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 unsigned LastIdx = NumVariables - 1; 36 37 for (unsigned R1 = 0; R1 < NumConstraints; R1++) { 38 SmallVector<int64_t, 8> &Row1 = Constraints[R1]; 39 int64_t LowerLast = Row1[LastIdx]; 40 if (LowerLast == 0) { 41 Row1.pop_back(); 42 NewSystem.push_back(std::move(Row1)); 43 continue; 44 } 45 46 // FIXME do not use copy 47 for (unsigned R2 = R1 + 1; R2 < NumConstraints; R2++) { 48 if (R1 == R2) 49 continue; 50 51 int64_t UpperLast = Constraints[R2][LastIdx]; 52 // FIXME: can we do better than just dropping things here? 53 if (UpperLast == 0) 54 continue; 55 56 int64_t LowerLast = Constraints[R1][LastIdx]; 57 if ((LowerLast < 0 && UpperLast < 0) || (LowerLast > 0 && UpperLast > 0)) 58 continue; 59 60 unsigned LowerR = R1; 61 unsigned UpperR = R2; 62 if (UpperLast < 0) { 63 std::swap(LowerR, UpperR); 64 std::swap(LowerLast, UpperLast); 65 } 66 67 SmallVector<int64_t, 8> NR; 68 for (unsigned I = 0; I < LastIdx; I++) { 69 int64_t M1, M2, N; 70 int64_t UpperV = Constraints[UpperR][I]; 71 if (MulOverflow(UpperV, ((-1) * LowerLast / GCD), M1)) 72 return false; 73 int64_t LowerV = Constraints[LowerR][I]; 74 if (MulOverflow(LowerV, (UpperLast / GCD), M2)) 75 return false; 76 if (AddOverflow(M1, M2, N)) 77 return false; 78 NR.push_back(N); 79 80 NewGCD = 81 APIntOps::GreatestCommonDivisor({32, (uint32_t)N}, {32, NewGCD}) 82 .getZExtValue(); 83 } 84 NewSystem.push_back(std::move(NR)); 85 // Give up if the new system gets too big. 86 if (NewSystem.size() > 500) 87 return false; 88 } 89 } 90 Constraints = std::move(NewSystem); 91 GCD = NewGCD; 92 93 return true; 94 } 95 96 bool ConstraintSystem::mayHaveSolutionImpl() { 97 while (!Constraints.empty() && Constraints[0].size() > 1) { 98 if (!eliminateUsingFM()) 99 return true; 100 } 101 102 if (Constraints.empty() || Constraints[0].size() > 1) 103 return true; 104 105 return all_of(Constraints, [](auto &R) { return R[0] >= 0; }); 106 } 107 108 void ConstraintSystem::dump(ArrayRef<std::string> Names) const { 109 if (Constraints.empty()) 110 return; 111 112 for (const auto &Row : Constraints) { 113 SmallVector<std::string, 16> Parts; 114 for (unsigned I = 1, S = Row.size(); I < S; ++I) { 115 if (Row[I] == 0) 116 continue; 117 std::string Coefficient; 118 if (Row[I] != 1) 119 Coefficient = std::to_string(Row[I]) + " * "; 120 Parts.push_back(Coefficient + Names[I - 1]); 121 } 122 assert(!Parts.empty() && "need to have at least some parts"); 123 LLVM_DEBUG(dbgs() << join(Parts, std::string(" + ")) 124 << " <= " << std::to_string(Row[0]) << "\n"); 125 } 126 } 127 128 void ConstraintSystem::dump() const { 129 SmallVector<std::string, 16> Names; 130 for (unsigned i = 1; i < Constraints.back().size(); ++i) 131 Names.push_back("x" + std::to_string(i)); 132 LLVM_DEBUG(dbgs() << "---\n"); 133 dump(Names); 134 } 135 136 bool ConstraintSystem::mayHaveSolution() { 137 LLVM_DEBUG(dump()); 138 bool HasSolution = mayHaveSolutionImpl(); 139 LLVM_DEBUG(dbgs() << (HasSolution ? "sat" : "unsat") << "\n"); 140 return HasSolution; 141 } 142 143 bool ConstraintSystem::isConditionImplied(SmallVector<int64_t, 8> R) const { 144 // If all variable coefficients are 0, we have 'C >= 0'. If the constant is >= 145 // 0, R is always true, regardless of the system. 146 if (all_of(ArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; })) 147 return R[0] >= 0; 148 149 // If there is no solution with the negation of R added to the system, the 150 // condition must hold based on the existing constraints. 151 R = ConstraintSystem::negate(R); 152 153 auto NewSystem = *this; 154 NewSystem.addVariableRow(R); 155 return !NewSystem.mayHaveSolution(); 156 } 157