[SCEV] Fix sorting order for AddRecExprs

[mkazantsev]

Summary

The existing sorting order in defined CompareSCEVComplexity sorts AddRecExprs by loop depth, but does not pay attention to dominance of loops. This can lead us to the following buggy situation:

for (...) { // loop1
  op1 = {A,+,B}
}
for (...) { // loop2
  op2 = {A,+,B}
  s = add op1, op2
}

In this case there is no guarantee that in operand list of s op2 comes before op1 (loop depth is the same, so they will be sorted just lexicographically), so we can incorrectly treat s as a recurrence of loop1, which is wrong.

This patch changes the sorting logic so that it places the dominated recs before the dominating recs. This ensures that when we pick the first recurrency in the operands order, it will be the bottom-most in terms of domination tree. The attached test set includes some tests that produce incorrect SCEV estimations and crashes with oldlogic.

[sanjoy]

Hi Max,

I'm not sure if such a large change is necessary. Why not do something surgical like this:

diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
index d712063..054571f 100644
--- a/lib/Analysis/ScalarEvolution.cpp
+++ b/lib/Analysis/ScalarEvolution.cpp
@@ -2448,6 +2448,15 @@ const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
     // Scan all of the other operands to this add and add them to the vector if
     // they are loop invariant w.r.t. the recurrence.
     SmallVector<const SCEV *, 8> LIOps;
+    int BotIdx = Idx;
+    for (int I = Idx + 1; I < Ops.size() && isa<SCEVAddRecExpr>(Ops[I]); ++I)
+      if (DT.dominates(
+              cast<SCEVAddRecExpr>(Ops[BotIdx])->getLoop()->getHeader(),
+              cast<SCEVAddRecExpr>(Ops[I])->getLoop()->getHeader()))
+        BotIdx = I;
+
+    std::swap(Ops[Idx], Ops[BotIdx]);
+
     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
     const Loop *AddRecLoop = AddRec->getLoop();
     for (unsigned i = 0, e = Ops.size(); i != e; ++i)

that uses the Ops array as a scratch space to get the invariant you need?

The other option (that I like more) is to change CompareSCEVComplexity to get this invariant directly from GroupByComplexity. After that, we can have an assert in getAddExpr to check that GroupByComplexity did what we wanted.

[mkazantsev]

Thanks Sanjoy, it seems that the approach with sorting order works well. I followed this approach and also added 2 more tests with nested loops.

[sanjoy]

lgtm with one comment.

lib/Analysis/ScalarEvolution.cpp

638

Can we assert DT.dominates(LHead, RHead) || DT.dominates(RHead, LHead) here?

[mkazantsev]

lib/Analysis/ScalarEvolution.cpp

638

Yes, I thought of that. It should be true as long as we only use this method to compare operands of one instruction. I propose to land this as is, and then I'll make a follow-up patch with this change. This will allow us to separate the potential problems (if any of these changes can bring them).

[sanjoy]

I have two more comments:

• Can you also add an assert in getAddExpr checking that the expressions are sorted like we expected?
• Can you please add a comment in CompareSCEVComplexity on why the ordering is needed? A one-liner that "we need this in getAddExpr" is sufficient.

[mkazantsev]

lib/Analysis/ScalarEvolution.cpp

638

Done as https://reviews.llvm.org/D33228

[mkazantsev]

Addressed the last comment.

lib/Analysis/ScalarEvolution.cpp

 }
 
 // Return negative, zero, or positive, if LHS is less than, equal to, or greater
 // than RHS, respectively. A three-way result allows recursive comparisons to be
 // more efficient.
 static int CompareSCEVComplexity(
     SmallSet<std::pair<const SCEV *, const SCEV *>, 8> &EqCacheSCEV,
     const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
-    unsigned Depth = 0) {
+    DominatorTree &DT, unsigned Depth = 0) {
   // Fast-path: SCEVs are uniqued so we can do a quick equality check.
   if (LHS == RHS)
     return 0;
 
   // Primarily, sort the SCEVs by their getSCEVType().
   unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
   if (LType != RType)
     return (int)LType - (int)RType;
if (LBitWidth != RBitWidth)
       return (int)LBitWidth - (int)RBitWidth;
     return LA.ult(RA) ? -1 : 1;
   }
 
   case scAddRecExpr: {
     const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
     const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
 
