remove constant terms

The delinearization is needed only to remove the non linearity induced by
expressions involving multiplications of parameters and induction variables.
There is no problem in dealing with constant times parameters, or constant times
an induction variable.

For this reason, the current patch discards all constant terms and multipliers
before running the delinearization algorithm on the terms. The only thing
remaining in the term expressions are parameters and multiply expressions of
parameters: these simplified term expressions are passed to the array shape
recognizer that will not recognize constant dimensions anymore: these will be
recognized as different strides in parametric subscripts.

The only important special case of a constant dimension is the size of elements.
Instead of relying on the delinearization to infer the size of an element,
compute the element size from the base address type. This is a much more precise
way of computing the element size than before, as we would have mixed together
the size of an element with the strides of the innermost dimension.

llvm-svn: 209691

diff --git a/llvm/include/llvm/Analysis/DependenceAnalysis.h b/llvm/include/llvm/Analysis/DependenceAnalysis.h
index 78a03ff..279755e 100644 (file)
--- a/llvm/include/llvm/Analysis/DependenceAnalysis.h
+++ b/llvm/include/llvm/Analysis/DependenceAnalysis.h
@@ -910,7 +910,8 @@ namespace llvm {
                          const Constraint &CurConstraint) const;
 
     bool tryDelinearize(const SCEV *SrcSCEV, const SCEV *DstSCEV,
-                        SmallVectorImpl<Subscript> &Pair) const;
+                        SmallVectorImpl<Subscript> &Pair,
+                        const SCEV *ElementSize) const;
 
   public:
     static char ID; // Class identification, replacement for typeinfo

diff --git a/llvm/include/llvm/Analysis/ScalarEvolution.h b/llvm/include/llvm/Analysis/ScalarEvolution.h
index 4db8686..0570826 100644 (file)
--- a/llvm/include/llvm/Analysis/ScalarEvolution.h
+++ b/llvm/include/llvm/Analysis/ScalarEvolution.h
@@ -894,10 +894,14 @@ namespace llvm {
     /// indirect operand.
     bool hasOperand(const SCEV *S, const SCEV *Op) const;
 
+    /// Return the size of an element read or written by Inst.
+    const SCEV *getElementSize(Instruction *Inst);
+
     /// Compute the array dimensions Sizes from the set of Terms extracted from
     /// the memory access function of this SCEVAddRecExpr.
     void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
-                             SmallVectorImpl<const SCEV *> &Sizes) const;
+                             SmallVectorImpl<const SCEV *> &Sizes,
+                             const SCEV *ElementSize) const;
 
     bool runOnFunction(Function &F) override;
     void releaseMemory() override;

diff --git a/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h b/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h
index ba32e92..b468fcd 100644 (file)
--- a/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h
+++ b/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h
@@ -434,7 +434,8 @@ namespace llvm {
     /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
     const SCEV *delinearize(ScalarEvolution &SE,
                             SmallVectorImpl<const SCEV *> &Subscripts,
-                            SmallVectorImpl<const SCEV *> &Sizes) const;
+                            SmallVectorImpl<const SCEV *> &Sizes,
+                            const SCEV *ElementSize) const;
   };
 
   //===--------------------------------------------------------------------===//

diff --git a/llvm/lib/Analysis/Delinearization.cpp b/llvm/lib/Analysis/Delinearization.cpp
index 1a58821..6c87027 100644 (file)
--- a/llvm/lib/Analysis/Delinearization.cpp
+++ b/llvm/lib/Analysis/Delinearization.cpp
@@ -108,8 +108,8 @@ void Delinearization::print(raw_ostream &O, const Module *) const {
       O << "AddRec: " << *AR << "\n";
 
       SmallVector<const SCEV *, 3> Subscripts, Sizes;
-      const SCEV *Res = AR->delinearize(*SE, Subscripts, Sizes);
-      if (Res == AR || Subscripts.size() == 0 || Sizes.size() == 0 ||
+      const SCEV *Res = AR->delinearize(*SE, Subscripts, Sizes, SE->getElementSize(Inst));
+      if (Subscripts.size() == 0 || Sizes.size() == 0 ||
           Subscripts.size() != Sizes.size()) {
         O << "failed to delinearize\n";
         continue;

diff --git a/llvm/lib/Analysis/DependenceAnalysis.cpp b/llvm/lib/Analysis/DependenceAnalysis.cpp
index 57231b8..33cb206 100644 (file)
--- a/llvm/lib/Analysis/DependenceAnalysis.cpp
+++ b/llvm/lib/Analysis/DependenceAnalysis.cpp
@@ -3180,9 +3180,10 @@ void DependenceAnalysis::updateDirection(Dependence::DVEntry &Level,
 /// source and destination array references are recurrences on a nested loop,
 /// this function flattens the nested recurrences into separate recurrences
 /// for each loop level.
-bool
-DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV, const SCEV *DstSCEV,
-                                   SmallVectorImpl<Subscript> &Pair) const {
+bool DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV,
+                                        const SCEV *DstSCEV,
+                                        SmallVectorImpl<Subscript> &Pair,
+                                        const SCEV *ElementSize) const {
   const SCEVAddRecExpr *SrcAR = dyn_cast<SCEVAddRecExpr>(SrcSCEV);
   const SCEVAddRecExpr *DstAR = dyn_cast<SCEVAddRecExpr>(DstSCEV);
   if (!SrcAR || !DstAR || !SrcAR->isAffine() || !DstAR->isAffine())
@@ -3195,7 +3196,7 @@ DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV, const SCEV *DstSCEV,
 
