LLVM  15.0.0git
ConstraintSystem.cpp
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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 
10 #include "llvm/ADT/SmallVector.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();
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) {
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 
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 (auto &Row : Constraints) {
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 {
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 
138  LLVM_DEBUG(dump());
139  bool HasSolution = mayHaveSolutionImpl();
140  LLVM_DEBUG(dbgs() << (HasSolution ? "sat" : "unsat") << "\n");
141  return HasSolution;
142 }
143 
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(makeArrayRef(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.
153 
154  auto NewSystem = *this;
155  NewSystem.addVariableRow(R);
156  return !NewSystem.mayHaveSolution();
157 }
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MathExtras.h
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Definition: AddressRanges.h:17
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Definition: SmallVector.h:1185
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Definition: Debug.cpp:163
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Definition: README_ALTIVEC.txt:86
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Definition: MathExtras.h:911
llvm::ConstraintSystem::size
unsigned size() const
Returns the number of rows in the constraint system.
Definition: ConstraintSystem.h:91
ConstraintSystem.h
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Definition: ConstraintSystem.h:71
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Implement std::swap in terms of BitVector swap.
Definition: BitVector.h:853
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bool isConditionImplied(SmallVector< int64_t, 8 > R) const
Definition: ConstraintSystem.cpp:144
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Definition: README.txt:210
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Multiply two signed integers, computing the two's complement truncated result, returning true if an o...
Definition: MathExtras.h:963
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Definition: ArrayRef.h:475
SmallVector.h
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Definition: APInt.cpp:759
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Returns true if there may be a solution for the constraints in the system.
Definition: ConstraintSystem.cpp:137
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Debug.h