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android / platform / external / tensorflow / e1ab44a457e / . / 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/Analysis/AffineStructures.h"
#include "mlir/Analysis/Utils.h"
#include "mlir/IR/AffineExprVisitor.h"
#include "mlir/IR/BuiltinOps.h"
#include "mlir/IR/Statements.h"
#include "mlir/StandardOps/StandardOps.h"
#include "mlir/Support/MathExtras.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/Support/raw_ostream.h"
using namespace mlir;
/// Constructs an affine expression from a flat ArrayRef. If there are local
/// identifiers (neither dimensional nor symbolic) that appear in the sum of
/// products expression, 'localExprs' is expected to have the AffineExpr
/// for it, and is substituted into. The ArrayRef 'eq' is expected to be in the
/// format [dims, symbols, locals, constant term].
// TODO(bondhugula): refactor getAddMulPureAffineExpr to reuse it from here.
static AffineExpr toAffineExpr(ArrayRef<int64_t> eq, unsigned numDims,
unsigned numSymbols,
ArrayRef<AffineExpr> localExprs,
MLIRContext *context) {
// Assert expected numLocals = eq.size() - numDims - numSymbols - 1
assert(eq.size() - numDims - numSymbols - 1 == localExprs.size() &&
"unexpected number of local expressions");
auto expr = getAffineConstantExpr(0, context);
// Dimensions and symbols.
for (unsigned j = 0; j < numDims + numSymbols; j++) {
if (eq[j] == 0) {
continue;
}
auto id = j < numDims ? getAffineDimExpr(j, context)
: getAffineSymbolExpr(j - numDims, context);
expr = expr + id * eq[j];
}
// Local identifiers.
for (unsigned j = numDims + numSymbols; j < eq.size() - 1; j++) {
if (eq[j] == 0) {
continue;
}
auto term = localExprs[j - numDims - numSymbols] * eq[j];
expr = expr + term;
}
// Constant term.
int64_t constTerm = eq[eq.size() - 1];
if (constTerm != 0)
expr = expr + constTerm;
return expr;
}
namespace {
// This class is used to flatten a pure affine expression (AffineExpr,
// which is in a tree form) into a sum of products (w.r.t constants) when
// possible, and in that process simplifying the expression. The simplification
// performed includes the accumulation of contributions for each dimensional and
// symbolic identifier together, the simplification of floordiv/ceildiv/mod
// expressions and other simplifications that in turn happen as a result. A
// simplification that this flattening naturally performs is of simplifying the
// numerator and denominator of floordiv/ceildiv, and folding a modulo
// expression to a zero, if possible. Three examples are below:
//
// (d0 + 3 * d1) + d0) - 2 * d1) - d0 simplified to d0 + d1
// (d0 - d0 mod 4 + 4) mod 4 simplified to 0.
// (3*d0 + 2*d1 + d0) floordiv 2 + d1 simplified to 2*d0 + 2*d1
//
// For a modulo, floordiv, or a ceildiv expression, an additional identifier
// (called a local identifier) is introduced to rewrite it as a sum of products
// (w.r.t constants). For example, for the second example above, d0 % 4 is
// replaced by d0 - 4*q with q being introduced: the expression then simplifies
// to: (d0 - (d0 - 4q) + 4) = 4q + 4, modulo of which w.r.t 4 simplifies to
// zero. Note that an affine expression may not always be expressible in a sum
// of products form due to the presence of modulo/floordiv/ceildiv expressions
// that may not be eliminated after simplification; in such cases, the final
// expression can be reconstructed by replacing the local identifier with its
// explicit form stored in localExprs (note that the explicit form itself would
// have been simplified and not necessarily the original form).
//
// This is a linear time post order walk for an affine expression that attempts
// the above simplifications through visit methods, with partial results being
// stored in 'operandExprStack'. When a parent expr is visited, the flattened
// expressions corresponding to its two operands would already be on the stack -
// the parent expr looks at the two flattened expressions and combines the two.
// It pops off the operand expressions and pushes the combined result (although
// this is done in-place on its LHS operand expr. When the walk is completed,
// the flattened form of the top-level expression would be left on the stack.
//
class AffineExprFlattener : public AffineExprVisitor<AffineExprFlattener> {
public:
// Flattend expression layout: [dims, symbols, locals, constant]
// Stack that holds the LHS and RHS operands while visiting a binary op expr.
// In future, consider adding a prepass to determine how big the SmallVector's
// will be, and linearize this to std::vector<int64_t> to prevent
// SmallVector moves on re-allocation.
std::vector<SmallVector<int64_t, 32>> operandExprStack;
// Constraints connecting newly introduced local variables to existing
// (dimensional and symbolic) ones.
