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[MLIR][FlatAffineConstraints][NFC] Move some static functions to be a…
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…vailable to Presburger/

This patch moves some static functions from AffineStructures.cpp to
Presburger/Utils.cpp and some to be private members of FlatAffineConstraints
(which will later be moved to IntegerPolyhedron) to allow for a smoother
transition for moving FlatAffineConstraints math functionality to
Presburger/IntegerPolyhedron.

This patch is part of a series of patches for moving math functionality to
Presburger directory.

Reviewed By: arjunp, bondhugula

Differential Revision: https://reviews.llvm.org/D115869
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@Groverkss
Groverkss committed Dec 25, 2021
1 parent d86e2cc commit 5b2e611
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Showing 7 changed files with 289 additions and 223 deletions.
20 changes: 10 additions & 10 deletions mlir/include/mlir/Analysis/AffineStructures.h
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Original file line number Diff line number Diff line change
Expand Up @@ -292,16 +292,6 @@ class FlatAffineConstraints : public IntegerPolyhedron {
unsigned symStartPos, ArrayRef<AffineExpr> localExprs,
MLIRContext *context) const;

/// Gather positions of all lower and upper bounds of the identifier at `pos`,
/// and optionally any equalities on it. In addition, the bounds are to be
/// independent of identifiers in position range [`offset`, `offset` + `num`).
void
getLowerAndUpperBoundIndices(unsigned pos,
SmallVectorImpl<unsigned> *lbIndices,
SmallVectorImpl<unsigned> *ubIndices,
SmallVectorImpl<unsigned> *eqIndices = nullptr,
unsigned offset = 0, unsigned num = 0) const;

/// Removes constraints that are independent of (i.e., do not have a
/// coefficient) identifiers in the range [pos, pos + num).
void removeIndependentConstraints(unsigned pos, unsigned num);
Expand Down Expand Up @@ -419,6 +409,16 @@ class FlatAffineConstraints : public IntegerPolyhedron {
/// Normalized each constraints by the GCD of its coefficients.
void normalizeConstraintsByGCD();

/// Searches for a constraint with a non-zero coefficient at `colIdx` in
/// equality (isEq=true) or inequality (isEq=false) constraints.
/// Returns true and sets row found in search in `rowIdx`, false otherwise.
bool findConstraintWithNonZeroAt(unsigned colIdx, bool isEq,
unsigned *rowIdx) const;

/// Returns true if the pos^th column is all zero for both inequalities and
/// equalities.
bool isColZero(unsigned pos) const;

/// A parameter that controls detection of an unrealistic number of
/// constraints. If the number of constraints is this many times the number of
/// variables, we consider such a system out of line with the intended use
Expand Down
10 changes: 10 additions & 0 deletions mlir/include/mlir/Analysis/Presburger/IntegerPolyhedron.h
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Original file line number Diff line number Diff line change
Expand Up @@ -185,6 +185,16 @@ class IntegerPolyhedron {
/// Removes all equalities and inequalities.
void clearConstraints();

/// Gather positions of all lower and upper bounds of the identifier at `pos`,
/// and optionally any equalities on it. In addition, the bounds are to be
/// independent of identifiers in position range [`offset`, `offset` + `num`).
void
getLowerAndUpperBoundIndices(unsigned pos,
SmallVectorImpl<unsigned> *lbIndices,
SmallVectorImpl<unsigned> *ubIndices,
SmallVectorImpl<unsigned> *eqIndices = nullptr,
unsigned offset = 0, unsigned num = 0) const;

protected:
/// Return the index at which the specified kind of id starts.
unsigned getIdKindOffset(IdKind kind) const;
Expand Down
40 changes: 40 additions & 0 deletions mlir/include/mlir/Analysis/Presburger/Utils.h
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Original file line number Diff line number Diff line change
@@ -0,0 +1,40 @@
//===- Utils.h - General utilities for Presburger library ------*- 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
//
//===----------------------------------------------------------------------===//
//
// Utility functions required by the Presburger Library.
//
//===----------------------------------------------------------------------===//

