[Polly] [DependenceInfo] change WAR, WAW generation to correct semantics

= Change of WAR, WAW generation: =

- `buildFlow(Sink, MustSource, MaySource, Sink)` treates any flow of the form
    `sink <- may source <- must source` as a *may* dependence.

- we used to call:
```lang=cpp, name=old-flow-call.cpp
Flow = buildFlow(MustWrite, MustWrite, Read, Schedule);
WAW = isl_union_flow_get_must_dependence(Flow);
WAR = isl_union_flow_get_may_dependence(Flow);
```

- This caused some WAW dependences to be treated as WAR dependences.
- Incorrect semantics.

- Now, we call WAR and WAW correctly.

== Correct WAW: ==
```lang=cpp, name=new-waw-call.cpp
   Flow = buildFlow(Write, MustWrite, MayWrite, Schedule);
   WAW = isl_union_flow_get_may_dependence(Flow);
   isl_union_flow_free(Flow);
```

== Correct WAR: ==
```lang=cpp, name=new-war-call.cpp
    Flow = buildFlow(Write, Read, MustaWrite, Schedule);
    WAR = isl_union_flow_get_must_dependence(Flow);
    isl_union_flow_free(Flow);
```

- We want the "shortest" WAR possible (exact dependences).
- We mark all the *must-writes* as may-source, reads as must-souce.
- Then, we ask for *must* dependence.
- This removes all the reads that flow through a *must-write*
  before reaching a sink.
- Note that we only block ealier writes with *must-writes*. This is
  intuitively correct, as we do not want may-writes to block
  must-writes.
- Leaves us with direct (R -> W).

- This affects reduction generation since RED is built using WAW and WAR.

= New StrictWAW for Reductions: =

- We used to call:
```lang=cpp,name=old-waw-war-call.cpp
      Flow = buildFlow(MustWrite, MustWrite, Read, Schedule);
      WAW = isl_union_flow_get_must_dependence(Flow);
      WAR = isl_union_flow_get_may_dependence(Flow);
```

- This *is* the right model of WAW we need for reductions, just not in general.
- Reductions need to track only *strict* WAW, without any interfering reductions.

= Explanation: Why the new WAR dependences in tests are correct: =

- We no longer set WAR = WAR - WAW
- Hence, we will have WAR dependences that were originally removed.
- These may look incorrect, but in fact make sense.

== Code: ==
```lang=llvm, name=new-war-dependence.ll
  ;    void manyreductions(long *A) {
  ;      for (long i = 0; i < 1024; i++)
  ;        for (long j = 0; j < 1024; j++)
  ; S0:          *A += 42;
  ;
  ;      for (long i = 0; i < 1024; i++)
  ;        for (long j = 0; j < 1024; j++)
  ; S1:          *A += 42;
  ;
```
=== WAR dependence: ===
  {  S0[1023, 1023] -> S1[0, 0] }

- Between `S0[1023, 1023]` and `S1[0, 0]`, we will have the dependences:

```lang=cpp, name=dependence-incorrect, counterexample
        S0[1023, 1023]:
    *-- tmp = *A (load0)--*
WAR 2   add = tmp + 42    |
    *-> *A = add (store0) |
                         WAR 1
        S1[0, 0]:         |
        tmp = *A (load1)  |
        add = tmp + 42    |
        A = add (store1)<-*
```

- One may assume that WAR2 *hides* WAR1 (since store0 happens before
  store1). However, within a statement, Polly has no idea about the
  ordering of loads and stores.

- Hence, according to Polly, the code may have looked like this:
```lang=cpp, name=dependence-correct
    S0[1023, 1023]:
    A = add (store0)
    tmp = A (load0) ---*
    add = A + 42       |
                     WAR 1
    S1[0, 0]:          |
    tmp = A (load1)    |
    add = A + 42       |
    A = add (store1) <-*
```

- So, Polly  generates (correct) WAR dependences. It does not make sense
  to remove these dependences, since they are correct with respect to
  Polly's model.

    Reviewers: grosser, Meinersbur

    tags: #polly

    Differential revision: https://reviews.llvm.org/D31386

llvm-svn: 299429

polly/lib/Analysis/DependenceInfo.cpp

@@ -289,7 +289,8 @@ static __isl_give isl_union_flow *buildFlow(__isl_keep isl_union_map *Snk,
   isl_union_access_info *AI;
 
   AI = isl_union_access_info_from_sink(isl_union_map_copy(Snk));
-  AI = isl_union_access_info_set_may_source(AI, isl_union_map_copy(MaySrc));
+  if (MaySrc)
+    AI = isl_union_access_info_set_may_source(AI, isl_union_map_copy(MaySrc));
   if (Src)
     AI = isl_union_access_info_set_must_source(AI, isl_union_map_copy(Src));
   AI = isl_union_access_info_set_schedule(AI, isl_schedule_copy(Schedule));
@@ -358,55 +359,132 @@ void Dependences::calculateDependences(Scop &S) {
         dbgs() << "MayWrite: " << MayWrite << "\n";
         dbgs() << "Schedule: " << Schedule << "\n");
 
+  isl_union_map *StrictWAW = nullptr;
   {
     IslMaxOperationsGuard MaxOpGuard(IslCtx.get(), OptComputeOut);
 
