From: Matthias Springer Date: Thu, 23 Mar 2023 08:25:01 +0000 (+0100) Subject: [mlir][Analysis][NFC] Split FlatAffineValueConstraints into multiple classes X-Git-Tag: upstream/17.0.6~13920 X-Git-Url: http://review.tizen.org/git/?a=commitdiff_plain;h=5b0055a4ae8d27bf2a8db903eed22ff642fc27c3;p=platform%2Fupstream%2Fllvm.git [mlir][Analysis][NFC] Split FlatAffineValueConstraints into multiple classes The new class hierarchy is as follows: * `IntegerRelation` (no change) * `IntegerPolyhedron` (no change) * `FlatLinearConstraints`: provides an AffineExpr-based API * `FlatLinearValueConstraints`: stores an additional mapping of non-local vars to SSA values * `FlatAffineValueConstraints`: provides additional helper functions for Affine dialect ops * `FlatAffineRelation` (no change) `FlatConstraints` and `FlatValueConstraints` are moved from `MLIRAffineAnalysis` to `MLIRAnalysis` and can be used without depending on the Affine dialect. This change is in preparation of D145681, which adds an MLIR interface that depends on `FlatConstraints` (and cannot depend on the Affine dialect or any other dialect). Differential Revision: https://reviews.llvm.org/D146201 --- diff --git a/mlir/docs/Rationale/UsageOfConst.md b/mlir/docs/Rationale/UsageOfConst.md index 102b948..7a54a4e 100644 --- a/mlir/docs/Rationale/UsageOfConst.md +++ b/mlir/docs/Rationale/UsageOfConst.md @@ -235,9 +235,9 @@ if (auto *dimOp = inst->dyn_cast()) { It is much better to eliminate them entirely, and just pass around `DimOp` directly. For example, instead of: -```C++ +```c++ LogicalResult mlir::getIndexSet(MutableArrayRef> forOps, - FlatAffineConstraints *domain) { + FlatAffineValueConstraints *domain) { ``` @@ -245,7 +245,7 @@ It is a lot nicer to just have: ```c++ LogicalResult mlir::getIndexSet(MutableArrayRef forOps, - FlatAffineConstraints *domain) { + FlatAffineValueConstraints *domain) { ``` Particularly since all of the `FooOp` classes are already semantically a smart diff --git a/mlir/include/mlir/Analysis/FlatLinearValueConstraints.h b/mlir/include/mlir/Analysis/FlatLinearValueConstraints.h new file mode 100644 index 0000000..a6900ab --- /dev/null +++ b/mlir/include/mlir/Analysis/FlatLinearValueConstraints.h @@ -0,0 +1,560 @@ +//===- FlatLinearValueConstraints.h - Linear Constraints --------*- C++ -*-===// +// +// 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 +// +//===----------------------------------------------------------------------===// + +#ifndef MLIR_ANALYSIS_FLATLINEARVALUECONSTRAINTS_H +#define MLIR_ANALYSIS_FLATLINEARVALUECONSTRAINTS_H + +#include "mlir/Analysis/Presburger/IntegerRelation.h" +#include "mlir/Analysis/Presburger/Matrix.h" +#include "mlir/IR/AffineExpr.h" +#include "mlir/IR/OpDefinition.h" +#include "mlir/Support/LogicalResult.h" +#include + +namespace mlir { + +class AffineMap; +class IntegerSet; +class MLIRContext; +class Value; +class MemRefType; +struct MutableAffineMap; + +namespace presburger { +class MultiAffineFunction; +} // namespace presburger + +/// FlatLinearConstraints is an extension of IntegerPolyhedron. It provides an +/// AffineExpr-based API. +class FlatLinearConstraints : public presburger::IntegerPolyhedron { +public: + /// Constructs a constraint system reserving memory for the specified number + /// of constraints and variables. `valArgs` are the optional SSA values + /// associated with each dimension/symbol. These must either be empty or match + /// the number of dimensions and symbols. + FlatLinearConstraints(unsigned numReservedInequalities, + unsigned numReservedEqualities, + unsigned numReservedCols, unsigned numDims, + unsigned numSymbols, unsigned numLocals) + : IntegerPolyhedron(numReservedInequalities, numReservedEqualities, + numReservedCols, + presburger::PresburgerSpace::getSetSpace( + numDims, numSymbols, numLocals)) { + assert(numReservedCols >= getNumVars() + 1); + } + + /// Constructs a constraint system with the specified number of dimensions + /// and symbols. `valArgs` are the optional SSA values associated with each + /// dimension/symbol. These must either be empty or match the number of + /// dimensions and symbols. + FlatLinearConstraints(unsigned numDims = 0, unsigned numSymbols = 0, + unsigned numLocals = 0) + : FlatLinearConstraints(/*numReservedInequalities=*/0, + /*numReservedEqualities=*/0, + /*numReservedCols=*/numDims + numSymbols + + numLocals + 1, + numDims, numSymbols, numLocals) {} + + FlatLinearConstraints(const IntegerPolyhedron &fac) + : IntegerPolyhedron(fac) {} + + /// Return the kind of this object. + Kind getKind() const override { return Kind::FlatLinearConstraints; } + + static bool classof(const IntegerRelation *cst) { + return cst->getKind() >= Kind::FlatLinearConstraints && + cst->getKind() <= Kind::FlatAffineRelation; + } + + /// Clones this object. + std::unique_ptr clone() const; + + /// Adds a bound for the variable at the specified position with constraints + /// being drawn from the specified bound map. In case of an EQ bound, the + /// bound map is expected to have exactly one result. In case of a LB/UB, the + /// bound map may have more than one result, for each of which an inequality + /// is added. + /// + /// The bound can be added as open or closed by specifying isClosedBound. In + /// case of a LB/UB, isClosedBound = false means the bound is added internally + /// as a closed bound by +1/-1 respectively. In case of an EQ bound, it can + /// only be added as a closed bound. + /// + /// Note: The dimensions/symbols of this FlatLinearConstraints must match the + /// dimensions/symbols of the affine map. + LogicalResult addBound(BoundType type, unsigned pos, AffineMap boundMap, + bool isClosedBound); + + /// Adds a bound for the variable at the specified position with constraints + /// being drawn from the specified bound map. In case of an EQ bound, the + /// bound map is expected to have exactly one result. In case of a LB/UB, the + /// bound map may have more than one result, for each of which an inequality + /// is added. + /// Note: The dimensions/symbols of this FlatLinearConstraints must match the + /// dimensions/symbols of the affine map. By default the lower bound is closed + /// and the upper bound is open. + LogicalResult addBound(BoundType type, unsigned pos, AffineMap boundMap); + + /// The `addBound` overload above hides the inherited overloads by default, so + /// we explicitly introduce them here. + using IntegerPolyhedron::addBound; + + /// Returns the constraint system as an integer set. Returns a null integer + /// set if the system has no constraints, or if an integer set couldn't be + /// constructed as a result of a local variable's explicit representation not + /// being known and such a local variable appearing in any of the constraints. + IntegerSet getAsIntegerSet(MLIRContext *context) const; + + /// Computes the lower and upper bounds of the first `num` dimensional + /// variables (starting at `offset`) as an affine map of the remaining + /// variables (dimensional and symbolic). This method is able to detect + /// variables as floordiv's and mod's of affine expressions of other + /// variables with respect to (positive) constants. Sets bound map to a + /// null AffineMap if such a bound can't be found (or yet unimplemented). + /// + /// By default the returned lower bounds are closed and upper bounds are open. + /// If `closedUb` is true, the upper bound is closed. + void getSliceBounds(unsigned offset, unsigned num, MLIRContext *context, + SmallVectorImpl *lbMaps, + SmallVectorImpl *ubMaps, + bool closedUB = false); + + /// Composes an affine map whose dimensions and symbols match one to one with + /// the dimensions and symbols of this FlatLinearConstraints. The results of + /// the map `other` are added as the leading dimensions of this constraint + /// system. Returns failure if `other` is a semi-affine map. + LogicalResult composeMatchingMap(AffineMap other); + + /// Gets the lower and upper bound of the `offset` + `pos`th variable + /// treating [0, offset) U [offset + num, symStartPos) as dimensions and + /// [symStartPos, getNumDimAndSymbolVars) as symbols, and `pos` lies in + /// [0, num). The multi-dimensional maps in the returned pair represent the + /// max and min of potentially multiple affine expressions. `localExprs` holds + /// pre-computed AffineExpr's for all local variables in the system. + /// + /// By default the returned lower bounds are closed and upper bounds are open. + /// If `closedUb` is true, the upper bound is closed. + std::pair + getLowerAndUpperBound(unsigned pos, unsigned offset, unsigned num, + unsigned symStartPos, ArrayRef localExprs, + MLIRContext *context, bool closedUB = false) const; + + /// Insert variables of the specified kind at position `pos`. Positions are + /// relative to the kind of variable. The coefficient columns corresponding + /// to the added variables are initialized to zero. `vals` are the Values + /// corresponding to the variables. Values should not be used with + /// VarKind::Local since values can only be attached to non-local variables. + /// Return the absolute column position (i.e., not relative to the kind of + /// variable) of the first added variable. + /// + /// Note: Empty Values are allowed in `vals`. + unsigned insertDimVar(unsigned pos, unsigned num = 1) { + return insertVar(VarKind::SetDim, pos, num); + } + unsigned insertSymbolVar(unsigned pos, unsigned num = 1) { + return insertVar(VarKind::Symbol, pos, num); + } + unsigned insertLocalVar(unsigned pos, unsigned num = 1) { + return insertVar(VarKind::Local, pos, num); + } + + /// Append variables of the specified kind after the last variable of that + /// kind. The coefficient columns corresponding to the added variables are + /// initialized to zero. `vals` are the Values corresponding to the + /// variables. Return the absolute column position (i.e., not relative to the + /// kind of variable) of the first appended variable. + /// + /// Note: Empty Values are allowed in `vals`. + unsigned appendDimVar(unsigned num = 1) { + return appendVar(VarKind::SetDim, num); + } + unsigned appendSymbolVar(unsigned num = 1) { + return appendVar(VarKind::Symbol, num); + } + unsigned appendLocalVar(unsigned num = 1) { + return appendVar(VarKind::Local, num); + } + +protected: + using VarKind = presburger::VarKind; + + /// 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. + LogicalResult computeLocalVars(SmallVectorImpl &memo, + MLIRContext *context) const; + + /// Given an affine map that is aligned with this constraint system: + /// * Flatten the map. + /// * Add newly introduced local columns at the beginning of this constraint + /// system (local column pos 0). + /// * Add equalities that define the new local columns to this constraint + /// system. + /// * Return the flattened expressions via `flattenedExprs`. + /// + /// Note: This is a shared helper function of `addLowerOrUpperBound` and + /// `composeMatchingMap`. + LogicalResult flattenAlignedMapAndMergeLocals( + AffineMap map, std::vector> *flattenedExprs); + + /// Prints the number of constraints, dimensions, symbols and locals in the + /// FlatLinearConstraints. Also, prints for each variable whether there is + /// an SSA Value attached to it. + void printSpace(raw_ostream &os) const override; +}; + +/// FlatLinearValueConstraints represents an extension of FlatLinearConstraints +/// where each non-local variable can have an SSA Value attached to it. +class FlatLinearValueConstraints : public FlatLinearConstraints { +public: + /// Constructs a constraint system reserving memory for the specified number + /// of constraints and variables. `valArgs` are the optional SSA values + /// associated with each dimension/symbol. These must either be empty or match + /// the number of dimensions and symbols. + FlatLinearValueConstraints(unsigned numReservedInequalities, + unsigned numReservedEqualities, + unsigned numReservedCols, unsigned numDims, + unsigned numSymbols, unsigned numLocals, + ArrayRef> valArgs) + : FlatLinearConstraints(numReservedInequalities, numReservedEqualities, + numReservedCols, numDims, numSymbols, numLocals) { + assert(valArgs.empty() || valArgs.size() == getNumDimAndSymbolVars()); + values.reserve(numReservedCols); + if (valArgs.empty()) + values.resize(getNumDimAndSymbolVars(), std::nullopt); + else + values.append(valArgs.begin(), valArgs.end()); + } + + /// Constructs a constraint system reserving memory for the specified number + /// of constraints and variables. `valArgs` are the optional SSA values + /// associated with each dimension/symbol. These must either be empty or match + /// the number of dimensions and symbols. + FlatLinearValueConstraints(unsigned numReservedInequalities, + unsigned numReservedEqualities, + unsigned numReservedCols, unsigned numDims, + unsigned numSymbols, unsigned numLocals, + ArrayRef valArgs) + : FlatLinearConstraints(numReservedInequalities, numReservedEqualities, + numReservedCols, numDims, numSymbols, numLocals) { + assert(valArgs.empty() || valArgs.size() == getNumDimAndSymbolVars()); + values.reserve(numReservedCols); + if (valArgs.empty()) + values.resize(getNumDimAndSymbolVars(), std::nullopt); + else + values.append(valArgs.begin(), valArgs.end()); + } + + /// Constructs a constraint system with the specified number of dimensions + /// and symbols. `valArgs` are the optional SSA values associated with each + /// dimension/symbol. These must either be empty or match the number of + /// dimensions and symbols. + FlatLinearValueConstraints(unsigned numDims, unsigned numSymbols, + unsigned numLocals, + ArrayRef> valArgs) + : FlatLinearValueConstraints(/*numReservedInequalities=*/0, + /*numReservedEqualities=*/0, + /*numReservedCols=*/numDims + numSymbols + + numLocals + 1, + numDims, numSymbols, numLocals, valArgs) {} + + /// Constructs a constraint system with the specified number of dimensions + /// and symbols. `valArgs` are the optional SSA values associated with each + /// dimension/symbol. These must either be empty or match the number of + /// dimensions and symbols. + FlatLinearValueConstraints(unsigned numDims = 0, unsigned numSymbols = 0, + unsigned numLocals = 0, + ArrayRef valArgs = {}) + : FlatLinearValueConstraints(/*numReservedInequalities=*/0, + /*numReservedEqualities=*/0, + /*numReservedCols=*/numDims + numSymbols + + numLocals + 1, + numDims, numSymbols, numLocals, valArgs) {} + + FlatLinearValueConstraints(const IntegerPolyhedron &fac, + ArrayRef> valArgs = {}) + : FlatLinearConstraints(fac) { + assert(valArgs.empty() || valArgs.size() == getNumDimAndSymbolVars()); + if (valArgs.empty()) + values.resize(getNumDimAndSymbolVars(), std::nullopt); + else + values.append(valArgs.begin(), valArgs.end()); + } + + /// Creates an affine constraint system from an IntegerSet. + explicit FlatLinearValueConstraints(IntegerSet set, ValueRange operands = {}); + + // 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. + static FlatLinearValueConstraints + getHyperrectangular(ValueRange ivs, ValueRange lbs, ValueRange ubs); + + /// Return the kind of this object. + Kind getKind() const override { return Kind::FlatLinearValueConstraints; } + + static bool classof(const IntegerRelation *cst) { + return cst->getKind() >= Kind::FlatLinearValueConstraints && + cst->getKind() <= Kind::FlatAffineRelation; + } + + /// Replaces the contents of this FlatLinearValueConstraints with `other`. + void clearAndCopyFrom(const IntegerRelation &other) override; + + /// Adds a constant bound for the variable associated with the given Value. + void addBound(BoundType type, Value val, int64_t value); + using FlatLinearConstraints::addBound; + + /// Returns the Value associated with the pos^th variable. Asserts if + /// no Value variable was associated. + inline Value getValue(unsigned pos) const { + assert(pos < getNumDimAndSymbolVars() && "Invalid position"); + assert(hasValue(pos) && "variable's Value not set"); + return *values[pos]; + } + + /// Returns the Values associated with variables in range [start, end). + /// Asserts if no Value was associated with one of these variables. + inline void getValues(unsigned start, unsigned end, + SmallVectorImpl *values) const { + assert(end <= getNumDimAndSymbolVars() && "invalid end position"); + assert(start <= end && "invalid start position"); + values->clear(); + values->reserve(end - start); + for (unsigned i = start; i < end; i++) + values->push_back(getValue(i)); + } + inline void getAllValues(SmallVectorImpl *values) const { + getValues(0, getNumDimAndSymbolVars(), values); + } + + inline ArrayRef> getMaybeValues() const { + return {values.data(), values.size()}; + } + + inline ArrayRef> + getMaybeValues(presburger::VarKind kind) const { + assert(kind != VarKind::Local && + "Local variables do not have any value attached to them."); + return {values.data() + getVarKindOffset(kind), getNumVarKind(kind)}; + } + + /// Returns true if the pos^th variable has an associated Value. + inline bool hasValue(unsigned pos) const { + assert(pos < getNumDimAndSymbolVars() && "Invalid position"); + return values[pos].has_value(); + } + + /// Returns true if at least one variable has an associated Value. + bool hasValues() const; + + unsigned appendDimVar(ValueRange vals); + using FlatLinearConstraints::appendDimVar; + + unsigned appendSymbolVar(ValueRange vals); + using FlatLinearConstraints::appendSymbolVar; + + unsigned insertDimVar(unsigned pos, ValueRange vals); + using FlatLinearConstraints::insertDimVar; + + unsigned insertSymbolVar(unsigned pos, ValueRange vals); + using FlatLinearConstraints::insertSymbolVar; + + unsigned insertVar(presburger::VarKind kind, unsigned pos, + unsigned num = 1) override; + unsigned insertVar(presburger::VarKind kind, unsigned pos, ValueRange vals); + + /// Removes variables in the column range [varStart, varLimit), and copies any + /// remaining valid data into place, updates member variables, and resizes + /// arrays as needed. + void removeVarRange(presburger::VarKind kind, unsigned varStart, + unsigned varLimit) override; + using IntegerPolyhedron::removeVarRange; + + /// Sets the Value associated with the pos^th variable. + inline void setValue(unsigned pos, Value val) { + assert(pos < getNumDimAndSymbolVars() && "invalid var position"); + values[pos] = val; + } + + /// Sets the Values associated with the variables in the range [start, end). + /// The range must contain only dim and symbol variables. + void setValues(unsigned start, unsigned end, ArrayRef values) { + assert(end <= getNumVars() && "invalid end position"); + assert(start <= end && "invalid start position"); + assert(values.size() == end - start && + "value should be provided for each variable in the range."); + for (unsigned i = start; i < end; ++i) + setValue(i, values[i - start]); + } + + /// Looks up the position of the variable with the specified Value. Returns + /// true if found (false otherwise). `pos` is set to the (column) position of + /// the variable. + bool findVar(Value val, unsigned *pos) const; + + /// Returns true if a variable with the specified Value exists, false + /// otherwise. + bool containsVar(Value val) const; + + /// Projects out the variable that is associate with Value. + void projectOut(Value val); + using IntegerPolyhedron::projectOut; + + /// Swap the posA^th variable with the posB^th variable. + void swapVar(unsigned posA, unsigned posB) override; + + /// Prints the number of constraints, dimensions, symbols and locals in the + /// FlatAffineValueConstraints. Also, prints for each variable whether there + /// is an SSA Value attached to it. + void printSpace(raw_ostream &os) const override; + + /// Align `map` with this constraint system based on `operands`. Each operand + /// must already have a corresponding dim/symbol in this constraint system. + AffineMap computeAlignedMap(AffineMap map, ValueRange operands) const; + + /// Merge and align the variables of `this` and `other` 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 `this`'s original variables appearing first followed + /// by any of `other`'s variables that didn't appear in `this`. Local + /// variables in `other` that have the same division representation as local + /// variables in `this` are merged into one. + // E.g.: Input: `this` has (%i, %j) [%M, %N] + // `other` has (%k, %j) [%P, %N, %M] + // Output: both `this`, `other` have (%i, %j, %k) [%M, %N, %P] + // + void mergeAndAlignVarsWithOther(unsigned offset, + FlatLinearValueConstraints *other); + + /// 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 mergeSymbolVars(FlatLinearValueConstraints &other); + + /// Returns true if this constraint system and `other` are in the same + /// space, i.e., if they are associated with the same set of variables, + /// appearing in the same order. Returns false otherwise. + bool areVarsAlignedWithOther(const FlatLinearConstraints &other); + + /// Updates the constraints to be the smallest bounding (enclosing) box that + /// contains the points of `this` set and that of `other`, with the symbols + /// being treated specially. For each of the dimensions, the min of the lower + /// bounds (symbolic) and the max of the upper bounds (symbolic) is computed + /// to determine such a bounding box. `other` is expected to have the same + /// dimensional variables as this constraint system (in the same order). + /// + /// E.g.: + /// 1) this = {0 <= d0 <= 127}, + /// other = {16 <= d0 <= 192}, + /// output = {0 <= d0 <= 192} + /// 2) this = {s0 + 5 <= d0 <= s0 + 20}, + /// other = {s0 + 1 <= d0 <= s0 + 9}, + /// output = {s0 + 1 <= d0 <= s0 + 20} + /// 3) this = {0 <= d0 <= 5, 1 <= d1 <= 9} + /// other = {2 <= d0 <= 6, 5 <= d1 <= 15}, + /// output = {0 <= d0 <= 6, 1 <= d1 <= 15} + LogicalResult unionBoundingBox(const FlatLinearValueConstraints &other); + using IntegerPolyhedron::unionBoundingBox; + +protected: + /// Eliminates the variable at the specified position using Fourier-Motzkin + /// variable elimination, but uses Gaussian elimination if there is an + /// equality involving that variable. If the result of the elimination is + /// integer exact, `*isResultIntegerExact` is set to true. If `darkShadow` is + /// set to true, a potential under approximation (subset) of the rational + /// shadow / exact integer shadow is computed. + // See implementation comments for more details. + void fourierMotzkinEliminate(unsigned pos, bool darkShadow = false, + bool *isResultIntegerExact = nullptr) override; + + /// Returns false if the fields corresponding to various variable counts, or + /// equality/inequality buffer sizes aren't consistent; true otherwise. This + /// is meant to be used within an assert internally. + bool hasConsistentState() const override; + + /// Values corresponding to the (column) non-local variables of this + /// constraint system appearing in the order the variables correspond to + /// columns. Variables that aren't associated with any Value are set to + /// None. + SmallVector, 8> values; +}; + +/// Flattens 'expr' into 'flattenedExpr', which contains the coefficients of the +/// dimensions, symbols, and additional variables that represent floor divisions +/// of dimensions, symbols, and in turn other floor divisions. Returns failure +/// if 'expr' could not be flattened (i.e., semi-affine is not yet handled). +/// 'cst' contains constraints that connect newly introduced local variables +/// to existing dimensional and symbolic variables. See documentation for +/// AffineExprFlattener on how mod's and div's are flattened. +LogicalResult getFlattenedAffineExpr(AffineExpr expr, unsigned numDims, + unsigned numSymbols, + SmallVectorImpl *flattenedExpr, + FlatLinearConstraints *cst = nullptr); + +/// Flattens the result expressions of the map to their corresponding flattened +/// forms and set in 'flattenedExprs'. Returns failure if any expression in the +/// map could not be flattened (i.e., semi-affine is not yet handled). 