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llvm-project/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp

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//===- AffineStructures.cpp - MLIR Affine Structures Class-----------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// Structures for affine/polyhedral analysis of affine dialect ops.
//
//===----------------------------------------------------------------------===//
#include "mlir/Dialect/Affine/Analysis/AffineStructures.h"
#include "mlir/Analysis/Presburger/LinearTransform.h"
#include "mlir/Analysis/Presburger/Simplex.h"
#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Dialect/Affine/IR/AffineOps.h"
#include "mlir/Dialect/Affine/IR/AffineValueMap.h"
#include "mlir/Dialect/Arithmetic/IR/Arithmetic.h"
#include "mlir/IR/AffineExprVisitor.h"
#include "mlir/IR/IntegerSet.h"
#include "mlir/Support/LLVM.h"
#include "mlir/Support/MathExtras.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#define DEBUG_TYPE "affine-structures"
using namespace mlir;
using namespace presburger;
namespace {
// See comments for SimpleAffineExprFlattener.
// An AffineExprFlattener extends a SimpleAffineExprFlattener by recording
// constraint information associated with mod's, floordiv's, and ceildiv's
// in FlatAffineValueConstraints 'localVarCst'.
struct AffineExprFlattener : public SimpleAffineExprFlattener {
public:
// Constraints connecting newly introduced local variables (for mod's and
// div's) to existing (dimensional and symbolic) ones. These are always
// inequalities.
IntegerPolyhedron localVarCst;
AffineExprFlattener(unsigned nDims, unsigned nSymbols)
: SimpleAffineExprFlattener(nDims, nSymbols),
localVarCst(PresburgerSpace::getSetSpace(nDims, nSymbols)) {}
private:
// Add a local variable (needed to flatten a mod, floordiv, ceildiv expr).
// The local variable added is always a floordiv of a pure add/mul affine
// function of other variables, coefficients of which are specified in
// `dividend' and with respect to the positive constant `divisor'. localExpr
// is the simplified tree expression (AffineExpr) corresponding to the
// quantifier.
void addLocalFloorDivId(ArrayRef<int64_t> dividend, int64_t divisor,
AffineExpr localExpr) override {
SimpleAffineExprFlattener::addLocalFloorDivId(dividend, divisor, localExpr);
// Update localVarCst.
localVarCst.addLocalFloorDiv(dividend, divisor);
}
};
} // namespace
// Flattens the expressions in map. Returns failure if 'expr' was unable to be
// flattened (i.e., semi-affine expressions not handled yet).
static LogicalResult
getFlattenedAffineExprs(ArrayRef<AffineExpr> exprs, unsigned numDims,
unsigned numSymbols,
std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
FlatAffineValueConstraints *localVarCst) {
if (exprs.empty()) {
localVarCst->reset(numDims, numSymbols);
return success();
}
AffineExprFlattener flattener(numDims, numSymbols);
// Use the same flattener to simplify each expression successively. This way
// local variables / expressions are shared.
for (auto expr : exprs) {
if (!expr.isPureAffine())
return failure();
flattener.walkPostOrder(expr);
}
assert(flattener.operandExprStack.size() == exprs.size());
flattenedExprs->clear();
flattenedExprs->assign(flattener.operandExprStack.begin(),
flattener.operandExprStack.end());
if (localVarCst)
localVarCst->clearAndCopyFrom(flattener.localVarCst);
return success();
}
// Flattens 'expr' into 'flattenedExpr'. Returns failure if 'expr' was unable to
// be flattened (semi-affine expressions not handled yet).
LogicalResult
mlir::getFlattenedAffineExpr(AffineExpr expr, unsigned numDims,
unsigned numSymbols,
SmallVectorImpl<int64_t> *flattenedExpr,
FlatAffineValueConstraints *localVarCst) {
std::vector<SmallVector<int64_t, 8>> flattenedExprs;
LogicalResult ret = ::getFlattenedAffineExprs({expr}, numDims, numSymbols,
&flattenedExprs, localVarCst);
*flattenedExpr = flattenedExprs[0];
return ret;
}
/// Flattens the expressions in map. Returns failure if 'expr' was unable to be
/// flattened (i.e., semi-affine expressions not handled yet).
LogicalResult mlir::getFlattenedAffineExprs(
AffineMap map, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
FlatAffineValueConstraints *localVarCst) {
if (map.getNumResults() == 0) {
localVarCst->reset(map.getNumDims(), map.getNumSymbols());
return success();
}
return ::getFlattenedAffineExprs(map.getResults(), map.getNumDims(),
map.getNumSymbols(), flattenedExprs,
localVarCst);
}
LogicalResult mlir::getFlattenedAffineExprs(
IntegerSet set, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
FlatAffineValueConstraints *localVarCst) {
if (set.getNumConstraints() == 0) {
localVarCst->reset(set.getNumDims(), set.getNumSymbols());
return success();
}
return ::getFlattenedAffineExprs(set.getConstraints(), set.getNumDims(),
set.getNumSymbols(), flattenedExprs,
localVarCst);
}
//===----------------------------------------------------------------------===//
// FlatAffineConstraints / FlatAffineValueConstraints.
//===----------------------------------------------------------------------===//
std::unique_ptr<FlatAffineValueConstraints>
FlatAffineValueConstraints::clone() const {
return std::make_unique<FlatAffineValueConstraints>(*this);
}
// Construct from an IntegerSet.
FlatAffineValueConstraints::FlatAffineValueConstraints(IntegerSet set)
: IntegerPolyhedron(set.getNumInequalities(), set.getNumEqualities(),
set.getNumDims() + set.getNumSymbols() + 1,
PresburgerSpace::getSetSpace(set.getNumDims(),
set.getNumSymbols(),
/*numLocals=*/0)) {
// Resize values.
values.resize(getNumDimAndSymbolVars(), None);
// Flatten expressions and add them to the constraint system.
std::vector<SmallVector<int64_t, 8>> flatExprs;
FlatAffineValueConstraints localVarCst;
if (failed(getFlattenedAffineExprs(set, &flatExprs, &localVarCst))) {
assert(false && "flattening unimplemented for semi-affine integer sets");
return;
}
assert(flatExprs.size() == set.getNumConstraints());
insertVar(VarKind::Local, getNumVarKind(VarKind::Local),
/*num=*/localVarCst.getNumLocalVars());
for (unsigned i = 0, e = flatExprs.size(); i < e; ++i) {
const auto &flatExpr = flatExprs[i];
assert(flatExpr.size() == getNumCols());
if (set.getEqFlags()[i]) {
addEquality(flatExpr);
} else {
addInequality(flatExpr);
}
}
// Add the other constraints involving local vars from flattening.
append(localVarCst);
}
// Construct a hyperrectangular constraint set from ValueRanges that represent
// induction variables, lower and upper bounds. `ivs`, `lbs` and `ubs` are
// expected to match one to one. The order of variables and constraints is:
//
// ivs | lbs | ubs | eq/ineq
// ----+-----+-----+---------
// 1 -1 0 >= 0
// ----+-----+-----+---------
// -1 0 1 >= 0
//
// All dimensions as set as VarKind::SetDim.