-    // Compare addrec loop depths.
+    // If there is a dominance relationship between the loops, sort by the
+    // dominance. Otherwise, sort by depth.
     const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
     if (LLoop != RLoop) {
+      const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
+      assert(LHead != RHead && "Two loops share the same header?");
+      if (DT.dominates(LHead, RHead))
+        return 1;
+      else if (DT.dominates(RHead, LHead))
+        return -1;
       unsigned LDepth = LLoop->getLoopDepth(), RDepth = RLoop->getLoopDepth();
       if (LDepth != RDepth)
         return (int)LDepth - (int)RDepth;
     }
 
     // Addrec complexity grows with operand count.
     unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
     if (LNumOps != RNumOps)
       return (int)LNumOps - (int)RNumOps;
 
     // Lexicographically compare.
     for (unsigned i = 0; i != LNumOps; ++i) {
       int X = CompareSCEVComplexity(EqCacheSCEV, LI, LA->getOperand(i),
-                                    RA->getOperand(i), Depth + 1);
+                                    RA->getOperand(i), DT,  Depth + 1);
       if (X != 0)
         return X;
     }
     EqCacheSCEV.insert({LHS, RHS});
     return 0;
   }
 
   case scAddExpr:
   case scMulExpr:
   case scSMaxExpr:
   case scUMaxExpr: {
     const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
     const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
 
     // Lexicographically compare n-ary expressions.
     unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
     if (LNumOps != RNumOps)
       return (int)LNumOps - (int)RNumOps;
 
     for (unsigned i = 0; i != LNumOps; ++i) {
       if (i >= RNumOps)
         return 1;
       int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(i),
-                                    RC->getOperand(i), Depth + 1);
+                                    RC->getOperand(i), DT, Depth + 1);
       if (X != 0)
         return X;
     }
     EqCacheSCEV.insert({LHS, RHS});
     return 0;
   }
 
   case scUDivExpr: {
     const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
     const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
 
     // Lexicographically compare udiv expressions.
     int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getLHS(), RC->getLHS(),
-                                  Depth + 1);
+                                  DT, Depth + 1);
     if (X != 0)
       return X;
-    X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getRHS(), RC->getRHS(),
+    X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getRHS(), RC->getRHS(), DT,
                               Depth + 1);
     if (X == 0)
       EqCacheSCEV.insert({LHS, RHS});
     return X;
   }
 
   case scTruncate:
   case scZeroExtend:
   case scSignExtend: {
     const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
     const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
 
     // Compare cast expressions by operand.
     int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(),
-                                  RC->getOperand(), Depth + 1);
+                                  RC->getOperand(), DT, Depth + 1);
     if (X == 0)
       EqCacheSCEV.insert({LHS, RHS});
     return X;
   }
 
   case scCouldNotCompute:
     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
   }
   llvm_unreachable("Unknown SCEV kind!");
 }
 
 /// Given a list of SCEV objects, order them by their complexity, and group
 /// objects of the same complexity together by value.  When this routine is
 /// finished, we know that any duplicates in the vector are consecutive and that
 /// complexity is monotonically increasing.
 ///
 /// Note that we go take special precautions to ensure that we get deterministic
 /// results from this routine.  In other words, we don't want the results of
 /// this to depend on where the addresses of various SCEV objects happened to
 /// land in memory.
 ///
 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
-                              LoopInfo *LI) {
+                              LoopInfo *LI, DominatorTree &DT) {
   if (Ops.size() < 2) return;  // Noop
 
   SmallSet<std::pair<const SCEV *, const SCEV *>, 8> EqCache;
   if (Ops.size() == 2) {
     // This is the common case, which also happens to be trivially simple.
     // Special case it.
     const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
-    if (CompareSCEVComplexity(EqCache, LI, RHS, LHS) < 0)
+    if (CompareSCEVComplexity(EqCache, LI, RHS, LHS, DT) < 0)
       std::swap(LHS, RHS);
     return;
   }
 
   // Do the rough sort by complexity.
   std::stable_sort(Ops.begin(), Ops.end(),
-                   [&EqCache, LI](const SCEV *LHS, const SCEV *RHS) {
-                     return CompareSCEVComplexity(EqCache, LI, LHS, RHS) < 0;
+                   [&EqCache, LI, &DT](const SCEV *LHS, const SCEV *RHS) {
+                     return
+                         CompareSCEVComplexity(EqCache, LI, LHS, RHS, DT) < 0;
                    });
 
   // Now that we are sorted by complexity, group elements of the same
   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
   // be extremely short in practice.  Note that we take this approach because we
   // do not want to depend on the addresses of the objects we are grouping.
   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
     const SCEV *S = Ops[i];

