*]]
+; CHECK:       if.then.peel4:
+; CHECK-NEXT:    call void @f1()
+; CHECK-NEXT:    br label [[FOR_INC_PEEL5]]
+; CHECK:       for.inc.peel5:
+; CHECK-NEXT:    [[INC_PEEL6:%.*]] = add nsw i32 [[INC_PEEL]], 1
+; CHECK-NEXT:    [[CMP_PEEL7:%.*]] = icmp slt i32 [[INC_PEEL6]], [[K]]
+; CHECK-NEXT:    br i1 [[CMP_PEEL7]], label [[FOR_BODY_PEEL_NEXT1:%.*]], label [[FOR_END]]
+; CHECK:       for.body.peel.next1:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL9:%.*]]
+; CHECK:       for.body.peel9:
+; CHECK-NEXT:    [[CMP1_PEEL10:%.*]] = icmp ne i32 [[INC_PEEL6]], 3
+; CHECK-NEXT:    br i1 [[CMP1_PEEL10]], label [[IF_THEN_PEEL11:%.*]], label [[FOR_INC_PEEL12:%.*]]
+; CHECK:       if.then.peel11:
+; CHECK-NEXT:    call void @f1()
+; CHECK-NEXT:    br label [[FOR_INC_PEEL12]]
+; CHECK:       for.inc.peel12:
+; CHECK-NEXT:    [[INC_PEEL13:%.*]] = add nsw i32 [[INC_PEEL6]], 1
+; CHECK-NEXT:    [[CMP_PEEL14:%.*]] = icmp slt i32 [[INC_PEEL13]], [[K]]
+; CHECK-NEXT:    br i1 [[CMP_PEEL14]], label [[FOR_BODY_PEEL_NEXT8:%.*]], label [[FOR_END]]
+; CHECK:       for.body.peel.next8:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_NEXT15:%.*]]
+; CHECK:       for.body.peel.next15:
+; CHECK-NEXT:    br label [[FOR_BODY_LR_PH_PEEL_NEWPH:%.*]]
+; CHECK:       for.body.lr.ph.peel.newph:
 ; CHECK-NEXT:    br label [[FOR_BODY:%.*]]
 ; CHECK:       for.body:
-; CHECK-NEXT:    [[I_05:%.*]] = phi i32 [ 0, [[FOR_BODY_LR_PH:%.*]] ], [ [[INC:%.*]], [[FOR_INC:%.*]] ]
+; CHECK-NEXT:    [[I_05:%.*]] = phi i32 [ [[INC_PEEL13]], [[FOR_BODY_LR_PH_PEEL_NEWPH]] ], [ [[INC:%.*]], [[FOR_INC:%.*]] ]
 ; CHECK-NEXT:    [[CMP1:%.*]] = icmp ne i32 [[I_05]], 3
 ; CHECK-NEXT:    br i1 [[CMP1]], label [[IF_THEN:%.*]], label [[FOR_INC]]
 ; CHECK:       if.then:
 ; CHECK-NEXT:    call void @f1()
 ; CHECK-NEXT:    br label [[FOR_INC]]
 ; CHECK:       for.inc:
-; CHECK-NEXT:    [[INC]] = add nsw i32 [[I_05]], 1
-; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i32 [[INC]], [[K:%.*]]
-; CHECK-NEXT:    br i1 [[CMP]], label [[FOR_BODY]], label [[FOR_END:%.*]]
+; CHECK-NEXT:    [[INC]] = add nuw nsw i32 [[I_05]], 1
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i32 [[INC]], [[K]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[FOR_BODY]], label [[FOR_END_LOOPEXIT:%.*]], !llvm.loop !6
+; CHECK:       for.end.loopexit:
+; CHECK-NEXT:    br label [[FOR_END]]
 ; CHECK:       for.end:
 ; CHECK-NEXT:    ret void
 ;
@@ -567,18 +611,62 @@
 ;        i == 3 becomes true.