FlatAffineValueConstraints
FlatAffineValueConstraints::getHyperrectangular(ValueRange ivs, ValueRange lbs,
ValueRange ubs) {
FlatAffineValueConstraints res;
unsigned nIvs = ivs.size();
assert(nIvs == lbs.size() && "expected as many lower bounds as ivs");
assert(nIvs == ubs.size() && "expected as many upper bounds as ivs");
if (nIvs == 0)
return res;
res.appendDimVar(ivs);
unsigned lbsStart = res.appendDimVar(lbs);
unsigned ubsStart = res.appendDimVar(ubs);
MLIRContext *ctx = ivs.front().getContext();
for (int ivIdx = 0, e = nIvs; ivIdx < e; ++ivIdx) {
// iv - lb >= 0
AffineMap lb = AffineMap::get(/*dimCount=*/3 * nIvs, /*symbolCount=*/0,
getAffineDimExpr(lbsStart + ivIdx, ctx));
if (failed(res.addBound(BoundType::LB, ivIdx, lb)))
llvm_unreachable("Unexpected FlatAffineValueConstraints creation error");
// -iv + ub >= 0
AffineMap ub = AffineMap::get(/*dimCount=*/3 * nIvs, /*symbolCount=*/0,
getAffineDimExpr(ubsStart + ivIdx, ctx));
if (failed(res.addBound(BoundType::UB, ivIdx, ub)))
llvm_unreachable("Unexpected FlatAffineValueConstraints creation error");
}
return res;
}
void FlatAffineValueConstraints::reset(unsigned numReservedInequalities,
unsigned numReservedEqualities,
unsigned newNumReservedCols,
unsigned newNumDims,
unsigned newNumSymbols,
unsigned newNumLocals) {
assert(newNumReservedCols >= newNumDims + newNumSymbols + newNumLocals + 1 &&
"minimum 1 column");
*this = FlatAffineValueConstraints(numReservedInequalities,
numReservedEqualities, newNumReservedCols,
newNumDims, newNumSymbols, newNumLocals);
}
void FlatAffineValueConstraints::reset(unsigned newNumDims,
unsigned newNumSymbols,
unsigned newNumLocals) {
reset(/*numReservedInequalities=*/0, /*numReservedEqualities=*/0,
/*numReservedCols=*/newNumDims + newNumSymbols + newNumLocals + 1,
newNumDims, newNumSymbols, newNumLocals);
}
void FlatAffineValueConstraints::reset(
unsigned numReservedInequalities, unsigned numReservedEqualities,
unsigned newNumReservedCols, unsigned newNumDims, unsigned newNumSymbols,
unsigned newNumLocals, ArrayRef<Value> valArgs) {
assert(newNumReservedCols >= newNumDims + newNumSymbols + newNumLocals + 1 &&
"minimum 1 column");
SmallVector<Optional<Value>, 8> newVals;
if (!valArgs.empty())
newVals.assign(valArgs.begin(), valArgs.end());
*this = FlatAffineValueConstraints(
numReservedInequalities, numReservedEqualities, newNumReservedCols,
newNumDims, newNumSymbols, newNumLocals, newVals);
}
void FlatAffineValueConstraints::reset(unsigned newNumDims,
unsigned newNumSymbols,
unsigned newNumLocals,
ArrayRef<Value> valArgs) {
reset(0, 0, newNumDims + newNumSymbols + newNumLocals + 1, newNumDims,
newNumSymbols, newNumLocals, valArgs);
}
unsigned FlatAffineValueConstraints::appendDimVar(ValueRange vals) {
unsigned pos = getNumDimVars();
insertVar(VarKind::SetDim, pos, vals);
return pos;
}
unsigned FlatAffineValueConstraints::appendSymbolVar(ValueRange vals) {
unsigned pos = getNumSymbolVars();
insertVar(VarKind::Symbol, pos, vals);
return pos;
}
unsigned FlatAffineValueConstraints::insertDimVar(unsigned pos,
ValueRange vals) {
return insertVar(VarKind::SetDim, pos, vals);
}
unsigned FlatAffineValueConstraints::insertSymbolVar(unsigned pos,
ValueRange vals) {
return insertVar(VarKind::Symbol, pos, vals);
}
unsigned FlatAffineValueConstraints::insertVar(VarKind kind, unsigned pos,
unsigned num) {
unsigned absolutePos = IntegerPolyhedron::insertVar(kind, pos, num);
if (kind != VarKind::Local) {
values.insert(values.begin() + absolutePos, num, None);
assert(values.size() == getNumDimAndSymbolVars());
}
return absolutePos;
}
unsigned FlatAffineValueConstraints::insertVar(VarKind kind, unsigned pos,
ValueRange vals) {
assert(!vals.empty() && "expected ValueRange with Values.");
assert(kind != VarKind::Local &&
"values cannot be attached to local variables.");
unsigned num = vals.size();
unsigned absolutePos = IntegerPolyhedron::insertVar(kind, pos, num);
// If a Value is provided, insert it; otherwise use None.
for (unsigned i = 0; i < num; ++i)
values.insert(values.begin() + absolutePos + i,
vals[i] ? Optional<Value>(vals[i]) : None);
assert(values.size() == getNumDimAndSymbolVars());
return absolutePos;
}
bool FlatAffineValueConstraints::hasValues() const {
return llvm::find_if(values, [](Optional<Value> var) {
return var.has_value();
}) != values.end();
}
/// Checks if two constraint systems are in the same space, i.e., if they are
/// associated with the same set of variables, appearing in the same order.
static bool areVarsAligned(const FlatAffineValueConstraints &a,
const FlatAffineValueConstraints &b) {
return a.getNumDimVars() == b.getNumDimVars() &&
a.getNumSymbolVars() == b.getNumSymbolVars() &&
a.getNumVars() == b.getNumVars() &&
a.getMaybeValues().equals(b.getMaybeValues());
}
/// Calls areVarsAligned to check if two constraint systems have the same set
/// of variables in the same order.
bool FlatAffineValueConstraints::areVarsAlignedWithOther(
const FlatAffineValueConstraints &other) {
return areVarsAligned(*this, other);
}
/// Checks if the SSA values associated with `cst`'s variables in range
/// [start, end) are unique.
static bool LLVM_ATTRIBUTE_UNUSED areVarsUnique(
const FlatAffineValueConstraints &cst, unsigned start, unsigned end) {
assert(start <= cst.getNumDimAndSymbolVars() &&
"Start position out of bounds");
assert(end <= cst.getNumDimAndSymbolVars() && "End position out of bounds");
if (start >= end)
return true;
SmallPtrSet<Value, 8> uniqueVars;
ArrayRef<Optional<Value>> maybeValues =
cst.getMaybeValues().slice(start, end - start);
for (Optional<Value> val : maybeValues) {
if (val && !uniqueVars.insert(*val).second)
return false;
}
return true;
}
/// Checks if the SSA values associated with `cst`'s variables are unique.
static bool LLVM_ATTRIBUTE_UNUSED
areVarsUnique(const FlatAffineValueConstraints &cst) {
return areVarsUnique(cst, 0, cst.getNumDimAndSymbolVars());
}
/// Checks if the SSA values associated with `cst`'s variables of kind `kind`
/// are unique.
static bool LLVM_ATTRIBUTE_UNUSED
areVarsUnique(const FlatAffineValueConstraints &cst, VarKind kind) {
if (kind == VarKind::SetDim)
return areVarsUnique(cst, 0, cst.getNumDimVars());
if (kind == VarKind::Symbol)
return areVarsUnique(cst, cst.getNumDimVars(),
cst.getNumDimAndSymbolVars());
llvm_unreachable("Unexpected VarKind");
}
/// Merge and align the variables of A and B starting at 'offset', so that
/// both constraint systems get the union of the contained variables that is
/// dimension-wise and symbol-wise unique; both constraint systems are updated
/// so that they have the union of all variables, with A's original
/// variables appearing first followed by any of B's variables that didn't
/// appear in A. Local variables in B that have the same division
/// representation as local variables in A are merged into one.
// E.g.: Input: A has ((%i, %j) [%M, %N]) and B has (%k, %j) [%P, %N, %M])
// Output: both A, B have (%i, %j, %k) [%M, %N, %P]
static void mergeAndAlignVars(unsigned offset, FlatAffineValueConstraints *a,
FlatAffineValueConstraints *b) {
assert(offset <= a->getNumDimVars() && offset <= b->getNumDimVars());
// A merge/align isn't meaningful if a cst's vars aren't distinct.
assert(areVarsUnique(*a) && "A's values aren't unique");
assert(areVarsUnique(*b) && "B's values aren't unique");
assert(std::all_of(a->getMaybeValues().begin() + offset,
a->getMaybeValues().end(),
[](Optional<Value> var) { return var.has_value(); }));
assert(std::all_of(b->getMaybeValues().begin() + offset,
b->getMaybeValues().end(),
[](Optional<Value> var) { return var.has_value(); }));
SmallVector<Value, 4> aDimValues;
a->getValues(offset, a->getNumDimVars(), &aDimValues);
{
// Merge dims from A into B.
unsigned d = offset;
for (auto aDimValue : aDimValues) {
unsigned loc;
if (b->findVar(aDimValue, &loc)) {
assert(loc >= offset && "A's dim appears in B's aligned range");
assert(loc < b->getNumDimVars() &&
"A's dim appears in B's non-dim position");
b->swapVar(d, loc);
} else {
b->insertDimVar(d, aDimValue);
}
d++;
}
// Dimensions that are in B, but not in A, are added at the end.
for (unsigned t = a->getNumDimVars(), e = b->getNumDimVars(); t < e; t++) {
a->appendDimVar(b->getValue(t));
}
assert(a->getNumDimVars() == b->getNumDimVars() &&
"expected same number of dims");
}
// Merge and align symbols of A and B
a->mergeSymbolVars(*b);
// Merge and align locals of A and B
a->mergeLocalVars(*b);
assert(areVarsAligned(*a, *b) && "IDs expected to be aligned");
}
// Call 'mergeAndAlignVars' to align constraint systems of 'this' and 'other'.
void FlatAffineValueConstraints::mergeAndAlignVarsWithOther(
unsigned offset, FlatAffineValueConstraints *other) {
mergeAndAlignVars(offset, this, other);
}
LogicalResult
FlatAffineValueConstraints::composeMap(const AffineValueMap *vMap) {
return composeMatchingMap(
computeAlignedMap(vMap->getAffineMap(), vMap->getOperands()));
}
// Similar to `composeMap` except that no Values need be associated with the
// constraint system nor are they looked at -- the dimensions and symbols of
// `other` are expected to correspond 1:1 to `this` system.
