| //===- AffineAnalysis.cpp - Affine structures analysis routines -----------===// |
| // |
| // Copyright 2019 The MLIR Authors. |
| // |
| // Licensed under the Apache License, Version 2.0 (the "License"); |
| // you may not use this file except in compliance with the License. |
| // You may obtain a copy of the License at |
| // |
| // http://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, software |
| // distributed under the License is distributed on an "AS IS" BASIS, |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| // See the License for the specific language governing permissions and |
| // limitations under the License. |
| // ============================================================================= |
| // |
| // This file implements miscellaneous analysis routines for affine structures |
| // (expressions, maps, sets), and other utilities relying on such analysis. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #include "mlir/Analysis/AffineAnalysis.h" |
| #include "mlir/AffineOps/AffineOps.h" |
| #include "mlir/Analysis/AffineStructures.h" |
| #include "mlir/Analysis/Utils.h" |
| #include "mlir/IR/AffineExprVisitor.h" |
| #include "mlir/IR/Builders.h" |
| #include "mlir/IR/Instruction.h" |
| #include "mlir/IR/IntegerSet.h" |
| #include "mlir/StandardOps/Ops.h" |
| #include "mlir/Support/MathExtras.h" |
| #include "mlir/Support/STLExtras.h" |
| #include "llvm/ADT/DenseMap.h" |
| #include "llvm/Support/Debug.h" |
| #include "llvm/Support/raw_ostream.h" |
| |
| #define DEBUG_TYPE "affine-analysis" |
| |
| using namespace mlir; |
| |
| using llvm::dbgs; |
| |
| /// Returns the sequence of AffineApplyOp Instructions operation in |
| /// 'affineApplyOps', which are reachable via a search starting from 'operands', |
| /// and ending at operands which are not defined by AffineApplyOps. |
| // TODO(andydavis) Add a method to AffineApplyOp which forward substitutes |
| // the AffineApplyOp into any user AffineApplyOps. |
| void mlir::getReachableAffineApplyOps( |
| ArrayRef<Value *> operands, |
| SmallVectorImpl<Instruction *> &affineApplyOps) { |
| struct State { |
| // The ssa value for this node in the DFS traversal. |
| Value *value; |
| // The operand index of 'value' to explore next during DFS traversal. |
| unsigned operandIndex; |
| }; |
| SmallVector<State, 4> worklist; |
| for (auto *operand : operands) { |
| worklist.push_back({operand, 0}); |
| } |
| |
| while (!worklist.empty()) { |
| State &state = worklist.back(); |
| auto *opInst = state.value->getDefiningInst(); |
| // Note: getDefiningInst will return nullptr if the operand is not an |
| // Instruction (i.e. AffineForOp), which is a terminator for the search. |
| if (opInst == nullptr || !opInst->isa<AffineApplyOp>()) { |
| worklist.pop_back(); |
| continue; |
| } |
| if (auto affineApplyOp = opInst->dyn_cast<AffineApplyOp>()) { |
| if (state.operandIndex == 0) { |
| // Pre-Visit: Add 'opInst' to reachable sequence. |
| affineApplyOps.push_back(opInst); |
| } |
| if (state.operandIndex < opInst->getNumOperands()) { |
| // Visit: Add next 'affineApplyOp' operand to worklist. |
| // Get next operand to visit at 'operandIndex'. |
| auto *nextOperand = opInst->getOperand(state.operandIndex); |
| // Increment 'operandIndex' in 'state'. |
| ++state.operandIndex; |
| // Add 'nextOperand' to worklist. |
| worklist.push_back({nextOperand, 0}); |
| } else { |
| // Post-visit: done visiting operands AffineApplyOp, pop off stack. |
| worklist.pop_back(); |
| } |
| } |
| } |
| } |
| |
| // Builds a system of constraints with dimensional identifiers corresponding to |
| // the loop IVs of the forOps appearing in that order. Any symbols founds in |
| // the bound operands are added as symbols in the system. Returns failure for |
| // the yet unimplemented cases. |
| // TODO(andydavis,bondhugula) Handle non-unit steps through local variables or |
| // stride information in FlatAffineConstraints. (For eg., by using iv - lb % |
| // step = 0 and/or by introducing a method in FlatAffineConstraints |
| // setExprStride(ArrayRef<int64_t> expr, int64_t stride) |
| LogicalResult mlir::getIndexSet(MutableArrayRef<AffineForOp> forOps, |
| FlatAffineConstraints *domain) { |
| SmallVector<Value *, 4> indices; |
| extractForInductionVars(forOps, &indices); |
| // Reset while associated Values in 'indices' to the domain. |
| domain->reset(forOps.size(), /*numSymbols=*/0, /*numLocals=*/0, indices); |
| for (auto forOp : forOps) { |
| // Add constraints from forOp's bounds. |
| if (failed(domain->addAffineForOpDomain(forOp))) |
| return failure(); |
| } |
| return success(); |
