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llvm-project/mlir/lib/Analysis/AffineAnalysis.cpp
Nicolas Vasilache 00aac70159 Move makeNormalizedAffineApply 
This CL is the 3rd on the path to simplifying AffineMap composition.
This CL just moves `makeNormalizedAffineApply` from VectorAnalysis to
AffineAnalysis where it more naturally belongs.

PiperOrigin-RevId: 228277182
2019-03-29 15:04:38 -07:00

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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/Builders.h"
#include "mlir/IR/BuiltinOps.h"
#include "mlir/IR/Instructions.h"
#include "mlir/StandardOps/StandardOps.h"
#include "mlir/Support/Functional.h"
#include "mlir/Support/MathExtras.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/Support/Debug.h"
#define DEBUG_TYPE "affine-analysis"
using namespace mlir;
using llvm::dbgs;
/// 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, e = eq.size() - 1; j < e; 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;
}
AffineMap mlir::simplifyAffineMap(AffineMap map) {
auto exprs = functional::map(
[map](AffineExpr e) {
return simplifyAffineExpr(e, map.getNumDims(), map.getNumSymbols());
},
map.getResults());
auto sizes = functional::map(
[map](AffineExpr e) {
return simplifyAffineExpr(e, map.getNumDims(), map.getNumSymbols());
},
map.getRangeSizes());
return AffineMap::get(map.getNumDims(), map.getNumSymbols(), exprs, sizes);
}
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. For a modulo,
// floordiv, or a ceildiv expression, an additional identifier, called a local
// identifier, is introduced to rewrite the expression as a sum of product
// affine expression. Each local identifier is always and by construction a
// floordiv of a pure add/mul affine function of dimensional, symbolic, and
// other local identifiers, in a non-mutually recursive way. Hence, every local
// identifier can ultimately always be recovered as an affine function of
// dimensional and symbolic identifiers (involving floordiv's); note however
// that by AffineExpr construction, some floordiv combinations are converted to
// mod's. The result of the flattening is a flattened expression and a set of
// constraints involving just the local variables.
//
// d2 + (d0 + d1) floordiv 4 is flattened to d2 + q where 'q' is the local
// variable introduced, with localVarCst containing 4*q <= d0 + d1 <= 4*q + 3.
//
// 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
//
// The way the flattening works for the second example is as follows: 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 purely as
// a sum of products involving just the original dimensional and symbolic
// identifiers 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 identifiers with their
// corresponding explicit form stored in 'localExprs' (note that each of the
// explicit forms itself would have been simplified).
//
// The expression walk method here performs a linear time post order walk that
// performs 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 expression 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.
//
// A flattener can be repeatedly used for multiple affine expressions that bind
// to the same operands, for example, for all result expressions of an
// AffineMap or AffineValueMap. In such cases, using it for multiple expressions
// is more efficient than creating a new flattener for each expression since
// common idenical div and mod expressions appearing across different
// expressions are mapped to the same local identifier (same column position in
// 'localVarCst').
struct 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, 8>> operandExprStack;
// Constraints connecting newly introduced local variables (for mod's and
// div's) to existing (dimensional and symbolic) ones. These are always
// inequalities.
FlatAffineConstraints localVarCst;
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 can be readily used 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);
localVarCst.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, e = rhs.size(); i < e; i++) {
lhs[i] += rhs[i];
}
// Pop off the RHS.
operandExprStack.pop_back();
}
//
// t = expr mod c <=> t = expr - c*q and c*q <= expr <= c*q + c - 1
//
// A mod expression "expr mod c" is thus flattened by introducing a new local
// variable q (= expr floordiv c), such that expr mod c is replaced with
// 'expr - c * q' and c * q <= expr <= c * q + c - 1 are added to localVarCst.
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, e;
for (i = 0, e = lhs.size(); i < e; 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);
int loc;
auto floorDiv = a.floorDiv(b);
if ((loc = findLocalId(floorDiv)) == -1) {
addLocalId(floorDiv);
lhs[getLocalVarStartIndex() + numLocals - 1] = -rhsConst;
// Update localVarCst: 0 <= expr1 - c * expr2 <= c - 1.
localVarCst.addConstantLowerBound(lhs, 0);
localVarCst.addConstantUpperBound(lhs, rhsConst - 1);
} else {
// Reuse the existing local id.
lhs[getLocalVarStartIndex() + loc] = -rhsConst;
}
}
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:
// t = expr floordiv c <=> t = q, c * q <= expr <= c * q + c - 1
// A floordiv is thus flattened by introducing a new local variable q, and
// replacing that expression with 'q' while adding the constraints
// c * q <= expr <= c * q + c - 1 to localVarCst.