 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVAddExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
-  GroupByComplexity(Ops, &LI);
+  GroupByComplexity(Ops, &LI, DT);
 
   Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
     ++Idx;
     assert(Idx < Ops.size());

 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVMulExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
-  GroupByComplexity(Ops, &LI);
+  GroupByComplexity(Ops, &LI, DT);
 
   Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
 
     // C1*(C2+V) -> C1*C2 + C1*V

 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVSMaxExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
-  GroupByComplexity(Ops, &LI);
+  GroupByComplexity(Ops, &LI, DT);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
     ++Idx;
     assert(Idx < Ops.size());
     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
       // We found two constants, fold them together!

 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVUMaxExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
-  GroupByComplexity(Ops, &LI);
+  GroupByComplexity(Ops, &LI, DT);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
     ++Idx;
     assert(Idx < Ops.size());
     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
       // We found two constants, fold them together!

test/Analysis/ScalarEvolution/different-loops-recs.ll

+; RUN: opt -analyze -scalar-evolution < %s | FileCheck %s
+
+; This test set ensures that we can correctly operate with recurrencies from
+; different loops.
+
+; Check that we can evaluate a sum of phis from two different loops in any
+; order.
+
+define void @test_00() {
+
+; CHECK-LABEL: Classifying expressions for: @test_00
+; CHECK:       %sum1 = add i32 %phi1, %phi2
+; CHECK-NEXT:  -->  {14,+,3}<%loop1>
+; CHECK:       %sum2 = add i32 %sum1, %phi3
+; CHECK-NEXT:  -->  {20,+,6}<%loop1>
+; CHECK:       %sum3 = add i32 %phi4, %phi5
+; CHECK-NEXT:  -->  {116,+,3}<%loop2>
+; CHECK:       %sum4 = add i32 %sum3, %phi6
+; CHECK-NEXT:  -->  {159,+,6}<%loop2>
+; CHECK:       %s1 = add i32 %phi1, %phi4
+; CHECK-NEXT:  -->  {{{{}}73,+,1}<%loop1>,+,1}<%loop2>
+; CHECK:       %s2 = add i32 %phi5, %phi2
+; CHECK-NEXT:  -->  {{{{}}57,+,2}<%loop1>,+,2}<%loop2>
+; CHECK:       %s3 = add i32 %sum1, %sum3
+; CHECK-NEXT:  -->  {{{{}}130,+,3}<%loop1>,+,3}<%loop2>
+; CHECK:       %s4 = add i32 %sum4, %sum2
+; CHECK-NEXT:  -->  {{{{}}179,+,6}<%loop1>,+,6}<%loop2>
+; CHECK:       %s5 = add i32 %phi3, %sum3
+; CHECK-NEXT:  -->  {{{{}}122,+,3}<%loop1>,+,3}<%loop2>
+; CHECK:       %s6 = add i32 %sum2, %phi6
+; CHECK-NEXT:  -->  {{{{}}63,+,6}<%loop1>,+,3}<%loop2>
+
+entry:
+  br label %loop1
+
+loop1:
+  %phi1 = phi i32 [ 10, %entry ], [ %phi1.inc, %loop1 ]
+  %phi2 = phi i32 [ 4, %entry ], [ %phi2.inc, %loop1 ]