| } |
| |
| // Computes the iteration domain for 'opInst' and populates 'indexSet', which |
| // encapsulates the constraints involving loops surrounding 'opInst' and |
| // potentially involving any Function symbols. The dimensional identifiers in |
| // 'indexSet' correspond to the loops surounding 'inst' from outermost to |
| // innermost. |
| // TODO(andydavis) Add support to handle IfInsts surrounding 'inst'. |
| static LogicalResult getInstIndexSet(Instruction *inst, |
| FlatAffineConstraints *indexSet) { |
| // TODO(andydavis) Extend this to gather enclosing IfInsts and consider |
| // factoring it out into a utility function. |
| SmallVector<AffineForOp, 4> loops; |
| getLoopIVs(*inst, &loops); |
| return getIndexSet(loops, indexSet); |
| } |
| |
| // ValuePositionMap manages the mapping from Values which represent dimension |
| // and symbol identifiers from 'src' and 'dst' access functions to positions |
| // in new space where some Values are kept separate (using addSrc/DstValue) |
| // and some Values are merged (addSymbolValue). |
| // Position lookups return the absolute position in the new space which |
| // has the following format: |
| // |
| // [src-dim-identifiers] [dst-dim-identifiers] [symbol-identifers] |
| // |
| // Note: access function non-IV dimension identifiers (that have 'dimension' |
| // positions in the access function position space) are assigned as symbols |
| // in the output position space. Convienience access functions which lookup |
| // an Value in multiple maps are provided (i.e. getSrcDimOrSymPos) to handle |
| // the common case of resolving positions for all access function operands. |
| // |
| // TODO(andydavis) Generalize this: could take a template parameter for |
| // the number of maps (3 in the current case), and lookups could take indices |
| // of maps to check. So getSrcDimOrSymPos would be "getPos(value, {0, 2})". |
| class ValuePositionMap { |
| public: |
| void addSrcValue(Value *value) { |
| if (addValueAt(value, &srcDimPosMap, numSrcDims)) |
| ++numSrcDims; |
| } |
| void addDstValue(Value *value) { |
| if (addValueAt(value, &dstDimPosMap, numDstDims)) |
| ++numDstDims; |
| } |
| void addSymbolValue(Value *value) { |
| if (addValueAt(value, &symbolPosMap, numSymbols)) |
| ++numSymbols; |
| } |
| unsigned getSrcDimOrSymPos(Value *value) const { |
| return getDimOrSymPos(value, srcDimPosMap, 0); |
| } |
| unsigned getDstDimOrSymPos(Value *value) const { |
| return getDimOrSymPos(value, dstDimPosMap, numSrcDims); |
| } |
| unsigned getSymPos(Value *value) const { |
| auto it = symbolPosMap.find(value); |
| assert(it != symbolPosMap.end()); |
| return numSrcDims + numDstDims + it->second; |
| } |
| |
| unsigned getNumSrcDims() const { return numSrcDims; } |
| unsigned getNumDstDims() const { return numDstDims; } |
| unsigned getNumDims() const { return numSrcDims + numDstDims; } |
| unsigned getNumSymbols() const { return numSymbols; } |
| |
| private: |
| bool addValueAt(Value *value, DenseMap<Value *, unsigned> *posMap, |
| unsigned position) { |
| auto it = posMap->find(value); |
| if (it == posMap->end()) { |
| (*posMap)[value] = position; |
| return true; |
| } |
| return false; |
| } |
| unsigned getDimOrSymPos(Value *value, |
| const DenseMap<Value *, unsigned> &dimPosMap, |
| unsigned dimPosOffset) const { |
| auto it = dimPosMap.find(value); |
| if (it != dimPosMap.end()) { |
| return dimPosOffset + it->second; |
| } |
| it = symbolPosMap.find(value); |
| assert(it != symbolPosMap.end()); |
| return numSrcDims + numDstDims + it->second; |
| } |
| |
| unsigned numSrcDims = 0; |
| unsigned numDstDims = 0; |
| unsigned numSymbols = 0; |
| DenseMap<Value *, unsigned> srcDimPosMap; |
| DenseMap<Value *, unsigned> dstDimPosMap; |
| DenseMap<Value *, unsigned> symbolPosMap; |
| }; |
| |
| // Builds a map from Value to identifier position in a new merged identifier |
| // list, which is the result of merging dim/symbol lists from src/dst |
| // iteration domains, the format of which is as follows: |
| // |
| // [src-dim-identifiers, dst-dim-identifiers, symbol-identifiers, const_term] |
| // |
| // This method populates 'valuePosMap' with mappings from operand Values in |
| // 'srcAccessMap'/'dstAccessMap' (as well as those in 'srcDomain'/'dstDomain') |
| // to the position of these values in the merged list. |
| static void buildDimAndSymbolPositionMaps( |
| const FlatAffineConstraints &srcDomain, |
| const FlatAffineConstraints &dstDomain, const AffineValueMap &srcAccessMap, |
| const AffineValueMap &dstAccessMap, ValuePositionMap *valuePosMap, |
| FlatAffineConstraints *dependenceConstraints) { |