     RAW = WAW = WAR = RED = nullptr;
+    isl_union_map *Write = isl_union_map_union(isl_union_map_copy(MustWrite),
+                                               isl_union_map_copy(MayWrite));
+
+    // We are interested in detecting reductions that do not have intermediate
+    // computations that are captured by other statements.
+    //
+    // Example:
+    // void f(int *A, int *B) {
+    //     for(int i = 0; i <= 100; i++) {
+    //
+    //            *-WAR (S0[i] -> S0[i + 1] 0 <= i <= 100)------------*
+    //            |                                                   |
+    //            *-WAW (S0[i] -> S0[i + 1] 0 <= i <= 100)------------*
+    //            |                                                   |
+    //            v                                                   |
+    //     S0:    *A += i; >------------------*-----------------------*
+    //                                        |
+    //         if (i >= 98) {          WAR (S0[i] -> S1[i]) 98 <= i <= 100
+    //                                        |
+    //     S1:        *B = *A; <--------------*
+    //         }
+    //     }
+    // }
+    //
+    // S0[0 <= i <= 100] has a reduction. However, the values in
+    // S0[98 <= i <= 100] is captured in S1[98 <= i <= 100].
+    // Since we allow free reordering on our reduction dependences, we need to
+    // remove all instances of a reduction statement that have data dependences
+    // orignating from them.
+    // In the case of the example, we need to remove S0[98 <= i <= 100] from
+    // our reduction dependences.
+    //
+    // When we build up the WAW dependences that are used to detect reductions,
+    // we consider only **Writes that have no intermediate Reads**.
+    //
+    // `isl_union_flow_get_must_dependence` gives us dependences of the form:
+    // (sink <- must_source).
+    //
+    // It *will not give* dependences of the form:
+    // 1. (sink <- ... <- may_source <- ... <- must_source)
+    // 2. (sink <- ... <- must_source <- ... <- must_source)
+    //
+    // For a detailed reference on ISL's flow analysis, see:
+    // "Presburger Formulas and Polyhedral Compilation" - Approximate Dataflow
+    //  Analysis.
+    //
+    // Since we set "Write" as a must-source, "Read" as a may-source, and ask
+    // for must dependences, we get all Writes to Writes that **do not flow
+    // through a Read**.
+    //
+    // ScopInfo::checkForReductions makes sure that if something captures
+    // the reduction variable in the same basic block, then it is rejected
+    // before it is even handed here. This makes sure that there is exactly
+    // one read and one write to a reduction variable in a Statement.
+    // Example:
+    //     void f(int *sum, int A[N], int B[N]) {
+    //       for (int i = 0; i < N; i++) {
+    //         *sum += A[i]; < the store and the load is not tagged as a
+    //         B[i] = *sum;  < reductionLike acccess due to the overlap.
+    //       }
+    //     }
+
+    isl_union_flow *Flow = buildFlow(Write, Write, Read, Schedule);
+    StrictWAW = isl_union_flow_get_must_dependence(Flow);
+    isl_union_flow_free(Flow);
 
     if (OptAnalysisType == VALUE_BASED_ANALYSIS) {
-      isl_union_flow *Flow;
-
       Flow = buildFlow(Read, MustWrite, MayWrite, Schedule);
-
       RAW = isl_union_flow_get_may_dependence(Flow);
       isl_union_flow_free(Flow);
 
-      Flow = buildFlow(MustWrite, MustWrite, Read, Schedule);
+      Flow = buildFlow(Write, MustWrite, MayWrite, Schedule);
-
+      WAW = isl_union_flow_get_may_dependence(Flow);
-      WAW = isl_union_flow_get_must_dependence(Flow);
-      WAR = isl_union_flow_get_may_dependence(Flow);
-
-      // This subtraction is needed to obtain the same results as were given by
-      // isl_union_map_compute_flow. For large sets this may add some
-      // compile-time cost. As there does not seem to be a need to distinguish
-      // between WAW and WAR, refactoring Polly to only track general non-flow
-      // dependences may improve performance.
-      WAR = isl_union_map_subtract(WAR, isl_union_map_copy(WAW));
-
       isl_union_flow_free(Flow);
+
+      // We need exact WAR dependences. That is, if there are
+      // dependences of the form:
+      // must-W2 (sink) <- must-W1 (sink) <- R (source)
+      // We wish to generate *ONLY*:
+      // { R -> W1 },
+      // NOT:
+      // { R -> W2, R -> W1 }
+      //
+      // However, in the case of may-writes, we do *not* wish to allow
+      // may-writes to block must-writes. This makes sense, since perhaps the
+      // may-write will not happen. In that case, the exact dependence will
+      // be the (read -> must-write).
+      // Example:
+      // must-W2 (sink) <- may-W1 (sink) <- R (source)
+      // We wish to generate:
+      // { R-> W1, R -> W2 }
+      //
+      //
+      // To achieve this, we use the fact that *must* dependences are not
+      // allowed to flow through the may-source.
+      // Since we set the may-source to MustWrite, we are guarenteed that
+      // only the exact ("shortest") (must-write -> read) is captured.
+      // Any number of intermediate may-writes are allowed.
+      Flow = buildFlow(Write, Read, MustWrite, Schedule);
+      WAR = isl_union_flow_get_must_dependence(Flow);
+      isl_union_flow_free(Flow);
+
+      isl_union_map_free(Write);
       isl_schedule_free(Schedule);
     } else {
       isl_union_flow *Flow;
 
