1312 lines
50 KiB
C++
1312 lines
50 KiB
C++
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//===- FlatLinearValueConstraints.cpp - Linear Constraint -----------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#include "mlir/Analysis//FlatLinearValueConstraints.h"
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#include "mlir/Analysis/Presburger/LinearTransform.h"
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#include "mlir/Analysis/Presburger/Simplex.h"
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#include "mlir/Analysis/Presburger/Utils.h"
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#include "mlir/IR/AffineExprVisitor.h"
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#include "mlir/IR/Builders.h"
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#include "mlir/IR/IntegerSet.h"
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#include "mlir/Support/LLVM.h"
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#include "mlir/Support/MathExtras.h"
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#include "llvm/ADT/STLExtras.h"
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#include "llvm/ADT/SmallPtrSet.h"
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#include "llvm/ADT/SmallVector.h"
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#include "llvm/Support/Debug.h"
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#include "llvm/Support/raw_ostream.h"
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#include <optional>
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#define DEBUG_TYPE "flat-value-constraints"
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using namespace mlir;
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using namespace presburger;
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//===----------------------------------------------------------------------===//
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// AffineExprFlattener
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//===----------------------------------------------------------------------===//
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namespace {
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// See comments for SimpleAffineExprFlattener.
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// An AffineExprFlattener extends a SimpleAffineExprFlattener by recording
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// constraint information associated with mod's, floordiv's, and ceildiv's
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// in FlatLinearConstraints 'localVarCst'.
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struct AffineExprFlattener : public SimpleAffineExprFlattener {
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public:
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// Constraints connecting newly introduced local variables (for mod's and
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// div's) to existing (dimensional and symbolic) ones. These are always
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// inequalities.
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IntegerPolyhedron localVarCst;
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AffineExprFlattener(unsigned nDims, unsigned nSymbols)
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: SimpleAffineExprFlattener(nDims, nSymbols),
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localVarCst(PresburgerSpace::getSetSpace(nDims, nSymbols)) {}
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private:
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// Add a local variable (needed to flatten a mod, floordiv, ceildiv expr).
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// The local variable added is always a floordiv of a pure add/mul affine
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// function of other variables, coefficients of which are specified in
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// `dividend' and with respect to the positive constant `divisor'. localExpr
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// is the simplified tree expression (AffineExpr) corresponding to the
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// quantifier.
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void addLocalFloorDivId(ArrayRef<int64_t> dividend, int64_t divisor,
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AffineExpr localExpr) override {
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SimpleAffineExprFlattener::addLocalFloorDivId(dividend, divisor, localExpr);
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// Update localVarCst.
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localVarCst.addLocalFloorDiv(dividend, divisor);
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}
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};
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} // namespace
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// Flattens the expressions in map. Returns failure if 'expr' was unable to be
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// flattened. For example two specific cases:
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// 1. semi-affine expressions not handled yet.
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// 2. has poison expression (i.e., division by zero).
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static LogicalResult
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getFlattenedAffineExprs(ArrayRef<AffineExpr> exprs, unsigned numDims,
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unsigned numSymbols,
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std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
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FlatLinearConstraints *localVarCst) {
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if (exprs.empty()) {
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if (localVarCst)
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*localVarCst = FlatLinearConstraints(numDims, numSymbols);
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return success();
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}
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AffineExprFlattener flattener(numDims, numSymbols);
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// Use the same flattener to simplify each expression successively. This way
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// local variables / expressions are shared.
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for (auto expr : exprs) {
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if (!expr.isPureAffine())
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return failure();
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// has poison expression
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auto flattenResult = flattener.walkPostOrder(expr);
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if (failed(flattenResult))
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return failure();
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}
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assert(flattener.operandExprStack.size() == exprs.size());
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flattenedExprs->clear();
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flattenedExprs->assign(flattener.operandExprStack.begin(),
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flattener.operandExprStack.end());
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if (localVarCst)
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localVarCst->clearAndCopyFrom(flattener.localVarCst);
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return success();
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}
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// Flattens 'expr' into 'flattenedExpr'. Returns failure if 'expr' was unable to
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// be flattened (semi-affine expressions not handled yet).