LogicalResult FlatAffineValueConstraints::composeMatchingMap(AffineMap other) {
assert(other.getNumDims() == getNumDimVars() && "dim mismatch");
assert(other.getNumSymbols() == getNumSymbolVars() && "symbol mismatch");
std::vector<SmallVector<int64_t, 8>> flatExprs;
if (failed(flattenAlignedMapAndMergeLocals(other, &flatExprs)))
return failure();
assert(flatExprs.size() == other.getNumResults());
// Add dimensions corresponding to the map's results.
insertDimVar(/*pos=*/0, /*num=*/other.getNumResults());
// We add one equality for each result connecting the result dim of the map to
// the other variables.
// E.g.: if the expression is 16*i0 + i1, and this is the r^th
// iteration/result of the value map, we are adding the equality:
// d_r - 16*i0 - i1 = 0. Similarly, when flattening (i0 + 1, i0 + 8*i2), we
// add two equalities: d_0 - i0 - 1 == 0, d1 - i0 - 8*i2 == 0.
for (unsigned r = 0, e = flatExprs.size(); r < e; r++) {
const auto &flatExpr = flatExprs[r];
assert(flatExpr.size() >= other.getNumInputs() + 1);
SmallVector<int64_t, 8> eqToAdd(getNumCols(), 0);
// Set the coefficient for this result to one.
eqToAdd[r] = 1;
// Dims and symbols.
for (unsigned i = 0, f = other.getNumInputs(); i < f; i++) {
// Negate `eq[r]` since the newly added dimension will be set to this one.
eqToAdd[e + i] = -flatExpr[i];
}
// Local columns of `eq` are at the beginning.
unsigned j = getNumDimVars() + getNumSymbolVars();
unsigned end = flatExpr.size() - 1;
for (unsigned i = other.getNumInputs(); i < end; i++, j++) {
eqToAdd[j] = -flatExpr[i];
}
// Constant term.
eqToAdd[getNumCols() - 1] = -flatExpr[flatExpr.size() - 1];
// Add the equality connecting the result of the map to this constraint set.
addEquality(eqToAdd);
}
return success();
}
// Turn a symbol into a dimension.
static void turnSymbolIntoDim(FlatAffineValueConstraints *cst, Value value) {
unsigned pos;
if (cst->findVar(value, &pos) && pos >= cst->getNumDimVars() &&
pos < cst->getNumDimAndSymbolVars()) {
cst->swapVar(pos, cst->getNumDimVars());
cst->setDimSymbolSeparation(cst->getNumSymbolVars() - 1);
}
}
/// Merge and align symbols of `this` and `other` such that both get union of
/// of symbols that are unique. Symbols in `this` and `other` should be
/// unique. Symbols with Value as `None` are considered to be inequal to all
/// other symbols.
void FlatAffineValueConstraints::mergeSymbolVars(
FlatAffineValueConstraints &other) {
assert(areVarsUnique(*this, VarKind::Symbol) && "Symbol vars are not unique");
assert(areVarsUnique(other, VarKind::Symbol) && "Symbol vars are not unique");
SmallVector<Value, 4> aSymValues;
getValues(getNumDimVars(), getNumDimAndSymbolVars(), &aSymValues);
// Merge symbols: merge symbols into `other` first from `this`.
unsigned s = other.getNumDimVars();
for (Value aSymValue : aSymValues) {
unsigned loc;
// If the var is a symbol in `other`, then align it, otherwise assume that
// it is a new symbol
if (other.findVar(aSymValue, &loc) && loc >= other.getNumDimVars() &&
loc < other.getNumDimAndSymbolVars())
other.swapVar(s, loc);
else
other.insertSymbolVar(s - other.getNumDimVars(), aSymValue);
s++;
}
// Symbols that are in other, but not in this, are added at the end.
for (unsigned t = other.getNumDimVars() + getNumSymbolVars(),
e = other.getNumDimAndSymbolVars();
t < e; t++)
insertSymbolVar(getNumSymbolVars(), other.getValue(t));
assert(getNumSymbolVars() == other.getNumSymbolVars() &&
"expected same number of symbols");
assert(areVarsUnique(*this, VarKind::Symbol) && "Symbol vars are not unique");
assert(areVarsUnique(other, VarKind::Symbol) && "Symbol vars are not unique");
}
// Changes all symbol variables which are loop IVs to dim variables.
void FlatAffineValueConstraints::convertLoopIVSymbolsToDims() {
// Gather all symbols which are loop IVs.
SmallVector<Value, 4> loopIVs;
for (unsigned i = getNumDimVars(), e = getNumDimAndSymbolVars(); i < e; i++) {
if (hasValue(i) && getForInductionVarOwner(getValue(i)))
loopIVs.push_back(getValue(i));
}
// Turn each symbol in 'loopIVs' into a dim variable.
for (auto iv : loopIVs) {
turnSymbolIntoDim(this, iv);
}
}
void FlatAffineValueConstraints::addInductionVarOrTerminalSymbol(Value val) {
if (containsVar(val))
return;
// Caller is expected to fully compose map/operands if necessary.
assert((isTopLevelValue(val) || isForInductionVar(val)) &&
"non-terminal symbol / loop IV expected");
// Outer loop IVs could be used in forOp's bounds.
if (auto loop = getForInductionVarOwner(val)) {
appendDimVar(val);
if (failed(this->addAffineForOpDomain(loop)))
LLVM_DEBUG(
loop.emitWarning("failed to add domain info to constraint system"));
return;
}
// Add top level symbol.
appendSymbolVar(val);
// Check if the symbol is a constant.
if (auto constOp = val.getDefiningOp<arith::ConstantIndexOp>())
addBound(BoundType::EQ, val, constOp.value());
}
LogicalResult
FlatAffineValueConstraints::addAffineForOpDomain(AffineForOp forOp) {
unsigned pos;
// Pre-condition for this method.
if (!findVar(forOp.getInductionVar(), &pos)) {
assert(false && "Value not found");
return failure();
}
int64_t step = forOp.getStep();
if (step != 1) {
if (!forOp.hasConstantLowerBound())
LLVM_DEBUG(forOp.emitWarning("domain conservatively approximated"));
else {
// Add constraints for the stride.
// (iv - lb) % step = 0 can be written as:
// (iv - lb) - step * q = 0 where q = (iv - lb) / step.
// Add local variable 'q' and add the above equality.
// The first constraint is q = (iv - lb) floordiv step
SmallVector<int64_t, 8> dividend(getNumCols(), 0);
int64_t lb = forOp.getConstantLowerBound();
dividend[pos] = 1;
dividend.back() -= lb;
addLocalFloorDiv(dividend, step);
// Second constraint: (iv - lb) - step * q = 0.
SmallVector<int64_t, 8> eq(getNumCols(), 0);
eq[pos] = 1;
eq.back() -= lb;
// For the local var just added above.
eq[getNumCols() - 2] = -step;
addEquality(eq);
}
}
if (forOp.hasConstantLowerBound()) {
addBound(BoundType::LB, pos, forOp.getConstantLowerBound());
} else {
// Non-constant lower bound case.
if (failed(addBound(BoundType::LB, pos, forOp.getLowerBoundMap(),
forOp.getLowerBoundOperands())))
return failure();
}
if (forOp.hasConstantUpperBound()) {
addBound(BoundType::UB, pos, forOp.getConstantUpperBound() - 1);
return success();
}
// Non-constant upper bound case.
return addBound(BoundType::UB, pos, forOp.getUpperBoundMap(),
forOp.getUpperBoundOperands());
}
LogicalResult
FlatAffineValueConstraints::addDomainFromSliceMaps(ArrayRef<AffineMap> lbMaps,
ArrayRef<AffineMap> ubMaps,
ArrayRef<Value> operands) {
assert(lbMaps.size() == ubMaps.size());
assert(lbMaps.size() <= getNumDimVars());
for (unsigned i = 0, e = lbMaps.size(); i < e; ++i) {
AffineMap lbMap = lbMaps[i];
AffineMap ubMap = ubMaps[i];
assert(!lbMap || lbMap.getNumInputs() == operands.size());
assert(!ubMap || ubMap.getNumInputs() == operands.size());
// Check if this slice is just an equality along this dimension. If so,
// retrieve the existing loop it equates to and add it to the system.
if (lbMap && ubMap && lbMap.getNumResults() == 1 &&
ubMap.getNumResults() == 1 &&
lbMap.getResult(0) + 1 == ubMap.getResult(0) &&
// The condition above will be true for maps describing a single
// iteration (e.g., lbMap.getResult(0) = 0, ubMap.getResult(0) = 1).
// Make sure we skip those cases by checking that the lb result is not
// just a constant.
!lbMap.getResult(0).isa<AffineConstantExpr>()) {
// Limited support: we expect the lb result to be just a loop dimension.
// Not supported otherwise for now.