#ifndef MLIR_ANALYSIS_PRESBURGER_UTILS_H
#define MLIR_ANALYSIS_PRESBURGER_UTILS_H

#include "mlir/Support/LLVM.h"

namespace mlir {

class IntegerPolyhedron;

namespace presburger_utils {

/// Check if the pos^th identifier can be expressed as a floordiv of an affine
/// function of other identifiers (where the divisor is a positive constant).
/// `foundRepr` contains a boolean for each identifier indicating if the
/// explicit representation for that identifier has already been computed.
/// Returns the upper and lower bound inequalities using which the floordiv
/// can be computed. If the representation could be computed, `dividend` and
/// `denominator` are set. If the representation could not be computed,
/// `llvm::None` is returned.
Optional<std::pair<unsigned, unsigned>>
computeSingleVarRepr(const IntegerPolyhedron &cst, ArrayRef<bool> foundRepr,
unsigned pos, SmallVector<int64_t, 8> &dividend,
unsigned &divisor);

} // namespace presburger_utils
} // namespace mlir

#endif // MLIR_ANALYSIS_PRESBURGER_UTILS_H
231 changes: 18 additions & 213 deletions mlir/lib/Analysis/AffineStructures.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -13,6 +13,7 @@
#include "mlir/Analysis/AffineStructures.h"
#include "mlir/Analysis/LinearTransform.h"
#include "mlir/Analysis/Presburger/Simplex.h"
#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Dialect/Affine/IR/AffineOps.h"
#include "mlir/Dialect/Affine/IR/AffineValueMap.h"
#include "mlir/Dialect/Arithmetic/IR/Arithmetic.h"
Expand Down Expand Up @@ -700,14 +701,13 @@ void FlatAffineValueConstraints::addAffineIfOpDomain(AffineIfOp ifOp) {
// Searches for a constraint with a non-zero coefficient at `colIdx` in
// equality (isEq=true) or inequality (isEq=false) constraints.
// Returns true and sets row found in search in `rowIdx`, false otherwise.
static bool findConstraintWithNonZeroAt(const FlatAffineConstraints &cst,
unsigned colIdx, bool isEq,
unsigned *rowIdx) {
assert(colIdx < cst.getNumCols() && "position out of bounds");
bool FlatAffineConstraints::findConstraintWithNonZeroAt(
unsigned colIdx, bool isEq, unsigned *rowIdx) const {
assert(colIdx < getNumCols() && "position out of bounds");
auto at = [&](unsigned rowIdx) -> int64_t {
return isEq ? cst.atEq(rowIdx, colIdx) : cst.atIneq(rowIdx, colIdx);
return isEq ? atEq(rowIdx, colIdx) : atIneq(rowIdx, colIdx);
};
unsigned e = isEq ? cst.getNumEqualities() : cst.getNumInequalities();
unsigned e = isEq ? getNumEqualities() : getNumInequalities();
for (*rowIdx = 0; *rowIdx < e; ++(*rowIdx)) {
if (at(*rowIdx) != 0) {
return true;
Expand Down Expand Up @@ -1203,145 +1203,6 @@ bool FlatAffineConstraints::containsPoint(ArrayRef<int64_t> point) const {
return true;
}