FlatAffineConstraints cst;
inline unsigned getNumCols() const {
return numDims + numSymbols + numLocals + 1;
}
unsigned numDims;
unsigned numSymbols;
// Number of newly introduced identifiers to flatten mod/floordiv/ceildiv
// expressions that could not be simplified.
unsigned numLocals;
// AffineExpr's corresponding to the floordiv/ceildiv/mod expressions for
// which new identifiers were introduced; if the latter do not get canceled
// out, these expressions are needed to reconstruct the AffineExpr / tree
// form. Note that these expressions themselves would have been simplified
// (recursively) by this pass. Eg. d0 + (d0 + 2*d1 + d0) ceildiv 4 will be
// simplified to d0 + q, where q = (d0 + d1) ceildiv 2. (d0 + d1) ceildiv 2
// would be the local expression stored for q.
SmallVector<AffineExpr, 4> localExprs;
MLIRContext *context;
AffineExprFlattener(unsigned numDims, unsigned numSymbols,
MLIRContext *context)
: numDims(numDims), numSymbols(numSymbols), numLocals(0),
context(context) {
operandExprStack.reserve(8);
cst.reset(numDims, numSymbols, numLocals);
}
void visitMulExpr(AffineBinaryOpExpr expr) {
assert(operandExprStack.size() >= 2);
// This is a pure affine expr; the RHS will be a constant.
assert(expr.getRHS().isa<AffineConstantExpr>());
// Get the RHS constant.
auto rhsConst = operandExprStack.back()[getConstantIndex()];
operandExprStack.pop_back();
// Update the LHS in place instead of pop and push.
auto &lhs = operandExprStack.back();
for (unsigned i = 0, e = lhs.size(); i < e; i++) {
lhs[i] *= rhsConst;
}
}
void visitAddExpr(AffineBinaryOpExpr expr) {
assert(operandExprStack.size() >= 2);
const auto &rhs = operandExprStack.back();
auto &lhs = operandExprStack[operandExprStack.size() - 2];
assert(lhs.size() == rhs.size());
// Update the LHS in place.
for (unsigned i = 0; i < rhs.size(); i++) {
lhs[i] += rhs[i];
}
// Pop off the RHS.
operandExprStack.pop_back();
}
void visitModExpr(AffineBinaryOpExpr expr) {
assert(operandExprStack.size() >= 2);
// This is a pure affine expr; the RHS will be a constant.
assert(expr.getRHS().isa<AffineConstantExpr>());
auto rhsConst = operandExprStack.back()[getConstantIndex()];
operandExprStack.pop_back();
auto &lhs = operandExprStack.back();
// TODO(bondhugula): handle modulo by zero case when this issue is fixed
// at the other places in the IR.
assert(rhsConst != 0 && "RHS constant can't be zero");
// Check if the LHS expression is a multiple of modulo factor.
unsigned i;
for (i = 0; i < lhs.size(); i++)
if (lhs[i] % rhsConst != 0)
break;
// If yes, modulo expression here simplifies to zero.
if (i == lhs.size()) {
std::fill(lhs.begin(), lhs.end(), 0);
return;
}
// Add an existential quantifier. expr1 % c is replaced by (expr1 -
// q * c) where q is the existential quantifier introduced.
auto a = toAffineExpr(lhs, numDims, numSymbols, localExprs, context);
auto b = getAffineConstantExpr(rhsConst, context);
addLocalId(a.floorDiv(b));
lhs[getLocalVarStartIndex() + numLocals - 1] = -rhsConst;
// Update cst: 0 <= expr1 - c * expr2 <= c - 1.
cst.addConstantLowerBound(lhs, 0);
cst.addConstantUpperBound(lhs, rhsConst - 1);
}
void visitCeilDivExpr(AffineBinaryOpExpr expr) {
visitDivExpr(expr, /*isCeil=*/true);
}
void visitFloorDivExpr(AffineBinaryOpExpr expr) {
visitDivExpr(expr, /*isCeil=*/false);
}
void visitDimExpr(AffineDimExpr expr) {
operandExprStack.emplace_back(SmallVector<int64_t, 32>(getNumCols(), 0));
auto &eq = operandExprStack.back();
assert(expr.getPosition() < numDims && "Inconsistent number of dims");
eq[getDimStartIndex() + expr.getPosition()] = 1;
}
void visitSymbolExpr(AffineSymbolExpr expr) {
operandExprStack.emplace_back(SmallVector<int64_t, 32>(getNumCols(), 0));
auto &eq = operandExprStack.back();
assert(expr.getPosition() < numSymbols && "inconsistent number of symbols");
eq[getSymbolStartIndex() + expr.getPosition()] = 1;
}
void visitConstantExpr(AffineConstantExpr expr) {
operandExprStack.emplace_back(SmallVector<int64_t, 32>(getNumCols(), 0));
auto &eq = operandExprStack.back();
eq[getConstantIndex()] = expr.getValue();
}
private:
void visitDivExpr(AffineBinaryOpExpr expr, bool isCeil) {
assert(operandExprStack.size() >= 2);
assert(expr.getRHS().isa<AffineConstantExpr>());
// This is a pure affine expr; the RHS is a positive constant.