//
// A ceildiv is similarly flattened:
// t = expr ceildiv c <=> t = q, c * q - (c - 1) <= expr <= c * q
// Note that although t = expr ceildiv c, it is equivalent to
// (expr + c - 1) floordiv c.
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, e = lhs.size(); i < e; i++)
gcd = llvm::GreatestCommonDivisor64(gcd, std::abs(lhs[i]));
// Simplify the numerator and the denominator.
if (gcd != 1) {
for (unsigned i = 0, e = lhs.size(); i < e; i++)
lhs[i] = lhs[i] / static_cast<int64_t>(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);
int loc;
auto div = isCeil ? a.ceilDiv(b) : a.floorDiv(b);
if ((loc = findLocalId(div)) == -1) {
addLocalId(div);
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.
localVarCst.addLowerBound(lhs, bound);
bound[bound.size() - 1] = rhsConst - 1;
localVarCst.addUpperBound(lhs, bound);
} else {
// q = lhs ceildiv c <=> c*q - (c - 1) <= lhs <= c*q.
localVarCst.addUpperBound(lhs, bound);
bound[bound.size() - 1] = -(rhsConst - 1);
localVarCst.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);
if (loc == -1)
lhs[getLocalVarStartIndex() + numLocals - 1] = 1;
else
lhs[getLocalVarStartIndex() + loc] = 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++;
localVarCst.addLocalId(localVarCst.getNumLocalIds());
}
int findLocalId(AffineExpr localExpr) {
SmallVectorImpl<AffineExpr>::iterator it;
if ((it = std::find(localExprs.begin(), localExprs.end(), localExpr)) ==
localExprs.end())
return -1;
return it - localExprs.begin();
}
inline unsigned getNumCols() const {
return numDims + numSymbols + numLocals + 1;
}
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
/// Simplify the affine expression by flattening it and reconstructing it.
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 the expressions in map. Returns true on success or false
// if 'expr' was unable to be flattened (i.e., semi-affine expressions not
// handled yet).
static bool getFlattenedAffineExprs(
ArrayRef<AffineExpr> exprs, unsigned numDims, unsigned numSymbols,
std::vector<llvm::SmallVector<int64_t, 8>> *flattenedExprs,
FlatAffineConstraints *localVarCst) {
if (exprs.empty()) {
localVarCst->reset(numDims, numSymbols);
return true;
}
flattenedExprs->clear();
flattenedExprs->reserve(exprs.size());
AffineExprFlattener flattener(numDims, numSymbols, exprs[0].getContext());
// Use the same flattener to simplify each expression successively. This way
// local identifiers / expressions are shared.
for (auto expr : exprs) {
if (!expr.isPureAffine())
return false;
flattener.walkPostOrder(expr);
}
assert(flattener.operandExprStack.size() == exprs.size());
flattenedExprs->insert(flattenedExprs->end(),
flattener.operandExprStack.begin(),
flattener.operandExprStack.end());
if (localVarCst)
localVarCst->clearAndCopyFrom(flattener.localVarCst);
return true;
}
// Flattens 'expr' into 'flattenedExpr'. Returns true on success or false
// if 'expr' was unable to be flattened (semi-affine expressions not handled
// yet).
bool mlir::getFlattenedAffineExpr(AffineExpr expr, unsigned numDims,
unsigned numSymbols,
llvm::SmallVectorImpl<int64_t> *flattenedExpr,
FlatAffineConstraints *localVarCst) {
std::vector<SmallVector<int64_t, 8>> flattenedExprs;
bool ret = ::getFlattenedAffineExprs({expr}, numDims, numSymbols,
&flattenedExprs, localVarCst);
*flattenedExpr = flattenedExprs[0];
return ret;
}
/// Flattens the expressions in map. Returns true on success or false
/// if 'expr' was unable to be flattened (i.e., semi-affine expressions not
/// handled yet).