/// Check if the pos^th identifier can be represented as a division using upper
/// bound inequality at position `ubIneq` and lower bound inequality at position
/// `lbIneq`.
///
/// Let `id` be the pos^th identifier, then `id` is equivalent to
/// `expr floordiv divisor` if there are constraints of the form:
/// 0 <= expr - divisor * id <= divisor - 1
/// Rearranging, we have:
/// divisor * id - expr + (divisor - 1) >= 0 <-- Lower bound for 'id'
/// -divisor * id + expr >= 0 <-- Upper bound for 'id'
///
/// For example:
/// 32*k >= 16*i + j - 31 <-- Lower bound for 'k'
/// 32*k <= 16*i + j <-- Upper bound for 'k'
/// expr = 16*i + j, divisor = 32
/// k = ( 16*i + j ) floordiv 32
///
/// 4q >= i + j - 2 <-- Lower bound for 'q'
/// 4q <= i + j + 1 <-- Upper bound for 'q'
/// expr = i + j + 1, divisor = 4
/// q = (i + j + 1) floordiv 4
//
/// This function also supports detecting divisions from bounds that are
/// strictly tighter than the division bounds described above, since tighter
/// bounds imply the division bounds. For example:
/// 4q - i - j + 2 >= 0 <-- Lower bound for 'q'
/// -4q + i + j >= 0 <-- Tight upper bound for 'q'
///
/// To extract floor divisions with tighter bounds, we assume that that the
/// constraints are of the form:
/// c <= expr - divisior * id <= divisor - 1, where 0 <= c <= divisor - 1
/// Rearranging, we have:
/// divisor * id - expr + (divisor - 1) >= 0 <-- Lower bound for 'id'
/// -divisor * id + expr - c >= 0 <-- Upper bound for 'id'
///
/// If successful, `expr` is set to dividend of the division and `divisor` is
/// set to the denominator of the division.
static LogicalResult getDivRepr(const FlatAffineConstraints &cst, unsigned pos,
unsigned ubIneq, unsigned lbIneq,
SmallVector<int64_t, 8> &expr,
unsigned &divisor) {

assert(pos <= cst.getNumIds() && "Invalid identifier position");
assert(ubIneq <= cst.getNumInequalities() &&
"Invalid upper bound inequality position");
assert(lbIneq <= cst.getNumInequalities() &&
"Invalid upper bound inequality position");

// Extract divisor from the lower bound.
divisor = cst.atIneq(lbIneq, pos);

// First, check if the constraints are opposite of each other except the
// constant term.
unsigned i = 0, e = 0;
for (i = 0, e = cst.getNumIds(); i < e; ++i)
if (cst.atIneq(ubIneq, i) != -cst.atIneq(lbIneq, i))
break;

if (i < e)
return failure();

// Then, check if the constant term is of the proper form.
// Due to the form of the upper/lower bound inequalities, the sum of their
// constants is `divisor - 1 - c`. From this, we can extract c:
int64_t constantSum = cst.atIneq(lbIneq, cst.getNumCols() - 1) +
cst.atIneq(ubIneq, cst.getNumCols() - 1);
int64_t c = divisor - 1 - constantSum;

// Check if `c` satisfies the condition `0 <= c <= divisor - 1`. This also
// implictly checks that `divisor` is positive.
if (!(c >= 0 && c <= divisor - 1))
return failure();

// The inequality pair can be used to extract the division.
// Set `expr` to the dividend of the division except the constant term, which
// is set below.
expr.resize(cst.getNumCols(), 0);
for (i = 0, e = cst.getNumIds(); i < e; ++i)
if (i != pos)
expr[i] = cst.atIneq(ubIneq, i);

// From the upper bound inequality's form, its constant term is equal to the
// constant term of `expr`, minus `c`. From this,
// constant term of `expr` = constant term of upper bound + `c`.
expr.back() = cst.atIneq(ubIneq, cst.getNumCols() - 1) + c;

return success();
}

/// Check if the pos^th identifier can be expressed as a floordiv of an affine
/// function of other identifiers (where the divisor is a positive constant).
/// `foundRepr` contains a boolean for each identifier indicating if the
/// explicit representation for that identifier has already been computed.
/// Returns the upper and lower bound inequalities using which the floordiv can
/// be computed. If the representation could be computed, `dividend` and
/// `denominator` are set. If the representation could not be computed,
/// `llvm::None` is returned.
static Optional<std::pair<unsigned, unsigned>>
computeSingleVarRepr(const FlatAffineConstraints &cst,
const SmallVector<bool, 8> &foundRepr, unsigned pos,
SmallVector<int64_t, 8> &dividend, unsigned &divisor) {
assert(pos < cst.getNumIds() && "invalid position");
assert(foundRepr.size() == cst.getNumIds() &&
"Size of foundRepr does not match total number of variables");