-      isl_union_map *Write = isl_union_map_union(isl_union_map_copy(MustWrite),
-                                                 isl_union_map_copy(MayWrite));
-
       Flow = buildFlow(Read, nullptr, Write, Schedule);
-
       RAW = isl_union_flow_get_may_dependence(Flow);
       isl_union_flow_free(Flow);
 
       Flow = buildFlow(Write, nullptr, Read, Schedule);
-
       WAR = isl_union_flow_get_may_dependence(Flow);
       isl_union_flow_free(Flow);
 
       Flow = buildFlow(Write, nullptr, Write, Schedule);
-
       WAW = isl_union_flow_get_may_dependence(Flow);
       isl_union_flow_free(Flow);
-      isl_schedule_free(Schedule);
+
       isl_union_map_free(Write);
+      isl_schedule_free(Schedule);
     }
 
     isl_union_map_free(MustWrite);
@@ -424,7 +502,8 @@ void Dependences::calculateDependences(Scop &S) {
     isl_union_map_free(RAW);
     isl_union_map_free(WAW);
     isl_union_map_free(WAR);
-    RAW = WAW = WAR = nullptr;
+    isl_union_map_free(StrictWAW);
+    RAW = WAW = WAR = StrictWAW = nullptr;
     isl_ctx_reset_error(IslCtx.get());
   }
 
@@ -435,6 +514,7 @@ void Dependences::calculateDependences(Scop &S) {
     RED = isl_union_map_empty(isl_union_map_get_space(RAW));
     TC_RED = isl_union_map_empty(isl_union_set_get_space(TaggedStmtDomain));
     isl_union_set_free(TaggedStmtDomain);
+    isl_union_map_free(StrictWAW);
     return;
   }
 
@@ -457,9 +537,9 @@ void Dependences::calculateDependences(Scop &S) {
   // 2) Intersect them with the actual RAW & WAW dependences to the get the
   //    actual reduction dependences. This will ensure the load/store memory
   //    addresses were __identical__ in the two iterations of the statement.
-  // 3) Relax the original RAW and WAW dependences by subtracting the actual
+  // 3) Relax the original RAW, WAW and WAR dependences by subtracting the
-  //    reduction dependences. Binary reductions (sum += A[i]) cause both, and
+  //    actual reduction dependences. Binary reductions (sum += A[i]) cause
-  //    the same, RAW and WAW dependences.
+  //    the same, RAW, WAW and WAR dependences.
   // 4) Add the privatization dependences which are widened versions of
   //    already present dependences. They model the effect of manual
   //    privatization at the outermost possible place (namely after the last
@@ -480,13 +560,14 @@ void Dependences::calculateDependences(Scop &S) {
 
   // Step 2)
   RED = isl_union_map_intersect(RED, isl_union_map_copy(RAW));
-  RED = isl_union_map_intersect(RED, isl_union_map_copy(WAW));
+  RED = isl_union_map_intersect(RED, StrictWAW);
 
   if (!isl_union_map_is_empty(RED)) {
 
     // Step 3)
     RAW = isl_union_map_subtract(RAW, isl_union_map_copy(RED));
     WAW = isl_union_map_subtract(WAW, isl_union_map_copy(RED));
+    WAR = isl_union_map_subtract(WAR, isl_union_map_copy(RED));
 
     // Step 4)
     addPrivatizationDependences();

polly/lib/Transform/ScheduleOptimizer.cpp

@@ -781,12 +781,6 @@ static bool containsOnlyMatrMultAcc(__isl_keep isl_map *PartialSchedule,
 ///         and false, otherwise.
 static bool containsOnlyMatMulDep(__isl_keep isl_map *Schedule,
                                   const Dependences *D, int &Pos) {
-  auto *WAR = D->getDependences(Dependences::TYPE_WAR);
-  if (!isl_union_map_is_empty(WAR)) {
-    isl_union_map_free(WAR);
-    return false;
-  }
-  isl_union_map_free(WAR);
   auto *Dep = D->getDependences(Dependences::TYPE_RAW);
   auto *Red = D->getDependences(Dependences::TYPE_RED);
   if (Red)

polly/test/DependenceInfo/different_schedule_dimensions.ll

@@ -6,7 +6,7 @@
 ; CHECK: RAW dependences:
 ; CHECK:   { Stmt_bb9[0] -> Stmt_bb10[0] }
 ; CHECK: WAR dependences:
-; CHECK:   {  }
+; CHECK:   { Stmt_bb3[0] -> Stmt_bb10[0] }
 ; CHECK: WAW dependences:
 ; CHECK:   { Stmt_bb3[0] -> Stmt_bb10[0] }
 ; CHECK: Reduction dependences:
@@ -15,7 +15,7 @@
 ; FUNC: RAW dependences:
 ; FUNC-NEXT:   { Stmt_bb9[0] -> Stmt_bb10[0]; [Stmt_bb9[0] -> Stmt_bb9_Write0_MemRef_tmp11[]] -> [Stmt_bb10[0] -> Stmt_bb10_Read0_MemRef_tmp11[]] }
 ; FUNC-NEXT: WAR dependences:
-; FUNC-NEXT:   {  }
+; FUNC-NEXT:   { Stmt_bb3[0] -> Stmt_bb10[0]; [Stmt_bb3[0] -> Stmt_bb3_Read0_MemRef_arg1[]] -> [Stmt_bb10[0] -> Stmt_bb10_Write1_MemRef_arg1[]] }
 ; FUNC-NEXT: WAW dependences:
 ; FUNC-NEXT:   { Stmt_bb3[0] -> Stmt_bb10[0]; [Stmt_bb3[0] -> Stmt_bb3_Write1_MemRef_arg1[]] -> [Stmt_bb10[0] -> Stmt_bb10_Write1_MemRef_arg1[]] }
 ; FUNC-NEXT: Reduction dependences:

