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llvm-project/mlir/lib/Analysis/FlatLinearValueConstraints.cpp

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//===- FlatLinearValueConstraints.cpp - Linear Constraint -----------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "mlir/Analysis//FlatLinearValueConstraints.h"
#include "mlir/Analysis/Presburger/LinearTransform.h"
#include "mlir/Analysis/Presburger/PresburgerSpace.h"
#include "mlir/Analysis/Presburger/Simplex.h"
#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/IR/AffineExprVisitor.h"
#include "mlir/IR/Builders.h"
#include "mlir/IR/IntegerSet.h"
#include "mlir/Support/LLVM.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/InterleavedRange.h"
#include "llvm/Support/raw_ostream.h"
#include <optional>
#define DEBUG_TYPE "flat-value-constraints"
using namespace mlir;
using namespace presburger;
//===----------------------------------------------------------------------===//
// AffineExprFlattener
//===----------------------------------------------------------------------===//
namespace {
// See comments for SimpleAffineExprFlattener.
// An AffineExprFlattenerWithLocalVars extends a SimpleAffineExprFlattener by
// recording constraint information associated with mod's, floordiv's, and
// ceildiv's in FlatLinearConstraints 'localVarCst'.
struct AffineExprFlattener : public SimpleAffineExprFlattener {
using SimpleAffineExprFlattener::SimpleAffineExprFlattener;
// Constraints connecting newly introduced local variables (for mod's and
// div's) to existing (dimensional and symbolic) ones. These are always
// inequalities.
IntegerPolyhedron localVarCst;
AffineExprFlattener(unsigned nDims, unsigned nSymbols)
: SimpleAffineExprFlattener(nDims, nSymbols),
localVarCst(PresburgerSpace::getSetSpace(nDims, nSymbols)) {};
private:
// Add a local variable (needed to flatten a mod, floordiv, ceildiv expr).
// The local variable added is always a floordiv of a pure add/mul affine
// function of other variables, coefficients of which are specified in
// `dividend' and with respect to the positive constant `divisor'. localExpr
// is the simplified tree expression (AffineExpr) corresponding to the
// quantifier.
void addLocalFloorDivId(ArrayRef<int64_t> dividend, int64_t divisor,
AffineExpr localExpr) override {
SimpleAffineExprFlattener::addLocalFloorDivId(dividend, divisor, localExpr);
// Update localVarCst.
localVarCst.addLocalFloorDiv(dividend, divisor);
}
LogicalResult addLocalIdSemiAffine(ArrayRef<int64_t> lhs,
ArrayRef<int64_t> rhs,
AffineExpr localExpr) override {
// AffineExprFlattener does not support semi-affine expressions.
return failure();
}
};
// A SemiAffineExprFlattener is an AffineExprFlattenerWithLocalVars that adds
// conservative bounds for semi-affine expressions (given assumptions hold). If
// the assumptions required to add the semi-affine bounds are found not to hold
// the final constraints set will be empty/inconsistent. If the assumptions are
// never contradicted the final bounds still only will be correct if the
// assumptions hold.
struct SemiAffineExprFlattener : public AffineExprFlattener {
using AffineExprFlattener::AffineExprFlattener;
LogicalResult addLocalIdSemiAffine(ArrayRef<int64_t> lhs,
ArrayRef<int64_t> rhs,
AffineExpr localExpr) override {
auto result =
SimpleAffineExprFlattener::addLocalIdSemiAffine(lhs, rhs, localExpr);
assert(succeeded(result) &&
"unexpected failure in SimpleAffineExprFlattener");
(void)result;
if (localExpr.getKind() == AffineExprKind::Mod) {
// Given two numbers a and b, division is defined as:
//
// a = bq + r
// 0 <= r < |b| (where |x| is the absolute value of x)
//
// q = a floordiv b
// r = a mod b
// Add a new local variable (r) to represent the mod.