bool mlir::getFlattenedAffineExprs(
AffineMap map, std::vector<llvm::SmallVector<int64_t, 8>> *flattenedExprs,
FlatAffineConstraints *localVarCst) {
if (map.getNumResults() == 0) {
localVarCst->reset(map.getNumDims(), map.getNumSymbols());
return true;
}
return ::getFlattenedAffineExprs(map.getResults(), map.getNumDims(),
map.getNumSymbols(), flattenedExprs,
localVarCst);
}
bool mlir::getFlattenedAffineExprs(
IntegerSet set, std::vector<llvm::SmallVector<int64_t, 8>> *flattenedExprs,
FlatAffineConstraints *localVarCst) {
if (set.getNumConstraints() == 0) {
localVarCst->reset(set.getNumDims(), set.getNumSymbols());
return true;
}
return ::getFlattenedAffineExprs(set.getConstraints(), set.getNumDims(),
set.getNumSymbols(), flattenedExprs,
localVarCst);
}
/// Returns the sequence of AffineApplyOp OperationInsts 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<OperationInst *> &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
// OperationInst (i.e. ForInst), 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();
}
}
}
}
// Forward substitutes into 'valueMap' all AffineApplyOps reachable from the
// operands of 'valueMap'.
void mlir::forwardSubstituteReachableOps(AffineValueMap *valueMap) {
// Gather AffineApplyOps reachable from 'indices'.
SmallVector<OperationInst *, 4> affineApplyOps;
getReachableAffineApplyOps(valueMap->getOperands(), affineApplyOps);
// Compose AffineApplyOps in 'affineApplyOps'.
for (auto *opInst : affineApplyOps) {
assert(opInst->isa<AffineApplyOp>());
auto affineApplyOp = opInst->dyn_cast<AffineApplyOp>();
// Forward substitute 'affineApplyOp' into 'valueMap'.
valueMap->forwardSubstitute(*affineApplyOp);
}
}
// Builds a system of constraints with dimensional identifiers corresponding to
// the loop IVs of the forInsts appearing in that order. Any symbols founds in
// the bound operands are added as symbols in the system. Returns false 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)
bool mlir::getIndexSet(ArrayRef<ForInst *> forInsts,
FlatAffineConstraints *domain) {
SmallVector<Value *, 4> indices(forInsts.begin(), forInsts.end());
// Reset while associated Values in 'indices' to the domain.
domain->reset(forInsts.size(), /*numSymbols=*/0, /*numLocals=*/0, indices);
for (auto *forInst : forInsts) {
// Add constraints from forInst's bounds.
if (!domain->addForInstDomain(*forInst))
return false;
}
return true;
}
// 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 bool getInstIndexSet(const Instruction *inst,
FlatAffineConstraints *indexSet) {
// TODO(andydavis) Extend this to gather enclosing IfInsts and consider
// factoring it out into a utility function.
SmallVector<ForInst *, 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 (!isa<ForInst>(values[i])) {
assert(values[i]->isValidSymbol() &&
"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 (!isa<ForInst>(value)) {
assert(value->isValidSymbol() && "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 false if any AffineExpr cannot be flattened (due to it being
// semi-affine). Returns true otherwise.
// TODO(bondhugula): assumes that dependenceDomain doesn't have local
// variables already. Fix this soon.
static bool
addMemRefAccessConstraints(const AffineValueMap &srcAccessMap,
const AffineValueMap &dstAccessMap,
const ValuePositionMap &valuePosMap,
FlatAffineConstraints *dependenceDomain) {
if (dependenceDomain->getNumLocalIds() != 0)
return false;
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 (!getFlattenedAffineExprs(srcMap, &srcFlatExprs, &srcLocalVarCst) ||
!getFlattenedAffineExprs(dstMap, &destFlatExprs, &destLocalVarCst))
return false;
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 (isa<ForInst>(operands[i]))
continue;
auto *symbol = operands[i];
assert(symbol->isValidSymbol());
// 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 true;
}
// 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 (!isa<ForInst>(srcDomain.getIdValue(i)) ||
!isa<ForInst>(dstDomain.getIdValue(i)) ||
srcDomain.getIdValue(i) != dstDomain.getIdValue(i))
break;
++numCommonLoops;
}
return numCommonLoops;
}
// Returns Block common to 'srcAccess.opInst' and 'dstAccess.opInst'.
static const 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);
assert(isa<ForInst>(commonForValue));
return cast<ForInst>(commonForValue)->getBody();
}
// Returns true if the ancestor operation instruction of 'srcAccess' appears
// before the ancestor operation instruction of 'dstAccess' in the same
// instruction 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 srcAppearsBeforeDstInCommonBlock(
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);
// Do a linear scan to determine whether dstInst comes after srcInst.
auto aIter = Block::const_iterator(srcInst);
auto bIter = Block::const_iterator(dstInst);
auto aBlockStart = srcInst->getBlock()->begin();
while (bIter != aBlockStart) {
--bIter;
if (bIter == aIter)
return true;
}
return false;
}
// 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 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 ForInst 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) {
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 (!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 (!getInstIndexSet(srcAccess.opInst, &srcDomain))
return false;
// Get iteration domain for 'dstAccess' instruction.