polly/test/DependenceInfo/do_pluto_matmult.ll

@@ -69,7 +69,7 @@ do.end45:                                         ; preds = %do.cond42
 ; VALUE:      RAW dependences:
 ; VALUE-NEXT:     { Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2[i0, i1, 1 + i2] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34 }
 ; VALUE-NEXT: WAR dependences:
-; VALUE-NEXT:     {  }
+; VALUE-NEXT: { Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2[i0, i1, 1 + i2] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34 }
 ; VALUE-NEXT: WAW dependences:
 ; VALUE-NEXT:     { Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2[i0, i1, 1 + i2] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34 }
 
@@ -83,7 +83,7 @@ do.end45:                                         ; preds = %do.cond42
 ; FUNC-VALUE:      RAW dependences:
 ; FUNC-VALUE-NEXT:     { [Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2_Write3_MemRef_C[]] -> [Stmt_do_body2[i0, i1, 1 + i2] -> Stmt_do_body2_Read0_MemRef_C[]] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34; Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2[i0, i1, 1 + i2] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34 }
 ; FUNC-VALUE-NEXT: WAR dependences:
-; FUNC-VALUE-NEXT:     {  }
+; FUNC-VALUE-NEXT:     { [Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2_Read0_MemRef_C[]] -> [Stmt_do_body2[i0, i1, 1 + i2] -> Stmt_do_body2_Write3_MemRef_C[]] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34; Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2[i0, i1, 1 + i2] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34 }
 ; FUNC-VALUE-NEXT: WAW dependences:
 ; FUNC-VALUE-NEXT:     { [Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2_Write3_MemRef_C[]] -> [Stmt_do_body2[i0, i1, 1 + i2] -> Stmt_do_body2_Write3_MemRef_C[]] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34; Stmt_do_body2[i0, i1, i2] -> Stmt_do_body2[i0, i1, 1 + i2] : 0 <= i0 <= 35 and 0 <= i1 <= 35 and 0 <= i2 <= 34 }
 

polly/test/DependenceInfo/generate_may_write_dependence_info.ll

@@ -58,10 +58,10 @@ for.end:                                          ; preds = %for.cond
 ; VALUE: RAW dependences:
 ; VALUE-NEXT:   { Stmt_A_must_write_20[i0] -> Stmt_B_write_from_A[i0] : 0 <= i0 <= 2999; Stmt_compute_i_square__TO__B_write_from_A[i0] -> Stmt_B_write_from_A[i0] : 0 <= i0 <= 2999 }
 ; VALUE-NEXT: WAR dependences:
-; VALUE-NEXT:   { Stmt_A_must_write_20[i0] -> Stmt_A_must_write_42[i0] : 0 <= i0 <= 2999; Stmt_B_write_from_A[i0] -> Stmt_A_must_write_42[i0] : 0 <= i0 <= 2999 }
+; VALUE-NEXT:   { Stmt_B_write_from_A[i0] -> Stmt_A_must_write_42[i0] : 0 <= i0 <= 2999 }
 ; VALUE-NEXT: WAW dependences:
-; VALUE-NEXT:   {  }
+; VALUE-NEXT:   { Stmt_compute_i_square__TO__B_write_from_A[i0] -> Stmt_A_must_write_42[i0] : 0 <= i0 <= 2999; Stmt_A_must_write_20[i0] -> Stmt_A_must_write_42[i0] : 0 <= i0 <= 2999; Stmt_A_must_write_20[i0] -> Stmt_compute_i_square__TO__B_write_from_A[i0] : 0 <= i0 <= 2999 }
 ; VALUE-NEXT: Reduction dependences:
 ; VALUE-NEXT:   {  }
 ; VALUE-NEXT: Transitive closure of reduction dependences:
-; VALUE-NEXT:   {  }
+; VALUE-NEXT:   {  }