| auto updateValuePosMap = [&](ArrayRef<Value *> values, bool isSrc) { |
| for (unsigned i = 0, e = values.size(); i < e; ++i) { |
| auto *value = values[i]; |
| if (!isForInductionVar(values[i])) { |
| assert(isValidSymbol(values[i]) && |
| "access operand has to be either a loop IV or a symbol"); |
| valuePosMap->addSymbolValue(value); |
| } else if (isSrc) { |
| valuePosMap->addSrcValue(value); |
| } else { |
| valuePosMap->addDstValue(value); |
| } |
| } |
| }; |
| |
| SmallVector<Value *, 4> srcValues, destValues; |
| srcDomain.getAllIdValues(&srcValues); |
| dstDomain.getAllIdValues(&destValues); |
| |
| // Update value position map with identifiers from src iteration domain. |
| updateValuePosMap(srcValues, /*isSrc=*/true); |
| // Update value position map with identifiers from dst iteration domain. |
| updateValuePosMap(destValues, /*isSrc=*/false); |
| // Update value position map with identifiers from src access function. |
| updateValuePosMap(srcAccessMap.getOperands(), /*isSrc=*/true); |
| // Update value position map with identifiers from dst access function. |
| updateValuePosMap(dstAccessMap.getOperands(), /*isSrc=*/false); |
| } |
| |
| // Sets up dependence constraints columns appropriately, in the format: |
| // [src-dim-identifiers, dst-dim-identifiers, symbol-identifiers, const_term] |
| void initDependenceConstraints(const FlatAffineConstraints &srcDomain, |
| const FlatAffineConstraints &dstDomain, |
| const AffineValueMap &srcAccessMap, |
| const AffineValueMap &dstAccessMap, |
| const ValuePositionMap &valuePosMap, |
| FlatAffineConstraints *dependenceConstraints) { |
| // Calculate number of equalities/inequalities and columns required to |
| // initialize FlatAffineConstraints for 'dependenceDomain'. |
| unsigned numIneq = |
| srcDomain.getNumInequalities() + dstDomain.getNumInequalities(); |
| AffineMap srcMap = srcAccessMap.getAffineMap(); |
| assert(srcMap.getNumResults() == dstAccessMap.getAffineMap().getNumResults()); |
| unsigned numEq = srcMap.getNumResults(); |
| unsigned numDims = srcDomain.getNumDimIds() + dstDomain.getNumDimIds(); |
| unsigned numSymbols = valuePosMap.getNumSymbols(); |
| unsigned numIds = numDims + numSymbols; |
| unsigned numCols = numIds + 1; |
| |
| // Set flat affine constraints sizes and reserving space for constraints. |
| dependenceConstraints->reset(numIneq, numEq, numCols, numDims, numSymbols, |
| /*numLocals=*/0); |
| |
| // Set values corresponding to dependence constraint identifiers. |
| SmallVector<Value *, 4> srcLoopIVs, dstLoopIVs; |
| srcDomain.getIdValues(0, srcDomain.getNumDimIds(), &srcLoopIVs); |
| dstDomain.getIdValues(0, dstDomain.getNumDimIds(), &dstLoopIVs); |
| |
| dependenceConstraints->setIdValues(0, srcLoopIVs.size(), srcLoopIVs); |
| dependenceConstraints->setIdValues( |
| srcLoopIVs.size(), srcLoopIVs.size() + dstLoopIVs.size(), dstLoopIVs); |
| |
| // Set values for the symbolic identifier dimensions. |
| auto setSymbolIds = [&](ArrayRef<Value *> values) { |
| for (auto *value : values) { |
| if (!isForInductionVar(value)) { |
| assert(isValidSymbol(value) && "expected symbol"); |
| dependenceConstraints->setIdValue(valuePosMap.getSymPos(value), value); |
| } |
| } |
| }; |
| |
| setSymbolIds(srcAccessMap.getOperands()); |
| setSymbolIds(dstAccessMap.getOperands()); |
| |
| SmallVector<Value *, 8> srcSymbolValues, dstSymbolValues; |
| srcDomain.getIdValues(srcDomain.getNumDimIds(), |
| srcDomain.getNumDimAndSymbolIds(), &srcSymbolValues); |
| dstDomain.getIdValues(dstDomain.getNumDimIds(), |
| dstDomain.getNumDimAndSymbolIds(), &dstSymbolValues); |
| setSymbolIds(srcSymbolValues); |
| setSymbolIds(dstSymbolValues); |
| |
| for (unsigned i = 0, e = dependenceConstraints->getNumDimAndSymbolIds(); |
| i < e; i++) |
| assert(dependenceConstraints->getIds()[i].hasValue()); |
| } |
| |
| // Adds iteration domain constraints from 'srcDomain' and 'dstDomain' into |
| // 'dependenceDomain'. |
| // Uses 'valuePosMap' to determine the position in 'dependenceDomain' to which a |
| // srcDomain/dstDomain Value maps. |
| static void addDomainConstraints(const FlatAffineConstraints &srcDomain, |
| const FlatAffineConstraints &dstDomain, |
| const ValuePositionMap &valuePosMap, |
| FlatAffineConstraints *dependenceDomain) { |
| unsigned srcNumIneq = srcDomain.getNumInequalities(); |
| unsigned srcNumDims = srcDomain.getNumDimIds(); |
| unsigned srcNumSymbols = srcDomain.getNumSymbolIds(); |
| unsigned srcNumIds = srcNumDims + srcNumSymbols; |
| |
| unsigned dstNumIneq = dstDomain.getNumInequalities(); |
| unsigned dstNumDims = dstDomain.getNumDimIds(); |