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LogicalResult
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mlir::getFlattenedAffineExpr(AffineExpr expr, unsigned numDims,
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unsigned numSymbols,
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SmallVectorImpl<int64_t> *flattenedExpr,
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FlatLinearConstraints *localVarCst) {
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std::vector<SmallVector<int64_t, 8>> flattenedExprs;
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LogicalResult ret = ::getFlattenedAffineExprs({expr}, numDims, numSymbols,
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&flattenedExprs, localVarCst);
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*flattenedExpr = flattenedExprs[0];
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return ret;
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}
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/// Flattens the expressions in map. Returns failure if 'expr' was unable to be
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/// flattened (i.e., semi-affine expressions not handled yet).
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LogicalResult mlir::getFlattenedAffineExprs(
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AffineMap map, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
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FlatLinearConstraints *localVarCst) {
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if (map.getNumResults() == 0) {
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if (localVarCst)
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*localVarCst =
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FlatLinearConstraints(map.getNumDims(), map.getNumSymbols());
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return success();
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}
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return ::getFlattenedAffineExprs(map.getResults(), map.getNumDims(),
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map.getNumSymbols(), flattenedExprs,
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localVarCst);
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}
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LogicalResult mlir::getFlattenedAffineExprs(
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IntegerSet set, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
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FlatLinearConstraints *localVarCst) {
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if (set.getNumConstraints() == 0) {
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if (localVarCst)
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*localVarCst =
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FlatLinearConstraints(set.getNumDims(), set.getNumSymbols());
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return success();
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}
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return ::getFlattenedAffineExprs(set.getConstraints(), set.getNumDims(),
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set.getNumSymbols(), flattenedExprs,
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localVarCst);
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}
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//===----------------------------------------------------------------------===//
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// FlatLinearConstraints
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//===----------------------------------------------------------------------===//
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// Similar to `composeMap` except that no Values need be associated with the
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// constraint system nor are they looked at -- the dimensions and symbols of
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// `other` are expected to correspond 1:1 to `this` system.
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LogicalResult FlatLinearConstraints::composeMatchingMap(AffineMap other) {
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assert(other.getNumDims() == getNumDimVars() && "dim mismatch");
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assert(other.getNumSymbols() == getNumSymbolVars() && "symbol mismatch");
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std::vector<SmallVector<int64_t, 8>> flatExprs;
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if (failed(flattenAlignedMapAndMergeLocals(other, &flatExprs)))
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return failure();
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assert(flatExprs.size() == other.getNumResults());
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// Add dimensions corresponding to the map's results.
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insertDimVar(/*pos=*/0, /*num=*/other.getNumResults());
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// We add one equality for each result connecting the result dim of the map to
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// the other variables.
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// E.g.: if the expression is 16*i0 + i1, and this is the r^th
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// iteration/result of the value map, we are adding the equality:
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// d_r - 16*i0 - i1 = 0. Similarly, when flattening (i0 + 1, i0 + 8*i2), we
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// add two equalities: d_0 - i0 - 1 == 0, d1 - i0 - 8*i2 == 0.
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for (unsigned r = 0, e = flatExprs.size(); r < e; r++) {
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const auto &flatExpr = flatExprs[r];
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assert(flatExpr.size() >= other.getNumInputs() + 1);
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SmallVector<int64_t, 8> eqToAdd(getNumCols(), 0);
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// Set the coefficient for this result to one.
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eqToAdd[r] = 1;
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// Dims and symbols.
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for (unsigned i = 0, f = other.getNumInputs(); i < f; i++) {
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// Negate `eq[r]` since the newly added dimension will be set to this one.
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eqToAdd[e + i] = -flatExpr[i];
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}
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// Local columns of `eq` are at the beginning.
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unsigned j = getNumDimVars() + getNumSymbolVars();
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unsigned end = flatExpr.size() - 1;
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for (unsigned i = other.getNumInputs(); i < end; i++, j++) {
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eqToAdd[j] = -flatExpr[i];
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}
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// Constant term.
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eqToAdd[getNumCols() - 1] = -flatExpr[flatExpr.size() - 1];
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// Add the equality connecting the result of the map to this constraint set.