polly/test/DependenceInfo/may_writes_do_not_block_must_writes_for_war.ll

@@ -0,0 +1,73 @@
+; RUN: opt %loadPolly -polly-dependences -analyze < %s | FileCheck %s
+;
+; Verify that the presence of a may-write (S1) between a read (S0) and a
+; must-write (S2) does not block the generation of RAW dependences. This makes
+; sure that we capture as many RAW dependences as possible.
+;
+; For this example, we want both (S0(Read) -> S1 (May-Write)) as well as
+; (S0(Read) -> S2(Must-Write)).
+;
+; CHECK: WAR dependences:
+; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S2[i0] : 0 < i0 <= 2; Stmt_S0[i0] -> Stmt_if_end__TO__S2[i0] : 0 < i0 <= 2 }
+;
+;
+;    static const int N = 3000;
+;
+;    void f(int *sum, int *A, int *B, int *out) {
+;      for (int i = 0; i <= 2; i++) {
+;        if (i) {
+; S0:          *out += *sum;
+;        }
+;
+;        if (i * i) {
+; S1:          *sum = *A;
+;        }
+; S2:        *sum = *B;
+;      }
+;    }
+;
+target datalayout = "e-m:o-i64:64-f80:128-n8:16:32:64-S128"
+
+define void @f(i32* %sum, i32* %A, i32* %B, i32* %out) {
+entry:
+  br label %for.cond
+
+for.cond:                                         ; preds = %for.inc, %entry
+  %i.0 = phi i32 [ 0, %entry ], [ %inc, %for.inc ]
+  %exitcond = icmp ne i32 %i.0, 3
+  br i1 %exitcond, label %for.body, label %for.end
+
+for.body:                                         ; preds = %for.cond
+  %tobool = icmp eq i32 %i.0, 0
+  br i1 %tobool, label %if.end, label %S0
+
+S0:                                          ; preds = %for.body
+  %tmp = load i32, i32* %sum, align 4
+  %tmp1 = load i32, i32* %out, align 4
+  %add = add nsw i32 %tmp1, %tmp
+  store i32 %add, i32* %out, align 4
+  br label %if.end
+
+if.end:                                           ; preds = %for.body, %S0
+  %mul = mul nsw i32 %i.0, %i.0
+  %tobool1 = icmp eq i32 %mul, 0
+  br i1 %tobool1, label %S2, label %S1
+
+S1:                                         ; preds = %if.end
+  %tmp2 = load i32, i32* %A, align 4
+  store i32 %tmp2, i32* %sum, align 4
+  br label %S2
+
+S2:                                          ; preds = %if.end, %S1
+  %tmp3 = load i32, i32* %B, align 4
+  store i32 %tmp3, i32* %sum, align 4
+  br label %for.inc
+
+for.inc:                                          ; preds = %S2
+  %inc = add nuw nsw i32 %i.0, 1
+  br label %for.cond
+
+for.end:                                          ; preds = %for.cond
+  ret void
+}
+

polly/test/DependenceInfo/reduction_dependences_equal_non_reduction_dependences.ll

@@ -6,7 +6,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_for_body[i0] -> Stmt_for_body[1 + i0] : 0 <= i0 <= 1022 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:     { Stmt_for_body[i0] -> Stmt_for_body[1 + i0] : 0 <= i0 <= 1022 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_for_body[i0] -> Stmt_for_body[1 + i0] : 0 <= i0 <= 1022 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_multiple_reductions_2.ll

@@ -12,7 +12,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S1[i0, o1] : 0 <= i0 <= 1023 and 0 <= o1 <= 1023; Stmt_S2[i0, i1] -> Stmt_S3[i0] : 0 <= i0 <= 1023 and 0 <= i1 <= 1023; Stmt_S3[i0] -> Stmt_S0[1 + i0] : 0 <= i0 <= 1022; Stmt_S1[i0, 1023] -> Stmt_S2[i0, o1] : 0 <= i0 <= 1023 and 0 <= o1 <= 1023; Stmt_S1[i0, i1] -> Stmt_S2[i0, 0] : 0 <= i0 <= 1023 and 0 <= i1 <= 1022 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S1[i0, o1] : 0 <= i0 <= 1023 and 0 <= o1 <= 1023; Stmt_S2[i0, i1] -> Stmt_S3[i0] : 0 <= i0 <= 1023 and 0 <= i1 <= 1023; Stmt_S3[i0] -> Stmt_S0[1 + i0] : 0 <= i0 <= 1022; Stmt_S1[i0, 1023] -> Stmt_S2[i0, o1] : 0 <= i0 <= 1023 and 0 <= o1 <= 1023; Stmt_S1[i0, i1] -> Stmt_S2[i0, 0] : 0 <= i0 <= 1023 and 0 <= i1 <= 1022 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S1[i0, o1] : 0 <= i0 <= 1023 and 0 <= o1 <= 1023; Stmt_S2[i0, i1] -> Stmt_S3[i0] : 0 <= i0 <= 1023 and 0 <= i1 <= 1023; Stmt_S3[i0] -> Stmt_S0[1 + i0] : 0 <= i0 <= 1022; Stmt_S1[i0, 1023] -> Stmt_S2[i0, o1] : 0 <= i0 <= 1023 and 0 <= o1 <= 1023; Stmt_S1[i0, i1] -> Stmt_S2[i0, 0] : 0 <= i0 <= 1023 and 0 <= i1 <= 1022 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_privatization_deps.ll

@@ -3,9 +3,9 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S1[o0, i0 - o0] : i0 <= 1023 and 0 <= o0 <= i0; Stmt_S1[i0, i1] -> Stmt_S2[-1 + i0 + i1] : 0 <= i0 <= 1023 and i1 >= 0 and -i0 < i1 <= 1024 - i0 and i1 <= 1023 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     { Stmt_S2[i0] -> Stmt_S2[1 + i0] : 0 <= i0 <= 1022; Stmt_S1[i0, i1] -> Stmt_S2[i0 + i1] : i0 >= 0 and i1 >= 0 and -i0 < i1 <= 1023 - i0 }
+; CHECK-NEXT:     { Stmt_S2[i0] -> Stmt_S2[1 + i0] : 0 <= i0 <= 1022; Stmt_S1[0, 0] -> Stmt_S2[0] }
 ; CHECK-NEXT: WAW dependences:
-; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S1[o0, i0 - o0] : i0 <= 1023 and 0 <= o0 <= i0; Stmt_S1[0, 0] -> Stmt_S2[0] }
+; CHECK-NEXT:     { Stmt_S0[i0] -> Stmt_S1[o0, i0 - o0] : i0 <= 1023 and 0 <= o0 <= i0; Stmt_S1[i0, i1] -> Stmt_S2[i0 + i1] : i0 >= 0 and 0 <= i1 <= 1023 - i0 }
 ; CHECK-NEXT: Reduction dependences:
 ; CHECK-NEXT:     { Stmt_S1[i0, i1] -> Stmt_S1[1 + i0, -1 + i1] : 0 <= i0 <= 1022 and 0 < i1 <= 1023 }
 ;