SmallVector<unsigned, 4> lbIndices, ubIndices;
cst.getLowerAndUpperBoundIndices(pos, &lbIndices, &ubIndices);

for (unsigned ubPos : ubIndices) {
for (unsigned lbPos : lbIndices) {
// Attempt to get divison representation from ubPos, lbPos.
if (failed(getDivRepr(cst, pos, ubPos, lbPos, dividend, divisor)))
continue;

// Check if the inequalities depend on a variable for which
// an explicit representation has not been found yet.
// Exit to avoid circular dependencies between divisions.
unsigned c, f;
for (c = 0, f = cst.getNumIds(); c < f; ++c) {
if (c == pos)
continue;
if (!foundRepr[c] && dividend[c] != 0)
break;
}

// Expression can't be constructed as it depends on a yet unknown
// identifier.
// TODO: Visit/compute the identifiers in an order so that this doesn't
// happen. More complex but much more efficient.
if (c < f)
continue;

return std::make_pair(ubPos, lbPos);
}
}

return llvm::None;
}

void FlatAffineConstraints::getLocalReprs(
std::vector<llvm::Optional<std::pair<unsigned, unsigned>>> &repr) const {
std::vector<SmallVector<int64_t, 8>> dividends(getNumLocalIds());
Expand Down Expand Up @@ -1378,8 +1239,9 @@ void FlatAffineConstraints::getLocalReprs(
changed = false;
for (unsigned i = 0, e = getNumLocalIds(); i < e; ++i) {
if (!foundRepr[i + divOffset]) {
if (auto res = computeSingleVarRepr(*this, foundRepr, divOffset + i,
dividends[i], denominators[i])) {
if (auto res = presburger_utils::computeSingleVarRepr(
*this, foundRepr, divOffset + i, dividends[i],
denominators[i])) {
foundRepr[i + divOffset] = true;
repr[i] = res;
changed = true;
Expand Down Expand Up @@ -1437,11 +1299,9 @@ unsigned FlatAffineConstraints::gaussianEliminateIds(unsigned posStart,
for (pivotCol = posStart; pivotCol < posLimit; ++pivotCol) {
// Find a row which has a non-zero coefficient in column 'j'.
unsigned pivotRow;
if (!findConstraintWithNonZeroAt(*this, pivotCol, /*isEq=*/true,
&pivotRow)) {
if (!findConstraintWithNonZeroAt(pivotCol, /*isEq=*/true, &pivotRow)) {
// No pivot row in equalities with non-zero at 'pivotCol'.
if (!findConstraintWithNonZeroAt(*this, pivotCol, /*isEq=*/false,
&pivotRow)) {
if (!findConstraintWithNonZeroAt(pivotCol, /*isEq=*/false, &pivotRow)) {
// If inequalities are also non-zero in 'pivotCol', it can be
// eliminated.
continue;
Expand Down Expand Up @@ -1596,60 +1456,6 @@ static bool detectAsMod(const FlatAffineConstraints &cst, unsigned pos,
return false;
}

/// Gather all lower and upper bounds of the identifier at `pos`, and
/// optionally any equalities on it. In addition, the bounds are to be
/// independent of identifiers in position range [`offset`, `offset` + `num`).
void FlatAffineConstraints::getLowerAndUpperBoundIndices(
unsigned pos, SmallVectorImpl<unsigned> *lbIndices,
SmallVectorImpl<unsigned> *ubIndices, SmallVectorImpl<unsigned> *eqIndices,
unsigned offset, unsigned num) const {
assert(pos < getNumIds() && "invalid position");
assert(offset + num < getNumCols() && "invalid range");

// Checks for a constraint that has a non-zero coeff for the identifiers in
// the position range [offset, offset + num) while ignoring `pos`.
auto containsConstraintDependentOnRange = [&](unsigned r, bool isEq) {
unsigned c, f;
auto cst = isEq ? getEquality(r) : getInequality(r);
for (c = offset, f = offset + num; c < f; ++c) {
if (c == pos)
continue;
if (cst[c] != 0)
break;
}
return c < f;
};

