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+//===- ConstraintSytem.cpp - A system of linear constraints. ----*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/ConstraintSystem.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/Support/MathExtras.h"
+#include "llvm/ADT/StringExtras.h"
+#include "llvm/IR/Value.h"
+#include "llvm/Support/Debug.h"
+
+#include <string>
+
+using namespace llvm;
+
+#define DEBUG_TYPE "constraint-system"
+
+bool ConstraintSystem::eliminateUsingFM() {
+ // Implementation of Fourier–Motzkin elimination, with some tricks from the
+ // paper Pugh, William. "The Omega test: a fast and practical integer
+ // programming algorithm for dependence
+ // analysis."
+ // Supercomputing'91: Proceedings of the 1991 ACM/
+ // IEEE conference on Supercomputing. IEEE, 1991.
+ assert(!Constraints.empty() &&
+ "should only be called for non-empty constraint systems");
+
+ unsigned LastIdx = NumVariables - 1;
+
+ // First, either remove the variable in place if it is 0 or add the row to
+ // RemainingRows and remove it from the system.
+ SmallVector<SmallVector<Entry, 8>, 4> RemainingRows;
+ for (unsigned R1 = 0; R1 < Constraints.size();) {
+ SmallVector<Entry, 8> &Row1 = Constraints[R1];
+ if (getLastCoefficient(Row1, LastIdx) == 0) {
+ if (Row1.size() > 0 && Row1.back().Id == LastIdx)
+ Row1.pop_back();
+ R1++;
+ } else {
+ std::swap(Constraints[R1], Constraints.back());
+ RemainingRows.push_back(std::move(Constraints.back()));
+ Constraints.pop_back();
+ }
+ }
+
+ // Process rows where the variable is != 0.
+ unsigned NumRemainingConstraints = RemainingRows.size();
+ for (unsigned R1 = 0; R1 < NumRemainingConstraints; R1++) {
+ // FIXME do not use copy
+ for (unsigned R2 = R1 + 1; R2 < NumRemainingConstraints; R2++) {
+ if (R1 == R2)
+ continue;
+
+ int64_t UpperLast = getLastCoefficient(RemainingRows[R2], LastIdx);
+ int64_t LowerLast = getLastCoefficient(RemainingRows[R1], LastIdx);
+ assert(
+ UpperLast != 0 && LowerLast != 0 &&
+ "RemainingRows should only contain rows where the variable is != 0");
+
+ if ((LowerLast < 0 && UpperLast < 0) || (LowerLast > 0 && UpperLast > 0))
+ continue;
+
+ unsigned LowerR = R1;
+ unsigned UpperR = R2;
+ if (UpperLast < 0) {
+ std::swap(LowerR, UpperR);
+ std::swap(LowerLast, UpperLast);
+ }
+
+ SmallVector<Entry, 8> NR;
+ unsigned IdxUpper = 0;
+ unsigned IdxLower = 0;
+ auto &LowerRow = RemainingRows[LowerR];
+ auto &UpperRow = RemainingRows[UpperR];
+ while (true) {
+ if (IdxUpper >= UpperRow.size() || IdxLower >= LowerRow.size())
+ break;
+ int64_t M1, M2, N;
+ int64_t UpperV = 0;
+ int64_t LowerV = 0;
+ uint16_t CurrentId = std::numeric_limits<uint16_t>::max();
+ if (IdxUpper < UpperRow.size()) {
+ CurrentId = std::min(UpperRow[IdxUpper].Id, CurrentId);
+ }
+ if (IdxLower < LowerRow.size()) {
+ CurrentId = std::min(LowerRow[IdxLower].Id, CurrentId);
+ }
+
+ if (IdxUpper < UpperRow.size() && UpperRow[IdxUpper].Id == CurrentId) {
+ UpperV = UpperRow[IdxUpper].Coefficient;
+ IdxUpper++;
+ }
+
+ if (MulOverflow(UpperV, -1 * LowerLast, M1))
+ return false;
+ if (IdxLower < LowerRow.size() && LowerRow[IdxLower].Id == CurrentId) {
+ LowerV = LowerRow[IdxLower].Coefficient;
+ IdxLower++;
+ }
+
+ if (MulOverflow(LowerV, UpperLast, M2))
+ return false;
+ if (AddOverflow(M1, M2, N))
+ return false;
+ if (N == 0)
+ continue;
+ NR.emplace_back(N, CurrentId);
+ }
+ if (NR.empty())
+ continue;
+ Constraints.push_back(std::move(NR));
+ // Give up if the new system gets too big.