auto rhsConst = operandExprStack.back()[getConstantIndex()];
// TODO(bondhugula): handle division by zero at the same time the issue is
// fixed at other places.
assert(rhsConst != 0 && "RHS constant can't be zero");
operandExprStack.pop_back();
auto &lhs = operandExprStack.back();
// Simplify the floordiv, ceildiv if possible by canceling out the greatest
// common divisors of the numerator and denominator.
uint64_t gcd = std::abs(rhsConst);
for (unsigned i = 0; i < lhs.size(); i++)
gcd = llvm::GreatestCommonDivisor64(gcd, std::abs(lhs[i]));
// Simplify the numerator and the denominator.
if (gcd != 1) {
for (unsigned i = 0; i < lhs.size(); i++)
lhs[i] = lhs[i] / gcd;
}
int64_t denominator = rhsConst / gcd;
// If the denominator becomes 1, the updated LHS is the result. (The
// denominator can't be negative since rhsConst is positive).
if (denominator == 1)
return;
// If the denominator cannot be simplified to one, we will have to retain
// the ceil/floor expr (simplified up until here). Add an existential
// quantifier to express its result, i.e., expr1 div expr2 is replaced
// by a new identifier, q.
auto a = toAffineExpr(lhs, numDims, numSymbols, localExprs, context);
auto b = getAffineConstantExpr(denominator, context);
if (isCeil) {
addLocalId(a.ceilDiv(b));
} else {
addLocalId(a.floorDiv(b));
}
std::vector<int64_t> bound(lhs.size(), 0);
bound[getLocalVarStartIndex() + numLocals - 1] = rhsConst;
if (!isCeil) {
// q = lhs floordiv c <=> c*q <= lhs <= c*q + c - 1.
cst.addLowerBound(lhs, bound);
bound[bound.size() - 1] = rhsConst - 1;
cst.addUpperBound(lhs, bound);
} else {
// q = lhs ceildiv c <=> c*q - (c - 1) <= lhs <= c*q.
cst.addUpperBound(lhs, bound);
bound[bound.size() - 1] = -(rhsConst - 1);
cst.addLowerBound(lhs, bound);
}
// Set the expression on stack to the local var introduced to capture the
// result of the division (floor or ceil).
std::fill(lhs.begin(), lhs.end(), 0);
lhs[getLocalVarStartIndex() + numLocals - 1] = 1;
}
// Add an existential quantifier (used to flatten a mod, floordiv, ceildiv
// expr). localExpr is the simplified tree expression (AffineExpr)
// corresponding to the quantifier.
void addLocalId(AffineExpr localExpr) {
for (auto &subExpr : operandExprStack) {
subExpr.insert(subExpr.begin() + getLocalVarStartIndex() + numLocals, 0);
}
localExprs.push_back(localExpr);
numLocals++;
cst.addLocalId(cst.getNumLocalIds());
}
inline unsigned getConstantIndex() const { return getNumCols() - 1; }
inline unsigned getLocalVarStartIndex() const { return numDims + numSymbols; }
inline unsigned getSymbolStartIndex() const { return numDims; }
inline unsigned getDimStartIndex() const { return 0; }
};
} // end anonymous namespace
AffineExpr mlir::simplifyAffineExpr(AffineExpr expr, unsigned numDims,
unsigned numSymbols) {
// TODO(bondhugula): only pure affine for now. The simplification here can be
// extended to semi-affine maps in the future.
if (!expr.isPureAffine())
return expr;
AffineExprFlattener flattener(numDims, numSymbols, expr.getContext());
flattener.walkPostOrder(expr);
ArrayRef<int64_t> flattenedExpr = flattener.operandExprStack.back();
auto simplifiedExpr = toAffineExpr(flattenedExpr, numDims, numSymbols,
flattener.localExprs, expr.getContext());
flattener.operandExprStack.pop_back();
assert(flattener.operandExprStack.empty());
return simplifiedExpr;
}
// Flattens 'expr' into 'flattenedExpr'. Returns true on success or false
// if 'expr' was unable to be flattened (i.e., semi-affine expression has not
// been implemented yet).
bool mlir::getFlattenedAffineExpr(AffineExpr expr, unsigned numDims,
unsigned numSymbols,
llvm::SmallVectorImpl<int64_t> *flattenedExpr,
FlatAffineConstraints *cst) {
// TODO(bondhugula): only pure affine for now. The simplification here can be
// extended to semi-affine maps in the future.
if (!expr.isPureAffine())
return false;
AffineExprFlattener flattener(numDims, numSymbols, expr.getContext());
flattener.walkPostOrder(expr);
if (cst)
cst->clearAndCopyFrom(flattener.cst);
for (auto v : flattener.operandExprStack.back()) {
flattenedExpr->push_back(v);
}
return true;
}
/// Returns the sequence of AffineApplyOp OperationStmts 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<MLValue *> operands,
SmallVectorImpl<OperationStmt *> &affineApplyOps) {
struct State {
// The ssa value for this node in the DFS traversal.