FlatAffineConstraints dstDomain;
if (!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.
unsigned numCommonLoops = getNumCommonLoops(srcDomain, dstDomain);
assert(loopDepth <= numCommonLoops + 1);
if (loopDepth > numCommonLoops &&
!srcAppearsBeforeDstInCommonBlock(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 failure in the future
// when local variables for mod/div exprs are supported.
if (!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;
}
namespace {
/// A `SingleResultAffineNormalizer` is a helper class that is not visible to
/// the user and supports renumbering operands of single-result AffineApplyOp.
/// This operates on the assumption that only single-result unbounded AffineMap
/// are used for all operands.
/// This acts as a reindexing map of Value* to positional dims or symbols and
/// allows simplifications such as:
///
/// ```mlir
/// %1 = affine_apply (d0, d1) -> (d0 - d1) (%0, %0)
/// ```
///
/// into:
///
/// ```mlir
/// %1 = affine_apply () -> (0)
/// ```
struct SingleResultAffineNormalizer {
SingleResultAffineNormalizer(AffineMap map, ArrayRef<Value *> operands);
/// Returns the single result, unbounded, AffineMap resulting from
/// normalization.
AffineMap getAffineMap() {
return AffineMap::get(reorderedDims.size(), reorderedSymbols.size(), {expr},
{});
}
SmallVector<Value *, 8> getOperands() {
SmallVector<Value *, 8> res(reorderedDims);
res.append(reorderedSymbols.begin(), reorderedSymbols.end());
return res;
}
private:
/// Helper function to insert `v` into the coordinate system of the current
/// SingleResultAffineNormalizer (i.e. in the proper `xxxValueToPosition` and
/// the proper `reorderedXXX`).
/// Returns the AffineDimExpr or AffineSymbolExpr with the correponding
/// renumbered position.
template <typename DimOrSymbol> DimOrSymbol renumberOneIndex(Value *v);
/// Given an `other` normalizer, this rewrites `other.expr` in the coordinate
/// system of the current SingleResultAffineNormalizer.
/// Returns the rewritten AffineExpr.
AffineExpr renumber(const SingleResultAffineNormalizer &other);
/// Given an `app` with single result and unbounded AffineMap, this rewrites
/// the app's map single result AffineExpr in the coordinate system of the
/// current SingleResultAffineNormalizer.
/// Returns the rewritten AffineExpr.
AffineExpr renumber(AffineApplyOp *app);
/// Maps of Value* to position in the `expr`.
DenseMap<Value *, unsigned> dimValueToPosition;
DenseMap<Value *, unsigned> symValueToPosition;
/// Ordered dims and symbols matching positional dims and symbols in `expr`.
SmallVector<Value *, 8> reorderedDims;
SmallVector<Value *, 8> reorderedSymbols;
AffineExpr expr;
};
} // namespace
template <typename DimOrSymbol>
static DimOrSymbol make(unsigned position, MLIRContext *context);
template <> AffineDimExpr make(unsigned position, MLIRContext *context) {
return getAffineDimExpr(position, context).cast<AffineDimExpr>();
}
template <> AffineSymbolExpr make(unsigned position, MLIRContext *context) {
return getAffineSymbolExpr(position, context).cast<AffineSymbolExpr>();
}
template <typename DimOrSymbol>
DimOrSymbol SingleResultAffineNormalizer::renumberOneIndex(Value *v) {
static_assert(std::is_same<DimOrSymbol, AffineDimExpr>::value ||
std::is_same<DimOrSymbol, AffineSymbolExpr>::value,
"renumber<AffineDimExpr>(...) or renumber<AffineDimExpr>(...) "
"required");
DenseMap<Value *, unsigned> &pos =
std::is_same<DimOrSymbol, AffineSymbolExpr>::value ? symValueToPosition
: dimValueToPosition;
DenseMap<Value *, unsigned>::iterator iterPos;
bool inserted = false;
std::tie(iterPos, inserted) = pos.insert(std::make_pair(v, pos.size()));
if (inserted) {
std::is_same<DimOrSymbol, AffineDimExpr>::value
? reorderedDims.push_back(v)
: reorderedSymbols.push_back(v);
}
return make<DimOrSymbol>(iterPos->second, v->getFunction()->getContext());
}
AffineExpr SingleResultAffineNormalizer::renumber(
const SingleResultAffineNormalizer &other) {
SmallVector<AffineExpr, 8> dimRemapping, symRemapping;
for (auto *v : other.reorderedDims) {
auto kvp = other.dimValueToPosition.find(v);
if (dimRemapping.size() <= kvp->second)
dimRemapping.resize(kvp->second + 1);
dimRemapping[kvp->second] = renumberOneIndex<AffineDimExpr>(kvp->first);
}
for (auto *v : other.reorderedSymbols) {
auto kvp = other.symValueToPosition.find(v);
if (symRemapping.size() <= kvp->second)
symRemapping.resize(kvp->second + 1);
symRemapping[kvp->second] = renumberOneIndex<AffineSymbolExpr>(kvp->first);
}
return other.expr.replaceDimsAndSymbols(dimRemapping, symRemapping);
}
AffineExpr SingleResultAffineNormalizer::renumber(AffineApplyOp *app) {
// Sanity check, single result AffineApplyOp if one wants to use this.
