llvm/mlir/include/mlir/Analysis/Presburger/GeneratingFunction.h

//===- GeneratingFunction.h - Generating Functions over Q^d -----*- 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
//
//===----------------------------------------------------------------------===//
//
// Definition of the GeneratingFunction class for Barvinok's algorithm,
// which represents a function over Q^n, parameterized by d parameters.
//
//===----------------------------------------------------------------------===//

#ifndef MLIR_ANALYSIS_PRESBURGER_GENERATINGFUNCTION_H
#define MLIR_ANALYSIS_PRESBURGER_GENERATINGFUNCTION_H

#include "mlir/Analysis/Presburger/Fraction.h"
#include "mlir/Analysis/Presburger/Matrix.h"

namespace mlir {
namespace presburger {
namespace detail {

// A parametric point is a vector, each of whose elements
// is an affine function of n parameters. Each column
// in the matrix represents the affine function and
// has n+1 elements.
ParamPoint;

// A point is simply a vector.
Point;

// A class to describe the type of generating function
// used to enumerate the integer points in a polytope.
// Consists of a set of terms, where the ith term has
// * a sign, ±1, stored in `signs[i]`
// * a numerator, of the form x^{n},
//      where n, stored in `numerators[i]`,
//      is a parametric point.
// * a denominator, of the form (1 - x^{d1})...(1 - x^{dn}),
//      where each dj, stored in `denominators[i][j]`,
//      is a vector.
//
// Represents functions f_p : Q^n -> Q of the form
//
// f_p(x) = \sum_i s_i * (x^n_i(p)) / (\prod_j (1 - x^d_{ij})
//
// where s_i is ±1,
// n_i \in Q^d -> Q^n is an n-vector of affine functions on d parameters, and
// g_{ij} \in Q^n are vectors.
class GeneratingFunction { … };

} // namespace detail
} // namespace presburger
} // namespace mlir

#endif // MLIR_ANALYSIS_PRESBURGER_GENERATINGFUNCTION_H