[Mlir-commits] [mlir] [MLIR][Presburger] Generating functions and quasi-polynomials for Barvinok's algorithm (PR #75702)

[Arjun P]

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+//===- 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 {
+
+// A parametric point is a vector, each of whose elements
+// is an affine function of n parameters. Each row
+// in the matrix represents the affine function and
+// has n+1 elements.
+using ParamPoint = Matrix<Fraction>;
+
+// A point is simply a vector.
+using Point = SmallVector<Fraction>;
+
+// 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 {
+public:
+  GeneratingFunction(unsigned numParam, SmallVector<int, 8> signs,
+                     std::vector<ParamPoint> nums,
+                     std::vector<std::vector<Point>> dens)
+      : numParam(numParam), signs(signs), numerators(nums), denominators(dens) {
+    for (const ParamPoint &term : numerators)
+      assert(term.getNumColumns() == numParam + 1 &&
+             "dimensionality of numerator exponents does not match number of "
+             "parameters!");
+  }
+
+  unsigned getNumParams() { return numParam; }
+
+  SmallVector<int> getSigns() { return signs; }
+
+  std::vector<ParamPoint> getNumerators() { return numerators; }
+
+  std::vector<std::vector<Point>> getDenominators() { return denominators; }
+
+  GeneratingFunction operator+(const GeneratingFunction &gf) const {
+    assert(numParam == gf.getNumParams() &&
+           "two generating functions with different numbers of parameters "
+           "cannot be added!");
+    SmallVector<int> sumSigns = signs;
+    sumSigns.append(gf.signs);
+
+    std::vector<ParamPoint> sumNumerators = numerators;
+    sumNumerators.insert(sumNumerators.end(), gf.numerators.begin(),
+                         gf.numerators.end());
+
+    std::vector<std::vector<Point>> sumDenominators = denominators;
+    sumDenominators.insert(sumDenominators.end(), gf.denominators.begin(),
+                           gf.denominators.end());
+    return GeneratingFunction(sumSigns, sumNumerators, sumDenominators);
+  }
+
+  llvm::raw_ostream &print(llvm::raw_ostream &os) const {
+    for (unsigned i = 0, e = signs.size(); i < e; i++) {
+      if (signs[i] == 1)
+        os << " + ";
+      else
+        os << " - ";
+
+      os << "x^[";
+      for (unsigned j = 0, e = numerators[i].size(); j < e - 1; j++)
+        os << numerators[i][j] << ",";
+      os << numerators[i].back() << "]/";
+
+      for (Point den : denominators[i]) {
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Superty wrote:

don't copy here

https://github.com/llvm/llvm-project/pull/75702