add more comments around the delinearization of arrays

llvm-svn: 194612

llvm/lib/Analysis/Delinearization.cpp

@@ -83,6 +83,8 @@ void Delinearization::print(raw_ostream &O, const Module *) const {
   O << "Delinearization on function " << F->getName() << ":\n";
   for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) {
     Instruction *Inst = &(*I);
+
+    // Only analyze loads and stores.
     if (!isa<StoreInst>(Inst) && !isa<LoadInst>(Inst) &&
         !isa<GetElementPtrInst>(Inst))
       continue;
@@ -93,6 +95,8 @@ void Delinearization::print(raw_ostream &O, const Module *) const {
     for (Loop *L = LI->getLoopFor(BB); L != NULL; L = L->getParentLoop()) {
       const SCEV *AccessFn = SE->getSCEVAtScope(getPointerOperand(*Inst), L);
       const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(AccessFn);
+
+      // Do not try to delinearize memory accesses that are not AddRecs.
       if (!AR)
         break;
 

llvm/lib/Analysis/DependenceAnalysis.cpp

@@ -24,11 +24,11 @@
 // Both of these are conservative weaknesses;
 // that is, not a source of correctness problems.
 //
-// The implementation depends on the GEP instruction to
+// The implementation depends on the GEP instruction to differentiate
-// differentiate subscripts. Since Clang linearizes subscripts
+// subscripts. Since Clang linearizes some array subscripts, the dependence
-// for most arrays, we give up some precision (though the existing MIV tests
+// analysis is using SCEV->delinearize to recover the representation of multiple
-// will help). We trust that the GEP instruction will eventually be extended.
+// subscripts, and thus avoid the more expensive and less precise MIV tests. The
-// In the meantime, we should explore Maslov's ideas about delinearization.
+// delinearization is controlled by the flag -da-delinearize.
 //
 // We should pay some careful attention to the possibility of integer overflow
 // in the implementation of the various tests. This could happen with Add,
@@ -3206,10 +3206,21 @@ DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV, const SCEV *DstSCEV,
     DEBUG(errs() << *DstSubscripts[i]);
 #endif
 
+  // The delinearization transforms a single-subscript MIV dependence test into
+  // a multi-subscript SIV dependence test that is easier to compute. So we
+  // resize Pair to contain as many pairs of subscripts as the delinearization
+  // has found, and then initialize the pairs following the delinearization.
   Pair.resize(size);
   for (int i = 0; i < size; ++i) {
     Pair[i].Src = SrcSubscripts[i];
     Pair[i].Dst = DstSubscripts[i];
+
+    // FIXME: we should record the bounds SrcSizes[i] and DstSizes[i] that the
+    // delinearization has found, and add these constraints to the dependence
+    // check to avoid memory accesses overflow from one dimension into another.
+    // This is related to the problem of determining the existence of data
+    // dependences in array accesses using a different number of subscripts: in
+    // C one can access an array A[100][100]; as A[0][9999], *A[9999], etc.
   }
 
   return true;

llvm/lib/Analysis/ScalarEvolution.cpp

@@ -7070,27 +7070,66 @@ private:
 