AffineDimExpr result = lbMap.getResult(0).dyn_cast<AffineDimExpr>();
if (!result)
return failure();
AffineForOp loop =
getForInductionVarOwner(operands[result.getPosition()]);
if (!loop)
return failure();
if (failed(addAffineForOpDomain(loop)))
return failure();
continue;
}
// This slice refers to a loop that doesn't exist in the IR yet. Add its
// bounds to the system assuming its dimension variable position is the
// same as the position of the loop in the loop nest.
if (lbMap && failed(addBound(BoundType::LB, i, lbMap, operands)))
return failure();
if (ubMap && failed(addBound(BoundType::UB, i, ubMap, operands)))
return failure();
}
return success();
}
void FlatAffineValueConstraints::addAffineIfOpDomain(AffineIfOp ifOp) {
// Create the base constraints from the integer set attached to ifOp.
FlatAffineValueConstraints cst(ifOp.getIntegerSet());
// Bind vars in the constraints to ifOp operands.
SmallVector<Value, 4> operands = ifOp.getOperands();
cst.setValues(0, cst.getNumDimAndSymbolVars(), operands);
// Merge the constraints from ifOp to the current domain. We need first merge
// and align the IDs from both constraints, and then append the constraints
// from the ifOp into the current one.
mergeAndAlignVarsWithOther(0, &cst);
append(cst);
}
bool FlatAffineValueConstraints::hasConsistentState() const {
return IntegerPolyhedron::hasConsistentState() &&
values.size() == getNumDimAndSymbolVars();
}
void FlatAffineValueConstraints::removeVarRange(VarKind kind, unsigned varStart,
unsigned varLimit) {
IntegerPolyhedron::removeVarRange(kind, varStart, varLimit);
unsigned offset = getVarKindOffset(kind);
if (kind != VarKind::Local) {
values.erase(values.begin() + varStart + offset,
values.begin() + varLimit + offset);
}
}
// Determine whether the variable at 'pos' (say var_r) can be expressed as
// modulo of another known variable (say var_n) w.r.t a constant. For example,
// if the following constraints hold true:
// ```
// 0 <= var_r <= divisor - 1
// var_n - (divisor * q_expr) = var_r
// ```
// where `var_n` is a known variable (called dividend), and `q_expr` is an
// `AffineExpr` (called the quotient expression), `var_r` can be written as:
//
// `var_r = var_n mod divisor`.
//
// Additionally, in a special case of the above constaints where `q_expr` is an
// variable itself that is not yet known (say `var_q`), it can be written as a
// floordiv in the following way:
//
// `var_q = var_n floordiv divisor`.
//
// Returns true if the above mod or floordiv are detected, updating 'memo' with
// these new expressions. Returns false otherwise.
static bool detectAsMod(const FlatAffineValueConstraints &cst, unsigned pos,
int64_t lbConst, int64_t ubConst,
SmallVectorImpl<AffineExpr> &memo,
MLIRContext *context) {
assert(pos < cst.getNumVars() && "invalid position");
// Check if a divisor satisfying the condition `0 <= var_r <= divisor - 1` can
// be determined.
if (lbConst != 0 || ubConst < 1)
return false;
int64_t divisor = ubConst + 1;
// Check for the aforementioned conditions in each equality.
for (unsigned curEquality = 0, numEqualities = cst.getNumEqualities();
curEquality < numEqualities; curEquality++) {
int64_t coefficientAtPos = cst.atEq(curEquality, pos);
// If current equality does not involve `var_r`, continue to the next
// equality.
if (coefficientAtPos == 0)
continue;
// Constant term should be 0 in this equality.
if (cst.atEq(curEquality, cst.getNumCols() - 1) != 0)
continue;
// Traverse through the equality and construct the dividend expression
// `dividendExpr`, to contain all the variables which are known and are
// not divisible by `(coefficientAtPos * divisor)`. Hope here is that the
// `dividendExpr` gets simplified into a single variable `var_n` discussed
// above.
auto dividendExpr = getAffineConstantExpr(0, context);
// Track the terms that go into quotient expression, later used to detect
// additional floordiv.
unsigned quotientCount = 0;
int quotientPosition = -1;
int quotientSign = 1;
// Consider each term in the current equality.
unsigned curVar, e;
for (curVar = 0, e = cst.getNumDimAndSymbolVars(); curVar < e; ++curVar) {
// Ignore var_r.
if (curVar == pos)
continue;
int64_t coefficientOfCurVar = cst.atEq(curEquality, curVar);
// Ignore vars that do not contribute to the current equality.
if (coefficientOfCurVar == 0)
continue;
// Check if the current var goes into the quotient expression.
if (coefficientOfCurVar % (divisor * coefficientAtPos) == 0) {
quotientCount++;
quotientPosition = curVar;
quotientSign = (coefficientOfCurVar * coefficientAtPos) > 0 ? 1 : -1;
continue;
}
// Variables that are part of dividendExpr should be known.
if (!memo[curVar])
break;
// Append the current variable to the dividend expression.
dividendExpr = dividendExpr + memo[curVar] * coefficientOfCurVar;
}
// Can't construct expression as it depends on a yet uncomputed var.
if (curVar < e)
continue;
// Express `var_r` in terms of the other vars collected so far.
if (coefficientAtPos > 0)
dividendExpr = (-dividendExpr).floorDiv(coefficientAtPos);
else
dividendExpr = dividendExpr.floorDiv(-coefficientAtPos);
// Simplify the expression.
dividendExpr = simplifyAffineExpr(dividendExpr, cst.getNumDimVars(),
cst.getNumSymbolVars());
// Only if the final dividend expression is just a single var (which we call
// `var_n`), we can proceed.
// TODO: Handle AffineSymbolExpr as well. There is no reason to restrict it
// to dims themselves.
auto dimExpr = dividendExpr.dyn_cast<AffineDimExpr>();
if (!dimExpr)
continue;
// Express `var_r` as `var_n % divisor` and store the expression in `memo`.
if (quotientCount >= 1) {
auto ub = cst.getConstantBound(FlatAffineValueConstraints::BoundType::UB,
dimExpr.getPosition());
// If `var_n` has an upperbound that is less than the divisor, mod can be
// eliminated altogether.
if (ub && *ub < divisor)
memo[pos] = dimExpr;
else
memo[pos] = dimExpr % divisor;
// If a unique quotient `var_q` was seen, it can be expressed as
// `var_n floordiv divisor`.
if (quotientCount == 1 && !memo[quotientPosition])
memo[quotientPosition] = dimExpr.floorDiv(divisor) * quotientSign;
return true;
}
}
return false;
}
/// Check if the pos^th variable can be expressed as a floordiv of an affine
/// function of other variables (where the divisor is a positive constant)
/// given the initial set of expressions in `exprs`. If it can be, the
/// corresponding position in `exprs` is set as the detected affine expr. For
/// eg: 4q <= i + j <= 4q + 3 <=> q = (i + j) floordiv 4. An equality can
/// also yield a floordiv: eg. 4q = i + j <=> q = (i + j) floordiv 4. 32q + 28
/// <= i <= 32q + 31 => q = i floordiv 32.
static bool detectAsFloorDiv(const FlatAffineValueConstraints &cst,
unsigned pos, MLIRContext *context,
SmallVectorImpl<AffineExpr> &exprs) {
assert(pos < cst.getNumVars() && "invalid position");
// Get upper-lower bound pair for this variable.
SmallVector<bool, 8> foundRepr(cst.getNumVars(), false);
for (unsigned i = 0, e = cst.getNumVars(); i < e; ++i)
if (exprs[i])
foundRepr[i] = true;
SmallVector<int64_t, 8> dividend(cst.getNumCols());
unsigned divisor;
auto ulPair = computeSingleVarRepr(cst, foundRepr, pos, dividend, divisor);
// No upper-lower bound pair found for this var.
if (ulPair.kind == ReprKind::None || ulPair.kind == ReprKind::Equality)
return false;
// Construct the dividend expression.
auto dividendExpr = getAffineConstantExpr(dividend.back(), context);
for (unsigned c = 0, f = cst.getNumVars(); c < f; c++)
if (dividend[c] != 0)
dividendExpr = dividendExpr + dividend[c] * exprs[c];
// Successfully detected the floordiv.
exprs[pos] = dividendExpr.floorDiv(divisor);
return true;
}
std::pair<AffineMap, AffineMap>
FlatAffineValueConstraints::getLowerAndUpperBound(
unsigned pos, unsigned offset, unsigned num, unsigned symStartPos,
ArrayRef<AffineExpr> localExprs, MLIRContext *context) const {
assert(pos + offset < getNumDimVars() && "invalid dim start pos");
assert(symStartPos >= (pos + offset) && "invalid sym start pos");
assert(getNumLocalVars() == localExprs.size() &&
"incorrect local exprs count");
SmallVector<unsigned, 4> lbIndices, ubIndices, eqIndices;
getLowerAndUpperBoundIndices(pos + offset, &lbIndices, &ubIndices, &eqIndices,
offset, num);
/// Add to 'b' from 'a' in set [0, offset) U [offset + num, symbStartPos).