unsigned rPos = localVarCst.appendVar(VarKind::Local);
// r >= 0 (Can ALWAYS be added)
localVarCst.addBound(BoundType::LB, rPos, 0);
// r < b (Can be added if b > 0, which we assume here)
ArrayRef<int64_t> b = rhs;
SmallVector<int64_t> bSubR(b);
bSubR.insert(bSubR.begin() + rPos, -1);
// Note: bSubR = b - r
// So this adds the bound b - r >= 1 (equivalent to r < b)
localVarCst.addBound(BoundType::LB, bSubR, 1);
// Note: The assumption of b > 0 is based on the affine expression docs,
// which state "RHS of mod is always a constant or a symbolic expression
// with a positive value." (see AffineExprKind in AffineExpr.h). If this
// assumption does not hold constraints (added above) are a contradiction.
return success();
}
// TODO: Support other semi-affine expressions.
return failure();
}
};
} // namespace
// Flattens the expressions in map. Returns failure if 'expr' was unable to be
// flattened. For example two specific cases:
// 1. an unhandled semi-affine expressions is found.
// 2. has poison expression (i.e., division by zero).
static LogicalResult
getFlattenedAffineExprs(ArrayRef<AffineExpr> exprs, unsigned numDims,
unsigned numSymbols,
std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
FlatLinearConstraints *localVarCst,
bool addConservativeSemiAffineBounds = false) {
if (exprs.empty()) {
if (localVarCst)
*localVarCst = FlatLinearConstraints(numDims, numSymbols);
return success();
}
auto flattenExprs = [&](AffineExprFlattener &flattener) -> LogicalResult {
// Use the same flattener to simplify each expression successively. This way
// local variables / expressions are shared.
for (auto expr : exprs) {
auto flattenResult = flattener.walkPostOrder(expr);
if (failed(flattenResult))
return failure();
}
assert(flattener.operandExprStack.size() == exprs.size());
flattenedExprs->clear();
flattenedExprs->assign(flattener.operandExprStack.begin(),
flattener.operandExprStack.end());
if (localVarCst)
localVarCst->clearAndCopyFrom(flattener.localVarCst);
return success();
};
if (addConservativeSemiAffineBounds) {
SemiAffineExprFlattener flattener(numDims, numSymbols);
return flattenExprs(flattener);
}
AffineExprFlattener flattener(numDims, numSymbols);
return flattenExprs(flattener);
}
// Flattens 'expr' into 'flattenedExpr'. Returns failure if 'expr' was unable to
// be flattened (an unhandled semi-affine was found).
LogicalResult mlir::getFlattenedAffineExpr(
AffineExpr expr, unsigned numDims, unsigned numSymbols,
SmallVectorImpl<int64_t> *flattenedExpr, FlatLinearConstraints *localVarCst,
bool addConservativeSemiAffineBounds) {
std::vector<SmallVector<int64_t, 8>> flattenedExprs;
LogicalResult ret =
::getFlattenedAffineExprs({expr}, numDims, numSymbols, &flattenedExprs,
localVarCst, addConservativeSemiAffineBounds);
*flattenedExpr = flattenedExprs[0];
return ret;
}
/// Flattens the expressions in map. Returns failure if 'expr' was unable to be
/// flattened (i.e., an unhandled semi-affine was found).
LogicalResult mlir::getFlattenedAffineExprs(
AffineMap map, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
FlatLinearConstraints *localVarCst, bool addConservativeSemiAffineBounds) {
if (map.getNumResults() == 0) {
if (localVarCst)
*localVarCst =
FlatLinearConstraints(map.getNumDims(), map.getNumSymbols());
return success();
}
return ::getFlattenedAffineExprs(
map.getResults(), map.getNumDims(), map.getNumSymbols(), flattenedExprs,
localVarCst, addConservativeSemiAffineBounds);
}
LogicalResult mlir::getFlattenedAffineExprs(
IntegerSet set, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
FlatLinearConstraints *localVarCst) {
if (set.getNumConstraints() == 0) {
if (localVarCst)
*localVarCst =
FlatLinearConstraints(set.getNumDims(), set.getNumSymbols());
return success();
}
return ::getFlattenedAffineExprs(set.getConstraints(), set.getNumDims(),
set.getNumSymbols(), flattenedExprs,
localVarCst);
}
//===----------------------------------------------------------------------===//
// FlatLinearConstraints
//===----------------------------------------------------------------------===//
// Similar to `composeMap` except that no Values need be associated with the
// constraint system nor are they looked at -- the dimensions and symbols of
// `other` are expected to correspond 1:1 to `this` system.