 ; CHECK-LABEL: @test8(
 ; CHECK-NEXT:  for.body.lr.ph:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_BEGIN:%.*]]
+; CHECK:       for.body.peel.begin:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL:%.*]]
+; CHECK:       for.body.peel:
+; CHECK-NEXT:    [[CMP1_PEEL:%.*]] = icmp eq i32 0, 3
+; CHECK-NEXT:    br i1 [[CMP1_PEEL]], label [[IF_THEN_PEEL:%.*]], label [[FOR_INC_PEEL:%.*]]
+; CHECK:       if.then.peel:
+; CHECK-NEXT:    call void @f1()
+; CHECK-NEXT:    br label [[FOR_INC_PEEL]]
+; CHECK:       for.inc.peel:
+; CHECK-NEXT:    [[INC_PEEL:%.*]] = add nsw i32 0, 1
+; CHECK-NEXT:    [[CMP_PEEL:%.*]] = icmp slt i32 [[INC_PEEL]], [[K:%.*]]
+; CHECK-NEXT:    br i1 [[CMP_PEEL]], label [[FOR_BODY_PEEL_NEXT:%.*]], label [[FOR_END:%.*]]
+; CHECK:       for.body.peel.next:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL2:%.*]]
+; CHECK:       for.body.peel2:
+; CHECK-NEXT:    [[CMP1_PEEL3:%.*]] = icmp eq i32 [[INC_PEEL]], 3
+; CHECK-NEXT:    br i1 [[CMP1_PEEL3]], label [[IF_THEN_PEEL4:%.*]], label [[FOR_INC_PEEL5:%.*]]
+; CHECK:       if.then.peel4:
+; CHECK-NEXT:    call void @f1()
+; CHECK-NEXT:    br label [[FOR_INC_PEEL5]]
+; CHECK:       for.inc.peel5:
+; CHECK-NEXT:    [[INC_PEEL6:%.*]] = add nsw i32 [[INC_PEEL]], 1
+; CHECK-NEXT:    [[CMP_PEEL7:%.*]] = icmp slt i32 [[INC_PEEL6]], [[K]]
+; CHECK-NEXT:    br i1 [[CMP_PEEL7]], label [[FOR_BODY_PEEL_NEXT1:%.*]], label [[FOR_END]]
+; CHECK:       for.body.peel.next1:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL9:%.*]]
+; CHECK:       for.body.peel9:
+; CHECK-NEXT:    [[CMP1_PEEL10:%.*]] = icmp eq i32 [[INC_PEEL6]], 3
+; CHECK-NEXT:    br i1 [[CMP1_PEEL10]], label [[IF_THEN_PEEL11:%.*]], label [[FOR_INC_PEEL12:%.*]]
+; CHECK:       if.then.peel11:
+; CHECK-NEXT:    call void @f1()
+; CHECK-NEXT:    br label [[FOR_INC_PEEL12]]
+; CHECK:       for.inc.peel12:
+; CHECK-NEXT:    [[INC_PEEL13:%.*]] = add nsw i32 [[INC_PEEL6]], 1
+; CHECK-NEXT:    [[CMP_PEEL14:%.*]] = icmp slt i32 [[INC_PEEL13]], [[K]]
+; CHECK-NEXT:    br i1 [[CMP_PEEL14]], label [[FOR_BODY_PEEL_NEXT8:%.*]], label [[FOR_END]]
+; CHECK:       for.body.peel.next8:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_NEXT15:%.*]]
+; CHECK:       for.body.peel.next15:
+; CHECK-NEXT:    br label [[FOR_BODY_LR_PH_PEEL_NEWPH:%.*]]
+; CHECK:       for.body.lr.ph.peel.newph:
 ; CHECK-NEXT:    br label [[FOR_BODY:%.*]]
 ; CHECK:       for.body:
-; CHECK-NEXT:    [[I_05:%.*]] = phi i32 [ 0, [[FOR_BODY_LR_PH:%.*]] ], [ [[INC:%.*]], [[FOR_INC:%.*]] ]
+; CHECK-NEXT:    [[I_05:%.*]] = phi i32 [ [[INC_PEEL13]], [[FOR_BODY_LR_PH_PEEL_NEWPH]] ], [ [[INC:%.*]], [[FOR_INC:%.*]] ]
 ; CHECK-NEXT:    [[CMP1:%.*]] = icmp eq i32 [[I_05]], 3
 ; CHECK-NEXT:    br i1 [[CMP1]], label [[IF_THEN:%.*]], label [[FOR_INC]]
 ; CHECK:       if.then:
 ; CHECK-NEXT:    call void @f1()
 ; CHECK-NEXT:    br label [[FOR_INC]]
 ; CHECK:       for.inc:
-; CHECK-NEXT:    [[INC]] = add nsw i32 [[I_05]], 1
-; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i32 [[INC]], [[K:%.*]]
-; CHECK-NEXT:    br i1 [[CMP]], label [[FOR_BODY]], label [[FOR_END:%.*]]
