// efficient.
type factsTable struct {
	// unsat is true if facts contains a contradiction.
	//
	// Note that the factsTable logic is incomplete, so if unsat
	// is false, the assertions in factsTable could be satisfiable
	// *or* unsatisfiable.
	unsat      bool // true if facts contains a contradiction
	unsatDepth int  // number of unsat checkpoints

	facts map[pair]relation // current known set of relation

arrive at the idea of doing those exact calculations. Nowhere is it mentioned
that this test extends the 2-by-1 guess into a 3-by-2 guess. The proof of the
Good Guess Guarantee is only for the 2-by-1 guess and argues by contradiction,
making it difficult to understand how modifications like adding another digit
or adjusting the quotient range affects the overall bound.

All that said, Knuth remains the canonical reference. It is dense but packed

    if (!isa<func::FuncOp, IfOp, WhileOp>(contraction->getParentOp())) {
      return rewriter.notifyMatchFailure(
          contraction,
          "fused operation must be nested inside a function, If or While");
    }

    // If the contraction is used in multiple places, fusing it will only create
    // more contraction nodes, which is slower.
    if (!contraction.getResult().hasOneUse())

        const int y_col =
            !matmul_op.getAdjY() ? shape_y.back() : *(shape_y.rbegin() + 1);

        // Checks that matrix multiply can perform a valid contraction.
        if (x_col != y_row) {
          result_shape.clear();
          return false;
        }

        result_shape.push_back(x_row);
        result_shape.push_back(y_col);
        return true;

- [`KT-65255`](https://youtrack.jetbrains.com/issue/KT-65255) K2 / KJS: "IllegalArgumentException: Candidate is not successful, but system has no contradiction"
- [`KT-65195`](https://youtrack.jetbrains.com/issue/KT-65195) K2: Unexpected exception when executing dynamic array element inc/dec

	//
	// since all the yi for i > 1 are 0 by choice of k: If any of them
	// were > 0, then yh >= b^2 and thus y >= b^2. Then k' = k*2 would
	// be a larger valid threshold contradicting the assumption about k.
	//
	if k < n || m != n {
		tp := getNat(3 * k)
		t := *tp

		// add x0*y1*b
		x0 := x0.norm()
		y1 := y[k:]       // y1 is normalized because y is

  let hasVerifier = 1;
}

def TF_EinsumOp : TF_Op<"Einsum", [Pure]> {
  let summary = [{
Tensor contraction according to Einstein summation convention.
  }];

  let description = [{
Implements generalized Tensor contraction and reduction. Each input Tensor must
have a corresponding input subscript appearing in the comma-separated left-hand

				required("spec", "validation", "openAPIV3Schema", "properties[spanning-defaults-with-missing-typemeta]", "default", "embedded", "kind"),
			},
		},
		{
			name: "contradicting meta field types",
			resource: &apiextensions.CustomResourceDefinition{
				ObjectMeta: metav1.ObjectMeta{Name: "plural.group.com"},
				Spec: apiextensions.CustomResourceDefinitionSpec{
					Group:    "group.com",

        `batch_dims` case.
    *   Removing of dtype in the constructor of initializers and partition_info
        in call.
    *   Add `tf.math.nextafter` op.
    *   Turn on MKL-DNN contraction kernels by default. MKL-DNN dynamically
        dispatches the best kernel implementation based on CPU vector
        architecture. To disable them, build with
        `--define=tensorflow_mkldnn_contraction_kernel=0`.