LogicalResult FlatLinearConstraints::composeMatchingMap(AffineMap other) {
assert(other.getNumDims() == getNumDimVars() && "dim mismatch");
assert(other.getNumSymbols() == getNumSymbolVars() && "symbol mismatch");
std::vector<SmallVector<int64_t, 8>> flatExprs;
if (failed(flattenAlignedMapAndMergeLocals(other, &flatExprs)))
return failure();
assert(flatExprs.size() == other.getNumResults());
// Add dimensions corresponding to the map's results.
insertDimVar(/*pos=*/0, /*num=*/other.getNumResults());
// We add one equality for each result connecting the result dim of the map to
// the other variables.
// E.g.: if the expression is 16*i0 + i1, and this is the r^th
// iteration/result of the value map, we are adding the equality:
// d_r - 16*i0 - i1 = 0. Similarly, when flattening (i0 + 1, i0 + 8*i2), we
// add two equalities: d_0 - i0 - 1 == 0, d1 - i0 - 8*i2 == 0.
for (unsigned r = 0, e = flatExprs.size(); r < e; r++) {
const auto &flatExpr = flatExprs[r];
assert(flatExpr.size() >= other.getNumInputs() + 1);
SmallVector<int64_t, 8> eqToAdd(getNumCols(), 0);
// Set the coefficient for this result to one.
eqToAdd[r] = 1;
// Dims and symbols.
for (unsigned i = 0, f = other.getNumInputs(); i < f; i++) {
// Negate `eq[r]` since the newly added dimension will be set to this one.
eqToAdd[e + i] = -flatExpr[i];
}
// Local columns of `eq` are at the beginning.
unsigned j = getNumDimVars() + getNumSymbolVars();
unsigned end = flatExpr.size() - 1;
for (unsigned i = other.getNumInputs(); i < end; i++, j++) {
eqToAdd[j] = -flatExpr[i];
}
// Constant term.
eqToAdd[getNumCols() - 1] = -flatExpr[flatExpr.size() - 1];
// Add the equality connecting the result of the map to this constraint set.
addEquality(eqToAdd);
}
return success();
}
// Determine whether the variable at 'pos' (say var_r) can be expressed as
// modulo of another known variable (say var_n) w.r.t a constant. For example,
// if the following constraints hold true:
// ```
// 0 <= var_r <= divisor - 1
// var_n - (divisor * q_expr) = var_r
// ```
// where `var_n` is a known variable (called dividend), and `q_expr` is an
// `AffineExpr` (called the quotient expression), `var_r` can be written as:
//
// `var_r = var_n mod divisor`.
//
// Additionally, in a special case of the above constaints where `q_expr` is an
// variable itself that is not yet known (say `var_q`), it can be written as a
// floordiv in the following way:
//
// `var_q = var_n floordiv divisor`.
//
// First 'num' dimensional variables starting at 'offset' are
// derived/to-be-derived in terms of the remaining variables. The remaining
// variables are assigned trivial affine expressions in `memo`. For example,
// memo is initilized as follows for a `cst` with 5 dims, when offset=2, num=2:
// memo ==> d0 d1 . . d2 ...
// cst ==> c0 c1 c2 c3 c4 ...
//
// Returns true if the above mod or floordiv are detected, updating 'memo' with
// these new expressions. Returns false otherwise.
static bool detectAsMod(const FlatLinearConstraints &cst, unsigned pos,
unsigned offset, unsigned num, int64_t lbConst,
int64_t ubConst, MLIRContext *context,
SmallVectorImpl<AffineExpr> &memo) {
assert(pos < cst.getNumVars() && "invalid position");
// Check if a divisor satisfying the condition `0 <= var_r <= divisor - 1` can
// be determined.
if (lbConst != 0 || ubConst < 1)
return false;
int64_t divisor = ubConst + 1;
// Check for the aforementioned conditions in each equality.
for (unsigned curEquality = 0, numEqualities = cst.getNumEqualities();
curEquality < numEqualities; curEquality++) {
int64_t coefficientAtPos = cst.atEq64(curEquality, pos);
// If current equality does not involve `var_r`, continue to the next
// equality.
if (coefficientAtPos == 0)
continue;
// Constant term should be 0 in this equality.