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addEquality(eqToAdd);
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}
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return success();
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}
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// Determine whether the variable at 'pos' (say var_r) can be expressed as
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// modulo of another known variable (say var_n) w.r.t a constant. For example,
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// if the following constraints hold true:
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// ```
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// 0 <= var_r <= divisor - 1
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// var_n - (divisor * q_expr) = var_r
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// ```
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// where `var_n` is a known variable (called dividend), and `q_expr` is an
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// `AffineExpr` (called the quotient expression), `var_r` can be written as:
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//
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// `var_r = var_n mod divisor`.
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//
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// Additionally, in a special case of the above constaints where `q_expr` is an
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// variable itself that is not yet known (say `var_q`), it can be written as a
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// floordiv in the following way:
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//
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// `var_q = var_n floordiv divisor`.
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//
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// First 'num' dimensional variables starting at 'offset' are
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// derived/to-be-derived in terms of the remaining variables. The remaining
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// variables are assigned trivial affine expressions in `memo`. For example,
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// memo is initilized as follows for a `cst` with 5 dims, when offset=2, num=2:
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// memo ==> d0 d1 . . d2 ...
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// cst ==> c0 c1 c2 c3 c4 ...
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//
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// Returns true if the above mod or floordiv are detected, updating 'memo' with
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// these new expressions. Returns false otherwise.
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static bool detectAsMod(const FlatLinearConstraints &cst, unsigned pos,
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unsigned offset, unsigned num, int64_t lbConst,
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int64_t ubConst, MLIRContext *context,
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SmallVectorImpl<AffineExpr> &memo) {
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assert(pos < cst.getNumVars() && "invalid position");
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// Check if a divisor satisfying the condition `0 <= var_r <= divisor - 1` can
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// be determined.
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if (lbConst != 0 || ubConst < 1)
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return false;
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int64_t divisor = ubConst + 1;
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// Check for the aforementioned conditions in each equality.
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for (unsigned curEquality = 0, numEqualities = cst.getNumEqualities();
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curEquality < numEqualities; curEquality++) {
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int64_t coefficientAtPos = cst.atEq64(curEquality, pos);
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// If current equality does not involve `var_r`, continue to the next
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// equality.
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if (coefficientAtPos == 0)
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continue;
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// Constant term should be 0 in this equality.
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if (cst.atEq64(curEquality, cst.getNumCols() - 1) != 0)
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continue;
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// Traverse through the equality and construct the dividend expression
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// `dividendExpr`, to contain all the variables which are known and are
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// not divisible by `(coefficientAtPos * divisor)`. Hope here is that the
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// `dividendExpr` gets simplified into a single variable `var_n` discussed
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// above.
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auto dividendExpr = getAffineConstantExpr(0, context);
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// Track the terms that go into quotient expression, later used to detect
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// additional floordiv.
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unsigned quotientCount = 0;
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int quotientPosition = -1;
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int quotientSign = 1;
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// Consider each term in the current equality.
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unsigned curVar, e;
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for (curVar = 0, e = cst.getNumDimAndSymbolVars(); curVar < e; ++curVar) {
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// Ignore var_r.
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if (curVar == pos)
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continue;
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int64_t coefficientOfCurVar = cst.atEq64(curEquality, curVar);
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// Ignore vars that do not contribute to the current equality.
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if (coefficientOfCurVar == 0)
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continue;
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// Check if the current var goes into the quotient expression.
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if (coefficientOfCurVar % (divisor * coefficientAtPos) == 0) {
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quotientCount++;
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quotientPosition = curVar;
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quotientSign = (coefficientOfCurVar * coefficientAtPos) > 0 ? 1 : -1;
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continue;
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}
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// Variables that are part of dividendExpr should be known.
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if (!memo[curVar])
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break;
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// Append the current variable to the dividend expression.
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dividendExpr = dividendExpr + memo[curVar] * coefficientOfCurVar;
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}
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// Can't construct expression as it depends on a yet uncomputed var.
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if (curVar < e)
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continue;
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// Express `var_r` in terms of the other vars collected so far.
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if (coefficientAtPos > 0)
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dividendExpr = (-dividendExpr).floorDiv(coefficientAtPos);
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else
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dividendExpr = dividendExpr.floorDiv(-coefficientAtPos);
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// Simplify the expression.