+  %phi3 = phi i32 [ 6, %entry ], [ %phi3.inc, %loop1 ]
+  %phi1.inc = add i32 %phi1, 1
+  %phi2.inc = add i32 %phi2, 2
+  %phi3.inc = add i32 %phi3, 3
+  %sum1 = add i32 %phi1, %phi2
+  %sum2 = add i32 %sum1, %phi3
+  %cond1 = icmp ult i32 %sum2, 1000
+  br i1 %cond1, label %loop1, label %loop2
+
+loop2:
+  %phi4 = phi i32 [ 63, %loop1 ], [ %phi4.inc, %loop2 ]
+  %phi5 = phi i32 [ 53, %loop1 ], [ %phi5.inc, %loop2 ]
+  %phi6 = phi i32 [ 43, %loop1 ], [ %phi6.inc, %loop2 ]
+  %phi4.inc = add i32 %phi4, 1
+  %phi5.inc = add i32 %phi5, 2
+  %phi6.inc = add i32 %phi6, 3
+  %sum3 = add i32 %phi4, %phi5
+  %sum4 = add i32 %sum3, %phi6
+  %cond2 = icmp ult i32 %sum4, 1000
+  br i1 %cond2, label %loop2, label %exit
+
+exit:
+  %s1 = add i32 %phi1, %phi4
+  %s2 = add i32 %phi5, %phi2
+  %s3 = add i32 %sum1, %sum3
+  %s4 = add i32 %sum4, %sum2
+  %s5 = add i32 %phi3, %sum3
+  %s6 = add i32 %sum2, %phi6
+  ret void
+}
+
+; Check that we can evaluate a sum of phis+invariants from two different loops
+; in any order.
+
+define void @test_01(i32 %a, i32 %b) {
+
+; CHECK-LABEL: Classifying expressions for: @test_01
+; CHECK:       %sum1 = add i32 %phi1, %phi2
+; CHECK-NEXT:  -->  {(%a + %b),+,3}<%loop1>
+; CHECK:       %sum2 = add i32 %sum1, %phi3
+; CHECK-NEXT:  -->  {(6 + %a + %b),+,6}<%loop1>
+; CHECK:       %is1 = add i32 %sum2, %a
+; CHECK-NEXT:  -->  {(6 + (2 * %a) + %b),+,6}<%loop1>
+; CHECK:       %sum3 = add i32 %phi4, %phi5
+; CHECK-NEXT:  -->  {116,+,3}<%loop2>
+; CHECK:       %sum4 = add i32 %sum3, %phi6
+; CHECK-NEXT:  -->  {159,+,6}<%loop2>
+; CHECK:       %is2 = add i32 %sum4, %b
+; CHECK-NEXT:  -->  {(159 + %b),+,6}<%loop2>
+; CHECK:       %ec2 = add i32 %is1, %is2
+; CHECK-NEXT:  -->  {{{{}}(165 + (2 * %a) + (2 * %b)),+,6}<%loop1>,+,6}<%loop2>
+; CHECK:       %s1 = add i32 %phi1, %is1
+; CHECK-NEXT:  -->  {(6 + (3 * %a) + %b),+,7}<%loop1>
+; CHECK:       %s2 = add i32 %is2, %phi4
+; CHECK-NEXT:  -->  {(222 + %b),+,7}<%loop2>
+; CHECK:       %s3 = add i32 %is1, %phi5
+; CHECK-NEXT:  -->  {{{{}}(59 + (2 * %a) + %b),+,6}<%loop1>,+,2}<%loop2>
+; CHECK:       %s4 = add i32 %phi2, %is2
+; CHECK-NEXT:  -->  {{{{}}(159 + (2 * %b)),+,2}<%loop1>,+,6}<%loop2>
+; CHECK:       %s5 = add i32 %is1, %is2
+; CHECK-NEXT:  -->  {{{{}}(165 + (2 * %a) + (2 * %b)),+,6}<%loop1>,+,6}<%loop2>
+; CHECK:       %s6 = add i32 %is2, %is1
+; CHECK-NEXT:  -->  {{{{}}(165 + (2 * %a) + (2 * %b)),+,6}<%loop1>,+,6}<%loop2>
+
+entry:
+  br label %loop1
+
+loop1:
+  %phi1 = phi i32 [ %a, %entry ], [ %phi1.inc, %loop1 ]
+  %phi2 = phi i32 [ %b, %entry ], [ %phi2.inc, %loop1 ]
+  %phi3 = phi i32 [ 6, %entry ], [ %phi3.inc, %loop1 ]
+  %phi1.inc = add i32 %phi1, 1
+  %phi2.inc = add i32 %phi2, 2
+  %phi3.inc = add i32 %phi3, 3
+  %sum1 = add i32 %phi1, %phi2
+  %sum2 = add i32 %sum1, %phi3
+  %is1 = add i32 %sum2, %a