polly/test/DependenceInfo/reduction_privatization_deps_2.ll

@@ -6,7 +6,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S3[i0] -> Stmt_S2[1 + i0, o1] : 0 <= i0 <= 97 and 0 <= o1 <= 99; Stmt_S1[i0] -> Stmt_S3[i0] : 0 <= i0 <= 98 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:     { Stmt_S3[i0] -> Stmt_S2[1 + i0, o1] : 0 <= i0 <= 97 and 0 <= o1 <= 99; Stmt_S1[i0] -> Stmt_S3[i0] : 0 <= i0 <= 98 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_S3[i0] -> Stmt_S2[1 + i0, o1] : 0 <= i0 <= 97 and 0 <= o1 <= 99; Stmt_S1[i0] -> Stmt_S3[i0] : 0 <= i0 <= 98 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_privatization_deps_3.ll

@@ -3,7 +3,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0, i1] -> Stmt_S3[o0] : i1 <= 1 - i0 and -i1 < o0 <= 1 and o0 <= 1 + i0 - i1; Stmt_S3[i0] -> Stmt_S2[o0, 1 - i0] : 0 <= i0 <= 1 and i0 < o0 <= 98; Stmt_S1[i0] -> Stmt_S3[2 + i0] : 0 <= i0 <= 96 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:   { Stmt_S2[i0, i1] -> Stmt_S3[o0] : i1 <= 1 - i0 and -i1 < o0 <= 1 and o0 <= 1 + i0 - i1; Stmt_S3[i0] -> Stmt_S2[o0, 1 - i0] : 0 <= i0 <= 1 and i0 < o0 <= 98; Stmt_S1[i0] -> Stmt_S3[2 + i0] : 0 <= i0 <= 96 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0, i1] -> Stmt_S3[o0] : i1 <= 1 - i0 and -i1 < o0 <= 1 and o0 <= 1 + i0 - i1; Stmt_S3[i0] -> Stmt_S2[o0, 1 - i0] : 0 <= i0 <= 1 and i0 < o0 <= 98; Stmt_S1[i0] -> Stmt_S3[2 + i0] : 0 <= i0 <= 96 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_privatization_deps_4.ll

@@ -3,7 +3,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0, i1] -> Stmt_S1[i1] : i0 >= 0 and i0 < i1 <= 98; Stmt_S1[i0] -> Stmt_S2[i0, i0] : 0 <= i0 <= 98; Stmt_S2[i0, i0] -> Stmt_S3[i0] : 0 <= i0 <= 98; Stmt_S3[i0] -> Stmt_S2[o0, i0] : i0 >= 0 and i0 < o0 <= 98 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:   { Stmt_S2[i0, i1] -> Stmt_S1[i1] : i0 >= 0 and i0 < i1 <= 98; Stmt_S1[i0] -> Stmt_S2[i0, i0] : 0 <= i0 <= 98; Stmt_S2[i0, i0] -> Stmt_S3[i0] : 0 <= i0 <= 98; Stmt_S3[i0] -> Stmt_S2[o0, i0] : i0 >= 0 and i0 < o0 <= 98 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0, i1] -> Stmt_S1[i1] : i0 >= 0 and i0 < i1 <= 98; Stmt_S1[i0] -> Stmt_S2[i0, i0] : 0 <= i0 <= 98; Stmt_S2[i0, i0] -> Stmt_S3[i0] : 0 <= i0 <= 98; Stmt_S3[i0] -> Stmt_S2[o0, i0] : i0 >= 0 and i0 < o0 <= 98 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_privatization_deps_5.ll

@@ -3,7 +3,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0, 0] -> Stmt_S1[1 + i0, 0] : 0 <= i0 <= 97; Stmt_S1[i0, 0] -> Stmt_S2[i0, 0] : 0 <= i0 <= 98 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:     { Stmt_S2[i0, 0] -> Stmt_S1[1 + i0, 0] : 0 <= i0 <= 97; Stmt_S1[i0, 0] -> Stmt_S2[i0, 0] : 0 <= i0 <= 98 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0, 0] -> Stmt_S1[1 + i0, 0] : 0 <= i0 <= 97; Stmt_S1[i0, 0] -> Stmt_S2[i0, 0] : 0 <= i0 <= 98 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_sequence.ll

