MLIR  19.0.0git
GeneratingFunction.h
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1 //===- GeneratingFunction.h - Generating Functions over Q^d -----*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // Definition of the GeneratingFunction class for Barvinok's algorithm,
10 // which represents a function over Q^n, parameterized by d parameters.
11 //
12 //===----------------------------------------------------------------------===//
13
14 #ifndef MLIR_ANALYSIS_PRESBURGER_GENERATINGFUNCTION_H
15 #define MLIR_ANALYSIS_PRESBURGER_GENERATINGFUNCTION_H
16
19
20 namespace mlir {
21 namespace presburger {
22 namespace detail {
23
24 // A parametric point is a vector, each of whose elements
25 // is an affine function of n parameters. Each column
26 // in the matrix represents the affine function and
27 // has n+1 elements.
29
30 // A point is simply a vector.
32
33 // A class to describe the type of generating function
34 // used to enumerate the integer points in a polytope.
35 // Consists of a set of terms, where the ith term has
36 // * a sign, ±1, stored in signs[i]
37 // * a numerator, of the form x^{n},
38 // where n, stored in numerators[i],
39 // is a parametric point.
40 // * a denominator, of the form (1 - x^{d1})...(1 - x^{dn}),
41 // where each dj, stored in denominators[i][j],
42 // is a vector.
43 //
44 // Represents functions f_p : Q^n -> Q of the form
45 //
46 // f_p(x) = \sum_i s_i * (x^n_i(p)) / (\prod_j (1 - x^d_{ij})
47 //
48 // where s_i is ±1,
49 // n_i \in Q^d -> Q^n is an n-vector of affine functions on d parameters, and
50 // g_{ij} \in Q^n are vectors.
52 public:
53  GeneratingFunction(unsigned numParam, SmallVector<int> signs,
54  std::vector<ParamPoint> nums,
55  std::vector<std::vector<Point>> dens)
56  : numParam(numParam), signs(signs), numerators(nums), denominators(dens) {
57 #ifndef NDEBUG
58  for (const ParamPoint &term : numerators)
59  assert(term.getNumRows() == numParam + 1 &&
60  "dimensionality of numerator exponents does not match number of "
61  "parameters!");
62 #endif // NDEBUG
63  }
64
65  unsigned getNumParams() const { return numParam; }
66
67  SmallVector<int> getSigns() const { return signs; }
68
69  std::vector<ParamPoint> getNumerators() const { return numerators; }
70
71  std::vector<std::vector<Point>> getDenominators() const {
72  return denominators;
73  }
74
76  assert(numParam == gf.getNumParams() &&
77  "two generating functions with different numbers of parameters "
79  SmallVector<int> sumSigns = signs;
80  sumSigns.append(gf.signs);
81
82  std::vector<ParamPoint> sumNumerators = numerators;
83  sumNumerators.insert(sumNumerators.end(), gf.numerators.begin(),
84  gf.numerators.end());
85
86  std::vector<std::vector<Point>> sumDenominators = denominators;
87  sumDenominators.insert(sumDenominators.end(), gf.denominators.begin(),
88  gf.denominators.end());
89  return GeneratingFunction(numParam, sumSigns, sumNumerators,
90  sumDenominators);
91  }
92
93  llvm::raw_ostream &print(llvm::raw_ostream &os) const {
94  for (unsigned i = 0, e = signs.size(); i < e; i++) {
95  if (i == 0) {
96  if (signs[i] == -1)
97  os << "- ";
98  } else {
99  if (signs[i] == 1)
100  os << " + ";
101  else
102  os << " - ";
103  }
104
105  os << "x^[";
106  unsigned r = numerators[i].getNumRows();
107  for (unsigned j = 0; j < r - 1; j++) {
108  os << "[";
109  for (unsigned k = 0, c = numerators[i].getNumColumns(); k < c - 1; k++)
110  os << numerators[i].at(j, k) << ",";
111  os << numerators[i].getRow(j).back() << "],";
112  }
113  os << "[";
114  for (unsigned k = 0, c = numerators[i].getNumColumns(); k < c - 1; k++)
115  os << numerators[i].at(r - 1, k) << ",";
116  os << numerators[i].getRow(r - 1).back() << "]]/";
117
118  for (const Point &den : denominators[i]) {
119  os << "(x^[";
120  for (unsigned j = 0, e = den.size(); j < e - 1; j++)
121  os << den[j] << ",";
122  os << den.back() << "])";
123  }
124  }
125  return os;
126  }
127
128 private:
129  unsigned numParam;
130  SmallVector<int> signs;
131  std::vector<ParamPoint> numerators;
132  std::vector<std::vector<Point>> denominators;
133 };
134
135 } // namespace detail
136 } // namespace presburger
137 } // namespace mlir
138
139 #endif // MLIR_ANALYSIS_PRESBURGER_GENERATINGFUNCTION_H
llvm::raw_ostream & print(llvm::raw_ostream &os) const
GeneratingFunction operator+(const GeneratingFunction &gf) const
std::vector< ParamPoint > getNumerators() const
std::vector< std::vector< Point > > getDenominators() const
GeneratingFunction(unsigned numParam, SmallVector< int > signs, std::vector< ParamPoint > nums, std::vector< std::vector< Point >> dens)
Include the generated interface declarations.
Eliminates variable at the specified position using Fourier-Motzkin variable elimination.