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dividendExpr = simplifyAffineExpr(dividendExpr, cst.getNumDimVars(),
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cst.getNumSymbolVars());
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// Only if the final dividend expression is just a single var (which we call
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// `var_n`), we can proceed.
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// TODO: Handle AffineSymbolExpr as well. There is no reason to restrict it
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// to dims themselves.
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auto dimExpr = dyn_cast<AffineDimExpr>(dividendExpr);
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if (!dimExpr)
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continue;
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// Express `var_r` as `var_n % divisor` and store the expression in `memo`.
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if (quotientCount >= 1) {
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// Find the column corresponding to `dimExpr`. `num` columns starting at
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// `offset` correspond to previously unknown variables. The column
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// corresponding to the trivially known `dimExpr` can be on either side
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// of these.
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unsigned dimExprPos = dimExpr.getPosition();
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unsigned dimExprCol = dimExprPos < offset ? dimExprPos : dimExprPos + num;
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auto ub = cst.getConstantBound64(BoundType::UB, dimExprCol);
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// If `var_n` has an upperbound that is less than the divisor, mod can be
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// eliminated altogether.
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if (ub && *ub < divisor)
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memo[pos] = dimExpr;
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else
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memo[pos] = dimExpr % divisor;
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// If a unique quotient `var_q` was seen, it can be expressed as
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// `var_n floordiv divisor`.
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if (quotientCount == 1 && !memo[quotientPosition])
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memo[quotientPosition] = dimExpr.floorDiv(divisor) * quotientSign;
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return true;
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}
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}
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return false;
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}
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/// Check if the pos^th variable can be expressed as a floordiv of an affine
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/// function of other variables (where the divisor is a positive constant)
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/// given the initial set of expressions in `exprs`. If it can be, the
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/// corresponding position in `exprs` is set as the detected affine expr. For
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/// eg: 4q <= i + j <= 4q + 3 <=> q = (i + j) floordiv 4. An equality can
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/// also yield a floordiv: eg. 4q = i + j <=> q = (i + j) floordiv 4. 32q + 28
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/// <= i <= 32q + 31 => q = i floordiv 32.
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static bool detectAsFloorDiv(const FlatLinearConstraints &cst, unsigned pos,
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MLIRContext *context,
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SmallVectorImpl<AffineExpr> &exprs) {
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assert(pos < cst.getNumVars() && "invalid position");
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// Get upper-lower bound pair for this variable.
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SmallVector<bool, 8> foundRepr(cst.getNumVars(), false);
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for (unsigned i = 0, e = cst.getNumVars(); i < e; ++i)
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if (exprs[i])
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foundRepr[i] = true;
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SmallVector<int64_t, 8> dividend(cst.getNumCols());
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unsigned divisor;
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auto ulPair = computeSingleVarRepr(cst, foundRepr, pos, dividend, divisor);
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// No upper-lower bound pair found for this var.
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if (ulPair.kind == ReprKind::None || ulPair.kind == ReprKind::Equality)
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return false;
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// Construct the dividend expression.
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auto dividendExpr = getAffineConstantExpr(dividend.back(), context);
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for (unsigned c = 0, f = cst.getNumVars(); c < f; c++)
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if (dividend[c] != 0)
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dividendExpr = dividendExpr + dividend[c] * exprs[c];
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// Successfully detected the floordiv.
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exprs[pos] = dividendExpr.floorDiv(divisor);
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return true;
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}
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std::pair<AffineMap, AffineMap> FlatLinearConstraints::getLowerAndUpperBound(
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unsigned pos, unsigned offset, unsigned num, unsigned symStartPos,
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ArrayRef<AffineExpr> localExprs, MLIRContext *context,
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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<unsigned, 4> lbIndices, ubIndices, eqIndices;
|
||
|
getLowerAndUpperBoundIndices(pos + offset, &lbIndices, &ubIndices, &eqIndices,
|
||
|
offset, num);
|
||
|
|
||
|
/// Add to 'b' from 'a' in set [0, offset) U [offset + num, symbStartPos).