MLValue *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 *opStmt = state.value->getDefiningStmt();
// Note: getDefiningStmt will return nullptr if the operand is not an
// OperationStmt (i.e. ForStmt), which is a terminator for the search.
if (opStmt == nullptr || !opStmt->isa<AffineApplyOp>()) {
worklist.pop_back();
continue;
}
if (auto affineApplyOp = opStmt->dyn_cast<AffineApplyOp>()) {
if (state.operandIndex == 0) {
// Pre-Visit: Add 'opStmt' to reachable sequence.
affineApplyOps.push_back(opStmt);
}
if (state.operandIndex < opStmt->getNumOperands()) {
// Visit: Add next 'affineApplyOp' operand to worklist.
// Get next operand to visit at 'operandIndex'.
auto *nextOperand = opStmt->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();
}
}
}
}
// Forward substitutes into 'valueMap' all AffineApplyOps reachable from the
// operands of 'valueMap'.
void mlir::forwardSubstituteReachableOps(AffineValueMap *valueMap) {
// Gather AffineApplyOps reachable from 'indices'.
SmallVector<OperationStmt *, 4> affineApplyOps;
getReachableAffineApplyOps(valueMap->getOperands(), affineApplyOps);
// Compose AffineApplyOps in 'affineApplyOps'.
for (auto *opStmt : affineApplyOps) {
assert(opStmt->isa<AffineApplyOp>());
auto affineApplyOp = opStmt->dyn_cast<AffineApplyOp>();
// Forward substitute 'affineApplyOp' into 'valueMap'.
valueMap->forwardSubstitute(*affineApplyOp);
}
}
// Adds loop upper and lower bound inequalities to 'domain' for each ForStmt
// value in 'forStmts'. Requires that the first 'numDims' MLValues in 'forStmts'
// are ForStmts. Returns true if lower/upper bound inequalities were
// successfully added, returns false otherwise.
// TODO(andydavis) Get operands for loop bounds so we can add domain
// constraints for non-constant loop bounds.
// TODO(andydavis) Handle non-unit Step by adding local variable
// (iv - lb % step = 0 introducing a method in FlatAffineConstraints
// setExprStride(ArrayRef<int64_t> expr, int64_t stride)
bool mlir::addIndexSet(ArrayRef<const MLValue *> indices,
FlatAffineConstraints *domain) {
unsigned numIds = indices.size();
for (unsigned i = 0; i < numIds; ++i) {
const ForStmt *forStmt = dyn_cast<ForStmt>(indices[i]);
if (!forStmt || !forStmt->hasConstantBounds())
return false;
// Add inequality for lower bound.
domain->addConstantLowerBound(i, forStmt->getConstantLowerBound());
// Add inequality for upper bound. (ForStmt's upper bound is exclusive).
domain->addConstantUpperBound(i, forStmt->getConstantUpperBound() - 1);
}
return true;
}
// IterationDomainContext encapsulates the state required to represent
// the iteration domain of an OperationStmt.
// TODO(andydavis) Move this into FlatAffineConstraints when we have shared
// code to manage the operand values and positions to use FlatAffineConstraints
// and AffineValueMap.
struct IterationDomainContext {
// Set of inequality constraint pairs, where each pair represents the
// upper/lower bounds of a ForStmt in the iteration domain.
FlatAffineConstraints domain;
// The number of dimension identifiers in 'values'.
unsigned numDims;
// The list of MLValues in this iteration domain, with MLValues in
// [0, numDims) representing dimension identifiers, and MLValues in
// [numDims, values.size()) representing symbol identifiers.
SmallVector<const MLValue *, 4> values;
IterationDomainContext() : numDims(0) {}
unsigned getNumDims() const { return numDims; }
unsigned getNumSymbols() const { return values.size() - numDims; }
};
// Computes the iteration domain for 'opStmt' and populates 'ctx', which
// encapsulates the following state for each ForStmt in 'opStmt's iteration
// domain:
// *) adds inequality constraints representing the ForStmt upper/lower bounds.
// *) adds MLValues and symbols for the ForStmt and its operands to a list.
// TODO(andydavis) Add support for IfStmts in iteration domain.
