Make all template specialization of FPE compile for float

[peterrum]

as reported by exadg/exadg#252

FYI @jh66637

[bangerth]

This doesn't sound quite right to me. Shouldn't the operator just return a Tensor representation of what it stores internally, and then if someone wants this in another type they can later cast from that tensor to one with a different scalar?

Note that that's basically what you do in the implementation, which now looks as follows:

template <int order, int dim, int spacedim, typename Number>
template <typename Number2>
inline DerivativeForm<order, dim, spacedim, Number>::
operator Tensor<order + 1, dim, Number>() const
{
  Assert((dim == spacedim), ExcMessage("Only allowed when dim==spacedim."));

  Tensor<order + 1, dim, Number> t;       <<<<<<<<<<<<<<<<<< old tensor type
  if (dim == spacedim)
    for (unsigned int j = 0; j < dim; ++j)
      t[j] = (*this)[j];
  return t;                                        <<<<<<<<<<<< cast to Tensor<....,Number2> happens here
}

My preference would be to make the place that calls this function do the cast at the calling site, not internally here.

[kronbichler]

I tend to agree with @bangerth here, since this only converts the end result, I would prefer doing that explicitly in FEPointEvaluation (I was confused by the abbreviation FPE, which I read as floating point exception).

[peterrum]

That the tensor used the old number- type was not indended:

Tensor<order + 1, dim, Number> t;       <<<<<<<<<<<<<<<<<< old tensor type

I have adjusted that.

Since the operator() is for casting, the casting is already done explicitly done in FEPointEvaluation:

dealii/include/deal.II/matrix_free/fe_point_evaluation.h

Lines 950 to 954 in 1195dbb

	gradients[i + j] = static_cast<gradient_type>(
	apply_transformation(mapping_info->get_mapping_data()
	.inverse_jacobians[i + j]
	.transpose(),
	unit_gradients[i + j]));

The alternative would to cast from DerivativeForm to typename internal::FEPointEvaluation::EvaluatorTypeTraits<dim, n_components, double>::gradient_type (please note that one has to use double instead of Number in this long expression) and after that cast it to a float version (or do an assignment, which seems to broke in Tensor).

[bangerth]

I think what I meant to say is this: I consider the cast operator as saying "give me a tensor representation of this object", the emphasis being on "representation of this object" rather than "give me". The emphasis here is on the object. As a consequence, a DerivativeForm<...,double> should return a Tensor<...,double>.

In contrast, your implementation is for the question "I want to use this object as an X", in which the emphasis is on want to use -- a caller side consideration. I would prefer an explicit cast to Tensor<...,Number2> in such situations.

[peterrum]

Closing in favor of #14155. Whatever the outcome will be there.