if (cst.atEq64(curEquality, cst.getNumCols() - 1) != 0)
continue;
// Traverse through the equality and construct the dividend expression
// `dividendExpr`, to contain all the variables which are known and are
// not divisible by `(coefficientAtPos * divisor)`. Hope here is that the
// `dividendExpr` gets simplified into a single variable `var_n` discussed
// above.
auto dividendExpr = getAffineConstantExpr(0, context);
// Track the terms that go into quotient expression, later used to detect
// additional floordiv.
unsigned quotientCount = 0;
int quotientPosition = -1;
int quotientSign = 1;
// Consider each term in the current equality.
unsigned curVar, e;
for (curVar = 0, e = cst.getNumDimAndSymbolVars(); curVar < e; ++curVar) {
// Ignore var_r.
if (curVar == pos)
continue;
int64_t coefficientOfCurVar = cst.atEq64(curEquality, curVar);
// Ignore vars that do not contribute to the current equality.
if (coefficientOfCurVar == 0)
continue;
// Check if the current var goes into the quotient expression.
if (coefficientOfCurVar % (divisor * coefficientAtPos) == 0) {
quotientCount++;
quotientPosition = curVar;
quotientSign = (coefficientOfCurVar * coefficientAtPos) > 0 ? 1 : -1;
continue;
}
// Variables that are part of dividendExpr should be known.
if (!memo[curVar])
break;
// Append the current variable to the dividend expression.
dividendExpr = dividendExpr + memo[curVar] * coefficientOfCurVar;
}
// Can't construct expression as it depends on a yet uncomputed var.
if (curVar < e)
continue;
// Express `var_r` in terms of the other vars collected so far.
if (coefficientAtPos > 0)
dividendExpr = (-dividendExpr).floorDiv(coefficientAtPos);
else
dividendExpr = dividendExpr.floorDiv(-coefficientAtPos);
// Simplify the expression.
dividendExpr = simplifyAffineExpr(dividendExpr, cst.getNumDimVars(),
cst.getNumSymbolVars());
// Only if the final dividend expression is just a single var (which we call
// `var_n`), we can proceed.
// TODO: Handle AffineSymbolExpr as well. There is no reason to restrict it
// to dims themselves.
auto dimExpr = dyn_cast<AffineDimExpr>(dividendExpr);
if (!dimExpr)
continue;
// Express `var_r` as `var_n % divisor` and store the expression in `memo`.
if (quotientCount >= 1) {
// Find the column corresponding to `dimExpr`. `num` columns starting at
// `offset` correspond to previously unknown variables. The column
// corresponding to the trivially known `dimExpr` can be on either side
// of these.
unsigned dimExprPos = dimExpr.getPosition();
unsigned dimExprCol = dimExprPos < offset ? dimExprPos : dimExprPos + num;
auto ub = cst.getConstantBound64(BoundType::UB, dimExprCol);
// If `var_n` has an upperbound that is less than the divisor, mod can be
// eliminated altogether.
if (ub && *ub < divisor)
memo[pos] = dimExpr;
else
memo[pos] = dimExpr % divisor;
// If a unique quotient `var_q` was seen, it can be expressed as
// `var_n floordiv divisor`.
if (quotientCount == 1 && !memo[quotientPosition])
memo[quotientPosition] = dimExpr.floorDiv(divisor) * quotientSign;
return true;
}
}
return false;
}
/// Check if the pos^th variable can be expressed as a floordiv of an affine
/// function of other variables (where the divisor is a positive constant)
/// given the initial set of expressions in `exprs`. If it can be, the
/// corresponding position in `exprs` is set as the detected affine expr. For
/// eg: 4q <= i + j <= 4q + 3 <=> q = (i + j) floordiv 4. An equality can
/// also yield a floordiv: eg. 4q = i + j <=> q = (i + j) floordiv 4. 32q + 28
/// <= i <= 32q + 31 => q = i floordiv 32.
static bool detectAsFloorDiv(const FlatLinearConstraints &cst, unsigned pos,
MLIRContext *context,
SmallVectorImpl<AffineExpr> &exprs) {
assert(pos < cst.getNumVars() && "invalid position");
// Get upper-lower bound pair for this variable.