|
||
|
auto addCoeffs = [&](ArrayRef<int64_t> a, SmallVectorImpl<int64_t> &b) {
|
||
|
b.clear();
|
||
|
for (unsigned i = 0, e = a.size(); i < e; ++i) {
|
||
|
if (i < offset || i >= offset + num)
|
||
|
b.push_back(a[i]);
|
||
|
}
|
||
|
};
|
||
|
|
||
|
SmallVector<int64_t, 8> lb, ub;
|
||
|
SmallVector<AffineExpr, 4> lbExprs;
|
||
|
unsigned dimCount = symStartPos - num;
|
||
|
unsigned symCount = getNumDimAndSymbolVars() - symStartPos;
|
||
|
lbExprs.reserve(lbIndices.size() + eqIndices.size());
|
||
|
// Lower bound expressions.
|
||
|
for (auto idx : lbIndices) {
|
||
|
auto ineq = 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<int64_t>());
|
||
|
auto expr =
|
||
|
getAffineExprFromFlatForm(lb, dimCount, symCount, localExprs, context);
|
||
|
// expr ceildiv divisor is (expr + divisor - 1) floordiv divisor
|
||
|
int64_t divisor = std::abs(ineq[pos + offset]);
|
||
|
expr = (expr + divisor - 1).floorDiv(divisor);
|
||
|
lbExprs.push_back(expr);
|
||
|
}
|
||
|
|
||
|
SmallVector<AffineExpr, 4> ubExprs;
|
||
|
ubExprs.reserve(ubIndices.size() + eqIndices.size());
|
||
|
// Upper bound expressions.
|
||
|
for (auto idx : ubIndices) {
|
||
|
auto ineq = 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<int64_t, 4> 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<int64_t>());
|
||
|
|
||
|
// Extract the upper bound (in terms of other coeff's + const).
|
||
|
auto expr =
|
||
|
getAffineExprFromFlatForm(b, dimCount, symCount, localExprs, context);
|
||
|
expr = expr.floorDiv(std::abs(eq[pos + offset]));
|
||
|
// Upper bound is exclusive.
|
||
|
ubExprs.push_back(expr + 1);
|
||
|
// Lower bound.
|
||
|
expr =
|
||
|
getAffineExprFromFlatForm(b, dimCount, symCount, localExprs, context);
|
||
|
expr = expr.ceilDiv(std::abs(eq[pos + offset]));
|
||
|
lbExprs.push_back(expr);
|
||
|
}
|
||
|
|
||
|
auto lbMap = AffineMap::get(dimCount, symCount, lbExprs, context);
|
||
|
auto ubMap = AffineMap::get(dimCount, symCount, ubExprs, context);
|
||
|
|
||
|
return {lbMap, ubMap};
|
||
|
}
|
||
|
|
||
|
/// Computes the lower and upper bounds of the first 'num' dimensional
|
||
|
/// variables (starting at 'offset') as affine maps of the remaining
|
||
|
/// variables (dimensional and symbolic variables). Local variables are
|
||
|
/// themselves explicitly computed as affine functions of other variables in
|
||
|
/// this process if needed.
|
||
|
void FlatLinearConstraints::getSliceBounds(unsigned offset, unsigned num,
|
||
|
MLIRContext *context,
|
||
|
SmallVectorImpl<AffineMap> *lbMaps,
|
||
|
SmallVectorImpl<AffineMap> *ubMaps,
|
||
|
bool closedUB) {
|
||
|
assert(offset + num <= getNumDimVars() && "invalid range");
|
||
|
|
||
|
// Basic simplification.
|
||
|
normalizeConstraintsByGCD();
|
||
|
|
||
|
LLVM_DEBUG(llvm::dbgs() << "getSliceBounds for first " << num
|
||
|
<< " variables\n");
|
||
|
LLVM_DEBUG(dump());
|
||
|
|
||
|
// Record computed/detected variables.
|
||
|
SmallVector<AffineExpr, 8> memo(getNumVars());
|
||
|
// Initialize dimensional and symbolic variables.