   // Second step: find subscript sizes.
   SmallVector<const SCEV *, 4> Sizes;
-  SE->findArrayDimensions(Terms, Sizes);
+  SE->findArrayDimensions(Terms, Sizes, ElementSize);
 
   // Third step: compute the access functions for each subscript.
   SmallVector<const SCEV *, 4> SrcSubscripts, DstSubscripts;
@@ -3353,7 +3354,7 @@ Dependence *DependenceAnalysis::depends(Instruction *Src,
   }
 
   if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
-      tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair)) {
+      tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
     DEBUG(dbgs() << "    delinerized GEP\n");
     Pairs = Pair.size();
   }
@@ -3777,7 +3778,7 @@ const  SCEV *DependenceAnalysis::getSplitIteration(const Dependence *Dep,
   }
 
   if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
-      tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair)) {
+      tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair, SE->getElementSize(Src))) {
     DEBUG(dbgs() << "    delinerized GEP\n");
     Pairs = Pair.size();
   }

diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index 1087e5d..4e4eb21 100644 (file)
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -6944,7 +6944,7 @@ struct SCEVCollectTerms {
       : Terms(T) {}
 
   bool follow(const SCEV *S) {
-    if (isa<SCEVUnknown>(S) || isa<SCEVConstant>(S) || isa<SCEVMulExpr>(S)) {
+    if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
       if (!containsUndefs(S))
         Terms.push_back(S);
 
@@ -7356,13 +7356,46 @@ static inline int numberOfTerms(const SCEV *S) {
   return 1;
 }
 
+static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
+  if (isa<SCEVConstant>(T))
+    return nullptr;
+
+  if (isa<SCEVUnknown>(T))
+    return T;
+
+  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
+    SmallVector<const SCEV *, 2> Factors;
+    for (const SCEV *Op : M->operands())
+      if (!isa<SCEVConstant>(Op))
+        Factors.push_back(Op);
+
+    return SE.getMulExpr(Factors);
+  }
+
+  return T;
+}
+
+/// Return the size of an element read or written by Inst.
+const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
+  Type *Ty;
+  if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
+    Ty = Store->getValueOperand()->getType();
+  else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
+    Ty = Load->getPointerOperand()->getType();
+  else
+    return nullptr;
+
+  Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
+  return getSizeOfExpr(ETy, Ty);
+}
+
 /// Second step of delinearization: compute the array dimensions Sizes from the
 /// set of Terms extracted from the memory access function of this SCEVAddRec.
-void ScalarEvolution::findArrayDimensions(
-    SmallVectorImpl<const SCEV *> &Terms,
-    SmallVectorImpl<const SCEV *> &Sizes) const {
+void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
+                                          SmallVectorImpl<const SCEV *> &Sizes,
+                                          const SCEV *ElementSize) const {
 
-  if (Terms.size() < 2)
+  if (Terms.size() < 1)
     return;
 
   // Early return when Terms do not contain parameters: we do not delinearize
@@ -7385,20 +7418,37 @@ void ScalarEvolution::findArrayDimensions(
     return numberOfTerms(LHS) > numberOfTerms(RHS);
   });
 
+  ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
+
+  // Divide all terms by the element size.
+  for (const SCEV *&Term : Terms) {
+    const SCEV *Q, *R;
+    SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
+    Term = Q;
+  }
+
+  SmallVector<const SCEV *, 4> NewTerms;
+
+  // Remove constant factors.
+  for (const SCEV *T : Terms)
+    if (const SCEV *NewT = removeConstantFactors(SE, T))
+      NewTerms.push_back(NewT);
+
   DEBUG({
       dbgs() << "Terms after sorting:\n";
-      for (const SCEV *T : Terms)
+      for (const SCEV *T : NewTerms)
         dbgs() << *T << "\n";
     });
 
-  ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
-  bool Res = findArrayDimensionsRec(SE, Terms, Sizes);
-
-  if (!Res) {
+  if (NewTerms.empty() ||
+      !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
     Sizes.clear();
     return;
   }
 
+  // The last element to be pushed into Sizes is the size of an element.
+  Sizes.push_back(ElementSize);
+
   DEBUG({
       dbgs() << "Sizes:\n";
       for (const SCEV *S : Sizes)
@@ -7433,9 +7483,14 @@ const SCEV *SCEVAddRecExpr::computeAccessFunctions(
 
     Res = Q;
 
+    // Do not record the last subscript corresponding to the size of elements in
+    // the array.
     if (i == Last) {
-      // Do not record the last subscript corresponding to the size of elements
-      // in the array.
+
+      // Bail out if the remainder is too complex.
+      if (isa<SCEVAddRecExpr>(R))
+        return nullptr;
+
       Remainder = R;
       continue;
     }
@@ -7507,10 +7562,9 @@ const SCEV *SCEVAddRecExpr::computeAccessFunctions(
 /// asking for the SCEV of the memory access with respect to all enclosing
 /// loops, calling SCEV->delinearize on that and printing the results.
 
