[Mlir-commits] [mlir] 5b2e611 - [MLIR][FlatAffineConstraints][NFC] Move some static functions to be available to Presburger/
llvmlistbot at llvm.org
llvmlistbot at llvm.org
Sat Dec 25 09:17:03 PST 2021
Author: Groverkss
Date: 2021-12-25T22:36:23+05:30
New Revision: 5b2e611b734cb64c5600c1c8d0a6b4881a05f874
URL: https://github.com/llvm/llvm-project/commit/5b2e611b734cb64c5600c1c8d0a6b4881a05f874
DIFF: https://github.com/llvm/llvm-project/commit/5b2e611b734cb64c5600c1c8d0a6b4881a05f874.diff
LOG: [MLIR][FlatAffineConstraints][NFC] Move some static functions to be available 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
Added:
mlir/include/mlir/Analysis/Presburger/Utils.h
mlir/lib/Analysis/Presburger/Utils.cpp
Modified:
mlir/include/mlir/Analysis/AffineStructures.h
mlir/include/mlir/Analysis/Presburger/IntegerPolyhedron.h
mlir/lib/Analysis/AffineStructures.cpp
mlir/lib/Analysis/Presburger/CMakeLists.txt
mlir/lib/Analysis/Presburger/IntegerPolyhedron.cpp
Removed:
################################################################################
diff --git a/mlir/include/mlir/Analysis/AffineStructures.h b/mlir/include/mlir/Analysis/AffineStructures.h
index 9e7ffb125f7ec..ea20edd1036f1 100644
--- a/mlir/include/mlir/Analysis/AffineStructures.h
+++ b/mlir/include/mlir/Analysis/AffineStructures.h
@@ -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);
@@ -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
diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerPolyhedron.h b/mlir/include/mlir/Analysis/Presburger/IntegerPolyhedron.h
index 933f20e441225..c7eae0cd29ee2 100644
--- a/mlir/include/mlir/Analysis/Presburger/IntegerPolyhedron.h
+++ b/mlir/include/mlir/Analysis/Presburger/IntegerPolyhedron.h
@@ -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;
diff --git a/mlir/include/mlir/Analysis/Presburger/Utils.h b/mlir/include/mlir/Analysis/Presburger/Utils.h
new file mode 100644
index 0000000000000..0b9c2c707d3e3
--- /dev/null
+++ b/mlir/include/mlir/Analysis/Presburger/Utils.h
@@ -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> ÷nd,
+ unsigned &divisor);
+
+} // namespace presburger_utils
+} // namespace mlir
+
+#endif // MLIR_ANALYSIS_PRESBURGER_UTILS_H
diff --git a/mlir/lib/Analysis/AffineStructures.cpp b/mlir/lib/Analysis/AffineStructures.cpp
index f4d857479cdee..520262d6fddc7 100644
--- a/mlir/lib/Analysis/AffineStructures.cpp
+++ b/mlir/lib/Analysis/AffineStructures.cpp
@@ -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"
@@ -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;
@@ -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> ÷nd, 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());
@@ -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;
@@ -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;
@@ -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
@@ -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)
@@ -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;
}
@@ -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 {
@@ -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()) {
diff --git a/mlir/lib/Analysis/Presburger/CMakeLists.txt b/mlir/lib/Analysis/Presburger/CMakeLists.txt
index dd8c8d96d872c..d52d4ccdb1c2f 100644
--- a/mlir/lib/Analysis/Presburger/CMakeLists.txt
+++ b/mlir/lib/Analysis/Presburger/CMakeLists.txt
@@ -2,10 +2,12 @@ add_mlir_library(MLIRPresburger
IntegerPolyhedron.cpp
Matrix.cpp
Simplex.cpp
+ Utils.cpp
DEPENDS
MLIRBuiltinLocationAttributesIncGen
LINK_LIBS PUBLIC
MLIRIR
+ MLIRSupport
)
diff --git a/mlir/lib/Analysis/Presburger/IntegerPolyhedron.cpp b/mlir/lib/Analysis/Presburger/IntegerPolyhedron.cpp
index 3c4f512bf4fbe..958f52e2625eb 100644
--- a/mlir/lib/Analysis/Presburger/IntegerPolyhedron.cpp
+++ b/mlir/lib/Analysis/Presburger/IntegerPolyhedron.cpp
@@ -217,3 +217,57 @@ void IntegerPolyhedron::clearConstraints() {
equalities.resizeVertically(0);
inequalities.resizeVertically(0);
}
+
+/// 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 IntegerPolyhedron::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);
+ }
+}
diff --git a/mlir/lib/Analysis/Presburger/Utils.cpp b/mlir/lib/Analysis/Presburger/Utils.cpp
new file mode 100644
index 0000000000000..8fb9390a440ee
--- /dev/null
+++ b/mlir/lib/Analysis/Presburger/Utils.cpp
@@ -0,0 +1,155 @@
+//===- Utils.cpp - General utilities for Presburger library ---------------===//
+//
+// 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.
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Analysis/Presburger/Utils.h"
+#include "mlir/Analysis/Presburger/IntegerPolyhedron.h"
+#include "mlir/Support/LogicalResult.h"
+
+using namespace mlir;
+
+/// 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 IntegerPolyhedron &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.
+Optional<std::pair<unsigned, unsigned>> presburger_utils::computeSingleVarRepr(
+ const IntegerPolyhedron &cst, ArrayRef<bool> foundRepr, unsigned pos,
+ SmallVector<int64_t, 8> ÷nd, 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;
+}
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