+  %cond1 = icmp ult i32 %is1, 1000
+  br i1 %cond1, label %loop1, label %loop2
+
+loop2:
+  %phi4 = phi i32 [ 63, %loop1 ], [ %phi4.inc, %loop2 ]
+  %phi5 = phi i32 [ 53, %loop1 ], [ %phi5.inc, %loop2 ]
+  %phi6 = phi i32 [ 43, %loop1 ], [ %phi6.inc, %loop2 ]
+  %phi4.inc = add i32 %phi4, 1
+  %phi5.inc = add i32 %phi5, 2
+  %phi6.inc = add i32 %phi6, 3
+  %sum3 = add i32 %phi4, %phi5
+  %sum4 = add i32 %sum3, %phi6
+  %is2 = add i32 %sum4, %b
+  %ec2 = add i32 %is1, %is2
+  %cond2 = icmp ult i32 %ec2, 1000
+  br i1 %cond2, label %loop2, label %exit
+
+exit:
+  %s1 = add i32 %phi1, %is1
+  %s2 = add i32 %is2, %phi4
+  %s3 = add i32 %is1, %phi5
+  %s4 = add i32 %phi2, %is2
+  %s5 = add i32 %is1, %is2
+  %s6 = add i32 %is2, %is1
+  ret void
+}
+
+; Check that we can correctly evaluate a sum of phis+variants from two different
+; loops in any order.
+
+define void @test_02(i32 %a, i32 %b, i32* %p) {
+
+; CHECK-LABEL: Classifying expressions for: @test_02
+; CHECK:       %sum1 = add i32 %phi1, %phi2
+; CHECK-NEXT:  -->  {(%a + %b),+,3}<%loop1>
+; CHECK:       %sum2 = add i32 %sum1, %phi3
+; CHECK-NEXT:  -->  {(6 + %a + %b),+,6}<%loop1>
+; CHECK:       %is1 = add i32 %sum2, %v1
+; CHECK-NEXT:  -->  ({(6 + %a + %b),+,6}<%loop1> + %v1)
+; CHECK:       %sum3 = add i32 %phi4, %phi5
+; CHECK-NEXT:  -->  {(%a + %b),+,3}<%loop2>
+; CHECK:       %sum4 = add i32 %sum3, %phi6
+; CHECK-NEXT:  -->  {(43 + %a + %b),+,6}<%loop2>
+; CHECK:       %is2 = add i32 %sum4, %v2
+; CHECK-NEXT:  -->  ({(43 + %a + %b),+,6}<%loop2> + %v2)
+; CHECK:       %is3 = add i32 %v1, %sum2
+; CHECK-NEXT:  -->  ({(6 + %a + %b),+,6}<%loop1> + %v1)
+; CHECK:       %ec2 = add i32 %is1, %is3
+; CHECK-NEXT:  -->  (2 * ({(6 + %a + %b),+,6}<%loop1> + %v1))
+; CHECK:       %s1 = add i32 %phi1, %is1
+; CHECK-NEXT:  -->  ({(6 + (2 * %a) + %b),+,7}<%loop1> + %v1)
+; CHECK:       %s2 = add i32 %is2, %phi4
+; CHECK-NEXT:  -->  ({(43 + (2 * %a) + %b),+,7}<%loop2> + %v2)
+; CHECK:       %s3 = add i32 %is1, %phi5
+; CHECK-NEXT:  -->  {({(6 + (2 * %b) + %a),+,6}<%loop1> + %v1),+,2}<%loop2>
+; CHECK:       %s4 = add i32 %phi2, %is2
+; CHECK-NEXT:  -->  ({{{{}}(43 + (2 * %b) + %a),+,2}<%loop1>,+,6}<%loop2> + %v2)
+; CHECK:       %s5 = add i32 %is1, %is2
+; CHECK-NEXT:  -->  ({({(49 + (2 * %a) + (2 * %b)),+,6}<%loop1> + %v1),+,6}<%loop2> + %v2)
+; CHECK:       %s6 = add i32 %is2, %is1
+; CHECK-NEXT:  -->  ({({(49 + (2 * %a) + (2 * %b)),+,6}<%loop1> + %v1),+,6}<%loop2> + %v2)
+
+entry:
+  br label %loop1
+
+loop1:
+  %phi1 = phi i32 [ %a, %entry ], [ %phi1.inc, %loop1 ]
+  %phi2 = phi i32 [ %b, %entry ], [ %phi2.inc, %loop1 ]
+  %phi3 = phi i32 [ 6, %entry ], [ %phi3.inc, %loop1 ]
+  %phi1.inc = add i32 %phi1, 1
+  %phi2.inc = add i32 %phi2, 2
+  %phi3.inc = add i32 %phi3, 3
+  %v1 = load i32, i32* %p
+  %sum1 = add i32 %phi1, %phi2
