[Mlir-commits] [mlir] [MLIR][Presburger] Helper functions to compute the constant term of a generating function (PR #77819)

[llvmlistbot at llvm.org]

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@@ -144,3 +144,102 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
                             std::vector({numerator}),
                             std::vector({denominator}));
 }
+
+/// We use a recursive procedure to find a vector not orthogonal
+/// to a given set. Let the inputs be {x_1, ..., x_k}, all vectors of length n.
+///
+/// In the following,
+/// vs[:i] means the elements of vs up to and including the i'th one,
+/// <vs, us> means the dot product of v and u,
+/// vs ++ [v] means the vector vs with the new element v appended to it.
+///
+/// Suppose we have a vector vs which is not orthogonal to
+/// any of {x_1[:n-1], ..., x_k[:n-1]}.
+/// Then we need v s.t. <x_i, vs++[v]> != 0 for all i.
+/// => <x_i[:n-1], vs> + x_i[-1]*v != 0
+/// => v != - <x_i[:n-1], vs> / x_i[-1]
+/// We compute this value for all i, and then
+/// set v to be the maximum element of this set + 1. Thus
+/// v is outside the set as desired, and we append it to vs.
+///
+/// The base case is given in one dimension,
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Abhinav271828 wrote:

And if any vector is null, it's completely ignored (as documented).

https://github.com/llvm/llvm-project/pull/77819