Many of the previous inductive cases were wrong (e.g. `abs`, `sq`, `div` and `truediv`).
We rewrite it using the mathematical terms that allow to prove the relevant upper
and lower bounds.
Note that the inductive step can be seen as a not-too-difficult optimisation problem
with constraints, hence the naming of the functions.
For many of the other functions, we also simplify the formulas, which will be useful
when this code is generalised to work with symbolic shapes.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/91601
Approved by: https://github.com/jansel, https://github.com/eellison
Builds up sympy expressions computing the lower and upper bound of ranges, and then finds `op.to_dtype(x, torch.int64)` nodes whose dominated values can all be computed in a lower precision. I haven't gotten all the way to work with dynamic shapes but it should be a fairly small change. There's still additional work to get torchinductor to work with large tensors (see https://github.com/pytorch/torchdynamo/issues/1819) because we would need to add explicit dtype annotations to int64 which we're not doing right now.
Fix for https://github.com/pytorch/torchdynamo/issues/1293.
Performance Before OpBench aten.upsample_bilinear2d.vec float32:
(25th %, 50th %, 75th %)
Before
[0.7521964636710751, 0.8645357996607477, 2.8746003906598494]
After:
[0.9511363478204263, 1.0295566597806718, 3.2662165264101755]
Pull Request resolved: https://github.com/pytorch/pytorch/pull/91028
Approved by: https://github.com/jansel