auto addCoeffs = [&](ArrayRef<int64_t> a, SmallVectorImpl<int64_t> &b) {
b.clear();
for (unsigned i = 0, e = a.size(); i < e; ++i) {
if (i < offset || i >= offset + num)
b.push_back(a[i]);
}
};
SmallVector<int64_t, 8> lb, ub;
SmallVector<AffineExpr, 4> lbExprs;
unsigned dimCount = symStartPos - num;
unsigned symCount = getNumDimAndSymbolVars() - symStartPos;
lbExprs.reserve(lbIndices.size() + eqIndices.size());
// Lower bound expressions.
for (auto idx : lbIndices) {
auto ineq = getInequality(idx);
// Extract the lower bound (in terms of other coeff's + const), i.e., if
// i - j + 1 >= 0 is the constraint, 'pos' is for i the lower bound is j
// - 1.
addCoeffs(ineq, lb);
std::transform(lb.begin(), lb.end(), lb.begin(), std::negate<int64_t>());
auto expr =
getAffineExprFromFlatForm(lb, dimCount, symCount, localExprs, context);
// expr ceildiv divisor is (expr + divisor - 1) floordiv divisor
int64_t divisor = std::abs(ineq[pos + offset]);
expr = (expr + divisor - 1).floorDiv(divisor);
lbExprs.push_back(expr);
}
SmallVector<AffineExpr, 4> ubExprs;
ubExprs.reserve(ubIndices.size() + eqIndices.size());
// Upper bound expressions.
for (auto idx : ubIndices) {
auto ineq = getInequality(idx);
// Extract the upper bound (in terms of other coeff's + const).
addCoeffs(ineq, ub);
auto expr =
getAffineExprFromFlatForm(ub, dimCount, symCount, localExprs, context);
expr = expr.floorDiv(std::abs(ineq[pos + offset]));
// Upper bound is exclusive.
ubExprs.push_back(expr + 1);
}
// Equalities. It's both a lower and a upper bound.
SmallVector<int64_t, 4> b;
for (auto idx : eqIndices) {
auto eq = getEquality(idx);
addCoeffs(eq, b);
if (eq[pos + offset] > 0)
std::transform(b.begin(), b.end(), b.begin(), std::negate<int64_t>());
// Extract the upper bound (in terms of other coeff's + const).
auto expr =
getAffineExprFromFlatForm(b, dimCount, symCount, localExprs, context);
expr = expr.floorDiv(std::abs(eq[pos + offset]));
// Upper bound is exclusive.
ubExprs.push_back(expr + 1);
// Lower bound.
expr =
getAffineExprFromFlatForm(b, dimCount, symCount, localExprs, context);
expr = expr.ceilDiv(std::abs(eq[pos + offset]));
lbExprs.push_back(expr);
}
auto lbMap = AffineMap::get(dimCount, symCount, lbExprs, context);
auto ubMap = AffineMap::get(dimCount, symCount, ubExprs, context);
return {lbMap, ubMap};
}
/// Computes the lower and upper bounds of the first 'num' dimensional
/// variables (starting at 'offset') as affine maps of the remaining
/// variables (dimensional and symbolic variables). Local variables are
/// themselves explicitly computed as affine functions of other variables in
/// this process if needed.
void FlatAffineValueConstraints::getSliceBounds(
unsigned offset, unsigned num, MLIRContext *context,
SmallVectorImpl<AffineMap> *lbMaps, SmallVectorImpl<AffineMap> *ubMaps,
bool getClosedUB) {
assert(num < getNumDimVars() && "invalid range");
// Basic simplification.
normalizeConstraintsByGCD();
LLVM_DEBUG(llvm::dbgs() << "getSliceBounds for first " << num
<< " variables\n");
LLVM_DEBUG(dump());
// Record computed/detected variables.
SmallVector<AffineExpr, 8> memo(getNumVars());
// Initialize dimensional and symbolic variables.
for (unsigned i = 0, e = getNumDimVars(); i < e; i++) {
if (i < offset)
memo[i] = getAffineDimExpr(i, context);
else if (i >= offset + num)
memo[i] = getAffineDimExpr(i - num, context);
}
for (unsigned i = getNumDimVars(), e = getNumDimAndSymbolVars(); i < e; i++)
memo[i] = getAffineSymbolExpr(i - getNumDimVars(), context);
bool changed;
do {
changed = false;
// Identify yet unknown variables as constants or mod's / floordiv's of
// other variables if possible.
for (unsigned pos = 0; pos < getNumVars(); pos++) {
if (memo[pos])
continue;
auto lbConst = getConstantBound(BoundType::LB, pos);
auto ubConst = getConstantBound(BoundType::UB, pos);
if (lbConst.has_value() && ubConst.has_value()) {
// Detect equality to a constant.
if (lbConst.value() == ubConst.value()) {
memo[pos] = getAffineConstantExpr(lbConst.value(), context);
changed = true;
continue;
}
// Detect an variable as modulo of another variable w.r.t a
// constant.
if (detectAsMod(*this, pos, lbConst.value(), ubConst.value(), memo,
context)) {
changed = true;
continue;
}
}
// Detect an variable as a floordiv of an affine function of other
// variables (divisor is a positive constant).
if (detectAsFloorDiv(*this, pos, context, memo)) {
changed = true;
continue;
}
// Detect an variable as an expression of other variables.
unsigned idx;
if (!findConstraintWithNonZeroAt(pos, /*isEq=*/true, &idx)) {
continue;
}
// Build AffineExpr solving for variable 'pos' in terms of all others.
auto expr = getAffineConstantExpr(0, context);
unsigned j, e;
for (j = 0, e = getNumVars(); j < e; ++j) {
if (j == pos)
continue;
int64_t c = atEq(idx, j);
if (c == 0)
continue;
// If any of the involved IDs hasn't been found yet, we can't proceed.
if (!memo[j])
break;
expr = expr + memo[j] * c;
}
if (j < e)
// Can't construct expression as it depends on a yet uncomputed
// variable.
continue;
// Add constant term to AffineExpr.
expr = expr + atEq(idx, getNumVars());
int64_t vPos = atEq(idx, pos);
assert(vPos != 0 && "expected non-zero here");
if (vPos > 0)
expr = (-expr).floorDiv(vPos);
else
// vPos < 0.
expr = expr.floorDiv(-vPos);
// Successfully constructed expression.
memo[pos] = expr;
changed = true;
}
// This loop is guaranteed to reach a fixed point - since once an
// variable's explicit form is computed (in memo[pos]), it's not updated
// again.
} while (changed);
int64_t ubAdjustment = getClosedUB ? 0 : 1;
// Set the lower and upper bound maps for all the variables that were
// computed as affine expressions of the rest as the "detected expr" and
// "detected expr + 1" respectively; set the undetected ones to null.
Optional<FlatAffineValueConstraints> tmpClone;
for (unsigned pos = 0; pos < num; pos++) {
unsigned numMapDims = getNumDimVars() - num;
unsigned numMapSymbols = getNumSymbolVars();
AffineExpr expr = memo[pos + offset];
if (expr)
expr = simplifyAffineExpr(expr, numMapDims, numMapSymbols);
AffineMap &lbMap = (*lbMaps)[pos];
AffineMap &ubMap = (*ubMaps)[pos];
if (expr) {
lbMap = AffineMap::get(numMapDims, numMapSymbols, expr);
ubMap = AffineMap::get(numMapDims, numMapSymbols, expr + ubAdjustment);
} else {
// TODO: Whenever there are local variables in the dependence
// constraints, we'll conservatively over-approximate, since we don't
// always explicitly compute them above (in the while loop).
if (getNumLocalVars() == 0) {
// Work on a copy so that we don't update this constraint system.
if (!tmpClone) {
tmpClone.emplace(FlatAffineValueConstraints(*this));
// Removing redundant inequalities is necessary so that we don't get
// redundant loop bounds.
tmpClone->removeRedundantInequalities();
}
std::tie(lbMap, ubMap) = tmpClone->getLowerAndUpperBound(
pos, offset, num, getNumDimVars(), /*localExprs=*/{}, context);
}
// If the above fails, we'll just use the constant lower bound and the
// constant upper bound (if they exist) as the slice bounds.