| unsigned dstNumSymbols = dstDomain.getNumSymbolIds(); |
| unsigned dstNumIds = dstNumDims + dstNumSymbols; |
| |
| SmallVector<int64_t, 4> ineq(dependenceDomain->getNumCols()); |
| // Add inequalities from src domain. |
| for (unsigned i = 0; i < srcNumIneq; ++i) { |
| // Zero fill. |
| std::fill(ineq.begin(), ineq.end(), 0); |
| // Set coefficients for identifiers corresponding to src domain. |
| for (unsigned j = 0; j < srcNumIds; ++j) |
| ineq[valuePosMap.getSrcDimOrSymPos(srcDomain.getIdValue(j))] = |
| srcDomain.atIneq(i, j); |
| // Set constant term. |
| ineq[ineq.size() - 1] = srcDomain.atIneq(i, srcNumIds); |
| // Add inequality constraint. |
| dependenceDomain->addInequality(ineq); |
| } |
| // Add inequalities from dst domain. |
| for (unsigned i = 0; i < dstNumIneq; ++i) { |
| // Zero fill. |
| std::fill(ineq.begin(), ineq.end(), 0); |
| // Set coefficients for identifiers corresponding to dst domain. |
| for (unsigned j = 0; j < dstNumIds; ++j) |
| ineq[valuePosMap.getDstDimOrSymPos(dstDomain.getIdValue(j))] = |
| dstDomain.atIneq(i, j); |
| // Set constant term. |
| ineq[ineq.size() - 1] = dstDomain.atIneq(i, dstNumIds); |
| // Add inequality constraint. |
| dependenceDomain->addInequality(ineq); |
| } |
| } |
| |
| // Adds equality constraints that equate src and dst access functions |
| // represented by 'srcAccessMap' and 'dstAccessMap' for each result. |
| // Requires that 'srcAccessMap' and 'dstAccessMap' have the same results count. |
| // For example, given the following two accesses functions to a 2D memref: |
| // |
| // Source access function: |
| // (a0 * d0 + a1 * s0 + a2, b0 * d0 + b1 * s0 + b2) |
| // |
| // Destination acceses function: |
| // (c0 * d0 + c1 * s0 + c2, f0 * d0 + f1 * s0 + f2) |
| // |
| // This method constructs the following equality constraints in |
| // 'dependenceDomain', by equating the access functions for each result |
| // (i.e. each memref dim). Notice that 'd0' for the destination access function |
| // is mapped into 'd0' in the equality constraint: |
| // |
| // d0 d1 s0 c |
| // -- -- -- -- |
| // a0 -c0 (a1 - c1) (a1 - c2) = 0 |
| // b0 -f0 (b1 - f1) (b1 - f2) = 0 |
| // |
| // Returns failure if any AffineExpr cannot be flattened (due to it being |
| // semi-affine). Returns success otherwise. |
| // TODO(bondhugula): assumes that dependenceDomain doesn't have local |
| // variables already. Fix this soon. |
| static LogicalResult |
| addMemRefAccessConstraints(const AffineValueMap &srcAccessMap, |
| const AffineValueMap &dstAccessMap, |
| const ValuePositionMap &valuePosMap, |
| FlatAffineConstraints *dependenceDomain) { |
| if (dependenceDomain->getNumLocalIds() != 0) |
| return failure(); |
| AffineMap srcMap = srcAccessMap.getAffineMap(); |
| AffineMap dstMap = dstAccessMap.getAffineMap(); |
| assert(srcMap.getNumResults() == dstMap.getNumResults()); |
| unsigned numResults = srcMap.getNumResults(); |
| |
| unsigned srcNumIds = srcMap.getNumDims() + srcMap.getNumSymbols(); |
| ArrayRef<Value *> srcOperands = srcAccessMap.getOperands(); |
| |
| unsigned dstNumIds = dstMap.getNumDims() + dstMap.getNumSymbols(); |
| ArrayRef<Value *> dstOperands = dstAccessMap.getOperands(); |
| |
| std::vector<SmallVector<int64_t, 8>> srcFlatExprs; |
| std::vector<SmallVector<int64_t, 8>> destFlatExprs; |
| FlatAffineConstraints srcLocalVarCst, destLocalVarCst; |
| // Get flattened expressions for the source destination maps. |
| if (failed(getFlattenedAffineExprs(srcMap, &srcFlatExprs, &srcLocalVarCst)) || |
| failed(getFlattenedAffineExprs(dstMap, &destFlatExprs, &destLocalVarCst))) |
| return failure(); |
| |
| unsigned srcNumLocalIds = srcLocalVarCst.getNumLocalIds(); |
| unsigned dstNumLocalIds = destLocalVarCst.getNumLocalIds(); |
| unsigned numLocalIdsToAdd = srcNumLocalIds + dstNumLocalIds; |
| for (unsigned i = 0; i < numLocalIdsToAdd; i++) { |
| dependenceDomain->addLocalId(dependenceDomain->getNumLocalIds()); |
| } |
| |
| unsigned numDims = dependenceDomain->getNumDimIds(); |
| unsigned numSymbols = dependenceDomain->getNumSymbolIds(); |
| unsigned numSrcLocalIds = srcLocalVarCst.getNumLocalIds(); |
| |
| // Equality to add. |
| SmallVector<int64_t, 8> eq(dependenceDomain->getNumCols()); |
| for (unsigned i = 0; i < numResults; ++i) { |
| // Zero fill. |
| std::fill(eq.begin(), eq.end(), 0); |
| |
| // Flattened AffineExpr for src result 'i'. |
| const auto &srcFlatExpr = srcFlatExprs[i]; |
| // Set identifier coefficients from src access function. |
| for (unsigned j = 0, e = srcOperands.size(); j < e; ++j) |
| eq[valuePosMap.getSrcDimOrSymPos(srcOperands[j])] = srcFlatExpr[j]; |