// TODO(andydavis) Handle non-constant loop bounds by composing affine maps
// for each ForStmt loop bound and adding de-duped ids/symbols to iteration
// domain context.
static bool getIterationDomainContext(const Statement *stmt,
IterationDomainContext *ctx) {
// Walk up tree storing parent statements in 'loops'.
// TODO(andydavis) Extend this to gather enclosing IfStmts and consider
// factoring it out into a utility function.
SmallVector<const ForStmt *, 4> loops;
const auto *currStmt = stmt->getParentStmt();
while (currStmt != nullptr) {
if (isa<IfStmt>(currStmt))
return false;
assert(isa<ForStmt>(currStmt));
auto *forStmt = dyn_cast<ForStmt>(currStmt);
loops.push_back(forStmt);
currStmt = currStmt->getParentStmt();
}
// Iterate through 'loops' from outer-most loop to inner-most loop.
// Populate 'values'.
ctx->values.reserve(loops.size());
for (int i = static_cast<int>(loops.size()) - 1; i >= 0; --i) {
auto *forStmt = loops[i];
// TODO(andydavis) Compose affine maps into lower/upper bounds of 'forStmt'
// and add de-duped symbols to ctx.symbols.
if (!forStmt->hasConstantBounds())
return false;
ctx->values.push_back(forStmt);
ctx->numDims++;
}
// Resize flat affine constraint system based on num dims symbols found.
unsigned numDims = ctx->getNumDims();
unsigned numSymbols = ctx->getNumSymbols();
ctx->domain.reset(/*newNumReservedInequalities=*/2 * numDims,
/*newNumReservedEqualities=*/0,
/*newNumReservedCols=*/numDims + numSymbols + 1, numDims,
numSymbols);
return addIndexSet(ctx->values, &ctx->domain);
}
// ValuePositionMap manages the mapping from MLValues which represent dimension
// and symbol identifiers from 'src' and 'dst' access functions to positions
// in new space where some MLValues are kept separate (using addSrc/DstValue)
// and some MLValues 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 MLValue 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 MLValue *value) {
if (addValueAt(value, &srcDimPosMap, numSrcDims))
++numSrcDims;
}
void addDstValue(const MLValue *value) {
if (addValueAt(value, &dstDimPosMap, numDstDims))
++numDstDims;
}
void addSymbolValue(const MLValue *value) {
if (addValueAt(value, &symbolPosMap, numSymbols))
++numSymbols;
}
unsigned getSrcDimOrSymPos(const MLValue *value) const {
return getDimOrSymPos(value, srcDimPosMap, 0);
}
unsigned getDstDimOrSymPos(const MLValue *value) const {
return getDimOrSymPos(value, dstDimPosMap, numSrcDims);
}
unsigned getSymPos(const MLValue *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 MLValue *value,
DenseMap<const MLValue *, unsigned> *posMap,
unsigned position) {
auto it = posMap->find(value);
if (it == posMap->end()) {
(*posMap)[value] = position;
return true;
}
return false;
}
unsigned getDimOrSymPos(const MLValue *value,
const DenseMap<const MLValue *, 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 MLValue *, unsigned> srcDimPosMap;
DenseMap<const MLValue *, unsigned> dstDimPosMap;
DenseMap<const MLValue *, unsigned> symbolPosMap;
};
// Builds a map from MLValue 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 the new merged list is as follows:
//
// [src-dim-identifiers, dst-dim-identifiers, symbol-identifiers]
//
// This method populates 'valuePosMap' with mappings from operand MLValues in
// 'srcAccessMap'/'dstAccessMap' (as well as those in
// 'srcIterationDomainContext'/'dstIterationDomainContext') to the position of
// these values in the merged list.
static void buildDimAndSymbolPositionMaps(
const IterationDomainContext &srcIterationDomainContext,
const IterationDomainContext &dstIterationDomainContext,
const AffineValueMap &srcAccessMap, const AffineValueMap &dstAccessMap,
ValuePositionMap *valuePosMap) {
auto updateValuePosMap = [&](ArrayRef<const MLValue *> values, bool isSrc) {
for (unsigned i = 0, e = values.size(); i < e; ++i) {
auto *value = values[i];
if (!isa<ForStmt>(values[i]))
valuePosMap->addSymbolValue(value);
else if (isSrc)
valuePosMap->addSrcValue(value);
else
valuePosMap->addDstValue(value);
}
};
// Update value position map with identifiers from src iteration domain.
updateValuePosMap(srcIterationDomainContext.values, /*isSrc=*/true);
// Update value position map with identifiers from dst iteration domain.
updateValuePosMap(dstIterationDomainContext.values, /*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);
}
static unsigned getPos(const DenseMap<const MLValue *, unsigned> &posMap,
const MLValue *value) {
auto it = posMap.find(value);
assert(it != posMap.end());
return it->second;
}
// Adds iteration domain constraints from 'srcCtx' and 'dstCtx' into
// 'dependenceDomain'.