SmallVector<bool, 8> foundRepr(cst.getNumVars(), false);
for (unsigned i = 0, e = cst.getNumVars(); i < e; ++i)
if (exprs[i])
foundRepr[i] = true;
SmallVector<int64_t, 8> dividend(cst.getNumCols());
unsigned divisor;
auto ulPair = computeSingleVarRepr(cst, foundRepr, pos, dividend, divisor);
// No upper-lower bound pair found for this var.
if (ulPair.kind == ReprKind::None || ulPair.kind == ReprKind::Equality)
return false;
// Construct the dividend expression.
auto dividendExpr = getAffineConstantExpr(dividend.back(), context);
for (unsigned c = 0, f = cst.getNumVars(); c < f; c++)
if (dividend[c] != 0)
dividendExpr = dividendExpr + dividend[c] * exprs[c];
// Successfully detected the floordiv.
exprs[pos] = dividendExpr.floorDiv(divisor);
return true;
}
void FlatLinearConstraints::dumpRow(ArrayRef<int64_t> row,
bool fixedColWidth) const {
unsigned ncols = getNumCols();
bool firstNonZero = true;
for (unsigned j = 0; j < ncols; j++) {
if (j == ncols - 1) {
// Constant.
if (row[j] == 0 && !firstNonZero) {
if (fixedColWidth)
llvm::errs().indent(7);
} else {
llvm::errs() << ((row[j] >= 0) ? "+ " : "") << row[j] << ' ';
}
} else {
std::string var = std::string("c_") + std::to_string(j);
if (row[j] == 1)
llvm::errs() << "+ " << var << ' ';
else if (row[j] == -1)
llvm::errs() << "- " << var << ' ';
else if (row[j] >= 2)
llvm::errs() << "+ " << row[j] << '*' << var << ' ';
else if (row[j] <= -2)
llvm::errs() << "- " << -row[j] << '*' << var << ' ';
else if (fixedColWidth)
// Zero coeff.
llvm::errs().indent(7);
if (row[j] != 0)
firstNonZero = false;
}
}
}
void FlatLinearConstraints::dumpPretty() const {
assert(hasConsistentState());
llvm::errs() << "Constraints (" << getNumDimVars() << " dims, "
<< getNumSymbolVars() << " symbols, " << getNumLocalVars()
<< " locals), (" << getNumConstraints() << " constraints)\n";
auto dumpConstraint = [&](unsigned rowPos, bool isEq) {
// Is it the first non-zero entry?
SmallVector<int64_t> row =
isEq ? getEquality64(rowPos) : getInequality64(rowPos);
dumpRow(row);
llvm::errs() << (isEq ? "=" : ">=") << " 0\n";
};
for (unsigned i = 0, e = getNumInequalities(); i < e; i++)
dumpConstraint(i, /*isEq=*/false);
for (unsigned i = 0, e = getNumEqualities(); i < e; i++)
dumpConstraint(i, /*isEq=*/true);
llvm::errs() << '\n';
}
std::pair<AffineMap, AffineMap> FlatLinearConstraints::getLowerAndUpperBound(
unsigned pos, unsigned offset, unsigned num, unsigned symStartPos,
ArrayRef<AffineExpr> localExprs, MLIRContext *context,
bool closedUB) const {
assert(pos + offset < getNumDimVars() && "invalid dim start pos");
assert(symStartPos >= (pos + offset) && "invalid sym start pos");
assert(getNumLocalVars() == localExprs.size() &&
"incorrect local exprs count");
SmallVector<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};
}
/// Express the pos^th identifier of `cst` as an affine expression in
/// terms of other identifiers, if they are available in `exprs`, using the
/// equality at position `idx` in `cs`t. Populates `exprs` with such an
/// expression if possible, and return true. Returns false otherwise.
static bool detectAsExpr(const FlatLinearConstraints &cst, unsigned pos,
unsigned idx, MLIRContext *context,
SmallVectorImpl<AffineExpr> &exprs) {
// Initialize with a `0` expression.
auto expr = getAffineConstantExpr(0, context);
// Traverse `idx`th equality and construct the possible affine expression in
// terms of known identifiers.
unsigned j, e;
for (j = 0, e = cst.getNumVars(); j < e; ++j) {
if (j == pos)
continue;
int64_t c = cst.atEq64(idx, j);
if (c == 0)
continue;
// If any of the involved IDs hasn't been found yet, we can't proceed.