// TODO: being conservative for the moment in cases that
// lead to multiple bounds - until getConstDifference in LoopFusion.cpp is
// fixed (b/126426796).
if (!lbMap || lbMap.getNumResults() > 1) {
LLVM_DEBUG(llvm::dbgs()
<< "WARNING: Potentially over-approximating slice lb\n");
auto lbConst = getConstantBound(BoundType::LB, pos + offset);
if (lbConst.has_value()) {
lbMap =
AffineMap::get(numMapDims, numMapSymbols,
getAffineConstantExpr(lbConst.value(), context));
}
}
if (!ubMap || ubMap.getNumResults() > 1) {
LLVM_DEBUG(llvm::dbgs()
<< "WARNING: Potentially over-approximating slice ub\n");
auto ubConst = getConstantBound(BoundType::UB, pos + offset);
if (ubConst.has_value()) {
ubMap = AffineMap::get(
numMapDims, numMapSymbols,
getAffineConstantExpr(ubConst.value() + ubAdjustment, context));
}
}
}
LLVM_DEBUG(llvm::dbgs()
<< "lb map for pos = " << Twine(pos + offset) << ", expr: ");
LLVM_DEBUG(lbMap.dump(););
LLVM_DEBUG(llvm::dbgs()
<< "ub map for pos = " << Twine(pos + offset) << ", expr: ");
LLVM_DEBUG(ubMap.dump(););
}
}
LogicalResult FlatAffineValueConstraints::flattenAlignedMapAndMergeLocals(
AffineMap map, std::vector<SmallVector<int64_t, 8>> *flattenedExprs) {
FlatAffineValueConstraints localCst;
if (failed(getFlattenedAffineExprs(map, flattenedExprs, &localCst))) {
LLVM_DEBUG(llvm::dbgs()
<< "composition unimplemented for semi-affine maps\n");
return failure();
}
// Add localCst information.
if (localCst.getNumLocalVars() > 0) {
unsigned numLocalVars = getNumLocalVars();
// Insert local dims of localCst at the beginning.
insertLocalVar(/*pos=*/0, /*num=*/localCst.getNumLocalVars());
// Insert local dims of `this` at the end of localCst.
localCst.appendLocalVar(/*num=*/numLocalVars);
// Dimensions of localCst and this constraint set match. Append localCst to
// this constraint set.
append(localCst);
}
return success();
}
LogicalResult FlatAffineValueConstraints::addBound(BoundType type, unsigned pos,
AffineMap boundMap,
bool isClosedBound) {
assert(boundMap.getNumDims() == getNumDimVars() && "dim mismatch");
assert(boundMap.getNumSymbols() == getNumSymbolVars() && "symbol mismatch");
assert(pos < getNumDimAndSymbolVars() && "invalid position");
assert((type != BoundType::EQ || isClosedBound) &&
"EQ bound must be closed.");
// Equality follows the logic of lower bound except that we add an equality
// instead of an inequality.
assert((type != BoundType::EQ || boundMap.getNumResults() == 1) &&
"single result expected");
bool lower = type == BoundType::LB || type == BoundType::EQ;
std::vector<SmallVector<int64_t, 8>> flatExprs;
if (failed(flattenAlignedMapAndMergeLocals(boundMap, &flatExprs)))
return failure();
assert(flatExprs.size() == boundMap.getNumResults());
// Add one (in)equality for each result.
for (const auto &flatExpr : flatExprs) {
SmallVector<int64_t> ineq(getNumCols(), 0);
// Dims and symbols.
for (unsigned j = 0, e = boundMap.getNumInputs(); j < e; j++) {
ineq[j] = lower ? -flatExpr[j] : flatExpr[j];
}
// Invalid bound: pos appears in `boundMap`.
// TODO: This should be an assertion. Fix `addDomainFromSliceMaps` and/or
// its callers to prevent invalid bounds from being added.
if (ineq[pos] != 0)
continue;
ineq[pos] = lower ? 1 : -1;
// Local columns of `ineq` are at the beginning.
unsigned j = getNumDimVars() + getNumSymbolVars();
unsigned end = flatExpr.size() - 1;
for (unsigned i = boundMap.getNumInputs(); i < end; i++, j++) {
ineq[j] = lower ? -flatExpr[i] : flatExpr[i];
}
// Make the bound closed in if flatExpr is open. The inequality is always
// created in the upper bound form, so the adjustment is -1.
int64_t boundAdjustment = (isClosedBound || type == BoundType::EQ) ? 0 : -1;
// Constant term.
ineq[getNumCols() - 1] = (lower ? -flatExpr[flatExpr.size() - 1]
: flatExpr[flatExpr.size() - 1]) +
boundAdjustment;
type == BoundType::EQ ? addEquality(ineq) : addInequality(ineq);
}
return success();
}
LogicalResult FlatAffineValueConstraints::addBound(BoundType type, unsigned pos,
AffineMap boundMap) {
return addBound(type, pos, boundMap, /*isClosedBound=*/type != BoundType::UB);
}
AffineMap
FlatAffineValueConstraints::computeAlignedMap(AffineMap map,
ValueRange operands) const {
assert(map.getNumInputs() == operands.size() && "number of inputs mismatch");
SmallVector<Value> dims, syms;
#ifndef NDEBUG
SmallVector<Value> newSyms;
SmallVector<Value> *newSymsPtr = &newSyms;
#else
SmallVector<Value> *newSymsPtr = nullptr;
#endif // NDEBUG
dims.reserve(getNumDimVars());
syms.reserve(getNumSymbolVars());
for (unsigned i = getVarKindOffset(VarKind::SetDim),
e = getVarKindEnd(VarKind::SetDim);
i < e; ++i)
dims.push_back(values[i] ? *values[i] : Value());
for (unsigned i = getVarKindOffset(VarKind::Symbol),
e = getVarKindEnd(VarKind::Symbol);
i < e; ++i)
syms.push_back(values[i] ? *values[i] : Value());
AffineMap alignedMap =
alignAffineMapWithValues(map, operands, dims, syms, newSymsPtr);
// All symbols are already part of this FlatAffineConstraints.
assert(syms.size() == newSymsPtr->size() && "unexpected new/missing symbols");
assert(std::equal(syms.begin(), syms.end(), newSymsPtr->begin()) &&
"unexpected new/missing symbols");
return alignedMap;
}
LogicalResult FlatAffineValueConstraints::addBound(BoundType type, unsigned pos,
AffineMap boundMap,
ValueRange boundOperands) {
// Fully compose map and operands; canonicalize and simplify so that we
// transitively get to terminal symbols or loop IVs.
auto map = boundMap;
SmallVector<Value, 4> operands(boundOperands.begin(), boundOperands.end());
fullyComposeAffineMapAndOperands(&map, &operands);
map = simplifyAffineMap(map);
canonicalizeMapAndOperands(&map, &operands);
for (auto operand : operands)
addInductionVarOrTerminalSymbol(operand);
return addBound(type, pos, computeAlignedMap(map, operands));
}
// Adds slice lower bounds represented by lower bounds in 'lbMaps' and upper
// bounds in 'ubMaps' to each value in `values' that appears in the constraint
// system. Note that both lower/upper bounds share the same operand list
// 'operands'.
// This function assumes 'values.size' == 'lbMaps.size' == 'ubMaps.size', and
// skips any null AffineMaps in 'lbMaps' or 'ubMaps'.
// Note that both lower/upper bounds use operands from 'operands'.
// Returns failure for unimplemented cases such as semi-affine expressions or
// expressions with mod/floordiv.
LogicalResult FlatAffineValueConstraints::addSliceBounds(
ArrayRef<Value> values, ArrayRef<AffineMap> lbMaps,
ArrayRef<AffineMap> ubMaps, ArrayRef<Value> operands) {
assert(values.size() == lbMaps.size());
assert(lbMaps.size() == ubMaps.size());
for (unsigned i = 0, e = lbMaps.size(); i < e; ++i) {
unsigned pos;
if (!findVar(values[i], &pos))
continue;
AffineMap lbMap = lbMaps[i];
AffineMap ubMap = ubMaps[i];
assert(!lbMap || lbMap.getNumInputs() == operands.size());
assert(!ubMap || ubMap.getNumInputs() == operands.size());
// Check if this slice is just an equality along this dimension.
if (lbMap && ubMap && lbMap.getNumResults() == 1 &&
ubMap.getNumResults() == 1 &&
lbMap.getResult(0) + 1 == ubMap.getResult(0)) {
if (failed(addBound(BoundType::EQ, pos, lbMap, operands)))
return failure();
continue;
}
// If lower or upper bound maps are null or provide no results, it implies
// that the source loop was not at all sliced, and the entire loop will be a
// part of the slice.
if (lbMap && lbMap.getNumResults() != 0 && ubMap &&
ubMap.getNumResults() != 0) {
if (failed(addBound(BoundType::LB, pos, lbMap, operands)))
return failure();
if (failed(addBound(BoundType::UB, pos, ubMap, operands)))
return failure();
} else {
auto loop = getForInductionVarOwner(values[i]);
if (failed(this->addAffineForOpDomain(loop)))
return failure();
}
}
return success();
}
bool FlatAffineValueConstraints::findVar(Value val, unsigned *pos) const {
unsigned i = 0;
for (const auto &mayBeVar : values) {
if (mayBeVar && *mayBeVar == val) {
*pos = i;
return true;
}
i++;
}
return false;
}
bool FlatAffineValueConstraints::containsVar(Value val) const {
return llvm::any_of(values, [&](const Optional<Value> &mayBeVar) {
return mayBeVar && *mayBeVar == val;
});
}
void FlatAffineValueConstraints::swapVar(unsigned posA, unsigned posB) {
IntegerPolyhedron::swapVar(posA, posB);
if (getVarKindAt(posA) == VarKind::Local &&
getVarKindAt(posB) == VarKind::Local)
return;
// Treat value of a local variable as None.