'cst' +/// contains constraints that connect newly introduced local variables to +/// existing dimensional and / symbolic variables. See documentation for +/// AffineExprFlattener on how mod's and div's are flattened. For all affine +/// expressions that share the same operands (like those of an affine map), this +/// method should be used instead of repeatedly calling getFlattenedAffineExpr +/// since local variables added to deal with div's and mod's will be reused +/// across expressions. +LogicalResult +getFlattenedAffineExprs(AffineMap map, + std::vector> *flattenedExprs, + FlatLinearConstraints *cst = nullptr); +LogicalResult +getFlattenedAffineExprs(IntegerSet set, + std::vector> *flattenedExprs, + FlatLinearConstraints *cst = nullptr); + +LogicalResult +getMultiAffineFunctionFromMap(AffineMap map, + presburger::MultiAffineFunction &multiAff); + +/// Re-indexes the dimensions and symbols of an affine map with given `operands` +/// values to align with `dims` and `syms` values. +/// +/// Each dimension/symbol of the map, bound to an operand `o`, is replaced with +/// dimension `i`, where `i` is the position of `o` within `dims`. If `o` is not +/// in `dims`, replace it with symbol `i`, where `i` is the position of `o` +/// within `syms`. If `o` is not in `syms` either, replace it with a new symbol. +/// +/// Note: If a value appears multiple times as a dimension/symbol (or both), all +/// corresponding dim/sym expressions are replaced with the first dimension +/// bound to that value (or first symbol if no such dimension exists). +/// +/// The resulting affine map has `dims.size()` many dimensions and at least +/// `syms.size()` many symbols. +/// +/// The SSA values of the symbols of the resulting map are optionally returned +/// via `newSyms`. This is a concatenation of `syms` with the SSA values of the +/// newly added symbols. +/// +/// Note: As part of this re-indexing, dimensions may turn into symbols, or vice +/// versa. +AffineMap alignAffineMapWithValues(AffineMap map, ValueRange operands, + ValueRange dims, ValueRange syms, + SmallVector *newSyms = nullptr); + +} // namespace mlir + +#endif // MLIR_ANALYSIS_FLATLINEARVALUECONSTRAINTS_H diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h index 347be263..8b0c2a5 100644 --- a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h +++ b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h @@ -54,10 +54,12 @@ class IntegerRelation { public: /// All derived classes of IntegerRelation. enum class Kind { - FlatAffineConstraints, - FlatAffineValueConstraints, IntegerRelation, IntegerPolyhedron, + FlatLinearConstraints, + FlatLinearValueConstraints, + FlatAffineValueConstraints, + FlatAffineRelation }; /// Constructs a relation reserving memory for the specified number @@ -848,7 +850,8 @@ public: Kind getKind() const override { return Kind::IntegerPolyhedron; } static bool classof(const IntegerRelation *cst) { - return cst->getKind() == Kind::IntegerPolyhedron; + return cst->getKind() >= Kind::IntegerPolyhedron && + cst->getKind() <= Kind::FlatAffineRelation; } // Clones this object. diff --git a/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h b/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h index 1b302f5..6249428 100644 --- a/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h +++ b/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h @@ -13,6 +13,7 @@ #ifndef MLIR_DIALECT_AFFINE_ANALYSIS_AFFINESTRUCTURES_H #define MLIR_DIALECT_AFFINE_ANALYSIS_AFFINESTRUCTURES_H +#include "mlir/Analysis/FlatLinearValueConstraints.h" #include "mlir/Analysis/Presburger/IntegerRelation.h" #include "mlir/Analysis/Presburger/Matrix.h" #include "mlir/IR/AffineExpr.h" @@ -38,117 +39,20 @@ namespace presburger { class MultiAffineFunction; } // namespace presburger -/// FlatAffineValueConstraints represents an extension of IntegerPolyhedron -/// where each non-local variable can have an SSA Value attached to it. -class FlatAffineValueConstraints : public presburger::IntegerPolyhedron { +/// FlatAffineValueConstraints is an extension of FlatLinearValueConstraints +/// with helper functions for Affine dialect ops. +class FlatAffineValueConstraints : public FlatLinearValueConstraints { public: - /// Constructs a constraint system reserving memory for the specified number - /// of constraints and variables. `valArgs` are the optional SSA values - /// associated with each dimension/symbol. These must either be empty or match - /// the number of dimensions and symbols. - FlatAffineValueConstraints(unsigned numReservedInequalities, - unsigned numReservedEqualities, - unsigned numReservedCols, unsigned numDims, - unsigned numSymbols, unsigned numLocals, - ArrayRef> valArgs) - : IntegerPolyhedron(numReservedInequalities, numReservedEqualities, - numReservedCols, - presburger::PresburgerSpace::getSetSpace( - numDims, numSymbols, numLocals)) { - assert(numReservedCols >= getNumVars() + 1); - assert(valArgs.empty() || valArgs.size() == getNumDimAndSymbolVars()); - values.reserve(numReservedCols); - if (valArgs.empty()) - values.resize(getNumDimAndSymbolVars(), std::nullopt); - else - values.append(valArgs.begin(), valArgs.end()); - } - - /// Constructs a constraint system reserving memory for the specified number - /// of constraints and variables. `valArgs` are the optional SSA values - /// associated with each dimension/symbol. These must either be empty or match - /// the number of dimensions and symbols. - FlatAffineValueConstraints(unsigned numReservedInequalities, - unsigned numReservedEqualities, - unsigned numReservedCols, unsigned numDims, - unsigned numSymbols, unsigned numLocals, - ArrayRef valArgs = {}) - : IntegerPolyhedron(numReservedInequalities, numReservedEqualities, - numReservedCols, - presburger::PresburgerSpace::getSetSpace( - numDims, numSymbols, numLocals)) { - assert(numReservedCols >= getNumVars() + 1); - assert(valArgs.empty() || valArgs.size() == getNumDimAndSymbolVars()); - values.reserve(numReservedCols); - if (valArgs.empty()) - values.resize(getNumDimAndSymbolVars(), std::nullopt); - else - values.append(valArgs.begin(), valArgs.end()); - } + using FlatLinearValueConstraints::FlatLinearValueConstraints; - /// Constructs a constraint system with the specified number of dimensions - /// and symbols. `valArgs` are the optional SSA values associated with each - /// dimension/symbol. These must either be empty or match the number of - /// dimensions and symbols. - FlatAffineValueConstraints(unsigned numDims, unsigned numSymbols, - unsigned numLocals, - ArrayRef> valArgs) - : FlatAffineValueConstraints(/*numReservedInequalities=*/0, - /*numReservedEqualities=*/0, - /*numReservedCols=*/numDims + numSymbols + - numLocals + 1, - numDims, numSymbols, numLocals, valArgs) {} - - /// Constructs a constraint system with the specified number of dimensions - /// and symbols. `valArgs` are the optional SSA values associated with each - /// dimension/symbol. These must either be empty or match the number of - /// dimensions and symbols. - FlatAffineValueConstraints(unsigned numDims = 0, unsigned numSymbols = 0, - unsigned numLocals = 0, - ArrayRef valArgs = {}) - : FlatAffineValueConstraints(/*numReservedInequalities=*/0, - /*numReservedEqualities=*/0, - /*numReservedCols=*/numDims + numSymbols + - numLocals + 1, - numDims, numSymbols, numLocals, valArgs) {} - - FlatAffineValueConstraints(const IntegerPolyhedron &fac, - ArrayRef> valArgs = {}) - : IntegerPolyhedron(fac) { - assert(valArgs.empty() || valArgs.size() == getNumDimAndSymbolVars()); - if (valArgs.empty()) - values.resize(getNumDimAndSymbolVars(), std::nullopt); - else - values.append(valArgs.begin(), valArgs.end()); - } - - /// Creates an affine constraint system from an IntegerSet. - explicit FlatAffineValueConstraints(IntegerSet set, ValueRange operands = {}); - - // 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. - static FlatAffineValueConstraints - getHyperrectangular(ValueRange ivs, ValueRange lbs, ValueRange ubs); - - /// Return the kind of this FlatAffineConstraints. + /// Return the kind of this object. Kind getKind() const override { return Kind::FlatAffineValueConstraints; } static bool classof(const IntegerRelation *cst) { - return cst->getKind() == Kind::FlatAffineValueConstraints; + return cst->getKind() >= Kind::FlatAffineValueConstraints && + cst->getKind() <= Kind::FlatAffineRelation; } - /// Clones this object. - std::unique_ptr clone() const; - /// Adds constraints (lower and upper bounds) for the specified 'affine.for' /// operation's Value using IR information stored in its bound maps. The /// right variable is first looked up using `forOp`'s Value. Asserts if the @@ -192,94 +96,21 @@ public: void addAffineIfOpDomain(AffineIfOp ifOp); /// Adds a bound for the variable at the specified position with constraints - /// being drawn from the specified bound map. In case of an EQ bound, the - /// bound map is expected to have exactly one result. In case of a LB/UB, the - /// bound map may have more than one result, for each of which an inequality - /// is added. - /// - /// The bound can be added as open or closed by specifying isClosedBound. In - /// case of a LB/UB, isClosedBound = false means the bound is added internally - /// as a closed bound by +1/-1 respectively. In case of an EQ bound, it can - /// only be added as a closed bound. - /// - /// Note: The dimensions/symbols of this FlatAffineConstraints must match the - /// dimensions/symbols of the affine map. - LogicalResult addBound(BoundType type, unsigned pos, AffineMap boundMap, - bool isClosedBound); - - /// Adds a bound for the variable at the specified position with constraints - /// being drawn from the specified bound map. In case of an EQ bound, the - /// bound map is expected to have exactly one result. In case of a LB/UB, the - /// bound map may have more than one result, for each of which an inequality - /// is added. - /// Note: The dimensions/symbols of this FlatAffineConstraints must match the - /// dimensions/symbols of the affine map. By default the lower bound is closed - /// and the upper bound is open. - LogicalResult addBound(BoundType type, unsigned pos, AffineMap boundMap); - - /// Adds a bound for the variable at the specified position with constraints /// being drawn from the specified bound map and operands. In case of an /// EQ bound, the bound map is expected to have exactly one result. In case /// of a LB/UB, the bound map may have more than one result, for each of which /// an inequality is added. LogicalResult addBound(BoundType type, unsigned pos, AffineMap