if (!exprs[j])
break;
expr = expr + exprs[j] * c;
}
if (j < e)
// Can't construct expression as it depends on a yet uncomputed
// identifier.
return false;
// Add constant term to AffineExpr.
expr = expr + cst.atEq64(idx, cst.getNumVars());
int64_t vPos = cst.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.
exprs[pos] = expr;
return true;
}
/// Compute a representation of `num` identifiers starting at `offset` in `cst`
/// as affine expressions involving other known identifiers. Each identifier's
/// expression (in terms of known identifiers) is populated into `memo`.
static void computeUnknownVars(const FlatLinearConstraints &cst,
MLIRContext *context, unsigned offset,
unsigned num,
SmallVectorImpl<AffineExpr> &memo) {
// Initialize dimensional and symbolic variables.
for (unsigned i = 0, e = cst.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 = cst.getNumDimVars(), e = cst.getNumDimAndSymbolVars();
i < e; i++)
memo[i] = getAffineSymbolExpr(i - cst.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, f = cst.getNumVars(); pos < f; pos++) {
if (memo[pos])
continue;
auto lbConst = cst.getConstantBound64(BoundType::LB, pos);
auto ubConst = cst.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(cst, 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(cst, pos, context, memo)) {
changed = true;
continue;
}
// Detect a variable as an expression of other variables.
std::optional<unsigned> idx;
if (!(idx = cst.findConstraintWithNonZeroAt(pos, /*isEq=*/true)))
continue;
if (detectAsExpr(cst, pos, *idx, context, memo)) {
changed = true;
continue;
}
}
// 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);
}
/// 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 variables at positions ["
<< offset << ", " << offset + num << ")\n");
LLVM_DEBUG(dumpPretty());
// Record computed/detected variables.
SmallVector<AffineExpr, 8> memo(getNumVars());
computeUnknownVars(*this, context, offset, num, memo);
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() << "Slice bounds:\n");
LLVM_DEBUG(llvm::dbgs() << "lb map for pos = " << Twine(pos + offset)
<< ", expr: " << lbMap << '\n');
LLVM_DEBUG(llvm::dbgs() << "ub map for pos = " << Twine(pos + offset)
<< ", expr: " << ubMap << '\n');
}
}
LogicalResult FlatLinearConstraints::flattenAlignedMapAndMergeLocals(
AffineMap map, std::vector<SmallVector<int64_t, 8>> *flattenedExprs,
bool addConservativeSemiAffineBounds) {
FlatLinearConstraints localCst;
if (failed(getFlattenedAffineExprs(map, flattenedExprs, &localCst,
addConservativeSemiAffineBounds))) {
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,
AddConservativeSemiAffineBounds addSemiAffineBounds) {
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,
addSemiAffineBounds == AddConservativeSemiAffineBounds::Yes)))
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,
AddConservativeSemiAffineBounds addSemiAffineBounds) {
return addBound(type, pos, boundMap,
/*isClosedBound=*/type != BoundType::UB, addSemiAffineBounds);
}
/// 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; }));
}
/// Given an equality or inequality (`isEquality` used to disambiguate) of `cst`
/// at `idx`, traverse and sum up `AffineExpr`s of all known ids other than the
/// `pos`th. Known `AffineExpr`s are given in `exprs` (unknowns are null). If
/// the equality/inequality contains any unknown id, return None. Otherwise
/// return sum as `AffineExpr`.
static std::optional<AffineExpr> getAsExpr(const FlatLinearConstraints &cst,
unsigned pos, MLIRContext *context,
ArrayRef<AffineExpr> exprs,
unsigned idx, bool isEquality) {
// Initialize with a `0` expression.
auto expr = getAffineConstantExpr(0, context);
SmallVector<int64_t, 8> row =
isEquality ? cst.getEquality64(idx) : cst.getInequality64(idx);
// Traverse `idx`th equality and construct the possible affine expression in
// terms of known identifiers.
unsigned j, e;
for (j = 0, e = cst.getNumVars(); j < e; ++j) {
if (j == pos)
continue;
int64_t c = row[j];
if (c == 0)
continue;
// If any of the involved IDs hasn't been found yet, we can't proceed.
if (!exprs[j])
break;
expr = expr + exprs[j] * c;
}
if (j < e)
// Can't construct expression as it depends on a yet uncomputed
// identifier.