-const SCEV *
-SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
-                            SmallVectorImpl<const SCEV *> &Subscripts,
-                            SmallVectorImpl<const SCEV *> &Sizes) const {
+const SCEV *SCEVAddRecExpr::delinearize(
+    ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
+    SmallVectorImpl<const SCEV *> &Sizes, const SCEV *ElementSize) const {
   // First step: collect parametric terms.
   SmallVector<const SCEV *, 4> Terms;
   collectParametricTerms(SE, Terms);
@@ -7519,7 +7573,7 @@ SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
     return nullptr;
 
   // Second step: find subscript sizes.
-  SE.findArrayDimensions(Terms, Sizes);
+  SE.findArrayDimensions(Terms, Sizes, ElementSize);
 
   if (Sizes.empty())
     return nullptr;

diff --git a/llvm/test/Analysis/Delinearization/iv_times_constant_in_subscript.ll b/llvm/test/Analysis/Delinearization/iv_times_constant_in_subscript.ll
new file mode 100644 (file)
index 0000000..01a4b96
--- /dev/null
+++ b/llvm/test/Analysis/Delinearization/iv_times_constant_in_subscript.ll
@@ -0,0 +1,45 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; Derived from the following code:
+;
+; void foo(long n, long m, long b, double A[n][m]) {
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       A[2i+b][2j] = 1.0;
+; }
+
+; AddRec: {{((%m * %b * sizeof(double)) + %A),+,(2 * %m * sizeof(double))}<%for.i>,+,(2 * sizeof(double))}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{%b,+,2}<%for.i>][{0,+,2}<%for.j>]
+
+
+define void @foo(i64 %n, i64 %m, i64 %b, double* %A) {
+entry:
+  br label %for.i
+
+for.i:
+  %i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.inc ]
+  %outerdim = mul nsw i64 %i, 2
+  %outerdim2 = add nsw i64 %outerdim, %b
+  %tmp = mul nsw i64 %outerdim2, %m
+  br label %for.j
+
+for.j:
+  %j = phi i64 [ 0, %for.i ], [ %j.inc, %for.j ]
+  %prodj = mul i64 %j, 2
+  %vlaarrayidx.sum = add i64 %prodj, %tmp
+  %arrayidx = getelementptr inbounds double* %A, i64 %vlaarrayidx.sum
+  store double 1.0, double* %arrayidx
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %m
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %n
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:
+  ret void
+}

diff --git a/llvm/test/Analysis/DependenceAnalysis/GCD.ll b/llvm/test/Analysis/DependenceAnalysis/GCD.ll
index fd9173b..7eca18e 100644 (file)
--- a/llvm/test/Analysis/DependenceAnalysis/GCD.ll
+++ b/llvm/test/Analysis/DependenceAnalysis/GCD.ll
@@ -269,10 +269,10 @@ entry:
 ; CHECK: da analyze - none!
 
 ; DELIN: 'Dependence Analysis' for function 'gcd4'
-; DELIN: da analyze - none!
+; DELIN: da analyze - output [* *]!
 ; DELIN: da analyze - none!
 ; DELIN: da analyze - confused!
-; DELIN: da analyze - none!
+; DELIN: da analyze - input [* *]!
 ; DELIN: da analyze - confused!
 ; DELIN: da analyze - none!
 
@@ -339,10 +339,10 @@ entry:
 ; CHECK: da analyze - none!
 
 ; DELIN: 'Dependence Analysis' for function 'gcd5'
-; DELIN: da analyze - none!
+; DELIN: da analyze - output [* *]!
 ; DELIN: da analyze - flow [<> *]!
 ; DELIN: da analyze - confused!
-; DELIN: da analyze - none!
+; DELIN: da analyze - input [* *]!
 ; DELIN: da analyze - confused!
 ; DELIN: da analyze - none!
 
@@ -410,10 +410,10 @@ entry:
 ; CHECK: da analyze - output [* *]!
 
 ; DELIN: 'Dependence Analysis' for function 'gcd6'
+; DELIN: da analyze - output [* *]!
 ; DELIN: da analyze - none!
-; DELIN: da analyze - flow [=> =>|<]!
 ; DELIN: da analyze - confused!
-; DELIN: da analyze - none!
+; DELIN: da analyze - input [* *]!
 ; DELIN: da analyze - confused!
 ; DELIN: da analyze - output [* *]!