 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
 /// sizes of an array access. Returns the remainder of the delinearization that
-/// is the offset start of the array. For example
+/// is the offset start of the array.  The SCEV->delinearize algorithm computes
-/// delinearize ({(((-4 + (3 * %m)))),+,(%m)}<%for.i>) {
+/// the multiples of SCEV coefficients: that is a pattern matching of sub
-///   IV: {0,+,1}<%for.i>
+/// expressions in the stride and base of a SCEV corresponding to the
-///   Start: -4 + (3 * %m)
+/// computation of a GCD (greatest common divisor) of base and stride.  When
-///   Step: %m
+/// SCEV->delinearize fails, it returns the SCEV unchanged.
-///   SCEVUDiv (Start, Step) = 3 remainder -4
+///
-///   rem = delinearize (3) = 3
+/// For example: when analyzing the memory access A[i][j][k] in this loop nest
-///   Subscripts.push_back(IV + rem)
+///
-///   Sizes.push_back(Step)
+///  void foo(long n, long m, long o, double A[n][m][o]) {
-///   return remainder -4
+///
+///    for (long i = 0; i < n; i++)
+///      for (long j = 0; j < m; j++)
+///        for (long k = 0; k < o; k++)
+///          A[i][j][k] = 1.0;
 ///  }
-/// When delinearize fails, it returns the SCEV unchanged.
+///
+/// the delinearization input is the following AddRec SCEV:
+///
+///  AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
+///
+/// From this SCEV, we are able to say that the base offset of the access is %A
+/// because it appears as an offset that does not divide any of the strides in
+/// the loops:
+///
+///  CHECK: Base offset: %A
+///
+/// and then SCEV->delinearize determines the size of some of the dimensions of
+/// the array as these are the multiples by which the strides are happening:
+///
+///  CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
+///
+/// Note that the outermost dimension remains of UnknownSize because there are
+/// no strides that would help identifying the size of the last dimension: when
+/// the array has been statically allocated, one could compute the size of that
+/// dimension by dividing the overall size of the array by the size of the known
+/// dimensions: %m * %o * 8.
+///
+/// Finally delinearize provides the access functions for the array reference
+/// that does correspond to A[i][j][k] of the above C testcase:
+///
+///  CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
+///
+/// The testcases are checking the output of a function pass:
+/// DelinearizationPass that walks through all loads and stores of a function
+/// 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 {
+  // Early exit in case this SCEV is not an affine multivariate function.
   if (!this->isAffine())
     return this;
 
   const SCEV *Start = this->getStart();
   const SCEV *Step = this->getStepRecurrence(SE);
+
+  // Build the SCEV representation of the cannonical induction variable in the
+  // loop of this SCEV.
   const SCEV *Zero = SE.getConstant(this->getType(), 0);
   const SCEV *One = SE.getConstant(this->getType(), 1);
   const SCEV *IV =
@@ -7098,38 +7137,55 @@ SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
 
   DEBUG(dbgs() << "(delinearize: " << *this << "\n");
 
+  // Currently we fail to delinearize when the stride of this SCEV is 1. We
+  // could decide to not fail in this case: we could just return 1 for the size
+  // of the subscript, and this same SCEV for the access function.
   if (Step == One) {
     DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
     return this;
   }
 
+  // Find the GCD and Remainder of the Start and Step coefficients of this SCEV.
   const SCEV *Remainder = NULL;
   const SCEV *GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
 
   DEBUG(dbgs() << "GCD: " << *GCD << "\n");
   DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
 
+  // Same remark as above: we currently fail the delinearization, although we
+  // can very well handle this special case.
   if (GCD == One) {
     DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
     return this;
   }
 
+  // As findGCD computed Remainder, GCD divides "Start - Remainder." The
+  // Quotient is then this SCEV without Remainder, scaled down by the GCD.  The
+  // Quotient is what will be used in the next subscript delinearization.
   const SCEV *Quotient =
       SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
   DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
 
   const SCEV *Rem;
   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
+    // Recursively call delinearize on the Quotient until there are no more
+    // multiples that can be recognized.
     Rem = AR->delinearize(SE, Subscripts, Sizes);
   else
     Rem = Quotient;
 
+  // Scale up the cannonical induction variable IV by whatever remains from the
+  // Step after division by the GCD: the GCD is the size of all the sub-array.
   if (Step != GCD) {
     Step = SCEVDivision::divide(SE, Step, GCD);
     IV = SE.getMulExpr(IV, Step);
   }
+  // The access function in the current subscript is computed as the cannonical
+  // induction variable IV (potentially scaled up by the step) and offset by
+  // Rem, the offset of delinearization in the sub-array.
   const SCEV *Index = SE.getAddExpr(IV, Rem);
 
+  // Record the access function and the size of the current subscript.
   Subscripts.push_back(Index);
   Sizes.push_back(GCD);