|
||
|
for (unsigned i = 0, e = getNumDimVars(); i < e; i++) {
|
||
|
if (i < offset)
|
||
|
memo[i] = getAffineDimExpr(i, context);
|
||
|
else if (i >= offset + num)
|
||
|
memo[i] = getAffineDimExpr(i - num, context);
|
||
|
}
|
||
|
for (unsigned i = getNumDimVars(), e = getNumDimAndSymbolVars(); i < e; i++)
|
||
|
memo[i] = getAffineSymbolExpr(i - getNumDimVars(), context);
|
||
|
|
||
|
bool changed;
|
||
|
do {
|
||
|
changed = false;
|
||
|
// Identify yet unknown variables as constants or mod's / floordiv's of
|
||
|
// other variables if possible.
|
||
|
for (unsigned pos = 0; pos < getNumVars(); pos++) {
|
||
|
if (memo[pos])
|
||
|
continue;
|
||
|
|
||
|
auto lbConst = 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, offset, num, *lbConst, *ubConst, context,
|
||
|
memo)) {
|
||
|
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<FlatLinearConstraints> 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<SmallVector<int64_t, 8>> *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<SmallVector<int64_t, 8>> flatExprs;
|
||
|
if (failed(flattenAlignedMapAndMergeLocals(boundMap, &flatExprs)))
|
||
|
return failure();
|
||
|
assert(flatExprs.size() == boundMap.getNumResults());
|
||
|
|
||
|
// Add one (in)equality for each result.
|
||
|
for (const auto &flatExpr : flatExprs) {
|
||
|
SmallVector<int64_t> ineq(getNumCols(), 0);
|
||
|
// Dims and symbols.
|
||
|
for (unsigned j = 0, e = boundMap.getNumInputs(); j < e; j++) {
|
||
|
ineq[j] = lower ? -flatExpr[j] : flatExpr[j];
|
||
|
}
|
||
|
// Invalid bound: pos appears in `boundMap`.
|
||
|
// TODO: This should be an assertion. Fix `addDomainFromSliceMaps` and/or
|
||
|
// its callers to prevent invalid bounds from being added.
|
||
|
if (ineq[pos] != 0)
|
||
|
continue;
|
||
|
ineq[pos] = lower ? 1 : -1;
|
||
|
// Local columns of `ineq` are at the beginning.
|
||
|
unsigned j = getNumDimVars() + getNumSymbolVars();
|
||
|
unsigned end = flatExpr.size() - 1;
|
||
|
for (unsigned i = boundMap.getNumInputs(); i < end; i++, j++) {
|
||
|
ineq[j] = lower ? -flatExpr[i] : flatExpr[i];
|
||
|
}
|
||
|
// Make the bound closed in if flatExpr is open. The inequality is always
|
||
|
// created in the upper bound form, so the adjustment is -1.
|
||
|
int64_t boundAdjustment = (isClosedBound || type == BoundType::EQ) ? 0 : -1;
|
||
|
// Constant term.
|
||
|
ineq[getNumCols() - 1] = (lower ? -flatExpr[flatExpr.size() - 1]
|
||
|
: flatExpr[flatExpr.size() - 1]) +
|
||
|
boundAdjustment;
|
||
|
type == BoundType::EQ ? addEquality(ineq) : addInequality(ineq);
|
||
|
}
|
||
|
|
||
|
return success();
|
||
|
}
|
||
|
|
||
|
LogicalResult 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<AffineExpr> &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<AffineExpr> localExprs =
|
||
|
ArrayRef<AffineExpr>(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<AffineExpr, 8> memo(getNumVars(), AffineExpr());
|
||
|
|
||
|
if (failed(computeLocalVars(memo, context))) {
|
||
|
// Check if the local variables without an explicit representation have
|
||
|
// zero coefficients everywhere.
|
||
|
SmallVector<unsigned> noLocalRepVars;
|
||
|
unsigned numDimsSymbols = getNumDimAndSymbolVars();
|
||
|
for (unsigned i = numDimsSymbols, e = getNumVars(); i < e; ++i) {
|
||
|
if (!memo[i] && !isColZero(/*pos=*/i))
|
||
|
noLocalRepVars.push_back(i - numDimsSymbols);
|
||
|
}
|
||
|
if (!noLocalRepVars.empty()) {
|
||
|
LLVM_DEBUG({
|
||
|
llvm::dbgs() << "local variables at position(s) ";
|
||
|
llvm::interleaveComma(noLocalRepVars, llvm::dbgs());
|
||
|
llvm::dbgs() << " do not have an explicit representation in:\n";
|
||
|
this->dump();
|
||
|
});
|
||
|
return IntegerSet();
|
||
|
}
|
||
|
}
|
||
|
|
||
|
ArrayRef<AffineExpr> localExprs =
|
||
|
ArrayRef<AffineExpr>(memo).take_back(getNumLocalVars());
|
||
|
|
||
|
// Construct the IntegerSet from the equalities/inequalities.