+; CHECK-NEXT:    [[INC]] = add nuw nsw i32 [[I_05]], 1
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i32 [[INC]], [[K]]
+; CHECK-NEXT:    br i1 [[CMP]], label [[FOR_BODY]], label [[FOR_END_LOOPEXIT:%.*]], !llvm.loop !7
+; CHECK:       for.end.loopexit:
+; CHECK-NEXT:    br label [[FOR_END]]
 ; CHECK:       for.end:
 ; CHECK-NEXT:    ret void
 ;
@@ -687,7 +775,7 @@
 ; CHECK-NEXT:    call void @sink()
 ; CHECK-NEXT:    [[INC]] = add nuw nsw i32 [[I_06]], 1
 ; CHECK-NEXT:    [[EXITCOND:%.*]] = icmp eq i32 [[INC]], [[LEN]]
-; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT_LOOPEXIT:%.*]], label [[FOR_BODY]], !llvm.loop !6
+; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT_LOOPEXIT:%.*]], label [[FOR_BODY]], !llvm.loop !8
 ;
 entry:
   %cmp5 = icmp sgt i32 %len, 0
@@ -754,7 +842,7 @@
 ; CHECK-NEXT:    call void @sink()
 ; CHECK-NEXT:    [[INC]] = add nuw nsw i32 [[I_06]], 1
 ; CHECK-NEXT:    [[EXITCOND:%.*]] = icmp eq i32 [[INC]], [[LEN]]
-; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT_LOOPEXIT:%.*]], label [[FOR_BODY]], !llvm.loop !8
+; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT_LOOPEXIT:%.*]], label [[FOR_BODY]], !llvm.loop !10
 ;
 entry:
   %cmp5 = icmp sgt i32 %len, 0
@@ -785,15 +873,35 @@
 ; CHECK-NEXT:    [[CMP5:%.*]] = icmp sgt i32 [[LEN:%.*]], 0
 ; CHECK-NEXT:    br i1 [[CMP5]], label [[FOR_BODY_PREHEADER:%.*]], label [[FOR_COND_CLEANUP:%.*]]
 ; CHECK:       for.body.preheader:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_BEGIN:%.*]]
+; CHECK:       for.body.peel.begin:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL:%.*]]
+; CHECK:       for.body.peel:
+; CHECK-NEXT:    [[CMP1_PEEL:%.*]] = icmp eq i32 0, 0
+; CHECK-NEXT:    br i1 [[CMP1_PEEL]], label [[IF_THEN_PEEL:%.*]], label [[IF_END_PEEL:%.*]]
+; CHECK:       if.then.peel:
+; CHECK-NEXT:    call void @init()
+; CHECK-NEXT:    br label [[IF_END_PEEL]]
+; CHECK:       if.end.peel:
+; CHECK-NEXT:    call void @sink()
+; CHECK-NEXT:    [[INC_PEEL:%.*]] = add nuw nsw i32 0, 1
+; CHECK-NEXT:    [[EXITCOND_PEEL:%.*]] = icmp eq i32 [[INC_PEEL]], [[LEN]]
+; CHECK-NEXT:    br i1 [[EXITCOND_PEEL]], label [[FOR_COND_CLEANUP_LOOPEXIT:%.*]], label [[FOR_BODY_PEEL_NEXT:%.*]]
+; CHECK:       for.body.peel.next:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_NEXT1:%.*]]
+; CHECK:       for.body.peel.next1:
+; CHECK-NEXT:    br label [[FOR_BODY_PREHEADER_PEEL_NEWPH:%.*]]
+; CHECK:       for.body.preheader.peel.newph:
 ; CHECK-NEXT:    br label [[FOR_BODY:%.*]]
+; CHECK:       for.cond.cleanup.loopexit.loopexit:
+; CHECK-NEXT:    br label [[FOR_COND_CLEANUP_LOOPEXIT]]
 ; CHECK:       for.cond.cleanup.loopexit:
 ; CHECK-NEXT:    br label [[FOR_COND_CLEANUP]]
 ; CHECK:       for.cond.cleanup:
 ; CHECK-NEXT:    ret void
 ; CHECK:       for.body:
-; CHECK-NEXT:    [[I_06:%.*]] = phi i32 [ [[INC:%.*]], [[IF_END:%.*]] ], [ 0, [[FOR_BODY_PREHEADER]] ]
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp eq i32 [[I_06]], 0
-; CHECK-NEXT:    br i1 [[CMP1]], label [[IF_THEN:%.*]], label [[IF_END]]
+; CHECK-NEXT:    [[I_06:%.*]] = phi i32 [ [[INC:%.*]], [[IF_END:%.*]] ], [ [[INC_PEEL]], [[FOR_BODY_PREHEADER_PEEL_NEWPH]] ]
