derived dim (#118729)
With the current `Dim`-based dynamic shapes API for export, one can express that shapes of different input shapes must be equal by reusing the same `Dim`. However, non-trivial relationships between such input shapes cannot be expressed.
Recently we are seeing more and more examples of code that require this additional expressibility, e.g., where a pair of shapes might differ by one, or a shape might be double another (or simply even).
This PR introduces the concept of a "derived" `Dim`, i.e., a linear arithmetic expression over a `Dim`. By using a combination of `Dim`s and derived `Dim`s to specify input shapes, the desired relationships can be expressed naturally. E.g., a pair of shapes might be `dim` and `dim + 1`, or `dim` and `2*dim`, or even `2*dim` and `dim + 1`.
We extend the current infrastructure that translates `Dim`s to deprecated `dynamic_dim`-based constraints to work with derived `Dim`s. As usual, we raise constraint violation errors when shape guards cannot be verified given a dynamic shapes spec; suggest fixes; and raise runtime errors when future inputs violate the spec.
Importantly, some guards that used to cause forced specializations in the constraint solver because they were deemed "too complex" now do not do so, because they can now be specified as constraints. Since this was what motivated the introduction of a `disable_constraint_solver` flag to some internal APIs, we may not need that flag any more.
Note that shapes of placeholders in exported programs can now contain symbolic expressions and not just symbols.
Differential Revision: D53254587
Pull Request resolved: https://github.com/pytorch/pytorch/pull/118729
Approved by: https://github.com/ezyang