assert(app->getNumResults() == 1 && "Not a single result AffineApplyOp");
assert(app->getAffineMap().getRangeSizes().empty() &&
"Non-empty range sizes");
// Create the SingleResultAffineNormalizer for the operands of this
// AffineApplyOp and combine it with the current SingleResultAffineNormalizer.
using ValueTy = decltype(*(app->getOperands().begin()));
SingleResultAffineNormalizer normalizer(
app->getAffineMap(),
functional::map([](ValueTy v) { return static_cast<Value *>(v); },
app->getOperands()));
// We know this is a single result AffineMap, we need to append a
// renumbered AffineExpr.
return renumber(normalizer);
}
SingleResultAffineNormalizer::SingleResultAffineNormalizer(
AffineMap map, ArrayRef<Value *> operands) {
assert(map.getNumResults() == 1 && "Single-result map expected");
assert(map.getRangeSizes().empty() && "Unbounded map expected");
assert(map.getNumInputs() == operands.size() &&
"number of operands does not match the number of map inputs");
if (operands.empty()) {
return;
}
auto *context = operands[0]->getFunction()->getContext();
SmallVector<AffineExpr, 8> exprs;
for (auto en : llvm::enumerate(operands)) {
auto *t = en.value();
assert(t->getType().isIndex());
if (auto inst = t->getDefiningInst()) {
if (auto app = inst->dyn_cast<AffineApplyOp>()) {
// Sanity check, AffineApplyOp must always be composed by construction
// and there can only ever be a dependence chain of 1 AffineApply. So we
// can never get a second AffineApplyOp.
// This also guarantees we can build another
// SingleResultAffineNormalizer here that does not recurse a second
// time.
for (auto *pred : app->getOperands()) {
assert(!pred->getDefiningInst() ||
!pred->getDefiningInst()->isa<AffineApplyOp>() &&
"AffineApplyOp chain of length > 1");
(void)pred;
}
exprs.push_back(renumber(app));
} else if (auto constant = inst->dyn_cast<ConstantOp>()) {
// Constants remain constants.
auto affineConstant = inst->cast<ConstantIndexOp>();
exprs.push_back(
getAffineConstantExpr(affineConstant->getValue(), context));
} else {
// DimOp, top of the function symbols are all symbols.
exprs.push_back(renumberOneIndex<AffineSymbolExpr>(t));
}
} else if (en.index() < map.getNumDims()) {
assert(isa<ForInst>(t) && "ForInst expected for AffineDimExpr");
exprs.push_back(renumberOneIndex<AffineDimExpr>(t));
} else {
assert(!isa<ForInst>(t) && "unexpectd ForInst for a AffineSymbolExpr");
exprs.push_back(renumberOneIndex<AffineSymbolExpr>(t));
}
}
auto exprsMap = AffineMap::get(dimValueToPosition.size(),
symValueToPosition.size(), exprs, {});
expr = simplifyAffineExpr(map.getResult(0).compose(exprsMap),
exprsMap.getNumDims(), exprsMap.getNumSymbols());
LLVM_DEBUG(map.getResult(0).print(dbgs() << "\nCompose expr: "));
LLVM_DEBUG(exprsMap.print(dbgs() << "\nWith map: "));
LLVM_DEBUG(expr.print(dbgs() << "\nResult: "));
}
OpPointer<AffineApplyOp>
mlir::makeNormalizedAffineApply(FuncBuilder *b, Location loc, AffineMap map,
ArrayRef<Value *> operands) {
SingleResultAffineNormalizer normalizer(map, operands);
return b->create<AffineApplyOp>(loc, normalizer.getAffineMap(),
normalizer.getOperands());
}
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