return std::nullopt;
// Add constant term to AffineExpr.
expr = expr + row[cst.getNumVars()];
return expr;
}
std::optional<int64_t> FlatLinearConstraints::getConstantBoundOnDimSize(
MLIRContext *context, unsigned pos, AffineMap *lb, AffineMap *ub,
unsigned *minLbPos, unsigned *minUbPos) const {
assert(pos < getNumDimVars() && "Invalid identifier position");
auto freeOfUnknownLocalVars = [&](ArrayRef<int64_t> cst,
ArrayRef<AffineExpr> whiteListCols) {
for (int i = getNumDimAndSymbolVars(), e = cst.size() - 1; i < e; ++i) {
if (whiteListCols[i] && whiteListCols[i].isSymbolicOrConstant())
continue;
if (cst[i] != 0)
return false;
}
return true;
};
// Detect the necesary local variables first.
SmallVector<AffineExpr, 8> memo(getNumVars(), AffineExpr());
(void)computeLocalVars(memo, context);
// Find an equality for 'pos'^th identifier that equates it to some function
// of the symbolic identifiers (+ constant).
int eqPos = findEqualityToConstant(pos, /*symbolic=*/true);
// If the equality involves a local var that can not be expressed as a
// symbolic or constant affine expression, we bail out.
if (eqPos != -1 && freeOfUnknownLocalVars(getEquality64(eqPos), memo)) {
// This identifier can only take a single value.
if (lb && detectAsExpr(*this, pos, eqPos, context, memo)) {
AffineExpr equalityExpr =
simplifyAffineExpr(memo[pos], 0, getNumSymbolVars());
*lb = AffineMap::get(/*dimCount=*/0, getNumSymbolVars(), equalityExpr);
if (ub)
*ub = *lb;
}
if (minLbPos)
*minLbPos = eqPos;
if (minUbPos)
*minUbPos = eqPos;
return 1;
}
// Positions of constraints that are lower/upper bounds on the variable.
SmallVector<unsigned, 4> lbIndices, ubIndices;
// Note inequalities that give lower and upper bounds.
getLowerAndUpperBoundIndices(pos, &lbIndices, &ubIndices,
/*eqIndices=*/nullptr, /*offset=*/0,
/*num=*/getNumDimVars());
std::optional<int64_t> minDiff = std::nullopt;
unsigned minLbPosition = 0, minUbPosition = 0;
AffineExpr minLbExpr, minUbExpr;
// Traverse each lower bound and upper bound pair, to compute the difference
// between them.
for (unsigned ubPos : ubIndices) {
// Construct sum of all ids other than `pos`th in the given upper bound row.
std::optional<AffineExpr> maybeUbExpr =
getAsExpr(*this, pos, context, memo, ubPos, /*isEquality=*/false);
if (!maybeUbExpr.has_value() || !(*maybeUbExpr).isSymbolicOrConstant())
continue;
// Canonical form of an inequality that constrains the upper bound on
// an id `x_i` is of the form:
// `c_1*x_1 + c_2*x_2 + ... + c_0 >= 0`, where `c_i` <= -1.
// Therefore the upper bound on `x_i` will be
// `(
// sum(c_j*x_j) where j != i
// +
// c_0
// )
// /
// -(c_i)`. Divison here is a floorDiv.
AffineExpr ubExpr = maybeUbExpr->floorDiv(-atIneq64(ubPos, pos));
assert(-atIneq64(ubPos, pos) > 0 && "invalid upper bound index");
// Go over each lower bound.
for (unsigned lbPos : lbIndices) {
// Construct sum of all ids other than `pos`th in the given lower bound
// row.
std::optional<AffineExpr> maybeLbExpr =
getAsExpr(*this, pos, context, memo, lbPos, /*isEquality=*/false);
if (!maybeLbExpr.has_value() || !(*maybeLbExpr).isSymbolicOrConstant())
continue;
// Canonical form of an inequality that is constraining the lower bound
// on an id `x_i is of the form:
// `c_1*x_1 + c_2*x_2 + ... + c_0 >= 0`, where `c_i` >= 1.