+  %sum2 = add i32 %sum1, %phi3
+  %is1 = add i32 %sum2, %v1
+  %cond1 = icmp ult i32 %is1, 1000
+  br i1 %cond1, label %loop1, label %loop2
+
+loop2:
+  %phi4 = phi i32 [ %a, %loop1 ], [ %phi4.inc, %loop2 ]
+  %phi5 = phi i32 [ %b, %loop1 ], [ %phi5.inc, %loop2 ]
+  %phi6 = phi i32 [ 43, %loop1 ], [ %phi6.inc, %loop2 ]
+  %phi4.inc = add i32 %phi4, 1
+  %phi5.inc = add i32 %phi5, 2
+  %phi6.inc = add i32 %phi6, 3
+  %v2 = load i32, i32* %p
+  %sum3 = add i32 %phi4, %phi5
+  %sum4 = add i32 %sum3, %phi6
+  %is2 = add i32 %sum4, %v2
+  %is3 = add i32 %v1, %sum2
+  %ec2 = add i32 %is1, %is3
+  %cond2 = icmp ult i32 %ec2, 1000
+  br i1 %cond2, label %loop2, label %exit
+
+exit:
+  %s1 = add i32 %phi1, %is1
+  %s2 = add i32 %is2, %phi4
+  %s3 = add i32 %is1, %phi5
+  %s4 = add i32 %phi2, %is2
+  %s5 = add i32 %is1, %is2
+  %s6 = add i32 %is2, %is1
+  ret void
+}
+
+; Mix of previous use cases that demonstrates %s3 can be incorrectly treated as
+; a recurrence of loop1 because of operands order if we pick recurrencies in an
+; incorrect order.
+
+define void @test_03(i32 %a, i32 %b, i32 %c, i32* %p) {
+
+; CHECK-LABEL: Classifying expressions for: @test_03
+; CHECK:       %v1 = load i32, i32* %p
+; CHECK-NEXT:  -->  %v1
+; CHECK:       %s1 = add i32 %phi1, %v1
+; CHECK-NEXT:  -->  {(%a + %v1),+,1}<%loop1>
+; CHECK:       %s2 = add i32 %s1, %b
+; CHECK-NEXT:  -->  {(%a + %b + %v1),+,1}<%loop1>
+; CHECK:       %s3 = add i32 %s2, %phi2
+; CHECK-NEXT:  -->  ({{{{}}((2 * %a) + %b),+,1}<%loop1>,+,2}<%loop2> + %v1)
+
+entry:
+  br label %loop1
+
+loop1:
+  %phi1 = phi i32 [ %a, %entry ], [ %phi1.inc, %loop1 ]
+  %phi1.inc = add i32 %phi1, 1
+  %cond1 = icmp ult i32 %phi1, %c
+  br i1 %cond1, label %loop1, label %loop2
+
+loop2:
+  %phi2 = phi i32 [ %a, %loop1 ], [ %phi2.inc, %loop2 ]
+  %phi2.inc = add i32 %phi2, 2
+  %v1 = load i32, i32* %p
+  %s1 = add i32 %phi1, %v1
+  %s2 = add i32 %s1, %b
+  %s3 = add i32 %s2, %phi2
+  %cond2 = icmp ult i32 %s3, %c
+  br i1 %cond2, label %loop2, label %exit
+
+exit:
+
+  ret void
+}
+
+; Another mix of previous use cases that demonstrates that incorrect picking of
+; a loop for a recurrence may cause a crash of SCEV analysis.
+define void @test_04() {
+
+; CHECK-LABEL: Classifying expressions for: @test_04
+; CHECK:       %tmp = phi i64 [ 2, %bb ], [ %tmp4, %bb3 ]
+; CHECK-NEXT:  -->  {2,+,1}<nuw><nsw><%loop1>
+; CHECK:       %tmp2 = trunc i64 %tmp to i32
+; CHECK-NEXT:  -->  {2,+,1}<%loop1>
+; CHECK:       %tmp4 = add nuw nsw i64 %tmp, 1
+; CHECK-NEXT:  -->  {3,+,1}<nuw><%loop1>
+; CHECK:       %tmp7 = phi i64 [ %tmp15, %loop2 ], [ 2, %loop1 ]
+; CHECK-NEXT:  -->  {2,+,1}<nuw><nsw><%loop2>
+; CHECK:       %tmp10 = sub i64 %tmp9, %tmp7
+; CHECK-NEXT:  -->  ((sext i8 %tmp8 to i64) + {-2,+,-1}<nw><%loop2>)
+; CHECK:       %tmp11 = add i64 %tmp10, undef