@@ -61,7 +61,7 @@
 ; CHECK: 	RAW dependences:
 ; CHECK-NEXT: 		{ Stmt_bb150[1023, 1023] -> Stmt_bb162[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb150[i0, i1] -> Stmt_bb162[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb150[1023, 1023] -> Stmt_bb162[0, 0]; Stmt_bb174[1023, 1023] -> Stmt_bb186[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb174[i0, i1] -> Stmt_bb186[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb174[1023, 1023] -> Stmt_bb186[0, 0]; Stmt_bb102[1023, 1023] -> Stmt_bb114[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb102[i0, i1] -> Stmt_bb114[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb102[1023, 1023] -> Stmt_bb114[0, 0]; Stmt_bb42[1023, 1023] -> Stmt_bb54[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb42[i0, i1] -> Stmt_bb54[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb42[1023, 1023] -> Stmt_bb54[0, 0]; Stmt_bb54[1023, 1023] -> Stmt_bb66[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb54[i0, i1] -> Stmt_bb66[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb54[1023, 1023] -> Stmt_bb66[0, 0]; Stmt_bb31[1023, 1023] -> Stmt_bb42[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb31[i0, i1] -> Stmt_bb42[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb31[1023, 1023] -> Stmt_bb42[0, 0]; Stmt_bb162[1023, 1023] -> Stmt_bb174[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb162[i0, i1] -> Stmt_bb174[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb162[1023, 1023] -> Stmt_bb174[0, 0]; Stmt_bb126[1023, 1023] -> Stmt_bb138[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb126[i0, i1] -> Stmt_bb138[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb126[1023, 1023] -> Stmt_bb138[0, 0]; Stmt_bb90[1023, 1023] -> Stmt_bb102[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb90[i0, i1] -> Stmt_bb102[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb90[1023, 1023] -> Stmt_bb102[0, 0]; Stmt_bb138[1023, 1023] -> Stmt_bb150[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb138[i0, i1] -> Stmt_bb150[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb138[1023, 1023] -> Stmt_bb150[0, 0]; Stmt_bb66[1023, 1023] -> Stmt_bb78[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb66[i0, i1] -> Stmt_bb78[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb66[1023, 1023] -> Stmt_bb78[0, 0]; Stmt_bb78[1023, 1023] -> Stmt_bb90[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb78[i0, i1] -> Stmt_bb90[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb78[1023, 1023] -> Stmt_bb90[0, 0]; Stmt_bb114[1023, 1023] -> Stmt_bb126[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb114[i0, i1] -> Stmt_bb126[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb114[1023, 1023] -> Stmt_bb126[0, 0] }
 ; CHECK-NEXT: 	WAR dependences:
-; CHECK-NEXT: 		{  }
+; CHECK-NEXT:     { Stmt_bb150[1023, 1023] -> Stmt_bb162[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb150[i0, i1] -> Stmt_bb162[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb150[1023, 1023] -> Stmt_bb162[0, 0]; Stmt_bb174[1023, 1023] -> Stmt_bb186[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb174[i0, i1] -> Stmt_bb186[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb174[1023, 1023] -> Stmt_bb186[0, 0]; Stmt_bb102[1023, 1023] -> Stmt_bb114[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb102[i0, i1] -> Stmt_bb114[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb102[1023, 1023] -> Stmt_bb114[0, 0]; Stmt_bb42[1023, 1023] -> Stmt_bb54[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb42[i0, i1] -> Stmt_bb54[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb42[1023, 1023] -> Stmt_bb54[0, 0]; Stmt_bb54[1023, 1023] -> Stmt_bb66[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb54[i0, i1] -> Stmt_bb66[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb54[1023, 1023] -> Stmt_bb66[0, 0]; Stmt_bb31[1023, 1023] -> Stmt_bb42[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb31[i0, i1] -> Stmt_bb42[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb31[1023, 1023] -> Stmt_bb42[0, 0]; Stmt_bb162[1023, 1023] -> Stmt_bb174[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb162[i0, i1] -> Stmt_bb174[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb162[1023, 1023] -> Stmt_bb174[0, 0]; Stmt_bb126[1023, 1023] -> Stmt_bb138[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb126[i0, i1] -> Stmt_bb138[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb126[1023, 1023] -> Stmt_bb138[0, 0]; Stmt_bb90[1023, 1023] -> Stmt_bb102[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb90[i0, i1] -> Stmt_bb102[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb90[1023, 1023] -> Stmt_bb102[0, 0]; Stmt_bb138[1023, 1023] -> Stmt_bb150[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb138[i0, i1] -> Stmt_bb150[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb138[1023, 1023] -> Stmt_bb150[0, 0]; Stmt_bb66[1023, 1023] -> Stmt_bb78[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb66[i0, i1] -> Stmt_bb78[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb66[1023, 1023] -> Stmt_bb78[0, 0]; Stmt_bb78[1023, 1023] -> Stmt_bb90[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb78[i0, i1] -> Stmt_bb90[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb78[1023, 1023] -> Stmt_bb90[0, 0]; Stmt_bb114[1023, 1023] -> Stmt_bb126[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb114[i0, i1] -> Stmt_bb126[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb114[1023, 1023] -> Stmt_bb126[0, 0] }
 ; CHECK-NEXT: 	WAW dependences:
 ; CHECK-NEXT: 		{ Stmt_bb150[1023, 1023] -> Stmt_bb162[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb150[i0, i1] -> Stmt_bb162[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb150[1023, 1023] -> Stmt_bb162[0, 0]; Stmt_bb174[1023, 1023] -> Stmt_bb186[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb174[i0, i1] -> Stmt_bb186[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb174[1023, 1023] -> Stmt_bb186[0, 0]; Stmt_bb102[1023, 1023] -> Stmt_bb114[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb102[i0, i1] -> Stmt_bb114[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb102[1023, 1023] -> Stmt_bb114[0, 0]; Stmt_bb42[1023, 1023] -> Stmt_bb54[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb42[i0, i1] -> Stmt_bb54[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb42[1023, 1023] -> Stmt_bb54[0, 0]; Stmt_bb54[1023, 1023] -> Stmt_bb66[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb54[i0, i1] -> Stmt_bb66[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb54[1023, 1023] -> Stmt_bb66[0, 0]; Stmt_bb31[1023, 1023] -> Stmt_bb42[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb31[i0, i1] -> Stmt_bb42[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb31[1023, 1023] -> Stmt_bb42[0, 0]; Stmt_bb162[1023, 1023] -> Stmt_bb174[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb162[i0, i1] -> Stmt_bb174[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb162[1023, 1023] -> Stmt_bb174[0, 0]; Stmt_bb126[1023, 1023] -> Stmt_bb138[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb126[i0, i1] -> Stmt_bb138[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb126[1023, 1023] -> Stmt_bb138[0, 0]; Stmt_bb90[1023, 1023] -> Stmt_bb102[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb90[i0, i1] -> Stmt_bb102[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb90[1023, 1023] -> Stmt_bb102[0, 0]; Stmt_bb138[1023, 1023] -> Stmt_bb150[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb138[i0, i1] -> Stmt_bb150[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb138[1023, 1023] -> Stmt_bb150[0, 0]; Stmt_bb66[1023, 1023] -> Stmt_bb78[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb66[i0, i1] -> Stmt_bb78[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb66[1023, 1023] -> Stmt_bb78[0, 0]; Stmt_bb78[1023, 1023] -> Stmt_bb90[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb78[i0, i1] -> Stmt_bb90[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb78[1023, 1023] -> Stmt_bb90[0, 0]; Stmt_bb114[1023, 1023] -> Stmt_bb126[o0, o1] : o0 <= 1023 and o1 >= 0 and -1024o0 < o1 <= 1023; Stmt_bb114[i0, i1] -> Stmt_bb126[0, 0] : i0 >= 0 and 0 <= i1 <= 1048574 - 1024i0 and i1 <= 1023; Stmt_bb114[1023, 1023] -> Stmt_bb126[0, 0] }
 ; CHECK-NEXT: 	Reduction dependences:

