Commits on Jun 28, 2024

1. [XLA:GPU] Construct constraints for destructured summations in `Symbo… …

   …licTile` derivation.
   
   Take the summation expression
   
     `expr = sum(map(lambda [size, stride]: stride * size, sizes_and_strides))`.
   
   In order to assign a single stride for the summation expression, we need to
   ensure that the parameters (sizes) involved in the expression are such that
   the gap between them is always the same. Concretely, given a list of sizes
   `[s0, s1, ..., s{n}]` ordered in descending order of associated strides, we
   expect that each size `s{k}` is either:
   
   1. `1` (and the corresponding stride is irrelevant);
   2. fully captured---i.e. `s{k} = upper_bound(s{k})`. Assume `s{k}` is the
      leftmost fully captured dimension. In that case,
      `for i in {0, ..., n-k-1}`, `s{k+i+1}` is allowed to be fully captured if
      `s{k+i}` is also fully captured.  Otherwise, `s{k+i+1} = 1`. The resulting
      stride is the smallest stride associated with a fully captured
      dimension;
   3. partially captured---i.e. `1 < s{k} < upper_bound(s{k})`. In that case,
      `for i in {0, ..., k-1}`, `s{i} = 1`. `s{k+1}` is allowed to be fully
      captured (and thus the leftmost fully captured dimension), in which case
      we do as in `2.`. If `s{k+1}` is not fully captured, then
      `for i in {k+1, ..., n}`, `s{i} = 1`, and the stride of the expression is
       the stride associated with `s{k}`.
   
   As a regex-like summary, we expect the sizes to be as follows in row-major
   order (i.e. strictly decreasing order of strides):
   
   &nbsp;&nbsp;`(1*, partial_dim?, full_dims*, 1*)`
   
   and construct constraints as such.
   
   PiperOrigin-RevId: 647638017

   

   bchetioui authored and tensorflower-gardener committed Jun 28, 2024
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