|
||
|
unsigned numDims = getNumDimVars();
|
||
|
unsigned numSyms = getNumSymbolVars();
|
||
|
|
||
|
SmallVector<bool, 16> eqFlags(getNumConstraints());
|
||
|
std::fill(eqFlags.begin(), eqFlags.begin() + getNumEqualities(), true);
|
||
|
std::fill(eqFlags.begin() + getNumEqualities(), eqFlags.end(), false);
|
||
|
|
||
|
SmallVector<AffineExpr, 8> exprs;
|
||
|
exprs.reserve(getNumConstraints());
|
||
|
|
||
|
for (unsigned i = 0, e = getNumEqualities(); i < e; ++i)
|
||
|
exprs.push_back(getAffineExprFromFlatForm(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<SmallVector<int64_t, 8>> 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);
|
||
|
}
|
||
|
|
||
|
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 std::nullopt.
|
||
|
for (unsigned i = 0; i < num; ++i)
|
||
|
values.insert(values.begin() + absolutePos + i,
|
||
|
vals[i] ? std::optional<Value>(vals[i]) : std::nullopt);
|
||
|
|
||
|
assert(values.size() == getNumDimAndSymbolVars());
|
||
|
return absolutePos;
|
||
|
}
|
||
|
|
||
|
/// 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<Value, 8> uniqueVars;
|
||
|
ArrayRef<std::optional<Value>> maybeValues =
|
||
|
cst.getMaybeValues().slice(start, end - start);
|
||
|
for (std::optional<Value> val : maybeValues) {
|
||
|
if (val && !uniqueVars.insert(*val).second)
|
||
|
return false;
|
||
|
}
|
||
|
return true;
|
||
|
}
|
||
|
|
||
|
/// Checks if the SSA values associated with `cst`'s variables are unique.
|
||
|
static bool LLVM_ATTRIBUTE_UNUSED
|
||
|
areVarsUnique(const 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. We allow A
|
||
|
/// and B to have non-unique values for their variables; in such cases, they are
|
||
|
/// still aligned with the variables appearing first aligned with those
|
||
|
/// appearing first in the other system from left to right.
|
||
|
// 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());
|
||
|
|
||
|
assert(llvm::all_of(
|
||
|
llvm::drop_begin(a->getMaybeValues(), offset),
|
||
|
[](const std::optional<Value> &var) { return var.has_value(); }));
|
||
|
|
||
|
assert(llvm::all_of(
|
||
|
llvm::drop_begin(b->getMaybeValues(), offset),
|
||
|
[](const std::optional<Value> &var) { return var.has_value(); }));
|
||
|
|
||
|
SmallVector<Value, 4> aDimValues;
|
||
|
a->getValues(offset, a->getNumDimVars(), &aDimValues);
|
||
|
|
||
|
{
|
||
|
// Merge dims from A into B.
|
||
|
unsigned d = offset;
|
||
|
for (Value aDimValue : aDimValues) {
|
||
|
unsigned loc;
|
||
|
// Find from the position `d` since we'd like to also consider the
|
||
|
// possibility of multiple variables with the same `Value`. We align with
|
||
|
// the next appearing one.
|
||
|
if (b->findVar(aDimValue, &loc, d)) {
|
||
|
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. Existing symbols need not be unique; they will be aligned from
|
||
|
/// left to right with duplicates aligned in the same order. Symbols with Value
|
||
|
/// as `None` are considered to be inequal to all other symbols.
|
||
|
void FlatLinearValueConstraints::mergeSymbolVars(
|
||
|
FlatLinearValueConstraints &other) {
|
||
|
|
||
|
SmallVector<Value, 4> aSymValues;
|
||
|
getValues(getNumDimVars(), getNumDimAndSymbolVars(), &aSymValues);
|
||
|
|
||
|
// Merge symbols: merge symbols into `other` first from `this`.
