[Mlir-commits] [mlir] [MLIR][Presburger] Implement function to evaluate the number of terms in a generating function. (PR #78078)

[Arjun P]

================
@@ -245,3 +246,235 @@ QuasiPolynomial mlir::presburger::detail::getCoefficientInRationalFunction(
   }
   return coefficients[power].simplify();
 }
+
+/// Substitute x_i = t^μ_i in one term of a generating function, returning
+/// a quasipolynomial which represents the exponent of the numerator
+/// of the result, and a vector which represents the exponents of the
+/// denominator of the result.
+/// v represents the affine functions whose floors are multiplied by the
+/// generators, and ds represents the list of generators.
+std::pair<QuasiPolynomial, std::vector<Fraction>>
+substituteMuInTerm(unsigned numParams, ParamPoint v, std::vector<Point> ds,
+                   Point mu) {
+  unsigned numDims = mu.size();
+  for (const Point &d : ds)
+    assert(d.size() == numDims &&
+           "μ has to have the same number of dimensions as the generators!");
+
+  // First, the exponent in the numerator becomes
+  // - (μ • u_1) * (floor(first col of v))
+  // - (μ • u_2) * (floor(second col of v)) - ...
+  // - (μ • u_d) * (floor(d'th col of v))
+  // So we store the negation of the dot products.
+
+  // We have d terms, each of whose coefficient is the negative dot product,
+  SmallVector<Fraction> coefficients;
+  coefficients.reserve(numDims);
+  for (const Point &d : ds)
+    coefficients.push_back(-dotProduct(mu, d));
+
+  // Then, the affine function is a single floor expression, given by the
+  // corresponding column of v.
+  ParamPoint vTranspose = v.transpose();
+  std::vector<std::vector<SmallVector<Fraction>>> affine;
+  affine.reserve(numDims);
+  for (unsigned j = 0; j < numDims; ++j)
+    affine.push_back({SmallVector<Fraction>(vTranspose.getRow(j))});
+
+  QuasiPolynomial num(numParams, coefficients, affine);
+  num = num.simplify();
+
+  std::vector<Fraction> dens;
+  dens.reserve(ds.size());
+  // Similarly, each term in the denominator has exponent
+  // given by the dot product of μ with u_i.
+  for (const Point &d : ds) {
+    // This term in the denominator is
+    // (1 - t^dens.back())
+    dens.push_back(dotProduct(d, mu));
+  }
+
+  return {num, dens};
+}
+
+/// Normalize all denominator exponents `dens` to their absolute values
+/// by multiplying and dividing by the inverses.
+/// Also, take the factors (-s) out of each term of the product.
+void normalizeDenominatorExponents(int &sign, QuasiPolynomial &num,
+                                   std::vector<Fraction> &dens) {
+  // We track the number of exponents that are negative in the
+  // denominator, and convert them to their absolute values.
+  unsigned numNegExps = 0;
+  Fraction sumNegExps(0, 1);
+  for (unsigned j = 0, e = dens.size(); j < e; ++j) {
+    if (dens[j] < 0) {
+      numNegExps += 1;
+      sumNegExps += dens[j];
+    }
+  }
+
+  // If we have (1 - (s+1)^-c) in the denominator,
+  // multiply and divide by (s+1)^c.
+  // We convert all negative-exponent terms at once; therefore
+  // we multiply and divide by (s+1)^sumNegExps.
----------------
Superty wrote:

make sure this makes sense in context of the explanation above as to the meaning of the denominator vec

https://github.com/llvm/llvm-project/pull/78078