boundMap, ValueRange operands); + using FlatLinearValueConstraints::addBound; - /// Adds a constant bound for the variable associated with the given Value. - void addBound(BoundType type, Value val, int64_t value); - - /// The `addBound` overload above hides the inherited overloads by default, so - /// we explicitly introduce them here. - using IntegerPolyhedron::addBound; - - /// Returns the constraint system as an integer set. Returns a null integer - /// set if the system has no constraints, or if an integer set couldn't be - /// constructed as a result of a local variable's explicit representation not - /// being known and such a local variable appearing in any of the constraints. - IntegerSet getAsIntegerSet(MLIRContext *context) const; - - /// Computes the lower and upper bounds of the first `num` dimensional - /// variables (starting at `offset`) as an affine map of the remaining - /// variables (dimensional and symbolic). This method is able to detect - /// variables as floordiv's and mod's of affine expressions of other - /// variables with respect to (positive) constants. Sets bound map to a - /// null AffineMap if such a bound can't be found (or yet unimplemented). - /// - /// By default the returned lower bounds are closed and upper bounds are open. - /// If `closedUb` is true, the upper bound is closed. - void getSliceBounds(unsigned offset, unsigned num, MLIRContext *context, - SmallVectorImpl *lbMaps, - SmallVectorImpl *ubMaps, - bool closedUB = false); - - /// Composes an affine map whose dimensions and symbols match one to one with - /// the dimensions and symbols of this FlatAffineConstraints. The results of - /// the map `other` are added as the leading dimensions of this constraint - /// system. Returns failure if `other` is a semi-affine map. - LogicalResult composeMatchingMap(AffineMap other); - - /// Gets the lower and upper bound of the `offset` + `pos`th variable - /// treating [0, offset) U [offset + num, symStartPos) as dimensions and - /// [symStartPos, getNumDimAndSymbolVars) as symbols, and `pos` lies in - /// [0, num). The multi-dimensional maps in the returned pair represent the - /// max and min of potentially multiple affine expressions. `localExprs` holds - /// pre-computed AffineExpr's for all local variables in the system. - /// - /// By default the returned lower bounds are closed and upper bounds are open. - /// If `closedUb` is true, the upper bound is closed. - std::pair - getLowerAndUpperBound(unsigned pos, unsigned offset, unsigned num, - unsigned symStartPos, ArrayRef localExprs, - MLIRContext *context, bool closedUB = false) const; - - /// Returns the bound for the variable at `pos` from the inequality at - /// `ineqPos` as a 1-d affine value map (affine map + operands). The returned - /// affine value map can either be a lower bound or an upper bound depending - /// on the sign of atIneq(ineqPos, pos). Asserts if the row at `ineqPos` does - /// not involve the `pos`th variable. - void getIneqAsAffineValueMap(unsigned pos, unsigned ineqPos, - AffineValueMap &vmap, - MLIRContext *context) const; + /// Add the specified values as a dim or symbol var depending on its nature, + /// if it already doesn't exist in the system. `val` has to be either a + /// terminal symbol or a loop IV, i.e., it cannot be the result affine.apply + /// of any symbols or loop IVs. The variable is added to the end of the + /// existing dims or symbols. Additional information on the variable is + /// extracted from the IR and added to the constraint system. + void addInductionVarOrTerminalSymbol(Value val); /// Adds slice lower bounds represented by lower bounds in `lbMaps` and upper /// bounds in `ubMaps` to each variable in the constraint system which has @@ -292,79 +123,17 @@ public: ArrayRef ubMaps, ArrayRef operands); - /// Looks up the position of the variable with the specified Value. Returns - /// true if found (false otherwise). `pos` is set to the (column) position of - /// the variable. - bool findVar(Value val, unsigned *pos) const; - - /// Returns true if an variable with the specified Value exists, false - /// otherwise. - bool containsVar(Value val) const; - - /// Swap the posA^th variable with the posB^th variable. - void swapVar(unsigned posA, unsigned posB) override; - - /// Insert variables of the specified kind at position `pos`. Positions are - /// relative to the kind of variable. The coefficient columns corresponding - /// to the added variables are initialized to zero. `vals` are the Values - /// corresponding to the variables. Values should not be used with - /// VarKind::Local since values can only be attached to non-local variables. - /// Return the absolute column position (i.e., not relative to the kind of - /// variable) of the first added variable. - /// - /// Note: Empty Values are allowed in `vals`. - unsigned insertDimVar(unsigned pos, unsigned num = 1) { - return insertVar(VarKind::SetDim, pos, num); - } - unsigned insertSymbolVar(unsigned pos, unsigned num = 1) { - return insertVar(VarKind::Symbol, pos, num); - } - unsigned insertLocalVar(unsigned pos, unsigned num = 1) { - return insertVar(VarKind::Local, pos, num); - } - unsigned insertDimVar(unsigned pos, ValueRange vals); - unsigned insertSymbolVar(unsigned pos, ValueRange vals); - unsigned insertVar(presburger::VarKind kind, unsigned pos, - unsigned num = 1) override; - unsigned insertVar(presburger::VarKind kind, unsigned pos, ValueRange vals); - - /// Append variables of the specified kind after the last variable of that - /// kind. The coefficient columns corresponding to the added variables are - /// initialized to zero. `vals` are the Values corresponding to the - /// variables. Return the absolute column position (i.e., not relative to the - /// kind of variable) of the first appended variable. - /// - /// Note: Empty Values are allowed in `vals`. - unsigned appendDimVar(ValueRange vals); - unsigned appendSymbolVar(ValueRange vals); - unsigned appendDimVar(unsigned num = 1) { - return appendVar(VarKind::SetDim, num); - } - unsigned appendSymbolVar(unsigned num = 1) { - return appendVar(VarKind::Symbol, num); - } - unsigned appendLocalVar(unsigned num = 1) { - return appendVar(VarKind::Local, num); - } - - /// Removes variables in the column range [varStart, varLimit), and copies any - /// remaining valid data into place, updates member variables, and resizes - /// arrays as needed. - void removeVarRange(presburger::VarKind kind, unsigned varStart, - unsigned varLimit) override; - using IntegerPolyhedron::removeVarRange; - - /// Add the specified values as a dim or symbol var depending on its nature, - /// if it already doesn't exist in the system. `val` has to be either a - /// terminal symbol or a loop IV, i.e., it cannot be the result affine.apply - /// of any symbols or loop IVs. The variable is added to the end of the - /// existing dims or symbols. Additional information on the variable is - /// extracted from the IR and added to the constraint system. - void addInductionVarOrTerminalSymbol(Value val); + /// Changes all symbol variables which are loop IVs to dim variables. + void convertLoopIVSymbolsToDims(); - /// Align `map` with this constraint system based on `operands`. Each operand - /// must already have a corresponding dim/symbol in this constraint system. - AffineMap computeAlignedMap(AffineMap map, ValueRange operands) const; + /// Returns the bound for the variable at `pos` from the inequality at + /// `ineqPos` as a 1-d affine value map (affine map + operands). The returned + /// affine value map can either be a lower bound or an upper bound depending + /// on the sign of atIneq(ineqPos, pos). Asserts if the row at `ineqPos` does + /// not involve the `pos`th variable. + void getIneqAsAffineValueMap(unsigned pos, unsigned ineqPos, + AffineValueMap &vmap, + MLIRContext *context) const; /// Composes the affine value map with this FlatAffineValueConstrains, adding /// the results of the map as dimensions at the front @@ -373,168 +142,10 @@ public: /// /// Returns failure if the composition fails (when vMap is a semi-affine map). /// The vMap's operand Value's are used to look up the right positions in - /// the FlatAffineConstraints with which to associate. Every operand of vMap - /// should have a matching dim/symbol column in this constraint system (with - /// the same associated Value). + /// the FlatAffineValueConstraints with which to associate. Every operand of + /// vMap should have a matching dim/symbol column in this constraint system + /// (with the same associated Value). LogicalResult composeMap(const AffineValueMap *vMap); - - /// Projects out the variable that is associate with Value. - void projectOut(Value val); - using IntegerPolyhedron::projectOut; - - /// Changes all symbol variables which are loop IVs to dim variables. - void convertLoopIVSymbolsToDims(); - - /// Updates the constraints to be the smallest bounding (enclosing) box that - /// contains the points of `this` set and that of `other`, with the symbols - /// being treated specially. For each of the dimensions, the min of the lower - /// bounds (symbolic) and the max of the upper bounds (symbolic) is computed - /// to determine such a bounding box. `other` is expected to have the same - /// dimensional variables as this constraint system (in the same order). - /// - /// E.g.: - /// 1) this = {0 <= d0 <= 127}, - /// other = {16 <= d0 <= 192}, - /// output = {0 <= d0 <= 192} - /// 2) this = {s0 + 5 <= d0 <= s0 + 20}, - /// other = {s0 + 1 <= d0 <= s0 + 9}, - /// output = {s0 + 1 <= d0 <= s0 + 20} - /// 3) this = {0 <= d0 <= 5, 1 <= d1 <= 9} - /// other = {2 <= d0 <= 6, 5 <= d1 <= 15}, - /// output = {0 <= d0 <= 6, 1 <= d1 <= 15} - LogicalResult unionBoundingBox(const FlatAffineValueConstraints &other); - using IntegerPolyhedron::unionBoundingBox; - - /// Merge and align the variables of `this` and `other` 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 `this`'s original variables appearing first followed - /// by any of `other`'s variables that didn't appear in `this`. Local - /// variables in `other` that have the same division representation as local - /// variables in `this` are merged into one. - // E.g.: Input: `this` has (%i, %j) [%M, %N] - // `other` has (%k, %j) [%P, %N, %M] - // Output: both `this`, `other` have (%i, %j, %k) [%M, %N, %P] - // - void mergeAndAlignVarsWithOther(unsigned offset, - FlatAffineValueConstraints *other); - - /// Returns true if this constraint system and `other` are in the same - /// space, i.e., if they are associated with the same set of variables, - /// appearing in the same order. Returns false otherwise. - bool areVarsAlignedWithOther(const FlatAffineValueConstraints &other); - - /// Replaces the contents of this FlatAffineValueConstraints with `other`. - void clearAndCopyFrom(const IntegerRelation &other) override; - - /// Returns the Value associated with the pos^th variable. Asserts if - /// no Value variable was associated. - inline Value getValue(unsigned pos) const { - assert(pos < getNumDimAndSymbolVars() && "Invalid position"); - assert(hasValue(pos) && "variable's Value not set"); - return *values[pos]; - } - - /// Returns true if the pos^th variable has an associated Value. - inline bool hasValue(unsigned pos) const { - assert(pos < getNumDimAndSymbolVars() && "Invalid position"); - return values[pos].has_value(); - } - - /// Returns true if at least one variable has an associated Value. - bool hasValues() const; - - /// Returns the Values associated