+; CHECK-NEXT:    br i1 false, label [[IF_THEN:%.*]], label [[IF_END]]
 ; CHECK:       if.then:
 ; CHECK-NEXT:    call void @init()
 ; CHECK-NEXT:    br label [[IF_END]]
@@ -801,7 +909,7 @@
 ; CHECK-NEXT:    call void @sink()
 ; CHECK-NEXT:    [[INC]] = add nuw nsw i32 [[I_06]], 1
 ; CHECK-NEXT:    [[EXITCOND:%.*]] = icmp eq i32 [[INC]], [[LEN]]
-; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT:%.*]], label [[FOR_BODY]]
+; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT_LOOPEXIT:%.*]], label [[FOR_BODY]], !llvm.loop !11
 ;
 entry:
   %cmp5 = icmp sgt i32 %len, 0
@@ -832,15 +940,35 @@
 ; CHECK-NEXT:    [[CMP5:%.*]] = icmp sgt i32 [[LEN:%.*]], 0
 ; CHECK-NEXT:    br i1 [[CMP5]], label [[FOR_BODY_PREHEADER:%.*]], label [[FOR_COND_CLEANUP:%.*]]
 ; CHECK:       for.body.preheader:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_BEGIN:%.*]]
+; CHECK:       for.body.peel.begin:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL:%.*]]
+; CHECK:       for.body.peel:
+; CHECK-NEXT:    [[CMP1_PEEL:%.*]] = icmp ne i32 0, 0
+; CHECK-NEXT:    br i1 [[CMP1_PEEL]], label [[IF_END_PEEL:%.*]], label [[IF_THEN_PEEL:%.*]]
+; CHECK:       if.then.peel:
+; CHECK-NEXT:    call void @init()
+; CHECK-NEXT:    br label [[IF_END_PEEL]]
+; CHECK:       if.end.peel:
+; CHECK-NEXT:    call void @sink()
+; CHECK-NEXT:    [[INC_PEEL:%.*]] = add nuw nsw i32 0, 1
+; CHECK-NEXT:    [[EXITCOND_PEEL:%.*]] = icmp eq i32 [[INC_PEEL]], [[LEN]]
+; CHECK-NEXT:    br i1 [[EXITCOND_PEEL]], label [[FOR_COND_CLEANUP_LOOPEXIT:%.*]], label [[FOR_BODY_PEEL_NEXT:%.*]]
+; CHECK:       for.body.peel.next:
+; CHECK-NEXT:    br label [[FOR_BODY_PEEL_NEXT1:%.*]]
+; CHECK:       for.body.peel.next1:
+; CHECK-NEXT:    br label [[FOR_BODY_PREHEADER_PEEL_NEWPH:%.*]]
+; CHECK:       for.body.preheader.peel.newph:
 ; CHECK-NEXT:    br label [[FOR_BODY:%.*]]
+; CHECK:       for.cond.cleanup.loopexit.loopexit:
+; CHECK-NEXT:    br label [[FOR_COND_CLEANUP_LOOPEXIT]]
 ; CHECK:       for.cond.cleanup.loopexit:
 ; CHECK-NEXT:    br label [[FOR_COND_CLEANUP]]
 ; CHECK:       for.cond.cleanup:
 ; CHECK-NEXT:    ret void
 ; CHECK:       for.body:
-; CHECK-NEXT:    [[I_06:%.*]] = phi i32 [ [[INC:%.*]], [[IF_END:%.*]] ], [ 0, [[FOR_BODY_PREHEADER]] ]
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp ne i32 [[I_06]], 0
-; CHECK-NEXT:    br i1 [[CMP1]], label [[IF_END]], label [[IF_THEN:%.*]]
+; CHECK-NEXT:    [[I_06:%.*]] = phi i32 [ [[INC:%.*]], [[IF_END:%.*]] ], [ [[INC_PEEL]], [[FOR_BODY_PREHEADER_PEEL_NEWPH]] ]
+; CHECK-NEXT:    br i1 true, label [[IF_END]], label [[IF_THEN:%.*]]
 ; CHECK:       if.then:
 ; CHECK-NEXT:    call void @init()
 ; CHECK-NEXT:    br label [[IF_END]]
@@ -848,7 +976,7 @@
 ; CHECK-NEXT:    call void @sink()
 ; CHECK-NEXT:    [[INC]] = add nuw nsw i32 [[I_06]], 1
 ; CHECK-NEXT:    [[EXITCOND:%.*]] = icmp eq i32 [[INC]], [[LEN]]
-; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT:%.*]], label [[FOR_BODY]]
+; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_COND_CLEANUP_LOOPEXIT_LOOPEXIT:%.*]], label [[FOR_BODY]], !llvm.loop !12
 ;
 entry:
   %cmp5 = icmp sgt i32 %len, 0