|
||
|
unsigned s = other.getNumDimVars();
|
||
|
for (Value aSymValue : aSymValues) {
|
||
|
unsigned loc;
|
||
|
// If the var is a symbol in `other`, then align it, otherwise assume that
|
||
|
// it is a new symbol. Search in `other` starting at position `s` since the
|
||
|
// left of it is aligned.
|
||
|
if (other.findVar(aSymValue, &loc, s) && 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");
|
||
|
}
|
||
|
|
||
|
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<Value> dims, syms;
|
||
|
#ifndef NDEBUG
|
||
|
SmallVector<Value> newSyms;
|
||
|
SmallVector<Value> *newSymsPtr = &newSyms;
|
||
|
#else
|
||
|
SmallVector<Value> *newSymsPtr = nullptr;
|
||
|
#endif // NDEBUG
|
||
|
|
||
|
dims.reserve(getNumDimVars());
|
||
|
syms.reserve(getNumSymbolVars());
|
||
|
for (unsigned i = getVarKindOffset(VarKind::SetDim),
|
||
|
e = getVarKindEnd(VarKind::SetDim);
|
||
|
i < e; ++i)
|
||
|
dims.push_back(values[i] ? *values[i] : Value());
|
||
|
for (unsigned i = getVarKindOffset(VarKind::Symbol),
|
||
|
e = getVarKindEnd(VarKind::Symbol);
|
||
|
i < e; ++i)
|
||
|
syms.push_back(values[i] ? *values[i] : Value());
|
||
|
|
||
|
AffineMap alignedMap =
|
||
|
alignAffineMapWithValues(map, operands, dims, syms, newSymsPtr);
|
||
|
// All symbols are already part of this 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,
|
||
|
unsigned offset) const {
|
||
|
unsigned i = offset;
|
||
|
for (const auto &mayBeVar :
|
||
|
ArrayRef<std::optional<Value>>(values).drop_front(offset)) {
|
||
|
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<Value> &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<const FlatLinearValueConstraints>(&other)) {
|
||
|
*this = *otherValueSet;
|
||
|
} else {
|
||
|
*static_cast<IntegerRelation *>(this) = other;
|
||
|
values.clear();
|
||
|
values.resize(getNumDimAndSymbolVars(), std::nullopt);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
void FlatLinearValueConstraints::fourierMotzkinEliminate(
|
||
|
unsigned pos, bool darkShadow, bool *isResultIntegerExact) {
|
||
|
SmallVector<std::optional<Value>, 8> newVals = values;
|
||
|
if (getVarKindAt(pos) != VarKind::Local)
|
||
|
newVals.erase(newVals.begin() + pos);
|
||
|
// Note: Base implementation discards all associated Values.
|
||
|
IntegerPolyhedron::fourierMotzkinEliminate(pos, darkShadow,
|
||
|
isResultIntegerExact);
|
||
|
values = newVals;
|
||
|
assert(values.size() == getNumDimAndSymbolVars());
|
||
|
}
|
||
|
|
||
|
void 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<Value> *newSyms) {
|
||
|
assert(operands.size() == map.getNumInputs() &&
|
||
|
"expected same number of operands and map inputs");
|
||
|
MLIRContext *ctx = map.getContext();
|
||
|
Builder builder(ctx);
|
||
|
SmallVector<AffineExpr> dimReplacements(map.getNumDims(), {});
|
||
|
unsigned numSymbols = syms.size();
|
||
|
SmallVector<AffineExpr> symReplacements(map.getNumSymbols(), {});
|
||
|
if (newSyms) {
|
||
|
newSyms->clear();
|
||
|
newSyms->append(syms.begin(), syms.end());
|
||
|
}
|
||
|
|
||
|
for (const auto &operand : llvm::enumerate(operands)) {
|
||
|
// Compute replacement dim/sym of operand.
|
||
|
AffineExpr replacement;
|
||
|
auto dimIt = llvm::find(dims, operand.value());
|
||
|
auto symIt = llvm::find(syms, 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<SmallVector<int64_t, 8>> 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<MPInt> 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();
|
||
|
}
|