| // Local terms. |
| for (unsigned j = 0, e = srcNumLocalIds; j < e; j++) |
| eq[numDims + numSymbols + j] = srcFlatExpr[srcNumIds + j]; |
| // Set constant term. |
| eq[eq.size() - 1] = srcFlatExpr[srcFlatExpr.size() - 1]; |
| |
| // Flattened AffineExpr for dest result 'i'. |
| const auto &destFlatExpr = destFlatExprs[i]; |
| // Set identifier coefficients from dst access function. |
| for (unsigned j = 0, e = dstOperands.size(); j < e; ++j) |
| eq[valuePosMap.getDstDimOrSymPos(dstOperands[j])] -= destFlatExpr[j]; |
| // Local terms. |
| for (unsigned j = 0, e = dstNumLocalIds; j < e; j++) |
| eq[numDims + numSymbols + numSrcLocalIds + j] = |
| -destFlatExpr[dstNumIds + j]; |
| // Set constant term. |
| eq[eq.size() - 1] -= destFlatExpr[destFlatExpr.size() - 1]; |
| |
| // Add equality constraint. |
| dependenceDomain->addEquality(eq); |
| } |
| |
| // Add equality constraints for any operands that are defined by constant ops. |
| auto addEqForConstOperands = [&](ArrayRef<Value *> operands) { |
| for (unsigned i = 0, e = operands.size(); i < e; ++i) { |
| if (isForInductionVar(operands[i])) |
| continue; |
| auto *symbol = operands[i]; |
| assert(isValidSymbol(symbol)); |
| // Check if the symbol is a constant. |
| if (auto *opInst = symbol->getDefiningInst()) { |
| if (auto constOp = opInst->dyn_cast<ConstantIndexOp>()) { |
| dependenceDomain->setIdToConstant(valuePosMap.getSymPos(symbol), |
| constOp.getValue()); |
| } |
| } |
| } |
| }; |
| |
| // Add equality constraints for any src symbols defined by constant ops. |
| addEqForConstOperands(srcOperands); |
| // Add equality constraints for any dst symbols defined by constant ops. |
| addEqForConstOperands(dstOperands); |
| |
| // By construction (see flattener), local var constraints will not have any |
| // equalities. |
| assert(srcLocalVarCst.getNumEqualities() == 0 && |
| destLocalVarCst.getNumEqualities() == 0); |
| // Add inequalities from srcLocalVarCst and destLocalVarCst into the |
| // dependence domain. |
| SmallVector<int64_t, 8> ineq(dependenceDomain->getNumCols()); |
| for (unsigned r = 0, e = srcLocalVarCst.getNumInequalities(); r < e; r++) { |
| std::fill(ineq.begin(), ineq.end(), 0); |
| |
| // Set identifier coefficients from src local var constraints. |
| for (unsigned j = 0, e = srcOperands.size(); j < e; ++j) |
| ineq[valuePosMap.getSrcDimOrSymPos(srcOperands[j])] = |
| srcLocalVarCst.atIneq(r, j); |
| // Local terms. |
| for (unsigned j = 0, e = srcNumLocalIds; j < e; j++) |
| ineq[numDims + numSymbols + j] = srcLocalVarCst.atIneq(r, srcNumIds + j); |
| // Set constant term. |
| ineq[ineq.size() - 1] = |
| srcLocalVarCst.atIneq(r, srcLocalVarCst.getNumCols() - 1); |
| dependenceDomain->addInequality(ineq); |
| } |
| |
| for (unsigned r = 0, e = destLocalVarCst.getNumInequalities(); r < e; r++) { |
| std::fill(ineq.begin(), ineq.end(), 0); |
| // Set identifier coefficients from dest local var constraints. |
| for (unsigned j = 0, e = dstOperands.size(); j < e; ++j) |
| ineq[valuePosMap.getDstDimOrSymPos(dstOperands[j])] = |
| destLocalVarCst.atIneq(r, j); |
| // Local terms. |
| for (unsigned j = 0, e = dstNumLocalIds; j < e; j++) |
| ineq[numDims + numSymbols + numSrcLocalIds + j] = |
| destLocalVarCst.atIneq(r, dstNumIds + j); |
| // Set constant term. |
| ineq[ineq.size() - 1] = |
| destLocalVarCst.atIneq(r, destLocalVarCst.getNumCols() - 1); |
| |
| dependenceDomain->addInequality(ineq); |
| } |
| return success(); |
| } |
| |
| // Returns the number of outer loop common to 'src/dstDomain'. |
| static unsigned getNumCommonLoops(const FlatAffineConstraints &srcDomain, |
| const FlatAffineConstraints &dstDomain) { |
| // Find the number of common loops shared by src and dst accesses. |
| unsigned minNumLoops = |
| std::min(srcDomain.getNumDimIds(), dstDomain.getNumDimIds()); |
| unsigned numCommonLoops = 0; |
| for (unsigned i = 0; i < minNumLoops; ++i) { |
| if (!isForInductionVar(srcDomain.getIdValue(i)) || |
| !isForInductionVar(dstDomain.getIdValue(i)) || |
| srcDomain.getIdValue(i) != dstDomain.getIdValue(i)) |
| break; |
| ++numCommonLoops; |
| } |
| return numCommonLoops; |
| } |
| |
| // Returns Block common to 'srcAccess.opInst' and 'dstAccess.opInst'. |
| static Block *getCommonBlock(const MemRefAccess &srcAccess, |
| const MemRefAccess &dstAccess, |
| const FlatAffineConstraints &srcDomain, |
| unsigned numCommonLoops) { |
| if (numCommonLoops == 0) { |
| auto *block = srcAccess.opInst->getBlock(); |
| while (block->getContainingInst()) { |
| block = block->getContainingInst()->getBlock(); |
| } |
| return block; |
| } |
| auto *commonForValue = srcDomain.getIdValue(numCommonLoops - 1); |
| auto forOp = getForInductionVarOwner(commonForValue); |
| assert(forOp && "commonForValue was not an induction variable"); |
| return forOp.getBody(); |
| } |
| |
| // Returns true if the ancestor operation instruction of 'srcAccess' appears |
| // before the ancestor operation instruction of 'dstAccess' in the common |
| // ancestral block. Returns false otherwise. |
| // Note that because 'srcAccess' or 'dstAccess' may be nested in conditionals, |
| // the function is named 'srcAppearsBeforeDstInCommonBlock'. |
| // Note that 'numCommonLoops' is the number of contiguous surrounding outer |
| // loops. |
| static bool srcAppearsBeforeDstInAncestralBlock( |
| const MemRefAccess &srcAccess, const MemRefAccess &dstAccess, |
| const FlatAffineConstraints &srcDomain, unsigned numCommonLoops) { |
| // Get Block common to 'srcAccess.opInst' and 'dstAccess.opInst'. |
| auto *commonBlock = |
| getCommonBlock(srcAccess, dstAccess, srcDomain, numCommonLoops); |
| // Check the dominance relationship between the respective ancestors of the |
| // src and dst in the Block of the innermost among the common loops. |
| auto *srcInst = commonBlock->findAncestorInstInBlock(*srcAccess.opInst); |
| assert(srcInst != nullptr); |
| auto *dstInst = commonBlock->findAncestorInstInBlock(*dstAccess.opInst); |
| assert(dstInst != nullptr); |
| |
| // Determine whether dstInst comes after srcInst. |
| return srcInst->isBeforeInBlock(dstInst); |
| } |
| |
| // Adds ordering constraints to 'dependenceDomain' based on number of loops |
| // common to 'src/dstDomain' and requested 'loopDepth'. |
| // Note that 'loopDepth' cannot exceed the number of common loops plus one. |
| // EX: Given a loop nest of depth 2 with IVs 'i' and 'j': |
| // *) If 'loopDepth == 1' then one constraint is added: i' >= i + 1 |
| // *) If 'loopDepth == 2' then two constraints are added: i == i' and j' > j + 1 |
| // *) If 'loopDepth == 3' then two constraints are added: i == i' and j == j' |
| static void addOrderingConstraints(const FlatAffineConstraints &srcDomain, |
| const FlatAffineConstraints &dstDomain, |
| unsigned loopDepth, |
| FlatAffineConstraints *dependenceDomain) { |
| unsigned numCols = dependenceDomain->getNumCols(); |
| SmallVector<int64_t, 4> eq(numCols); |
| unsigned numSrcDims = srcDomain.getNumDimIds(); |
| unsigned numCommonLoops = getNumCommonLoops(srcDomain, dstDomain); |
| unsigned numCommonLoopConstraints = std::min(numCommonLoops, loopDepth); |
| for (unsigned i = 0; i < numCommonLoopConstraints; ++i) { |
| std::fill(eq.begin(), eq.end(), 0); |
| eq[i] = -1; |
| eq[i + numSrcDims] = 1; |
| if (i == loopDepth - 1) { |
| eq[numCols - 1] = -1; |
| dependenceDomain->addInequality(eq); |
| } else { |
| dependenceDomain->addEquality(eq); |
| } |
| } |
| } |
| |
| // Returns true if 'isEq' constraint in 'dependenceDomain' has a single |
| // non-zero coefficient at (rowIdx, idPos). Returns false otherwise. |
| // TODO(andydavis) Move this function to FlatAffineConstraints. |
| static bool hasSingleNonZeroAt(unsigned idPos, unsigned rowIdx, bool isEq, |
| FlatAffineConstraints *dependenceDomain) { |
| unsigned numCols = dependenceDomain->getNumCols(); |
| for (unsigned j = 0; j < numCols - 1; ++j) { |
| int64_t v = isEq ? dependenceDomain->atEq(rowIdx, j) |
| : dependenceDomain->atIneq(rowIdx, j); |
| if ((j == idPos && v == 0) || (j != idPos && v != 0)) |
| return false; |
| } |
| return true; |
| } |
| |
| // Computes distance and direction vectors in 'dependences', by adding |
| // variables to 'dependenceDomain' which represent the difference of the IVs, |
| // eliminating all other variables, and reading off distance vectors from |
| // equality constraints (if possible), and direction vectors from inequalities. |
| static void computeDirectionVector( |
| const FlatAffineConstraints &srcDomain, |
| const FlatAffineConstraints &dstDomain, unsigned loopDepth, |
| FlatAffineConstraints *dependenceDomain, |
| llvm::SmallVector<DependenceComponent, 2> *dependenceComponents) { |
| // Find the number of common loops shared by src and dst accesses. |
| unsigned numCommonLoops = getNumCommonLoops(srcDomain, dstDomain); |
| if (numCommonLoops == 0) |
| return; |
| // Compute direction vectors for requested loop depth. |
| unsigned numIdsToEliminate = dependenceDomain->getNumIds(); |
| // Add new variables to 'dependenceDomain' to represent the direction |
| // constraints for each shared loop. |
| for (unsigned j = 0; j < numCommonLoops; ++j) { |
| dependenceDomain->addDimId(j); |
| } |
| |
| // Add equality contraints for each common loop, setting newly introduced |
| // variable at column 'j' to the 'dst' IV minus the 'src IV. |
| SmallVector<int64_t, 4> eq; |
| eq.resize(dependenceDomain->getNumCols()); |
| for (unsigned j = 0; j < numCommonLoops; ++j) { |
| std::fill(eq.begin(), eq.end(), 0); |
| eq[j] = 1; |
| eq[j + numCommonLoops] = 1; |
| eq[j + 2 * numCommonLoops] = -1; |
| dependenceDomain->addEquality(eq); |
| } |
| |
| // Eliminate all variables other than the direction variables just added. |
| dependenceDomain->projectOut(numCommonLoops, numIdsToEliminate); |
| |
| // Scan each common loop variable column and set direction vectors based |
| // on eliminated constraint system. |
| dependenceComponents->resize(numCommonLoops); |
| for (unsigned j = 0; j < numCommonLoops; ++j) { |
| auto lbConst = dependenceDomain->getConstantLowerBound(j); |
| (*dependenceComponents)[j].lb = |
| lbConst.getValueOr(std::numeric_limits<int64_t>::min()); |
| auto ubConst = dependenceDomain->getConstantUpperBound(j); |
| (*dependenceComponents)[j].ub = |
| ubConst.getValueOr(std::numeric_limits<int64_t>::max()); |
| } |
| } |
| |
| // Populates 'accessMap' with composition of AffineApplyOps reachable from |
| // indices of MemRefAccess. |
| void MemRefAccess::getAccessMap(AffineValueMap *accessMap) const { |
| auto memrefType = memref->getType().cast<MemRefType>(); |
| // Create identity map with same number of dimensions as 'memrefType' rank. |
| auto map = AffineMap::getMultiDimIdentityMap(memrefType.getRank(), |
| memref->getType().getContext()); |
| SmallVector<Value *, 8> operands(indices.begin(), indices.end()); |
| fullyComposeAffineMapAndOperands(&map, &operands); |
| map = simplifyAffineMap(map); |
| canonicalizeMapAndOperands(&map, &operands); |
| accessMap->reset(map, operands); |
| } |
| |
| // Builds a flat affine constraint system to check if there exists a dependence |
| // between memref accesses 'srcAccess' and 'dstAccess'. |
| // Returns 'false' if the accesses can be definitively shown not to access the |
| // same element. Returns 'true' otherwise. |
| // If a dependence exists, returns in 'dependenceComponents' a direction |
| // vector for the dependence, with a component for each loop IV in loops |
| // common to both accesses (see Dependence in AffineAnalysis.h for details). |
| // |
| // The memref access dependence check is comprised of the following steps: |
| // *) Compute access functions for each access. Access functions are computed |
| // using AffineValueMaps initialized with the indices from an access, then |
| // composed with AffineApplyOps reachable from operands of that access, |
| // until operands of the AffineValueMap are loop IVs or symbols. |
| // *) Build iteration domain constraints for each access. Iteration domain |
| // constraints are pairs of inequality contraints representing the |
| // upper/lower loop bounds for each AffineForOp in the loop nest associated |
| // with each access. |
| // *) Build dimension and symbol position maps for each access, which map |
| // Values from access functions and iteration domains to their position |
| // in the merged constraint system built by this method. |
| // |
| // This method builds a constraint system with the following column format: |
| // |
| // [src-dim-identifiers, dst-dim-identifiers, symbols, constant] |
| // |
| // For example, given the following MLIR code with with "source" and |
| // "destination" accesses to the same memref labled, and symbols %M, %N, %K: |
| // |
| // affine.for %i0 = 0 to 100 { |
| // affine.for %i1 = 0 to 50 { |
| // %a0 = affine.apply |
| // (d0, d1) -> (d0 * 2 - d1 * 4 + s1, d1 * 3 - s0) (%i0, %i1)[%M, %N] |
| // // Source memref access. |
| // store %v0, %m[%a0#0, %a0#1] : memref<4x4xf32> |
| // } |
| // } |
| // |
| // affine.for %i2 = 0 to 100 { |
| // affine.for %i3 = 0 to 50 { |
| // %a1 = affine.apply |
| // (d0, d1) -> (d0 * 7 + d1 * 9 - s1, d1 * 11 + s0) (%i2, %i3)[%K, %M] |
| // // Destination memref access. |
| // %v1 = load %m[%a1#0, %a1#1] : memref<4x4xf32> |
| // } |
| // } |
| // |
| // The access functions would be the following: |
| // |
| // src: (%i0 * 2 - %i1 * 4 + %N, %i1 * 3 - %M) |
| // dst: (%i2 * 7 + %i3 * 9 - %M, %i3 * 11 - %K) |
| // |
| // The iteration domains for the src/dst accesses would be the following: |
| // |
| // src: 0 <= %i0 <= 100, 0 <= %i1 <= 50 |
| // dst: 0 <= %i2 <= 100, 0 <= %i3 <= 50 |
| // |
| // The symbols by both accesses would be assigned to a canonical position order |
| // which will be used in the dependence constraint system: |
| // |
| // symbol name: %M %N %K |
| // symbol pos: 0 1 2 |
| // |
| // Equality constraints are built by equating each result of src/destination |
| // access functions. For this example, the following two equality constraints |
| // will be added to the dependence constraint system: |
| // |
| // [src_dim0, src_dim1, dst_dim0, dst_dim1, sym0, sym1, sym2, const] |
| // 2 -4 -7 -9 1 1 0 0 = 0 |
| // 0 3 0 -11 -1 0 1 0 = 0 |
| // |
| // Inequality constraints from the iteration domain will be meged into |
| // the dependence constraint system |
| // |
| // [src_dim0, src_dim1, dst_dim0, dst_dim1, sym0, sym1, sym2, const] |
| // 1 0 0 0 0 0 0 0 >= 0 |
| // -1 0 0 0 0 0 0 100 >= 0 |
| // 0 1 0 0 0 0 0 0 >= 0 |
| // 0 -1 0 0 0 0 0 50 >= 0 |
| // 0 0 1 0 0 0 0 0 >= 0 |
| // 0 0 -1 0 0 0 0 100 >= 0 |
| // 0 0 0 1 0 0 0 0 >= 0 |
| // 0 0 0 -1 0 0 0 50 >= 0 |
| // |
| // |
| // TODO(andydavis) Support AffineExprs mod/floordiv/ceildiv. |
| bool mlir::checkMemrefAccessDependence( |
| const MemRefAccess &srcAccess, const MemRefAccess &dstAccess, |
| unsigned loopDepth, FlatAffineConstraints *dependenceConstraints, |
| llvm::SmallVector<DependenceComponent, 2> *dependenceComponents, |
| bool allowRAR) { |
| LLVM_DEBUG(llvm::dbgs() << "Checking for dependence at depth: " |
| << Twine(loopDepth) << " between:\n";); |
| LLVM_DEBUG(srcAccess.opInst->dump();); |
| LLVM_DEBUG(dstAccess.opInst->dump();); |
| |
| // Return 'false' if these accesses do not acces the same memref. |
| if (srcAccess.memref != dstAccess.memref) |
| return false; |
| // Return 'false' if one of these accesses is not a StoreOp. |
| if (!allowRAR && !srcAccess.opInst->isa<StoreOp>() && |
| !dstAccess.opInst->isa<StoreOp>()) |
| return false; |
| |
| // Get composed access function for 'srcAccess'. |
| AffineValueMap srcAccessMap; |
| srcAccess.getAccessMap(&srcAccessMap); |
| |
| // Get composed access function for 'dstAccess'. |
| AffineValueMap dstAccessMap; |
| dstAccess.getAccessMap(&dstAccessMap); |
| |
| // Get iteration domain for the 'srcAccess' instruction. |
| FlatAffineConstraints srcDomain; |
| if (failed(getInstIndexSet(srcAccess.opInst, &srcDomain))) |
| return false; |
| |
| // Get iteration domain for 'dstAccess' instruction. |
| FlatAffineConstraints dstDomain; |
| if (failed(getInstIndexSet(dstAccess.opInst, &dstDomain))) |
| return false; |
| |
| // Return 'false' if loopDepth > numCommonLoops and if the ancestor operation |
| // instruction of 'srcAccess' does not properly dominate the ancestor |
| // operation instruction of 'dstAccess' in the same common instruction block. |
| // Note: this check is skipped if 'allowRAR' is true, because because RAR |
| // deps can exist irrespective of lexicographic ordering b/w src and dst. |
| unsigned numCommonLoops = getNumCommonLoops(srcDomain, dstDomain); |
| assert(loopDepth <= numCommonLoops + 1); |
| if (!allowRAR && loopDepth > numCommonLoops && |
| !srcAppearsBeforeDstInAncestralBlock(srcAccess, dstAccess, srcDomain, |
| numCommonLoops)) { |
| return false; |
| } |
| // Build dim and symbol position maps for each access from access operand |
| // Value to position in merged contstraint system. |
| ValuePositionMap valuePosMap; |
| buildDimAndSymbolPositionMaps(srcDomain, dstDomain, srcAccessMap, |
| dstAccessMap, &valuePosMap, |
| dependenceConstraints); |
| |
| initDependenceConstraints(srcDomain, dstDomain, srcAccessMap, dstAccessMap, |
| valuePosMap, dependenceConstraints); |
| |
| assert(valuePosMap.getNumDims() == |
| srcDomain.getNumDimIds() + dstDomain.getNumDimIds()); |
| |
| // Create memref access constraint by equating src/dst access functions. |
| // Note that this check is conservative, and will fail in the future when |
| // local variables for mod/div exprs are supported. |
| if (failed(addMemRefAccessConstraints(srcAccessMap, dstAccessMap, valuePosMap, |
| dependenceConstraints))) |
| return true; |
| |
| // Add 'src' happens before 'dst' ordering constraints. |
| addOrderingConstraints(srcDomain, dstDomain, loopDepth, |
| dependenceConstraints); |
| // Add src and dst domain constraints. |
| addDomainConstraints(srcDomain, dstDomain, valuePosMap, |
| dependenceConstraints); |
| |
| // Return false if the solution space is empty: no dependence. |
| if (dependenceConstraints->isEmpty()) { |
| return false; |
| } |
| |
| // Compute dependence direction vector and return true. |
| if (dependenceComponents != nullptr) { |
| computeDirectionVector(srcDomain, dstDomain, loopDepth, |
| dependenceConstraints, dependenceComponents); |
| } |
| |
| LLVM_DEBUG(llvm::dbgs() << "Dependence polyhedron:\n"); |
| LLVM_DEBUG(dependenceConstraints->dump()); |
| return true; |
| } |