if (getVarKindAt(posA) == VarKind::Local)
values[posB] = None;
else if (getVarKindAt(posB) == VarKind::Local)
values[posA] = None;
else
std::swap(values[posA], values[posB]);
}
void FlatAffineValueConstraints::addBound(BoundType type, Value val,
int64_t value) {
unsigned pos;
if (!findVar(val, &pos))
// This is a pre-condition for this method.
assert(0 && "var not found");
addBound(type, pos, value);
}
void FlatAffineValueConstraints::printSpace(raw_ostream &os) const {
IntegerPolyhedron::printSpace(os);
os << "(";
for (unsigned i = 0, e = getNumDimAndSymbolVars(); i < e; i++) {
if (hasValue(i))
os << "Value ";
else
os << "None ";
}
for (unsigned i = getVarKindOffset(VarKind::Local),
e = getVarKindEnd(VarKind::Local);
i < e; ++i)
os << "Local ";
os << " const)\n";
}
void FlatAffineValueConstraints::clearAndCopyFrom(
const IntegerRelation &other) {
if (auto *otherValueSet =
dyn_cast<const FlatAffineValueConstraints>(&other)) {
*this = *otherValueSet;
} else {
*static_cast<IntegerRelation *>(this) = other;
values.clear();
values.resize(getNumDimAndSymbolVars(), None);
}
}
void FlatAffineValueConstraints::fourierMotzkinEliminate(
unsigned pos, bool darkShadow, bool *isResultIntegerExact) {
SmallVector<Optional<Value>, 8> newVals = values;
if (getVarKindAt(pos) != VarKind::Local)
newVals.erase(newVals.begin() + pos);
// Note: Base implementation discards all associated Values.
IntegerPolyhedron::fourierMotzkinEliminate(pos, darkShadow,
isResultIntegerExact);
values = newVals;
assert(values.size() == getNumDimAndSymbolVars());
}
void FlatAffineValueConstraints::projectOut(Value val) {
unsigned pos;
bool ret = findVar(val, &pos);
assert(ret);
(void)ret;
fourierMotzkinEliminate(pos);
}
LogicalResult FlatAffineValueConstraints::unionBoundingBox(
const FlatAffineValueConstraints &otherCst) {
assert(otherCst.getNumDimVars() == getNumDimVars() && "dims mismatch");
assert(otherCst.getMaybeValues()
.slice(0, getNumDimVars())
.equals(getMaybeValues().slice(0, getNumDimVars())) &&
"dim values mismatch");
assert(otherCst.getNumLocalVars() == 0 && "local vars not supported here");
assert(getNumLocalVars() == 0 && "local vars not supported yet here");
// Align `other` to this.
if (!areVarsAligned(*this, otherCst)) {
FlatAffineValueConstraints otherCopy(otherCst);
mergeAndAlignVars(/*offset=*/getNumDimVars(), this, &otherCopy);
return IntegerPolyhedron::unionBoundingBox(otherCopy);
}
return IntegerPolyhedron::unionBoundingBox(otherCst);
}
/// Compute an explicit representation for local vars. For all systems coming
/// from MLIR integer sets, maps, or expressions where local vars were
/// introduced to model floordivs and mods, this always succeeds.
static LogicalResult computeLocalVars(const FlatAffineValueConstraints &cst,
SmallVectorImpl<AffineExpr> &memo,
MLIRContext *context) {
unsigned numDims = cst.getNumDimVars();
unsigned numSyms = cst.getNumSymbolVars();
// Initialize dimensional and symbolic variables.
for (unsigned i = 0; i < numDims; i++)
memo[i] = getAffineDimExpr(i, context);
for (unsigned i = numDims, e = numDims + numSyms; i < e; i++)
memo[i] = getAffineSymbolExpr(i - numDims, context);
bool changed;
do {
// Each time `changed` is true at the end of this iteration, one or more
// local vars would have been detected as floordivs and set in memo; so the
// number of null entries in memo[...] strictly reduces; so this converges.
changed = false;
for (unsigned i = 0, e = cst.getNumLocalVars(); i < e; ++i)
if (!memo[numDims + numSyms + i] &&
detectAsFloorDiv(cst, /*pos=*/numDims + numSyms + i, context, memo))
changed = true;
} while (changed);
ArrayRef<AffineExpr> localExprs =
ArrayRef<AffineExpr>(memo).take_back(cst.getNumLocalVars());
return success(
llvm::all_of(localExprs, [](AffineExpr expr) { return expr; }));
}
void FlatAffineValueConstraints::getIneqAsAffineValueMap(
unsigned pos, unsigned ineqPos, AffineValueMap &vmap,
MLIRContext *context) const {
unsigned numDims = getNumDimVars();
unsigned numSyms = getNumSymbolVars();
assert(pos < numDims && "invalid position");
assert(ineqPos < getNumInequalities() && "invalid inequality position");
// Get expressions for local vars.
SmallVector<AffineExpr, 8> memo(getNumVars(), AffineExpr());
if (failed(computeLocalVars(*this, memo, context)))
assert(false &&
"one or more local exprs do not have an explicit representation");
auto localExprs = ArrayRef<AffineExpr>(memo).take_back(getNumLocalVars());
// Compute the AffineExpr lower/upper bound for this inequality.
ArrayRef<int64_t> inequality = getInequality(ineqPos);
SmallVector<int64_t, 8> bound;
bound.reserve(getNumCols() - 1);
// Everything other than the coefficient at `pos`.
bound.append(inequality.begin(), inequality.begin() + pos);
bound.append(inequality.begin() + pos + 1, inequality.end());
if (inequality[pos] > 0)
// Lower bound.
std::transform(bound.begin(), bound.end(), bound.begin(),
std::negate<int64_t>());
else
// Upper bound (which is exclusive).
bound.back() += 1;
// Convert to AffineExpr (tree) form.
auto boundExpr = getAffineExprFromFlatForm(bound, numDims - 1, numSyms,
localExprs, context);
// Get the values to bind to this affine expr (all dims and symbols).
SmallVector<Value, 4> operands;
getValues(0, pos, &operands);
SmallVector<Value, 4> trailingOperands;
getValues(pos + 1, getNumDimAndSymbolVars(), &trailingOperands);
operands.append(trailingOperands.begin(), trailingOperands.end());
vmap.reset(AffineMap::get(numDims - 1, numSyms, boundExpr), operands);
}
IntegerSet
FlatAffineValueConstraints::getAsIntegerSet(MLIRContext *context) const {
if (getNumConstraints() == 0)
// Return universal set (always true): 0 == 0.
return IntegerSet::get(getNumDimVars(), getNumSymbolVars(),
getAffineConstantExpr(/*constant=*/0, context),
/*eqFlags=*/true);
// Construct local references.
SmallVector<AffineExpr, 8> memo(getNumVars(), AffineExpr());
if (failed(computeLocalVars(*this, memo, context))) {
// Check if the local variables without an explicit representation have
// zero coefficients everywhere.
SmallVector<unsigned> noLocalRepVars;
unsigned numDimsSymbols = getNumDimAndSymbolVars();
for (unsigned i = numDimsSymbols, e = getNumVars(); i < e; ++i) {
if (!memo[i] && !isColZero(/*pos=*/i))
noLocalRepVars.push_back(i - numDimsSymbols);
}
if (!noLocalRepVars.empty()) {
LLVM_DEBUG({
llvm::dbgs() << "local variables at position(s) ";
llvm::interleaveComma(noLocalRepVars, llvm::dbgs());
llvm::dbgs() << " do not have an explicit representation in:\n";
this->dump();
});
return IntegerSet();
}
}
ArrayRef<AffineExpr> localExprs =
ArrayRef<AffineExpr>(memo).take_back(getNumLocalVars());
// Construct the IntegerSet from the equalities/inequalities.
unsigned numDims = getNumDimVars();
unsigned numSyms = getNumSymbolVars();
SmallVector<bool, 16> eqFlags(getNumConstraints());
std::fill(eqFlags.begin(), eqFlags.begin() + getNumEqualities(), true);
std::fill(eqFlags.begin() + getNumEqualities(), eqFlags.end(), false);
SmallVector<AffineExpr, 8> exprs;
exprs.reserve(getNumConstraints());
for (unsigned i = 0, e = getNumEqualities(); i < e; ++i)
exprs.push_back(getAffineExprFromFlatForm(getEquality(i), numDims, numSyms,
localExprs, context));
for (unsigned i = 0, e = getNumInequalities(); i < e; ++i)
exprs.push_back(getAffineExprFromFlatForm(getInequality(i), numDims,
numSyms, localExprs, context));
return IntegerSet::get(numDims, numSyms, exprs, eqFlags);
}
AffineMap mlir::alignAffineMapWithValues(AffineMap map, ValueRange operands,
ValueRange dims, ValueRange syms,
SmallVector<Value> *newSyms) {
assert(operands.size() == map.getNumInputs() &&
"expected same number of operands and map inputs");
MLIRContext *ctx = map.getContext();
Builder builder(ctx);
SmallVector<AffineExpr> dimReplacements(map.getNumDims(), {});
unsigned numSymbols = syms.size();
SmallVector<AffineExpr> symReplacements(map.getNumSymbols(), {});
if (newSyms) {
newSyms->clear();
newSyms->append(syms.begin(), syms.end());
}
for (const auto &operand : llvm::enumerate(operands)) {
// Compute replacement dim/sym of operand.