// Therefore upperBound on `x_i` will be
// `-(
// sum(c_j*x_j) where j != i
// +
// c_0
// )
// /
// c_i`. Divison here is a ceilDiv.
int64_t divisor = atIneq64(lbPos, pos);
// We convert the `ceilDiv` for floordiv with the formula:
// `expr ceildiv divisor is (expr + divisor - 1) floordiv divisor`,
// since uniformly keeping divisons as `floorDiv` helps their
// simplification.
AffineExpr lbExpr = (-(*maybeLbExpr) + divisor - 1).floorDiv(divisor);
assert(atIneq64(lbPos, pos) > 0 && "invalid lower bound index");
AffineExpr difference =
simplifyAffineExpr(ubExpr - lbExpr + 1, 0, getNumSymbolVars());
// If the difference is not constant, ignore the lower bound - upper bound
// pair.
auto constantDiff = dyn_cast<AffineConstantExpr>(difference);
if (!constantDiff)
continue;
int64_t diffValue = constantDiff.getValue();
// This bound is non-negative by definition.
diffValue = std::max<int64_t>(diffValue, 0);
if (!minDiff || diffValue < *minDiff) {
minDiff = diffValue;
minLbPosition = lbPos;
minUbPosition = ubPos;
minLbExpr = lbExpr;
minUbExpr = ubExpr;
}
}
}
// Populate outputs where available and needed.
if (lb && minDiff) {
*lb = AffineMap::get(/*dimCount=*/0, getNumSymbolVars(), minLbExpr);
}
if (ub)
*ub = AffineMap::get(/*dimCount=*/0, getNumSymbolVars(), minUbExpr);
if (minLbPos)
*minLbPos = minLbPosition;
if (minUbPos)
*minUbPos = minUbPosition;
return minDiff;
}
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::interleaved(noLocalRepVars)
<< " 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) {
assert((operands.empty() || set.getNumInputs() == operands.size()) &&
"operand count mismatch");
// Set the values for the non-local variables.
for (unsigned i = 0, e = operands.size(); i < e; ++i)
setValue(i, operands[i]);
// 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);
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, e = vals.size(); i < e; ++i)
if (vals[i])
setValue(absolutePos + i, vals[i]);
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) {
if (a.getNumDomainVars() != b.getNumDomainVars() ||
a.getNumRangeVars() != b.getNumRangeVars() ||
a.getNumSymbolVars() != b.getNumSymbolVars())
return false;
SmallVector<std::optional<Value>> aMaybeValues = a.getMaybeValues(),
bMaybeValues = b.getMaybeValues();
return std::equal(aMaybeValues.begin(), aMaybeValues.end(),
bMaybeValues.begin(), bMaybeValues.end());
}
/// 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;
SmallVector<std::optional<Value>, 8> maybeValuesAll = cst.getMaybeValues();
ArrayRef<std::optional<Value>> maybeValues = {maybeValuesAll.data() + start,
maybeValuesAll.data() + end};
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");
}
void FlatLinearValueConstraints::removeVarRange(VarKind kind, unsigned varStart,
unsigned varLimit) {
IntegerPolyhedron::removeVarRange(kind, varStart, varLimit);
}
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 = 0, e = getNumVarKind(VarKind::SetDim); i < e; ++i) {
Identifier id = space.getId(VarKind::SetDim, i);
dims.push_back(id.hasValue() ? Value(id.getValue<Value>()) : Value());
}
for (unsigned i = 0, e = getNumVarKind(VarKind::Symbol); i < e; ++i) {
Identifier id = space.getId(VarKind::Symbol, i);
syms.push_back(id.hasValue() ? Value(id.getValue<Value>()) : 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 {
SmallVector<std::optional<Value>> maybeValues = getMaybeValues();
for (unsigned i = offset, e = maybeValues.size(); i < e; ++i)
if (maybeValues[i] && maybeValues[i].value() == val) {
*pos = i;
return true;
}
return false;
}
bool FlatLinearValueConstraints::containsVar(Value val) const {
unsigned pos;
return findVar(val, &pos, 0);
}
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::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");
SmallVector<std::optional<Value>> maybeValues = getMaybeValues(),
otherMaybeValues =
otherCst.getMaybeValues();
assert(std::equal(maybeValues.begin(), maybeValues.begin() + getNumDimVars(),
otherMaybeValues.begin(),
otherMaybeValues.begin() + 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<DynamicAPInt> 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();
}
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