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author | Sebastian Pop <spop@codeaurora.org> | 2013-11-13 22:37:58 +0000 |
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committer | Sebastian Pop <spop@codeaurora.org> | 2013-11-13 22:37:58 +0000 |
commit | f44941d81dc30cfd357c12292059721c9644a27f (patch) | |
tree | b081d48e5604ff534147a37cac531f512268522c /lib/Analysis/ScalarEvolution.cpp | |
parent | c9024c6ebcea89746e01207195eeb52c60c3c3bb (diff) | |
download | llvm-f44941d81dc30cfd357c12292059721c9644a27f.tar.gz llvm-f44941d81dc30cfd357c12292059721c9644a27f.tar.bz2 llvm-f44941d81dc30cfd357c12292059721c9644a27f.tar.xz |
add more comments around the delinearization of arrays
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@194612 91177308-0d34-0410-b5e6-96231b3b80d8
Diffstat (limited to 'lib/Analysis/ScalarEvolution.cpp')
-rw-r--r-- | lib/Analysis/ScalarEvolution.cpp | 80 |
1 files changed, 68 insertions, 12 deletions
diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp index 9b2182f456..0f54d7ebda 100644 --- a/lib/Analysis/ScalarEvolution.cpp +++ b/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 -/// delinearize ({(((-4 + (3 * %m)))),+,(%m)}<%for.i>) { -/// IV: {0,+,1}<%for.i> -/// Start: -4 + (3 * %m) -/// Step: %m -/// SCEVUDiv (Start, Step) = 3 remainder -4 -/// rem = delinearize (3) = 3 -/// Subscripts.push_back(IV + rem) -/// Sizes.push_back(Step) -/// return remainder -4 -/// } -/// When delinearize fails, it returns the SCEV unchanged. +/// is the offset start of the array. The SCEV->delinearize algorithm computes +/// the multiples of SCEV coefficients: that is a pattern matching of sub +/// expressions in the stride and base of a SCEV corresponding to the +/// computation of a GCD (greatest common divisor) of base and stride. When +/// SCEV->delinearize fails, it returns the SCEV unchanged. +/// +/// For example: when analyzing the memory access A[i][j][k] in this loop nest +/// +/// void foo(long n, long m, long o, double A[n][m][o]) { +/// +/// 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; +/// } +/// +/// 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); |