// Uses 'valuePosMap' to map from operand values in 'ctx.values' to position in
// 'dependenceDomain'.
static void addDomainConstraints(const IterationDomainContext &srcCtx,
const IterationDomainContext &dstCtx,
const ValuePositionMap &valuePosMap,
FlatAffineConstraints *dependenceDomain) {
unsigned srcNumIneq = srcCtx.domain.getNumInequalities();
unsigned srcNumDims = srcCtx.domain.getNumDimIds();
unsigned srcNumSymbols = srcCtx.domain.getNumSymbolIds();
unsigned srcNumIds = srcNumDims + srcNumSymbols;
unsigned dstNumIneq = dstCtx.domain.getNumInequalities();
unsigned dstNumDims = dstCtx.domain.getNumDimIds();
unsigned dstNumSymbols = dstCtx.domain.getNumSymbolIds();
unsigned dstNumIds = dstNumDims + dstNumSymbols;
unsigned outputNumDims = dependenceDomain->getNumDimIds();
unsigned outputNumSymbols = dependenceDomain->getNumSymbolIds();
unsigned outputNumIds = outputNumDims + outputNumSymbols;
SmallVector<int64_t, 4> ineq;
ineq.resize(outputNumIds + 1);
// 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(srcCtx.values[j])] =
srcCtx.domain.atIneq(i, j);
// Set constant term.
ineq[outputNumIds] = srcCtx.domain.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(dstCtx.values[j])] =
dstCtx.domain.atIneq(i, j);
// Set constant term.
ineq[outputNumIds] = dstCtx.domain.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 false if any AffineExpr cannot be flattened (which will be removed
// when mod/floor/ceil support is added). Returns true otherwise.
static bool
addMemRefAccessConstraints(const AffineValueMap &srcAccessMap,
const AffineValueMap &dstAccessMap,
const ValuePositionMap &valuePosMap,
FlatAffineConstraints *dependenceDomain) {
AffineMap srcMap = srcAccessMap.getAffineMap();
AffineMap dstMap = dstAccessMap.getAffineMap();
assert(srcMap.getNumResults() == dstMap.getNumResults());
unsigned numResults = srcMap.getNumResults();
unsigned srcNumDims = srcMap.getNumDims();
unsigned srcNumSymbols = srcMap.getNumSymbols();
unsigned srcNumIds = srcNumDims + srcNumSymbols;
ArrayRef<MLValue *> srcOperands = srcAccessMap.getOperands();
unsigned dstNumDims = dstMap.getNumDims();
unsigned dstNumSymbols = dstMap.getNumSymbols();
unsigned dstNumIds = dstNumDims + dstNumSymbols;
ArrayRef<MLValue *> dstOperands = dstAccessMap.getOperands();
unsigned outputNumDims = dependenceDomain->getNumDimIds();
unsigned outputNumSymbols = dependenceDomain->getNumSymbolIds();
unsigned outputNumIds = outputNumDims + outputNumSymbols;
SmallVector<int64_t, 4> eq(outputNumIds + 1);
SmallVector<int64_t, 4> flattenedExpr;
for (unsigned i = 0; i < numResults; ++i) {
// Zero fill.
std::fill(eq.begin(), eq.end(), 0);
// Get flattened AffineExpr for result 'i' from src access function.
auto srcExpr = srcMap.getResult(i);
flattenedExpr.clear();
if (!getFlattenedAffineExpr(srcExpr, srcNumDims, srcNumSymbols,
&flattenedExpr))
return false;
// Set identifier coefficients from src access function.
for (unsigned j = 0, e = srcOperands.size(); j < e; ++j)
eq[valuePosMap.getSrcDimOrSymPos(srcOperands[j])] = flattenedExpr[j];
// Set constant term.
eq[outputNumIds] = flattenedExpr[srcNumIds];
// Get flattened AffineExpr for result 'i' from dst access function.
auto dstExpr = dstMap.getResult(i);
flattenedExpr.clear();
if (!getFlattenedAffineExpr(dstExpr, dstNumDims, dstNumSymbols,
&flattenedExpr))
return false;
// Set identifier coefficients from dst access function.
for (unsigned j = 0, e = dstOperands.size(); j < e; ++j)
eq[valuePosMap.getDstDimOrSymPos(dstOperands[j])] -= flattenedExpr[j];
// Set constant term.
eq[outputNumIds] -= flattenedExpr[dstNumIds];
// Add equality constraint.
dependenceDomain->addEquality(eq);
}
// Add equality constraints for any operands that are defined by constant ops.
