1 //===- ConstraintSytem.cpp - A system of linear constraints. ----*- C++ -*-===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 9 #include "llvm/Analysis/ConstraintSystem.h" 10 #include "llvm/ADT/SmallVector.h" 11 #include "llvm/Support/MathExtras.h" 12 #include "llvm/ADT/StringExtras.h" 13 #include "llvm/Support/Debug.h" 14 15 #include <string> 16 17 using namespace llvm; 18 19 #define DEBUG_TYPE "constraint-system" 20 21 bool ConstraintSystem::eliminateUsingFM() { 22 // Implementation of Fourier–Motzkin elimination, with some tricks from the 23 // paper Pugh, William. "The Omega test: a fast and practical integer 24 // programming algorithm for dependence 25 // analysis." 26 // Supercomputing'91: Proceedings of the 1991 ACM/ 27 // IEEE conference on Supercomputing. IEEE, 1991. 28 assert(!Constraints.empty() && 29 "should only be called for non-empty constraint systems"); 30 unsigned NumVariables = Constraints[0].size(); 31 SmallVector<SmallVector<int64_t, 8>, 4> NewSystem; 32 33 unsigned NumConstraints = Constraints.size(); 34 uint32_t NewGCD = 1; 35 // FIXME do not use copy 36 for (unsigned R1 = 0; R1 < NumConstraints; R1++) { 37 if (Constraints[R1][1] == 0) { 38 SmallVector<int64_t, 8> NR; 39 NR.push_back(Constraints[R1][0]); 40 for (unsigned i = 2; i < NumVariables; i++) { 41 NR.push_back(Constraints[R1][i]); 42 } 43 NewSystem.push_back(std::move(NR)); 44 continue; 45 } 46 47 // FIXME do not use copy 48 for (unsigned R2 = R1 + 1; R2 < NumConstraints; R2++) { 49 if (R1 == R2) 50 continue; 51 52 // FIXME: can we do better than just dropping things here? 53 if (Constraints[R2][1] == 0) 54 continue; 55 56 if ((Constraints[R1][1] < 0 && Constraints[R2][1] < 0) || 57 (Constraints[R1][1] > 0 && Constraints[R2][1] > 0)) 58 continue; 59 60 unsigned LowerR = R1; 61 unsigned UpperR = R2; 62 if (Constraints[UpperR][1] < 0) 63 std::swap(LowerR, UpperR); 64 65 SmallVector<int64_t, 8> NR; 66 for (unsigned I = 0; I < NumVariables; I++) { 67 if (I == 1) 68 continue; 69 70 int64_t M1, M2, N; 71 if (MulOverflow(Constraints[UpperR][I], 72 ((-1) * Constraints[LowerR][1] / GCD), M1)) 73 return false; 74 if (MulOverflow(Constraints[LowerR][I], 75 (Constraints[UpperR][1] / GCD), M2)) 76 return false; 77 if (AddOverflow(M1, M2, N)) 78 return false; 79 NR.push_back(N); 80 81 NewGCD = APIntOps::GreatestCommonDivisor({32, (uint32_t)NR.back()}, 82 {32, NewGCD}) 83 .getZExtValue(); 84 } 85 NewSystem.push_back(std::move(NR)); 86 // Give up if the new system gets too big. 87 if (NewSystem.size() > 500) 88 return false; 89 } 90 } 91 Constraints = std::move(NewSystem); 92 GCD = NewGCD; 93 94 return true; 95 } 96 97 bool ConstraintSystem::mayHaveSolutionImpl() { 98 while (!Constraints.empty() && Constraints[0].size() > 1) { 99 if (!eliminateUsingFM()) 100 return true; 101 } 102 103 if (Constraints.empty() || Constraints[0].size() > 1) 104 return true; 105 106 return all_of(Constraints, [](auto &R) { return R[0] >= 0; }); 107 } 108 109 void ConstraintSystem::dump(ArrayRef<std::string> Names) const { 110 if (Constraints.empty()) 111 return; 112 113 for (const auto &Row : Constraints) { 114 SmallVector<std::string, 16> Parts; 115 for (unsigned I = 1, S = Row.size(); I < S; ++I) { 116 if (Row[I] == 0) 117 continue; 118 std::string Coefficient; 119 if (Row[I] != 1) 120 Coefficient = std::to_string(Row[I]) + " * "; 121 Parts.push_back(Coefficient + Names[I - 1]); 122 } 123 assert(!Parts.empty() && "need to have at least some parts"); 124 LLVM_DEBUG(dbgs() << join(Parts, std::string(" + ")) 125 << " <= " << std::to_string(Row[0]) << "\n"); 126 } 127 } 128 129 void ConstraintSystem::dump() const { 130 SmallVector<std::string, 16> Names; 131 for (unsigned i = 1; i < Constraints.back().size(); ++i) 132 Names.push_back("x" + std::to_string(i)); 133 LLVM_DEBUG(dbgs() << "---\n"); 134 dump(Names); 135 } 136 137 bool ConstraintSystem::mayHaveSolution() { 138 LLVM_DEBUG(dump()); 139 bool HasSolution = mayHaveSolutionImpl(); 140 LLVM_DEBUG(dbgs() << (HasSolution ? "sat" : "unsat") << "\n"); 141 return HasSolution; 142 } 143 144 bool ConstraintSystem::isConditionImplied(SmallVector<int64_t, 8> R) const { 145 // If all variable coefficients are 0, we have 'C >= 0'. If the constant is >= 146 // 0, R is always true, regardless of the system. 147 if (all_of(ArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; })) 148 return R[0] >= 0; 149 150 // If there is no solution with the negation of R added to the system, the 151 // condition must hold based on the existing constraints. 152 R = ConstraintSystem::negate(R); 153 154 auto NewSystem = *this; 155 NewSystem.addVariableRow(R); 156 return !NewSystem.mayHaveSolution(); 157 } 158