with variables in range [start, end). - /// Asserts if no Value was associated with one of these variables. - inline void getValues(unsigned start, unsigned end, - SmallVectorImpl *values) const { - assert(end <= getNumDimAndSymbolVars() && "invalid end position"); - assert(start <= end && "invalid start position"); - values->clear(); - values->reserve(end - start); - for (unsigned i = start; i < end; i++) - values->push_back(getValue(i)); - } - inline void getAllValues(SmallVectorImpl *values) const { - getValues(0, getNumDimAndSymbolVars(), values); - } - - inline ArrayRef> getMaybeValues() const { - return {values.data(), values.size()}; - } - - inline ArrayRef> - getMaybeValues(presburger::VarKind kind) const { - assert(kind != VarKind::Local && - "Local variables do not have any value attached to them."); - return {values.data() + getVarKindOffset(kind), getNumVarKind(kind)}; - } - - /// Sets the Value associated with the pos^th variable. - inline void setValue(unsigned pos, Value val) { - assert(pos < getNumDimAndSymbolVars() && "invalid var position"); - values[pos] = val; - } - - /// Sets the Values associated with the variables in the range [start, end). - /// The range must contain only dim and symbol variables. - void setValues(unsigned start, unsigned end, ArrayRef values) { - assert(end <= getNumVars() && "invalid end position"); - assert(start <= end && "invalid start position"); - assert(values.size() == end - start && - "value should be provided for each variable in the range."); - for (unsigned i = start; i < end; ++i) - setValue(i, values[i - start]); - } - - /// 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 mergeSymbolVars(FlatAffineValueConstraints &other); - -protected: - using VarKind = presburger::VarKind; - - /// Returns false if the fields corresponding to various variable counts, or - /// equality/inequality buffer sizes aren't consistent; true otherwise. This - /// is meant to be used within an assert internally. - bool hasConsistentState() const override; - - /// Given an affine map that is aligned with this constraint system: - /// * Flatten the map. - /// * Add newly introduced local columns at the beginning of this constraint - /// system (local column pos 0). - /// * Add equalities that define the new local columns to this constraint - /// system. - /// * Return the flattened expressions via `flattenedExprs`. - /// - /// Note: This is a shared helper function of `addLowerOrUpperBound` and - /// `composeMatchingMap`. - LogicalResult flattenAlignedMapAndMergeLocals( - AffineMap map, std::vector> *flattenedExprs); - - /// Eliminates the variable at the specified position using Fourier-Motzkin - /// variable elimination, but uses Gaussian elimination if there is an - /// equality involving that variable. If the result of the elimination is - /// integer exact, `*isResultIntegerExact` is set to true. If `darkShadow` is - /// set to true, a potential under approximation (subset) of the rational - /// shadow / exact integer shadow is computed. - // See implementation comments for more details. - void fourierMotzkinEliminate(unsigned pos, bool darkShadow = false, - bool *isResultIntegerExact = nullptr) override; - - /// Prints the number of constraints, dimensions, symbols and locals in the - /// FlatAffineConstraints. Also, prints for each variable whether there is - /// an SSA Value attached to it. - void printSpace(raw_ostream &os) const override; - - /// Values corresponding to the (column) non-local variables of this - /// constraint system appearing in the order the variables correspond to - /// columns. Variables that aren't associated with any Value are set to - /// None. - SmallVector, 8> values; }; /// A FlatAffineRelation represents a set of ordered pairs (domain -> range) @@ -570,6 +181,13 @@ public: : FlatAffineValueConstraints(fac), numDomainDims(numDomainDims), numRangeDims(numRangeDims) {} + /// Return the kind of this object. + Kind getKind() const override { return Kind::FlatAffineRelation; } + + static bool classof(const IntegerRelation *cst) { + return cst->getKind() == Kind::FlatAffineRelation; + } + /// Returns a set corresponding to the domain/range of the affine relation. FlatAffineValueConstraints getDomainSet() const; FlatAffineValueConstraints getRangeSet() const; @@ -616,66 +234,6 @@ protected: unsigned numRangeDims; }; -/// Flattens 'expr' into 'flattenedExpr', which contains the coefficients of the -/// dimensions, symbols, and additional variables that represent floor divisions -/// of dimensions, symbols, and in turn other floor divisions. Returns failure -/// if 'expr' could not be flattened (i.e., semi-affine is not yet handled). -/// 'cst' contains constraints that connect newly introduced local variables -/// to existing dimensional and symbolic variables. See documentation for -/// AffineExprFlattener on how mod's and div's are flattened. -LogicalResult getFlattenedAffineExpr(AffineExpr expr, unsigned numDims, - unsigned numSymbols, - SmallVectorImpl *flattenedExpr, - FlatAffineValueConstraints *cst = nullptr); - -/// Flattens the result expressions of the map to their corresponding flattened -/// forms and set in 'flattenedExprs'. Returns failure if any expression in the -/// map could not be flattened (i.e., semi-affine is not yet handled). 'cst' -/// contains constraints that connect newly introduced local variables to -/// existing dimensional and / symbolic variables. See documentation for -/// AffineExprFlattener on how mod's and div's are flattened. For all affine -/// expressions that share the same operands (like those of an affine map), this -/// method should be used instead of repeatedly calling getFlattenedAffineExpr -/// since local variables added to deal with div's and mod's will be reused -/// across expressions. -LogicalResult -getFlattenedAffineExprs(AffineMap map, - std::vector> *flattenedExprs, - FlatAffineValueConstraints *cst = nullptr); -LogicalResult -getFlattenedAffineExprs(IntegerSet set, - std::vector> *flattenedExprs, - FlatAffineValueConstraints *cst = nullptr); - -LogicalResult -getMultiAffineFunctionFromMap(AffineMap map, - presburger::MultiAffineFunction &multiAff); - -/// Re-indexes the dimensions and symbols of an affine map with given `operands` -/// values to align with `dims` and `syms` values. -/// -/// Each dimension/symbol of the map, bound to an operand `o`, is replaced with -/// dimension `i`, where `i` is the position of `o` within `dims`. If `o` is not -/// in `dims`, replace it with symbol `i`, where `i` is the position of `o` -/// within `syms`. If `o` is not in `syms` either, replace it with a new symbol. -/// -/// Note: If a value appears multiple times as a dimension/symbol (or both), all -/// corresponding dim/sym expressions are replaced with the first dimension -/// bound to that value (or first symbol if no such dimension exists). -/// -/// The resulting affine map has `dims.size()` many dimensions and at least -/// `syms.size()` many symbols. -/// -/// The SSA values of the symbols of the resulting map are optionally returned -/// via `newSyms`. This is a concatenation of `syms` with the SSA values of the -/// newly added symbols. -/// -/// Note: As part of this re-indexing, dimensions may turn into symbols, or vice -/// versa. -AffineMap alignAffineMapWithValues(AffineMap map, ValueRange operands, - ValueRange dims, ValueRange syms, - SmallVector *newSyms = nullptr); - /// Builds a relation from the given AffineMap/AffineValueMap `map`, containing /// all pairs of the form `operands -> result` that satisfy `map`. `rel` is set /// to the relation built. For example, give the AffineMap: @@ -696,6 +254,6 @@ LogicalResult getRelationFromMap(AffineMap &map, FlatAffineRelation &rel); LogicalResult getRelationFromMap(const AffineValueMap &map, FlatAffineRelation &rel); -} // namespace mlir. +} // namespace mlir #endif // MLIR_DIALECT_AFFINE_ANALYSIS_AFFINESTRUCTURES_H diff --git a/mlir/include/mlir/IR/AffineExprVisitor.h b/mlir/include/mlir/IR/AffineExprVisitor.h index 30ee1b6..f621661 100644 --- a/mlir/include/mlir/IR/AffineExprVisitor.h +++ b/mlir/include/mlir/IR/AffineExprVisitor.h @@ -324,7 +324,7 @@ private: // 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 (done by - // FlatAffineConstraints::addLocalFloorDiv). + // IntegerRelation::addLocalFloorDiv). // // A ceildiv is similarly flattened: // t = expr ceildiv c <=> t = (expr + c - 1) floordiv c diff --git a/mlir/include/mlir/IR/IntegerSet.h b/mlir/include/mlir/IR/IntegerSet.h index b8affca..f814776 100644 --- a/mlir/include/mlir/IR/IntegerSet.h +++ b/mlir/include/mlir/IR/IntegerSet.h @@ -17,7 +17,7 @@ // This class is not meant for affine analysis and operations like set // operations, emptiness checks, or other math operations for analysis and -// transformation. For the latter, use FlatAffineConstraints. +// transformation. For the latter, use FlatAffineValueConstraints. // //===----------------------------------------------------------------------===// diff --git a/mlir/lib/Analysis/CMakeLists.txt b/mlir/lib/Analysis/CMakeLists.txt index 25263db..b68e03c 100644 --- a/mlir/lib/Analysis/CMakeLists.txt +++ b/mlir/lib/Analysis/CMakeLists.txt @@ -2,6 +2,7 @@ set(LLVM_OPTIONAL_SOURCES AliasAnalysis.cpp CallGraph.cpp DataLayoutAnalysis.cpp + FlatLinearValueConstraints.cpp Liveness.cpp SliceAnalysis.cpp @@ -14,11 +15,14 @@ set(LLVM_OPTIONAL_SOURCES DataFlow/SparseAnalysis.cpp ) +add_subdirectory(Presburger) + add_mlir_library(MLIRAnalysis AliasAnalysis.cpp CallGraph.cpp DataFlowFramework.cpp DataLayoutAnalysis.cpp + FlatLinearValueConstraints.cpp Liveness.cpp SliceAnalysis.cpp @@ -43,8 +47,8 @@ add_mlir_library(MLIRAnalysis MLIRInferIntRangeInterface MLIRInferTypeOpInterface MLIRLoopLikeInterface + MLIRPresburger MLIRSideEffectInterfaces MLIRViewLikeInterface ) -add_subdirectory(Presburger) diff --git a/mlir/lib/Analysis/FlatLinearValueConstraints.cpp b/mlir/lib/Analysis/FlatLinearValueConstraints.cpp new file mode 100644 index 0000000..b89b2d1 --- /dev/null +++ b/mlir/lib/Analysis/FlatLinearValueConstraints.cpp @@ -0,0 +1,1344 @@ +//===- FlatLinearValueConstraints.cpp - Linear Constraint -----------------===// +// +// 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 +// +//===----------------------------------------------------------------------===// + +#include "mlir/Analysis//FlatLinearValueConstraints.h" + +#include "mlir/Analysis/Presburger/LinearTransform.h" +#include "mlir/Analysis/Presburger/Simplex.h" +#include "mlir/Analysis/Presburger/Utils.h" +#include "mlir/IR/AffineExprVisitor.h" +#include "mlir/IR/Builders.