+; CHECK-NEXT:  -->  ((sext i8 %tmp8 to i64) + {(-2 + undef),+,-1}<nw><%loop2>)
+; CHECK:       %tmp13 = trunc i64 %tmp11 to i32
+; CHECK-NEXT:  -->  ((sext i8 %tmp8 to i32) + {(trunc i64 (-2 + undef) to i32),+,-1}<%loop2>)
+; CHECK:       %tmp14 = sub i32 %tmp13, %tmp2
+; CHECK-NEXT:  -->  ((sext i8 %tmp8 to i32) + {{{{}}(-2 + (trunc i64 (-2 + undef) to i32)),+,-1}<%loop1>,+,-1}<%loop2>)
+; CHECK:       %tmp15 = add nuw nsw i64 %tmp7, 1
+; CHECK-NEXT:  -->  {3,+,1}<nuw><nsw><%loop2>
+
+bb:
+  br label %loop1
+
+loop1:
+  %tmp = phi i64 [ 2, %bb ], [ %tmp4, %bb3 ]
+  %tmp2 = trunc i64 %tmp to i32
+  br i1 undef, label %loop2, label %bb3
+
+bb3:
+  %tmp4 = add nuw nsw i64 %tmp, 1
+  br label %loop1
+
+bb5:
+  ret void
+
+loop2:
+  %tmp7 = phi i64 [ %tmp15, %loop2 ], [ 2, %loop1 ]
+  %tmp8 = load i8, i8 addrspace(1)* undef, align 1
+  %tmp9 = sext i8 %tmp8 to i64
+  %tmp10 = sub i64 %tmp9, %tmp7
+  %tmp11 = add i64 %tmp10, undef
+  %tmp13 = trunc i64 %tmp11 to i32
+  %tmp14 = sub i32 %tmp13, %tmp2
+  %tmp15 = add nuw nsw i64 %tmp7, 1
+  %tmp16 = icmp slt i64 %tmp15, %tmp
+  br i1 %tmp16, label %loop2, label %bb5
+}
+
+@A = weak global [1000 x i32] zeroinitializer, align 32
+
+; Demonstrate a situation when we can add two recs with different degrees from
+; the same loop.
+define void @test_05(i32 %N) {
+
+; CHECK-LABEL: Classifying expressions for: @test_05
+; CHECK:       %SQ = mul i32 %i.0, %i.0
+; CHECK-NEXT:  -->  {4,+,5,+,2}<%bb3>
+; CHECK:       %tmp4 = mul i32 %i.0, 2
+; CHECK-NEXT:  -->  {4,+,2}<%bb3>
+; CHECK:       %tmp5 = sub i32 %SQ, %tmp4
+; CHECK-NEXT:  -->  {0,+,3,+,2}<%bb3>
+
+entry:
+        %"alloca point" = bitcast i32 0 to i32           ; <i32> [#uses=0]
+        br label %bb3
+
+bb:             ; preds = %bb3
+        %tmp = getelementptr [1000 x i32], [1000 x i32]* @A, i32 0, i32 %i.0          ; <i32*> [#uses=1]
+        store i32 123, i32* %tmp
+        %tmp2 = add i32 %i.0, 1         ; <i32> [#uses=1]
+        br label %bb3
+
+bb3:            ; preds = %bb, %entry
+        %i.0 = phi i32 [ 2, %entry ], [ %tmp2, %bb ]            ; <i32> [#uses=3]
+        %SQ = mul i32 %i.0, %i.0
+        %tmp4 = mul i32 %i.0, 2
+        %tmp5 = sub i32 %SQ, %tmp4
+        %tmp3 = icmp sle i32 %tmp5, 9999          ; <i1> [#uses=1]
+        br i1 %tmp3, label %bb, label %bb5
+
+bb5:            ; preds = %bb3
+        br label %return
+
+return:         ; preds = %bb5
+        ret void
+}
+
+; Check that we can add Phis from different loops with different nesting, nested
+; loop comes first.
+define void @test_06() {
+
+; CHECK-LABEL: Classifying expressions for: @test_06
+; CHECK:       %s1 = add i32 %phi1, %phi2
+; CHECK-NEXT:  -->  {{{{}}30,+,1}<%loop1>,+,2}<%loop2>
+; CHECK:       %s2 = add i32 %phi2, %phi1
+; CHECK-NEXT:  -->  {{{{}}30,+,1}<%loop1>,+,2}<%loop2>