auto addEqForConstOperands = [&](ArrayRef<const MLValue *> operands) {
for (unsigned i = 0, e = operands.size(); i < e; ++i) {
if (isa<ForStmt>(operands[i]))
continue;
auto *symbol = operands[i];
assert(symbol->isValidSymbol());
// Check if the symbol is a constant.
if (auto *opStmt = symbol->getDefiningStmt()) {
if (auto constOp = opStmt->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);
return true;
}
// Returns the number of outer loop common to 'src/dstIterationDomainContext'.
static unsigned
getNumCommonLoops(const IterationDomainContext &srcIterationDomainContext,
const IterationDomainContext &dstIterationDomainContext) {
// Find the number of common loops shared by src and dst accesses.
unsigned minNumLoops = std::min(srcIterationDomainContext.getNumDims(),
dstIterationDomainContext.getNumDims());
unsigned numCommonLoops = 0;
for (unsigned i = 0; i < minNumLoops; ++i) {
if (!isa<ForStmt>(srcIterationDomainContext.values[i]) ||
!isa<ForStmt>(dstIterationDomainContext.values[i]) ||
srcIterationDomainContext.values[i] !=
dstIterationDomainContext.values[i])
break;
++numCommonLoops;
}
return numCommonLoops;
}
// Returns true if the operation statement in 'srcAccess' properly dominates
// the operation statement in 'dstAccess'. Returns false otherwise.
// Note that 'numCommonLoops' is the number of contiguous surrounding outer
// loops.
static bool
srcHappensBeforeDst(const MemRefAccess &srcAccess,
const MemRefAccess &dstAccess,
const IterationDomainContext &srcIterationDomainContext,
unsigned numCommonLoops) {
if (numCommonLoops == 0) {
return mlir::properlyDominates(*srcAccess.opStmt, *dstAccess.opStmt);
}
auto *commonForValue = srcIterationDomainContext.values[numCommonLoops - 1];
assert(isa<ForStmt>(commonForValue));
auto *commonForStmt = dyn_cast<ForStmt>(commonForValue);
// Check the dominance relationship between the respective ancestors of the
// src and dst in the StmtBlock of the innermost among the common loops.
auto *srcStmt = commonForStmt->findAncestorStmtInBlock(*srcAccess.opStmt);
assert(srcStmt != nullptr);
auto *dstStmt = commonForStmt->findAncestorStmtInBlock(*dstAccess.opStmt);
assert(dstStmt != nullptr);
return mlir::properlyDominates(*srcStmt, *dstStmt);
}
// Adds ordering constraints to 'dependenceDomain' based on number of loops
// common to 'src/dstIterationDomainContext' 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 IterationDomainContext &srcIterationDomainContext,
const IterationDomainContext &dstIterationDomainContext,
const ValuePositionMap &valuePosMap, unsigned loopDepth,
FlatAffineConstraints *dependenceDomain) {
unsigned numCols = dependenceDomain->getNumCols();
SmallVector<int64_t, 4> eq(numCols);
unsigned numSrcDims = valuePosMap.getNumSrcDims();
unsigned numCommonLoops =
getNumCommonLoops(srcIterationDomainContext, dstIterationDomainContext);
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 IterationDomainContext &srcIterationDomainContext,
const IterationDomainContext &dstIterationDomainContext, unsigned loopDepth,
FlatAffineConstraints *dependenceDomain,
llvm::SmallVector<DependenceComponent, 2> *dependenceComponents) {
// Find the number of common loops shared by src and dst accesses.
unsigned numCommonLoops =
getNumCommonLoops(srcIterationDomainContext, dstIterationDomainContext);
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 add direction vectors based
// on eliminated constraint system.
unsigned numCols = dependenceDomain->getNumCols();
dependenceComponents->reserve(numCommonLoops);
for (unsigned j = 0; j < numCommonLoops; ++j) {
DependenceComponent depComp;
for (unsigned i = 0, e = dependenceDomain->getNumEqualities(); i < e; ++i) {
// Check for equality constraint with single non-zero in column 'j'.
if (!hasSingleNonZeroAt(j, i, /*isEq=*/true, dependenceDomain))
continue;
// Get direction variable coefficient at (i, j).
int64_t d = dependenceDomain->atEq(i, j);
// Get constant coefficient at (i, numCols - 1).
int64_t c = -dependenceDomain->atEq(i, numCols - 1);
assert(c % d == 0 && "No dependence should have existed");
depComp.lb = depComp.ub = c / d;
dependenceComponents->push_back(depComp);
break;
}
// Skip checking inequalities if we set 'depComp' based on equalities.
if (depComp.lb.hasValue() || depComp.ub.hasValue())
continue;
// TODO(andydavis) Call FlatAffineConstraints::getConstantLower/UpperBound
// Check inequalities to track direction range for each 'j'.
for (unsigned i = 0, e = dependenceDomain->getNumInequalities(); i < e;
++i) {
// Check for inequality constraint with single non-zero in column 'j'.