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" +#include + +#define DEBUG_TYPE "flat-value-constraints" + +using namespace mlir; +using namespace presburger; + +//===----------------------------------------------------------------------===// +// AffineExprFlattener +//===----------------------------------------------------------------------===// + +namespace { + +// See comments for SimpleAffineExprFlattener. +// An AffineExprFlattener extends a SimpleAffineExprFlattener by recording +// constraint information associated with mod's, floordiv's, and ceildiv's +// in FlatLinearConstraints '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 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 exprs, unsigned numDims, + unsigned numSymbols, + std::vector> *flattenedExprs, + FlatLinearConstraints *localVarCst) { + if (exprs.empty()) { + if (localVarCst) + *localVarCst = FlatLinearConstraints(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 *flattenedExpr, + FlatLinearConstraints *localVarCst) { + std::vector> 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> *flattenedExprs, + FlatLinearConstraints *localVarCst) { + if (map.getNumResults() == 0) { + if (localVarCst) + *localVarCst = + FlatLinearConstraints(map.getNumDims(), map.getNumSymbols()); + return success(); + } + return ::getFlattenedAffineExprs(map.getResults(), map.getNumDims(), + map.getNumSymbols(), flattenedExprs, + localVarCst); +} + +LogicalResult mlir::getFlattenedAffineExprs( + IntegerSet set, std::vector> *flattenedExprs, + FlatLinearConstraints *localVarCst) { + if (set.getNumConstraints() == 0) { + if (localVarCst) + *localVarCst = + FlatLinearConstraints(set.getNumDims(), set.getNumSymbols()); + return success(); + } + return ::getFlattenedAffineExprs(set.getConstraints(), set.getNumDims(), + set.getNumSymbols(), flattenedExprs, + localVarCst); +} + +//===----------------------------------------------------------------------===// +// FlatLinearConstraints +//===----------------------------------------------------------------------===// + +std::unique_ptr FlatLinearConstraints::clone() const { + return std::make_unique(*this); +} + +// 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 FlatLinearConstraints::composeMatchingMap(AffineMap other) { + assert(other.getNumDims() == getNumDimVars() && "dim mismatch"); + assert(other.getNumSymbols() == getNumSymbolVars() && "symbol mismatch"); + + std::vector> 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 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(); +} + +// 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 FlatLinearConstraints &cst, unsigned pos, + int64_t lbConst, int64_t ubConst, + SmallVectorImpl &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.atEq64(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.atEq64(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.atEq64(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(); + if (!dimExpr) + continue; + + // Express `var_r` as `var_n % divisor` and store the expression in `memo`. + if (quotientCount >= 1) { + auto ub = cst.getConstantBound64(FlatLinearConstraints::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 FlatLinearConstraints &cst, unsigned pos, + MLIRContext *context, + SmallVectorImpl &exprs) { + assert(pos < cst.getNumVars() && "invalid position"); + + // Get upper-lower bound pair for this variable. + SmallVector foundRepr(cst.getNumVars(), false); + for (unsigned i = 0, e = cst.getNumVars(); i < e; ++i) + if (exprs[i]) + foundRepr[i] = true; + + SmallVector 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 FlatLinearConstraints::getLowerAndUpperBound( + unsigned pos, unsigned offset, unsigned num, unsigned symStartPos, + ArrayRef localExprs, MLIRContext *context, + bool closedUB) 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 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 a, SmallVectorImpl &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 lb, ub; + SmallVector lbExprs; + unsigned dimCount = symStartPos - num; + unsigned symCount = getNumDimAndSymbolVars() - symStartPos; + lbExprs.reserve(lbIndices.size() + eqIndices.size()); + // Lower bound expressions. + for (auto idx : lbIndices) { + auto ineq = getInequality64(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()); + 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 ubExprs; + ubExprs.reserve(ubIndices.size() + eqIndices.size()); + // Upper bound expressions. + for (auto idx : ubIndices) { + auto ineq = getInequality64(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])); + int64_t ubAdjustment = closedUB ? 0 : 1; + ubExprs.push_back(expr + ubAdjustment); + } + + // Equalities. It's both a lower and a upper bound. + SmallVector b; + for (auto idx : eqIndices) { + auto eq = getEquality64(idx); + addCoeffs(eq, b); + if (eq[pos + offset] > 0) + std::transform(b.begin(), b.end(), b.begin(), std::negate()); + + // 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 FlatLinearConstraints::getSliceBounds(unsigned offset, unsigned num, + MLIRContext *context, + SmallVectorImpl *lbMaps, + SmallVectorImpl *ubMaps, + bool closedUB) { + 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 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 = getConstantBound64(BoundType::LB, pos); + auto ubConst = getConstantBound64(BoundType::UB, pos); + if (lbConst.has_value() && ubConst.has_value()) { + // Detect equality to a constant. + if (*lbConst == *ubConst) { + memo[pos] = getAffineConstantExpr(*lbConst, context); + changed = true; + continue; + } + + // Detect a variable as modulo of another variable w.r.t a + // constant. + if (detectAsMod(*this, pos, *lbConst, *ubConst, memo, context)) { + changed = true; + continue; + } + } + + // Detect a 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 a 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 = atEq64(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 + atEq64(idx, getNumVars()); + int64_t vPos = atEq64(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 = closedUB ? 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. + std::optional 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(FlatLinearConstraints(*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, + closedUB); + } + + // 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 = getConstantBound64(BoundType::LB, pos + offset); + if (lbConst.has_value()) { + lbMap = AffineMap::get(numMapDims, numMapSymbols, + getAffineConstantExpr(*lbConst, context)); + } + } + if (!ubMap || ubMap.getNumResults() > 1) { + LLVM_DEBUG(llvm::dbgs() + << "WARNING: Potentially over-approximating slice ub\n"); + auto ubConst = getConstantBound64(BoundType::UB, pos + offset); + if (ubConst.has_value()) { + ubMap = AffineMap::get( + numMapDims, numMapSymbols, + getAffineConstantExpr(*ubConst + 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 FlatLinearConstraints::flattenAlignedMapAndMergeLocals( + AffineMap map, std::vector> *flattenedExprs) { + FlatLinearConstraints 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 FlatLinearConstraints::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> 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 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 FlatLinearConstraints::addBound(BoundType type, unsigned pos, + AffineMap boundMap) { + return addBound(type, pos, boundMap, /*isClosedBound=*/type != BoundType::UB); +} + +/// 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. +LogicalResult +FlatLinearConstraints::computeLocalVars(SmallVectorImpl &memo, + MLIRContext *context) const { + unsigned numDims = getNumDimVars(); + unsigned numSyms = 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 = getNumLocalVars(); i < e; ++i) + if (!memo[numDims + numSyms + i] && + detectAsFloorDiv(*this, /*pos=*/numDims + numSyms + i, context, memo)) + changed = true; + } while (changed); + + ArrayRef localExprs = + ArrayRef(memo).take_back(getNumLocalVars()); + return success( + llvm::all_of(localExprs, [](AffineExpr expr) { return expr; })); +} + +IntegerSet FlatLinearConstraints::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 memo(getNumVars(), AffineExpr()); + + if (failed(computeLocalVars(memo, context))) { + // Check if the local variables without an explicit representation have + // zero coefficients everywhere. + SmallVector 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 localExprs = + ArrayRef(memo).take_back(getNumLocalVars()); + + // Construct the IntegerSet from the equalities/inequalities. + unsigned numDims = getNumDimVars(); + unsigned numSyms = getNumSymbolVars(); + + SmallVector eqFlags(getNumConstraints()); + std::fill(eqFlags.begin(), eqFlags.begin() + getNumEqualities(), true); + std::fill(eqFlags.begin() + getNumEqualities(), eqFlags.end(), false); + + SmallVector exprs; + exprs.reserve(getNumConstraints()); + + for (unsigned i = 0, e = getNumEqualities(); i < e; ++i) + exprs.push_back(getAffineExprFromFlatForm(getEquality64(i), numDims, + numSyms, localExprs, context)); + for (unsigned i = 0, e = getNumInequalities(); i < e; ++i) + exprs.push_back(getAffineExprFromFlatForm(getInequality64(i), numDims, + numSyms, localExprs, context)); + return IntegerSet::get(numDims, numSyms, exprs, eqFlags); +} + +//===----------------------------------------------------------------------===// +// FlatLinearValueConstraints +//===----------------------------------------------------------------------===// + +// Construct from an IntegerSet. +FlatLinearValueConstraints::FlatLinearValueConstraints(IntegerSet set, + ValueRange operands) + : FlatLinearConstraints(set.getNumInequalities(), set.getNumEqualities(), + set.getNumDims() + set.getNumSymbols() + 1, + set.getNumDims(), set.getNumSymbols(), + /*numLocals=*/0) { + // Populate values. + if (operands.empty()) { + values.resize(getNumDimAndSymbolVars(), std::nullopt); + } else { + assert(set.getNumInputs() == operands.size() && "operand count mismatch"); + values.assign(operands.begin(), operands.end()); + } + + // Flatten expressions and add them to the constraint system. + std::vector> flatExprs; + FlatLinearConstraints 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. +FlatLinearValueConstraints +FlatLinearValueConstraints::getHyperrectangular(ValueRange ivs, ValueRange lbs, + ValueRange ubs) { + FlatLinearValueConstraints 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 FlatLinearValueConstraints 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 FlatLinearValueConstraints creation error"); + } + return res; +} + +unsigned FlatLinearValueConstraints::appendDimVar(ValueRange vals) { + unsigned pos = getNumDimVars(); + return insertVar(VarKind::SetDim, pos, vals); +} + +unsigned FlatLinearValueConstraints::appendSymbolVar(ValueRange vals) { + unsigned pos = getNumSymbolVars(); + return insertVar(VarKind::Symbol, pos, vals); +} + +unsigned FlatLinearValueConstraints::insertDimVar(unsigned pos, + ValueRange vals) { + return insertVar(VarKind::SetDim, pos, vals); +} + +unsigned FlatLinearValueConstraints::insertSymbolVar(unsigned pos, + ValueRange vals) { + return insertVar(VarKind::Symbol, pos, vals); +} + +unsigned FlatLinearValueConstraints::insertVar(VarKind kind, unsigned pos, + unsigned num) { + unsigned absolutePos = IntegerPolyhedron::insertVar(kind, pos, num); + + if (kind != VarKind::Local) { + values.insert(values.begin() + absolutePos, num, std::nullopt); + assert(values.size() == getNumDimAndSymbolVars()); + } + + return absolutePos; +} + +unsigned FlatLinearValueConstraints::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] ? std::optional(vals[i]) : std::nullopt); + + assert(values.size() == getNumDimAndSymbolVars()); + return absolutePos; +} + +bool FlatLinearValueConstraints::hasValues() const { + return llvm::any_of( + values, [](const std::optional &var) { return var.has_value(); }); +} + +/// 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 FlatLinearValueConstraints &a, + const FlatLinearValueConstraints &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 FlatLinearValueConstraints::areVarsAlignedWithOther( + const FlatLinearConstraints &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 FlatLinearValueConstraints &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 uniqueVars; + ArrayRef> maybeValues = + cst.getMaybeValues().slice(start, end - start); + for (std::optional 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 