polly/test/DependenceInfo/reduction_simple_iv_debug_wrapped_dependences.ll

@@ -10,7 +10,7 @@
 ; CHECK-NEXT:     RAW dependences:
 ; CHECK-NEXT:         { [Stmt_for_cond[i0] -> MemRef_sum[0{{\]\]}} -> [Stmt_for_cond[1 + i0] -> MemRef_sum[0{{\]\]}} : 0 <= i0 <= 99 }
 ; CHECK-NEXT:     WAR dependences:
-; CHECK-NEXT:         {  }
+; CHECK-NEXT:         { [Stmt_for_cond[i0] -> MemRef_sum[0{{\]\]}} -> [Stmt_for_cond[1 + i0] -> MemRef_sum[0{{\]\]}} : 0 <= i0 <= 99 }
 ; CHECK-NEXT:     WAW dependences:
 ; CHECK-NEXT:         { [Stmt_for_cond[i0] -> MemRef_sum[0{{\]\]}} -> [Stmt_for_cond[1 + i0] -> MemRef_sum[0{{\]\]}} : 0 <= i0 <= 99 }
 ; CHECK-NEXT:     Reduction dependences:

polly/test/DependenceInfo/reduction_simple_privatization_deps_2.ll

@@ -3,7 +3,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0] -> Stmt_S0[1 + i0] : 0 <= i0 <= 98; Stmt_S0[i0] -> Stmt_S1[i0, o1] : 0 <= i0 <= 99 and 0 <= o1 <= 99; Stmt_S1[i0, i1] -> Stmt_S2[i0] : 0 <= i0 <= 99 and 0 <= i1 <= 99 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     {  }
+; CHECK-NEXT:     { Stmt_S2[i0] -> Stmt_S0[1 + i0] : 0 <= i0 <= 98; Stmt_S0[i0] -> Stmt_S1[i0, o1] : 0 <= i0 <= 99 and 0 <= o1 <= 99; Stmt_S1[i0, i1] -> Stmt_S2[i0] : 0 <= i0 <= 99 and 0 <= i1 <= 99 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     { Stmt_S2[i0] -> Stmt_S0[1 + i0] : 0 <= i0 <= 98; Stmt_S0[i0] -> Stmt_S1[i0, o1] : 0 <= i0 <= 99 and 0 <= o1 <= 99; Stmt_S1[i0, i1] -> Stmt_S2[i0] : 0 <= i0 <= 99 and 0 <= i1 <= 99 }
 ; CHECK-NEXT: Reduction dependences:

polly/test/DependenceInfo/reduction_simple_privatization_deps_w_parameter.ll

@@ -3,7 +3,7 @@
 ; CHECK:      RAW dependences:
 ; CHECK-NEXT:     [N] -> { Stmt_S0[] -> Stmt_S1[o0] : N >= 11 and 0 <= o0 <= 1023; Stmt_S1[i0] -> Stmt_S2[] : N >= 11 and 0 <= i0 <= 1023 }
 ; CHECK-NEXT: WAR dependences:
-; CHECK-NEXT:     [N] -> {  }
+; CHECK-NEXT:     [N] -> { Stmt_S1[i0] -> Stmt_S2[] : N >= 11 and 0 <= i0 <= 1023 }
 ; CHECK-NEXT: WAW dependences:
 ; CHECK-NEXT:     [N] -> { Stmt_S0[] -> Stmt_S1[o0] : N >= 11 and 0 <= o0 <= 1023; Stmt_S1[i0] -> Stmt_S2[] : N >= 11 and 0 <= i0 <= 1023 }
 ; CHECK-NEXT: Reduction dependences: