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llvm-project/mlir/lib/Analysis/AffineAnalysis.cpp

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//===- 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<OpPointer<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(const Instruction *inst,
FlatAffineConstraints *indexSet) {
// TODO(andydavis) Extend this to gather enclosing IfInsts and consider
// factoring it out into a utility function.
SmallVector<OpPointer<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(const Value *value) {
if (addValueAt(value, &srcDimPosMap, numSrcDims))
++numSrcDims;
}
void addDstValue(const Value *value) {
if (addValueAt(value, &dstDimPosMap, numDstDims))
++numDstDims;
}
void addSymbolValue(const Value *value) {
if (addValueAt(value, &symbolPosMap, numSymbols))
++numSymbols;
}
unsigned getSrcDimOrSymPos(const Value *value) const {
return getDimOrSymPos(value, srcDimPosMap, 0);
}
unsigned getDstDimOrSymPos(const Value *value) const {
return getDimOrSymPos(value, dstDimPosMap, numSrcDims);
}
unsigned getSymPos(const 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(const Value *value, DenseMap<const Value *, unsigned> *posMap,
unsigned position) {
auto it = posMap->find(value);
if (it == posMap->end()) {
(*posMap)[value] = position;
return true;
}
return false;
}
unsigned getDimOrSymPos(const Value *value,
const DenseMap<const 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<const Value *, unsigned> srcDimPosMap;
DenseMap<const Value *, unsigned> dstDimPosMap;
DenseMap<const 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<const 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:
//
// for %i0 = 0 to 100 {
// 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>
// }
// }
//
// for %i2 = 0 to 100 {
// 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;
}
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