FlatLinearValueConstraints &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 FlatLinearValueConstraints &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, FlatLinearValueConstraints *a, + FlatLinearValueConstraints *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(llvm::all_of( + llvm::drop_begin(a->getMaybeValues(), offset), + [](const std::optional &var) { return var.has_value(); })); + + assert(llvm::all_of( + llvm::drop_begin(b->getMaybeValues(), offset), + [](const std::optional &var) { return var.has_value(); })); + + SmallVector 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 FlatLinearValueConstraints::mergeAndAlignVarsWithOther( + unsigned offset, FlatLinearValueConstraints *other) { + mergeAndAlignVars(offset, this, other); +} + +/// 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 FlatLinearValueConstraints::mergeSymbolVars( + FlatLinearValueConstraints &other) { + + assert(areVarsUnique(*this, VarKind::Symbol) && "Symbol vars are not unique"); + assert(areVarsUnique(other, VarKind::Symbol) && "Symbol vars are not unique"); + + SmallVector 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"); +} + +bool FlatLinearValueConstraints::hasConsistentState() const { + return IntegerPolyhedron::hasConsistentState() && + values.size() == getNumDimAndSymbolVars(); +} + +void FlatLinearValueConstraints::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); + } +} + +AffineMap +FlatLinearValueConstraints::computeAlignedMap(AffineMap map, + ValueRange operands) const { + assert(map.getNumInputs() == operands.size() && "number of inputs mismatch"); + + SmallVector dims, syms; +#ifndef NDEBUG + SmallVector newSyms; + SmallVector *newSymsPtr = &newSyms; +#else + SmallVector *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 FlatAffineValueConstraints. + assert(syms.size() == newSymsPtr->size() && "unexpected new/missing symbols"); + assert(std::equal(syms.begin(), syms.end(), newSymsPtr->begin()) && + "unexpected new/missing symbols"); + return alignedMap; +} + +bool FlatLinearValueConstraints::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 FlatLinearValueConstraints::containsVar(Value val) const { + return llvm::any_of(values, [&](const std::optional &mayBeVar) { + return mayBeVar && *mayBeVar == val; + }); +} + +void FlatLinearValueConstraints::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 std::nullopt. + if (getVarKindAt(posA) == VarKind::Local) + values[posB] = std::nullopt; + else if (getVarKindAt(posB) == VarKind::Local) + values[posA] = std::nullopt; + else + std::swap(values[posA], values[posB]); +} + +void FlatLinearValueConstraints::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 FlatLinearConstraints::printSpace(raw_ostream &os) const { + IntegerPolyhedron::printSpace(os); + os << "("; + for (unsigned i = 0, e = getNumDimAndSymbolVars(); i < e; i++) + os << "None\t"; + for (unsigned i = getVarKindOffset(VarKind::Local), + e = getVarKindEnd(VarKind::Local); + i < e; ++i) + os << "Local\t"; + os << "const)\n"; +} + +void FlatLinearValueConstraints::printSpace(raw_ostream &os) const { + IntegerPolyhedron::printSpace(os); + os << "("; + for (unsigned i = 0, e = getNumDimAndSymbolVars(); i < e; i++) { + if (hasValue(i)) + os << "Value\t"; + else + os << "None\t"; + } + for (unsigned i = getVarKindOffset(VarKind::Local), + e = getVarKindEnd(VarKind::Local); + i < e; ++i) + os << "Local\t"; + os << "const)\n"; +} + +void FlatLinearValueConstraints::clearAndCopyFrom( + const IntegerRelation &other) { + + if (auto *otherValueSet = + dyn_cast(&other)) { + *this = *otherValueSet; + } else { + *static_cast(this) = other; + values.clear(); + values.resize(getNumDimAndSymbolVars(), std::nullopt); + } +} + +void FlatLinearValueConstraints::fourierMotzkinEliminate( + unsigned pos, bool darkShadow, bool *isResultIntegerExact) { + SmallVector, 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 FlatLinearValueConstraints::projectOut(Value val) { + unsigned pos; + bool ret = findVar(val, &pos); + assert(ret); + (void)ret; + fourierMotzkinEliminate(pos); +} + +LogicalResult FlatLinearValueConstraints::unionBoundingBox( + const FlatLinearValueConstraints &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)) { + FlatLinearValueConstraints otherCopy(otherCst); + mergeAndAlignVars(/*offset=*/getNumDimVars(), this, &otherCopy); + return IntegerPolyhedron::unionBoundingBox(otherCopy); + } + + return IntegerPolyhedron::unionBoundingBox(otherCst); +} + +//===----------------------------------------------------------------------===// +// Helper functions +//===----------------------------------------------------------------------===// + +AffineMap mlir::alignAffineMapWithValues(AffineMap map, ValueRange operands, + ValueRange dims, ValueRange syms, + SmallVector *newSyms) { + assert(operands.size() == map.getNumInputs() && + "expected same number of operands and map inputs"); + MLIRContext *ctx = map.getContext(); + Builder builder(ctx); + SmallVector dimReplacements(map.getNumDims(), {}); + unsigned numSymbols = syms.size(); + SmallVector 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); +} + +LogicalResult +mlir::getMultiAffineFunctionFromMap(AffineMap map, + MultiAffineFunction &multiAff) { + FlatLinearConstraints cst; + std::vector> flattenedExprs; + LogicalResult result = getFlattenedAffineExprs(map, &flattenedExprs, &cst); + + if (result.failed()) + return failure(); + + DivisionRepr divs = cst.getLocalReprs(); + assert(divs.hasAllReprs() && + "AffineMap cannot produce divs without local representation"); + + // TODO: We shouldn't have to do this conversion. + Matrix mat(map.getNumResults(), map.getNumInputs() + divs.getNumDivs() + 1); + for (unsigned i = 0, e = flattenedExprs.size(); i < e; ++i) + for (unsigned j = 0, f = flattenedExprs[i].size(); j < f; ++j) + mat(i, j) = flattenedExprs[i][j]; + + multiAff = MultiAffineFunction( + PresburgerSpace::getRelationSpace(map.getNumDims(), map.getNumResults(), + map.getNumSymbols(), divs.getNumDivs()), + mat, divs); + + return success(); +} diff --git a/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp b/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp index 03b8b1d..f087dca 100644 --- a/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp +++ b/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp @@ -33,504 +33,6 @@ 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 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 exprs, unsigned numDims, - unsigned numSymbols, - std::vector> *flattenedExprs, - FlatAffineValueConstraints *localVarCst) { - if (exprs.empty()) { - if (localVarCst) - *localVarCst = FlatAffineValueConstraints(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 *flattenedExpr, - FlatAffineValueConstraints *localVarCst) { - std::vector> 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> *flattenedExprs, - FlatAffineValueConstraints *localVarCst) { - if (map.getNumResults() == 0) { - if (localVarCst) - *localVarCst = - FlatAffineValueConstraints(map.getNumDims(), map.getNumSymbols()); - return success(); - } - return ::getFlattenedAffineExprs(map.getResults(), map.getNumDims(), - map.getNumSymbols(), flattenedExprs, - localVarCst); -} - -LogicalResult mlir::getFlattenedAffineExprs( - IntegerSet set, std::vector> *flattenedExprs, - FlatAffineValueConstraints *localVarCst) { - if (set.getNumConstraints() == 0) { - if (localVarCst) - *localVarCst = - FlatAffineValueConstraints(set.getNumDims(), set.getNumSymbols()); - return success(); - } - return ::getFlattenedAffineExprs(set.getConstraints(), set.getNumDims(), - set.getNumSymbols(), flattenedExprs, - localVarCst); -} - -//===----------------------------------------------------------------------===// -// FlatAffineConstraints / FlatAffineValueConstraints. -//===----------------------------------------------------------------------===// - -std::unique_ptr -FlatAffineValueConstraints::clone() const { - return std::make_unique(*this); -} - -// Construct from an IntegerSet. -FlatAffineValueConstraints::FlatAffineValueConstraints(IntegerSet set, - ValueRange operands) - : IntegerPolyhedron(set.getNumInequalities(), set.getNumEqualities(), - set.getNumDims() + set.getNumSymbols() + 1, - PresburgerSpace::getSetSpace(set.getNumDims(), - set.getNumSymbols(), - /*numLocals=*/0)) { - // Populate values. - if (operands.empty()) { - values.resize(getNumDimAndSymbolVars(), std::nullopt); - } else { - assert(set.getNumInputs() == operands.size() && "operand count mismatch"); - values.assign(operands.begin(), operands.end()); - } - - // Flatten expressions and add them to the constraint system. - std::vector> 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; -} - -unsigned FlatAffineValueConstraints::appendDimVar(ValueRange vals) { - unsigned pos = getNumDimVars(); - return insertVar(VarKind::SetDim, pos, vals); -} - -unsigned FlatAffineValueConstraints::appendSymbolVar(ValueRange vals) { - unsigned pos = getNumSymbolVars(); - return insertVar(VarKind::Symbol, pos, vals); -} - -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, std::nullopt); - 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] ? std::optional(vals[i]) : std::nullopt); - - assert(values.size() == getNumDimAndSymbolVars()); - return absolutePos; -} - -bool FlatAffineValueConstraints::hasValues() const { - return llvm::any_of( - values, [](const std::optional &var) { return var.has_value(); }); -} - -/// 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 uniqueVars; - ArrayRef> maybeValues = - cst.getMaybeValues().slice(start, end - start); - for (std::optional 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(llvm::all_of( - llvm::drop_begin(a->getMaybeValues(), offset), - [](const std::optional &var) { return var.has_value(); })); - - assert(llvm::all_of( - llvm::drop_begin(b->getMaybeValues(), offset), - [](const std::optional &var) { return var.has_value(); })); - - SmallVector 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> 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 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 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 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)) @@ -709,559 +211,6 @@ void FlatAffineValueConstraints::addAffineIfOpDomain(AffineIfOp ifOp) { 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 &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.atEq64(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.atEq64(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.atEq64(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(); - if (!dimExpr) - continue; - - // Express `var_r` as `var_n % divisor` and store the expression in `memo`. - if (quotientCount >= 1) { - auto ub = cst.getConstantBound64( - 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 &exprs) { - assert(pos < cst.getNumVars() && "invalid position"); - - // Get upper-lower bound pair for this variable. - SmallVector foundRepr(cst.getNumVars(), false); - for (unsigned i = 0, e = cst.getNumVars(); i < e; ++i) - if (exprs[i]) - foundRepr[i] = true; - - SmallVector 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 -FlatAffineValueConstraints::getLowerAndUpperBound( - unsigned pos, unsigned offset, unsigned num, unsigned symStartPos, - ArrayRef localExprs, MLIRContext *context, - bool closedUB) 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 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 a, SmallVectorImpl &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 lb, ub; - SmallVector lbExprs; - unsigned dimCount = symStartPos - num; - unsigned symCount = getNumDimAndSymbolVars() - symStartPos; - lbExprs.reserve(lbIndices.size() + eqIndices.size()); - // Lower bound expressions. - for (auto idx : lbIndices) { - auto ineq = getInequality64(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()); - 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 ubExprs; - ubExprs.reserve(ubIndices.size() + eqIndices.size()); - // Upper bound expressions. - for (auto idx : ubIndices) { - auto ineq = getInequality64(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])); - int64_t ubAdjustment = closedUB ? 0 : 1; - ubExprs.push_back(expr + ubAdjustment); - } - - // Equalities. It's both a lower and a upper bound. - SmallVector b; - for (auto idx : eqIndices) { - auto eq = getEquality64(idx); - addCoeffs(eq, b); - if (eq[pos + offset] > 0) - std::transform(b.begin(), b.end(), b.begin(), std::negate()); - - // 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 *lbMaps, SmallVectorImpl *ubMaps, - bool closedUB) { - 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 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 = getConstantBound64(BoundType::LB, pos); - auto ubConst = getConstantBound64(BoundType::UB, pos); - if (lbConst.has_value() && ubConst.has_value()) { - // Detect equality to a constant. - if (*lbConst == *ubConst) { - memo[pos] = getAffineConstantExpr(*lbConst, context); - changed = true; - continue; - } - - // Detect an variable as modulo of another variable w.r.t a - // constant. - if (detectAsMod(*this, pos, *lbConst, *ubConst, 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 = atEq64(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 + atEq64(idx, getNumVars()); - int64_t vPos = atEq64(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 = closedUB ? 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. - std::optional 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, - closedUB); - } - - // 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 = getConstantBound64(BoundType::LB, pos + offset); - if (lbConst.has_value()) { - lbMap = AffineMap::get(numMapDims, numMapSymbols, - getAffineConstantExpr(*lbConst, context)); - } - } - if (!ubMap || ubMap.getNumResults() > 1) { - LLVM_DEBUG(llvm::dbgs() - << "WARNING: Potentially over-approximating slice ub\n"); - auto ubConst = getConstantBound64(BoundType::UB, pos + offset); - if (ubConst.has_value()) { - ubMap = AffineMap::get( - numMapDims, numMapSymbols, - getAffineConstantExpr(*ubConst + 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> *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> 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 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 dims, syms; -#ifndef NDEBUG - SmallVector newSyms; - SmallVector *newSymsPtr = &newSyms; -#else - SmallVector *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) { @@ -1329,149 +278,34 @@ LogicalResult FlatAffineValueConstraints::addSliceBounds( 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 std::optional &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 std::nullopt. - if (getVarKindAt(posA) == VarKind::Local) - values[posB] = std::nullopt; - else if (getVarKindAt(posB) == VarKind::Local) - values[posA] = std::nullopt; - else - std::swap(values[posA], values[posB]); +LogicalResult +FlatAffineValueConstraints::composeMap(const AffineValueMap *vMap) { + return composeMatchingMap( + computeAlignedMap(vMap->getAffineMap(), vMap->getOperands())); } -void FlatAffineValueConstraints::addBound(BoundType type, Value val, - int64_t value) { +// Turn a symbol into a dimension. +static void turnSymbolIntoDim(FlatAffineValueConstraints *cst, Value 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\t"; - else - os << "None\t"; + if (cst->findVar(value, &pos) && pos >= cst->getNumDimVars() && + pos < cst->getNumDimAndSymbolVars()) { + cst->swapVar(pos, cst->getNumDimVars()); + cst->setDimSymbolSeparation(cst->getNumSymbolVars() - 1); } - for (unsigned i = getVarKindOffset(VarKind::Local), - e = getVarKindEnd(VarKind::Local); - i < e; ++i) - os << "Local\t"; - os << "const)\n"; } -void FlatAffineValueConstraints::clearAndCopyFrom( - const IntegerRelation &other) { - - if (auto *otherValueSet = - dyn_cast(&other)) { - *this = *otherValueSet; - } else { - *static_cast(this) = other; - values.clear(); - values.resize(getNumDimAndSymbolVars(), std::nullopt); +// Changes all symbol variables which are loop IVs to dim variables. +void FlatAffineValueConstraints::convertLoopIVSymbolsToDims() { + // Gather all symbols which are loop IVs. + SmallVector loopIVs; + for (unsigned i = getNumDimVars(), e = getNumDimAndSymbolVars(); i < e; i++) { + if (hasValue(i) && getForInductionVarOwner(getValue(i))) + loopIVs.push_back(getValue(i)); } -} - -void FlatAffineValueConstraints::fourierMotzkinEliminate( - unsigned pos, bool darkShadow, bool *isResultIntegerExact) { - SmallVector, 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); + // Turn each symbol in 'loopIVs' into a dim variable. + for (auto iv : loopIVs) { + turnSymbolIntoDim(this, iv); } - - 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 &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 localExprs = - ArrayRef(memo).take_back(cst.getNumLocalVars()); - return success( - llvm::all_of(localExprs, [](AffineExpr expr) { return expr; })); } void FlatAffineValueConstraints::getIneqAsAffineValueMap( @@ -1485,7 +319,7 @@ void FlatAffineValueConstraints::getIneqAsAffineValueMap( // Get expressions for local vars. SmallVector memo(getNumVars(), AffineExpr()); - if (failed(computeLocalVars(*this, memo, context))) + if (failed(computeLocalVars(memo, context))) assert(false && "one or more local exprs do not have an explicit representation"); auto localExprs = ArrayRef(memo).take_back(getNumLocalVars()); @@ -1519,105 +353,6 @@ void FlatAffineValueConstraints::getIneqAsAffineValueMap( 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 memo(getNumVars(), AffineExpr()); - - if (failed(computeLocalVars(*this, memo, context))) { - // Check if the local variables without an explicit representation have - // zero coefficients everywhere. - SmallVector 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 localExprs = - ArrayRef(memo).take_back(getNumLocalVars()); - - // Construct the IntegerSet from the equalities/inequalities. - unsigned numDims = getNumDimVars(); - unsigned numSyms = getNumSymbolVars(); - - SmallVector eqFlags(getNumConstraints()); - std::fill(eqFlags.begin(), eqFlags.begin() + getNumEqualities(), true); - std::fill(eqFlags.begin() + getNumEqualities(), eqFlags.end(), false); - - SmallVector exprs; - exprs.reserve(getNumConstraints()); - - for (unsigned i = 0, e = getNumEqualities(); i < e; ++i) - exprs.push_back(getAffineExprFromFlatForm(getEquality64(i), numDims, - numSyms, localExprs, context)); - for (unsigned i = 0, e = getNumInequalities(); i < e; ++i) - exprs.push_back(getAffineExprFromFlatForm(getInequality64(i), numDims, - numSyms, localExprs, context)); - return IntegerSet::get(numDims, numSyms, exprs, eqFlags); -} - -AffineMap mlir::alignAffineMapWithValues(AffineMap map, ValueRange operands, - ValueRange dims, ValueRange syms, - SmallVector *newSyms) { - assert(operands.size() == map.getNumInputs() && - "expected same number of operands and map inputs"); - MLIRContext *ctx = map.getContext(); - Builder builder(ctx); - SmallVector dimReplacements(map.getNumDims(), {}); - unsigned numSymbols = syms.size(); - SmallVector 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. @@ -1806,31 +541,3 @@ LogicalResult mlir::getRelationFromMap(const AffineValueMap &map, return success(); } - -LogicalResult -mlir::getMultiAffineFunctionFromMap(AffineMap map, - MultiAffineFunction &multiAff) { - FlatAffineValueConstraints cst; - std::vector> flattenedExprs; - LogicalResult result = getFlattenedAffineExprs(map, &flattenedExprs, &cst); - - if (result.failed()) - return failure(); - - DivisionRepr divs = cst.getLocalReprs(); - assert(divs.hasAllReprs() && - "AffineMap cannot produce divs without local representation"); - - // TODO: We shouldn't have to do this conversion. - Matrix mat(map.getNumResults(), map.getNumInputs() + divs.getNumDivs() + 1); - for (unsigned i = 0, e = flattenedExprs.size(); i < e; ++i) - for (unsigned j = 0, f = flattenedExprs[i].size(); j < f; ++j) - mat(i, j) = flattenedExprs[i][j]; - - multiAff = MultiAffineFunction( - PresburgerSpace::getRelationSpace(map.getNumDims(), map.getNumResults(), - map.getNumSymbols(), divs.getNumDivs()), - mat, divs); - - return success(); -} diff --git a/mlir/lib/IR/AffineExpr.cpp b/mlir/lib/IR/AffineExpr.cpp index 554452c..8564bac 100644 --- a/mlir/lib/IR/AffineExpr.cpp +++ b/mlir/lib/IR/AffineExpr.cpp @@ -1290,7 +1290,7 @@ void SimpleAffineExprFlattener::addLocalVariableSemiAffine( // 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 (done by -// FlatAffineConstraints::addLocalFloorDiv). +// IntegerRelation::addLocalFloorDiv). // // A ceildiv is similarly flattened: // t = expr ceildiv c <=> t = (expr + c - 1) floordiv c diff --git a/mlir/lib/IR/AffineMap.cpp b/mlir/lib/IR/AffineMap.cpp index c924d2b..39c8ab9 100644 --- a/mlir/lib/IR/AffineMap.cpp +++ b/mlir/lib/IR/AffineMap.cpp @@ -829,7 +829,7 @@ bool MutableAffineMap::isMultipleOf(unsigned idx, int64_t factor) const { if (results[idx].isMultipleOf(factor)) return true; - // TODO: use simplifyAffineExpr and FlatAffineConstraints to + // TODO: use simplifyAffineExpr and FlatAffineValueConstraints to // complete this (for a more powerful analysis). return false; } diff --git a/mlir/test/Transforms/memref-bound-check.mlir b/mlir/test/Transforms/memref-bound-check.mlir index fce6bdb..80909ab 100644 --- a/mlir/test/Transforms/memref-bound-check.mlir +++ b/mlir/test/Transforms/memref-bound-check.mlir @@ -201,7 +201,7 @@ func.func @out_of_bounds() { // This test case accesses within bounds. Without removal of a certain type of // trivially redundant constraints (those differing only in their constant // term), the number of constraints here explodes, and this would return out of -// bounds errors conservatively due to FlatAffineConstraints::kExplosionFactor. +// bounds errors conservatively due to IntegerRelation::kExplosionFactor. #map3 = affine_map<(d0, d1) -> ((d0 * 72 + d1) floordiv 2304 + ((((d0 * 72 + d1) mod 2304) mod 1152) mod 9) floordiv 3)> #map4 = affine_map<(d0, d1) -> ((d0 * 72 + d1) mod 2304 - (((d0 * 72 + d1) mod 2304) floordiv 1152) * 1151 - ((((d0 * 72 + d1) mod 2304) mod 1152) floordiv 9) * 9 - (((((d0 * 72 + d1) mod 2304) mod 1152) mod 9) floordiv 3) * 3)> #map5 = affine_map<(d0, d1) -> (((((d0 * 72 + d1) mod 2304) mod 1152) floordiv 9) floordiv 8)> diff --git a/mlir/test/Transforms/memref-dependence-check.mlir b/mlir/test/Transforms/memref-dependence-check.mlir index 3a16a33..f272277 100644 --- a/mlir/test/Transforms/memref-dependence-check.mlir +++ b/mlir/test/Transforms/memref-dependence-check.mlir @@ -636,7 +636,7 @@ func.func @mod_deps() { affine.for %i0 = 0 to 10 { %a0 = affine.apply affine_map<(d0) -> (d0 mod 2)> (%i0) // Results are conservative here since we currently don't have a way to - // represent strided sets in FlatAffineConstraints. + // represent strided sets in FlatAffineValueConstraints. %v0 = affine.load %m[%a0] : memref<100xf32> // expected-remark@above {{dependence from 0 to 0 at depth 1 = false}} // expected-remark@above {{dependence from 0 to 0 at depth 2 = false}}