+; CHECK:       %s3 = add i32 %phi1, %phi3
+; CHECK-NEXT:  -->  {{{{}}40,+,1}<%loop1>,+,3}<%loop3>
+; CHECK:       %s4 = add i32 %phi3, %phi1
+; CHECK-NEXT:  -->  {{{{}}40,+,1}<%loop1>,+,3}<%loop3>
+; CHECK:       %s5 = add i32 %phi2, %phi3
+; CHECK-NEXT:  -->  {{{{}}50,+,2}<%loop2>,+,3}<%loop3>
+; CHECK:       %s6 = add i32 %phi3, %phi2
+; CHECK-NEXT:  -->  {{{{}}50,+,2}<%loop2>,+,3}<%loop3>
+
+entry:
+  br label %loop1
+
+loop1:
+  %phi1 = phi i32 [ 10, %entry ], [ %phi1.inc, %loop1.exit ]
+  br label %loop2
+
+loop2:
+  %phi2 = phi i32 [ 20, %loop1 ], [ %phi2.inc, %loop2 ]
+  %phi2.inc = add i32 %phi2, 2
+  %cond2 = icmp ult i32 %phi2.inc, 1000
+  br i1 %cond2, label %loop2, label %loop1.exit
+
+loop1.exit:
+  %phi1.inc = add i32 %phi1, 1
+  %cond1 = icmp ult i32 %phi1.inc, 1000
+  br i1 %cond1, label %loop1, label %loop3
+
+loop3:
+  %phi3 = phi i32 [ 30, %loop1.exit ], [ %phi3.inc, %loop3 ]
+  %phi3.inc = add i32 %phi3, 3
+  %cond3 = icmp ult i32 %phi3.inc, 1000
+  br i1 %cond3, label %loop3, label %exit
+
+exit:
+  %s1 = add i32 %phi1, %phi2
+  %s2 = add i32 %phi2, %phi1
+  %s3 = add i32 %phi1, %phi3
+  %s4 = add i32 %phi3, %phi1
+  %s5 = add i32 %phi2, %phi3
+  %s6 = add i32 %phi3, %phi2
+  ret void
+}
+
+; Check that we can add Phis from different loops with different nesting, nested
+; loop comes second.
+define void @test_07() {
+
+; CHECK-LABEL: Classifying expressions for: @test_07
+; CHECK:       %s1 = add i32 %phi1, %phi2
+; CHECK-NEXT:  -->  {{{{}}30,+,1}<%loop1>,+,2}<%loop2>
+; CHECK:       %s2 = add i32 %phi2, %phi1
+; CHECK-NEXT:  -->  {{{{}}30,+,1}<%loop1>,+,2}<%loop2>
+; CHECK:       %s3 = add i32 %phi1, %phi3
+; CHECK-NEXT:  -->  {{{{}}40,+,3}<%loop3>,+,1}<%loop1>
+; CHECK:       %s4 = add i32 %phi3, %phi1
+; CHECK-NEXT:  -->  {{{{}}40,+,3}<%loop3>,+,1}<%loop1>
+; CHECK:       %s5 = add i32 %phi2, %phi3
+; CHECK-NEXT:  -->  {{{{}}50,+,3}<%loop3>,+,2}<%loop2>
+; CHECK:       %s6 = add i32 %phi3, %phi2
+; CHECK-NEXT:  -->  {{{{}}50,+,3}<%loop3>,+,2}<%loop2>
+
+entry:
+  br label %loop3
+
+loop3:
+  %phi3 = phi i32 [ 30, %entry ], [ %phi3.inc, %loop3 ]
+  %phi3.inc = add i32 %phi3, 3
+  %cond3 = icmp ult i32 %phi3.inc, 1000
+  br i1 %cond3, label %loop3, label %loop1
+
+loop1:
+  %phi1 = phi i32 [ 10, %loop3 ], [ %phi1.inc, %loop1.exit ]
+  br label %loop2
+
+loop2:
+  %phi2 = phi i32 [ 20, %loop1 ], [ %phi2.inc, %loop2 ]
+  %phi2.inc = add i32 %phi2, 2
+  %cond2 = icmp ult i32 %phi2.inc, 1000
+  br i1 %cond2, label %loop2, label %loop1.exit
+
+loop1.exit:
+  %phi1.inc = add i32 %phi1, 1
+  %cond1 = icmp ult i32 %phi1.inc, 1000
+  br i1 %cond1, label %exit, label %loop1
+
+exit:
+  %s1 = add i32 %phi1, %phi2
+  %s2 = add i32 %phi2, %phi1
+  %s3 = add i32 %phi1, %phi3
+  %s4 = add i32 %phi3, %phi1
+  %s5 = add i32 %phi2, %phi3
+  %s6 = add i32 %phi3, %phi2
+  ret void
+}