// Gather all lower bounds and upper bounds of the variable. Since the
// canonical form c_1*x_1 + c_2*x_2 + ... + c_0 >= 0, a constraint is a lower
// bound for x_i if c_i >= 1, and an upper bound if c_i <= -1.
for (unsigned r = 0, e = getNumInequalities(); r < e; r++) {
// The bounds are to be independent of [offset, offset + num) columns.
if (containsConstraintDependentOnRange(r, /*isEq=*/false))
continue;
if (atIneq(r, pos) >= 1) {
// Lower bound.
lbIndices->push_back(r);
} else if (atIneq(r, pos) <= -1) {
// Upper bound.
ubIndices->push_back(r);
}
}

// An equality is both a lower and upper bound. Record any equalities
// involving the pos^th identifier.
if (!eqIndices)
return;

for (unsigned r = 0, e = getNumEqualities(); r < e; r++) {
if (atEq(r, pos) == 0)
continue;
if (containsConstraintDependentOnRange(r, /*isEq=*/true))
continue;
eqIndices->push_back(r);
}
}

/// Check if the pos^th identifier can be expressed as a floordiv of an affine
/// function of other identifiers (where the divisor is a positive constant)
/// given the initial set of expressions in `exprs`. If it can be, the
Expand All @@ -1670,7 +1476,8 @@ static bool detectAsFloorDiv(const FlatAffineConstraints &cst, unsigned pos,

SmallVector<int64_t, 8> dividend;
unsigned divisor;
auto ulPair = computeSingleVarRepr(cst, foundRepr, pos, dividend, divisor);
auto ulPair = presburger_utils::computeSingleVarRepr(cst, foundRepr, pos,
dividend, divisor);

// No upper-lower bound pair found for this var.
if (!ulPair)
Expand Down Expand Up @@ -2109,7 +1916,7 @@ void FlatAffineConstraints::getSliceBounds(unsigned offset, unsigned num,

// Detect an identifier as an expression of other identifiers.
unsigned idx;
if (!findConstraintWithNonZeroAt(*this, pos, /*isEq=*/true, &idx)) {
if (!findConstraintWithNonZeroAt(pos, /*isEq=*/true, &idx)) {
continue;
}

Expand Down Expand Up @@ -3447,12 +3254,10 @@ void FlatAffineValueConstraints::getIneqAsAffineValueMap(
vmap.reset(AffineMap::get(numDims - 1, numSyms, boundExpr), operands);
}

/// Returns true if the pos^th column is all zero for both inequalities and
/// equalities..
static bool isColZero(const FlatAffineConstraints &cst, unsigned pos) {
bool FlatAffineConstraints::isColZero(unsigned pos) const {
unsigned rowPos;
return !findConstraintWithNonZeroAt(cst, pos, /*isEq=*/false, &rowPos) &&
!findConstraintWithNonZeroAt(cst, pos, /*isEq=*/true, &rowPos);
return !findConstraintWithNonZeroAt(pos, /*isEq=*/false, &rowPos) &&
!findConstraintWithNonZeroAt(pos, /*isEq=*/true, &rowPos);
}

IntegerSet FlatAffineConstraints::getAsIntegerSet(MLIRContext *context) const {
Expand All @@ -3471,7 +3276,7 @@ IntegerSet FlatAffineConstraints::getAsIntegerSet(MLIRContext *context) const {
SmallVector<unsigned> noLocalRepVars;
unsigned numDimsSymbols = getNumDimAndSymbolIds();
for (unsigned i = numDimsSymbols, e = getNumIds(); i < e; ++i) {
if (!memo[i] && !isColZero(*this, /*pos=*/i))
if (!memo[i] && !isColZero(/*pos=*/i))
noLocalRepVars.push_back(i - numDimsSymbols);
}
if (!noLocalRepVars.empty()) {
Expand Down
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