AffineExpr replacement;
auto dimIt = std::find(dims.begin(), dims.end(), operand.value());
auto symIt = std::find(syms.begin(), syms.end(), operand.value());
if (dimIt != dims.end()) {
replacement =
builder.getAffineDimExpr(std::distance(dims.begin(), dimIt));
} else if (symIt != syms.end()) {
replacement =
builder.getAffineSymbolExpr(std::distance(syms.begin(), symIt));
} else {
// This operand is neither a dimension nor a symbol. Add it as a new
// symbol.
replacement = builder.getAffineSymbolExpr(numSymbols++);
if (newSyms)
newSyms->push_back(operand.value());
}
// Add to corresponding replacements vector.
if (operand.index() < map.getNumDims()) {
dimReplacements[operand.index()] = replacement;
} else {
symReplacements[operand.index() - map.getNumDims()] = replacement;
}
}
return map.replaceDimsAndSymbols(dimReplacements, symReplacements,
dims.size(), numSymbols);
}
FlatAffineValueConstraints FlatAffineRelation::getDomainSet() const {
FlatAffineValueConstraints domain = *this;
// Convert all range variables to local variables.
domain.convertToLocal(VarKind::SetDim, getNumDomainDims(),
getNumDomainDims() + getNumRangeDims());
return domain;
}
FlatAffineValueConstraints FlatAffineRelation::getRangeSet() const {
FlatAffineValueConstraints range = *this;
// Convert all domain variables to local variables.
range.convertToLocal(VarKind::SetDim, 0, getNumDomainDims());
return range;
}
void FlatAffineRelation::compose(const FlatAffineRelation &other) {
assert(getNumDomainDims() == other.getNumRangeDims() &&
"Domain of this and range of other do not match");
assert(std::equal(values.begin(), values.begin() + getNumDomainDims(),
other.values.begin() + other.getNumDomainDims()) &&
"Domain of this and range of other do not match");
FlatAffineRelation rel = other;
// Convert `rel` from
// [otherDomain] -> [otherRange]
// to
// [otherDomain] -> [otherRange thisRange]
// and `this` from
// [thisDomain] -> [thisRange]
// to
// [otherDomain thisDomain] -> [thisRange].
unsigned removeDims = rel.getNumRangeDims();
insertDomainVar(0, rel.getNumDomainDims());
rel.appendRangeVar(getNumRangeDims());
// Merge symbol and local variables.
mergeSymbolVars(rel);
mergeLocalVars(rel);
// Convert `rel` from [otherDomain] -> [otherRange thisRange] to
// [otherDomain] -> [thisRange] by converting first otherRange range vars
// to local vars.
rel.convertToLocal(VarKind::SetDim, rel.getNumDomainDims(),
rel.getNumDomainDims() + removeDims);
// Convert `this` from [otherDomain thisDomain] -> [thisRange] to
// [otherDomain] -> [thisRange] by converting last thisDomain domain vars
// to local vars.
convertToLocal(VarKind::SetDim, getNumDomainDims() - removeDims,
getNumDomainDims());
auto thisMaybeValues = getMaybeValues(VarKind::SetDim);
auto relMaybeValues = rel.getMaybeValues(VarKind::SetDim);
// Add and match domain of `rel` to domain of `this`.
for (unsigned i = 0, e = rel.getNumDomainDims(); i < e; ++i)
if (relMaybeValues[i].has_value())
setValue(i, relMaybeValues[i].value());
// Add and match range of `this` to range of `rel`.
for (unsigned i = 0, e = getNumRangeDims(); i < e; ++i) {
unsigned rangeIdx = rel.getNumDomainDims() + i;
if (thisMaybeValues[rangeIdx].has_value())
rel.setValue(rangeIdx, thisMaybeValues[rangeIdx].value());
}
// Append `this` to `rel` and simplify constraints.
rel.append(*this);
rel.removeRedundantLocalVars();
*this = rel;
}
void FlatAffineRelation::inverse() {
unsigned oldDomain = getNumDomainDims();
unsigned oldRange = getNumRangeDims();
// Add new range vars.
appendRangeVar(oldDomain);
// Swap new vars with domain.
for (unsigned i = 0; i < oldDomain; ++i)
swapVar(i, oldDomain + oldRange + i);
// Remove the swapped domain.
removeVarRange(0, oldDomain);
// Set domain and range as inverse.
numDomainDims = oldRange;
numRangeDims = oldDomain;
}
void FlatAffineRelation::insertDomainVar(unsigned pos, unsigned num) {
assert(pos <= getNumDomainDims() &&
"Var cannot be inserted at invalid position");
insertDimVar(pos, num);
numDomainDims += num;
}
void FlatAffineRelation::insertRangeVar(unsigned pos, unsigned num) {
assert(pos <= getNumRangeDims() &&
"Var cannot be inserted at invalid position");
insertDimVar(getNumDomainDims() + pos, num);
numRangeDims += num;
}
void FlatAffineRelation::appendDomainVar(unsigned num) {
insertDimVar(getNumDomainDims(), num);
numDomainDims += num;
}
void FlatAffineRelation::appendRangeVar(unsigned num) {
insertDimVar(getNumDimVars(), num);
numRangeDims += num;
}
void FlatAffineRelation::removeVarRange(VarKind kind, unsigned varStart,
unsigned varLimit) {
assert(varLimit <= getNumVarKind(kind));
if (varStart >= varLimit)
return;
FlatAffineValueConstraints::removeVarRange(kind, varStart, varLimit);
// If kind is not SetDim, domain and range don't need to be updated.
if (kind != VarKind::SetDim)
return;
// Compute number of domain and range variables to remove. This is done by
// intersecting the range of domain/range vars with range of vars to remove.
unsigned intersectDomainLHS = std::min(varLimit, getNumDomainDims());
unsigned intersectDomainRHS = varStart;
unsigned intersectRangeLHS = std::min(varLimit, getNumDimVars());
unsigned intersectRangeRHS = std::max(varStart, getNumDomainDims());
if (intersectDomainLHS > intersectDomainRHS)
numDomainDims -= intersectDomainLHS - intersectDomainRHS;
if (intersectRangeLHS > intersectRangeRHS)
numRangeDims -= intersectRangeLHS - intersectRangeRHS;
}
LogicalResult mlir::getRelationFromMap(AffineMap &map,
FlatAffineRelation &rel) {
// Get flattened affine expressions.
std::vector<SmallVector<int64_t, 8>> flatExprs;
FlatAffineValueConstraints localVarCst;
if (failed(getFlattenedAffineExprs(map, &flatExprs, &localVarCst)))
return failure();
unsigned oldDimNum = localVarCst.getNumDimVars();
unsigned oldCols = localVarCst.getNumCols();
unsigned numRangeVars = map.getNumResults();
unsigned numDomainVars = map.getNumDims();
// Add range as the new expressions.
localVarCst.appendDimVar(numRangeVars);
// Add equalities between source and range.
SmallVector<int64_t, 8> eq(localVarCst.getNumCols());
for (unsigned i = 0, e = map.getNumResults(); i < e; ++i) {
// Zero fill.
std::fill(eq.begin(), eq.end(), 0);
// Fill equality.
for (unsigned j = 0, f = oldDimNum; j < f; ++j)
eq[j] = flatExprs[i][j];
for (unsigned j = oldDimNum, f = oldCols; j < f; ++j)
eq[j + numRangeVars] = flatExprs[i][j];
// Set this dimension to -1 to equate lhs and rhs and add equality.
eq[numDomainVars + i] = -1;
localVarCst.addEquality(eq);
}
// Create relation and return success.
rel = FlatAffineRelation(numDomainVars, numRangeVars, localVarCst);
return success();
}
LogicalResult mlir::getRelationFromMap(const AffineValueMap &map,
FlatAffineRelation &rel) {
AffineMap affineMap = map.getAffineMap();
if (failed(getRelationFromMap(affineMap, rel)))
return failure();
// Set symbol values for domain dimensions and symbols.
for (unsigned i = 0, e = rel.getNumDomainDims(); i < e; ++i)
rel.setValue(i, map.getOperand(i));
for (unsigned i = rel.getNumDimVars(), e = rel.getNumDimAndSymbolVars();
i < e; ++i)
rel.setValue(i, map.getOperand(i - rel.getNumRangeDims()));
return success();
}
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