if (!hasSingleNonZeroAt(j, i, /*isEq=*/false, dependenceDomain))
continue;
// Get direction variable coefficient at (i, j).
int64_t d = dependenceDomain->atIneq(i, j);
// Get constant coefficient at (i, numCols - 1).
int64_t c = dependenceDomain->atIneq(i, numCols - 1);
if (d < 0) {
// Upper bound: add tightest upper bound.
auto ub = mlir::floorDiv(c, -d);
if (!depComp.ub.hasValue() || ub < depComp.ub.getValue())
depComp.ub = ub;
} else {
// Lower bound: add tightest lower bound.
auto lb = mlir::ceilDiv(-c, d);
if (!depComp.lb.hasValue() || lb > depComp.lb.getValue())
depComp.lb = lb;
}
}
if (depComp.lb.hasValue() || depComp.ub.hasValue()) {
if (depComp.lb.hasValue() && depComp.ub.hasValue())
assert(depComp.lb.getValue() <= depComp.ub.getValue());
dependenceComponents->push_back(depComp);
}
}
}
// 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());
// Reset 'accessMap' and 'map' and access 'indices'.
accessMap->reset(map, indices);
// Compose 'accessMap' with reachable AffineApplyOps.
forwardSubstituteReachableOps(accessMap);
}
// 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 ForStmt in the loop nest associated
// with each access.
// *) Build dimension and symbol position maps for each access, which map
// MLValues from access functions and iteration domains to their position
// in the merged constraint system build 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)
// src: (%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 folloing 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,
llvm::SmallVector<DependenceComponent, 2> *dependenceComponents) {
// 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 (!srcAccess.opStmt->isa<StoreOp>() && !dstAccess.opStmt->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 context for 'srcAccess'.
IterationDomainContext srcIterationDomainContext;
if (!getIterationDomainContext(srcAccess.opStmt, &srcIterationDomainContext))
return false;
// Get iteration domain context for 'dstAccess'.
IterationDomainContext dstIterationDomainContext;
if (!getIterationDomainContext(dstAccess.opStmt, &dstIterationDomainContext))
return false;
// Return if loopDepth > numCommonLoops and 'srcAccess' does not properly
// dominate 'dstAccess' (i.e. no execution path from src to dst access).
unsigned numCommonLoops =
getNumCommonLoops(srcIterationDomainContext, dstIterationDomainContext);
assert(loopDepth <= numCommonLoops + 1);
if (loopDepth > numCommonLoops &&
!srcHappensBeforeDst(srcAccess, dstAccess, srcIterationDomainContext,
numCommonLoops)) {
return false;
}
// Build dim and symbol position maps for each access from access operand
// MLValue to position in merged contstraint system.
ValuePositionMap valuePosMap;
buildDimAndSymbolPositionMaps(srcIterationDomainContext,
dstIterationDomainContext, srcAccessMap,
dstAccessMap, &valuePosMap);
// Calculate number of equalities/inequalities and columns required to
// initialize FlatAffineConstraints for 'dependenceDomain'.
unsigned numIneq = srcIterationDomainContext.domain.getNumInequalities() +
dstIterationDomainContext.domain.getNumInequalities();
AffineMap srcMap = srcAccessMap.getAffineMap();
assert(srcMap.getNumResults() == dstAccessMap.getAffineMap().getNumResults());
unsigned numEq = srcMap.getNumResults();
unsigned numDims = valuePosMap.getNumDims();
unsigned numSymbols = valuePosMap.getNumSymbols();
unsigned numIds = numDims + numSymbols;
unsigned numCols = numIds + 1;
// Create flat affine constraints reserving space for 'numEq' and 'numIneq'.
FlatAffineConstraints dependenceDomain(numIneq, numEq, numCols, numDims,
numSymbols);
// Create memref access constraint by equating src/dst access functions.
// Note that this check is conservative, and will failure in the future
// when local variables for mod/div exprs are supported.
if (!addMemRefAccessConstraints(srcAccessMap, dstAccessMap, valuePosMap,
&dependenceDomain))
return true;
// Add 'src' happens before 'dst' ordering constraints.
addOrderingConstraints(srcIterationDomainContext, dstIterationDomainContext,
valuePosMap, loopDepth, &dependenceDomain);
// Add src and dst domain constraints.
addDomainConstraints(srcIterationDomainContext, dstIterationDomainContext,
valuePosMap, &dependenceDomain);
// Return false if the solution space is empty: no dependence.
if (dependenceDomain.isEmpty()) {
return false;
}
// Compute dependence direction vector and return true.
computeDirectionVector(srcIterationDomainContext, dstIterationDomainContext,
loopDepth, &dependenceDomain, dependenceComponents);
return true;
}