+ if (Constraints.size() > 500)
+ return false;
+ }
+ }
+ NumVariables -= 1;
+
+ return true;
+}
+
+bool ConstraintSystem::mayHaveSolutionImpl() {
+ while (!Constraints.empty() && NumVariables > 1) {
+ if (!eliminateUsingFM())
+ return true;
+ }
+
+ if (Constraints.empty() || NumVariables > 1)
+ return true;
+
+ return all_of(Constraints, [](auto &R) {
+ if (R.empty())
+ return true;
+ if (R[0].Id == 0)
+ return R[0].Coefficient >= 0;
+ return true;
+ });
+}
+
+SmallVector<std::string> ConstraintSystem::getVarNamesList() const {
+ SmallVector<std::string> Names(Value2Index.size(), "");
+#ifndef NDEBUG
+ for (auto &[V, Index] : Value2Index) {
+ std::string OperandName;
+ if (V->getName().empty())
+ OperandName = V->getNameOrAsOperand();
+ else
+ OperandName = std::string("%") + V->getName().str();
+ Names[Index - 1] = OperandName;
+ }
+#endif
+ return Names;
+}
+
+void ConstraintSystem::dump() const {
+#ifndef NDEBUG
+ if (Constraints.empty())
+ return;
+ SmallVector<std::string> Names = getVarNamesList();
+ for (const auto &Row : Constraints) {
+ SmallVector<std::string, 16> Parts;
+ for (unsigned I = 0, S = Row.size(); I < S; ++I) {
+ if (Row[I].Id >= NumVariables)
+ break;
+ if (Row[I].Id == 0)
+ continue;
+ std::string Coefficient;
+ if (Row[I].Coefficient != 1)
+ Coefficient = std::to_string(Row[I].Coefficient) + " * ";
+ Parts.push_back(Coefficient + Names[Row[I].Id - 1]);
+ }
+ // assert(!Parts.empty() && "need to have at least some parts");
+ int64_t ConstPart = 0;
+ if (Row[0].Id == 0)
+ ConstPart = Row[0].Coefficient;
+ LLVM_DEBUG(dbgs() << join(Parts, std::string(" + "))
+ << " <= " << std::to_string(ConstPart) << "\n");
+ }
+#endif
+}
+
+bool ConstraintSystem::mayHaveSolution() {
+ LLVM_DEBUG(dbgs() << "---\n");
+ LLVM_DEBUG(dump());
+ bool HasSolution = mayHaveSolutionImpl();
+ LLVM_DEBUG(dbgs() << (HasSolution ? "sat" : "unsat") << "\n");
+ return HasSolution;
+}
+
+bool ConstraintSystem::isConditionImplied(SmallVector<int64_t, 8> R) const {
+ // If all variable coefficients are 0, we have 'C >= 0'. If the constant is >=
+ // 0, R is always true, regardless of the system.
+ if (all_of(ArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; }))
+ return R[0] >= 0;
+
+ // If there is no solution with the negation of R added to the system, the
+ // condition must hold based on the existing constraints.
+ R = ConstraintSystem::negate(R);
+ if (R.empty())
+ return false;
+
+ auto NewSystem = *this;
+ NewSystem.addVariableRow(R);
+ return !NewSystem.mayHaveSolution();
+}