Matthias Boehm created SYSTEMML-1782:

             Summary: Extend parfor block indexing analysis
                 Key: SYSTEMML-1782
             Project: SystemML
          Issue Type: Task
            Reporter: Matthias Boehm

This task aims to better support arbitrary block indexing in a parfor context, 
for expressions as this example from SYSTEMML-1774:

 parfor (j in 1:parallel_batches, log=DEBUG) {
        # Get a mini-batch in this group
        beg = ((j-1) * batch_size) %% nrow(X_group_batch) + 1
        end = min(nrow(X_group_batch), beg + batch_size - 1)
        X_batch = X_group_batch[beg:end,]
        y_batch = y_group_batch[beg:end,]

Currently, we're unable to determine a constant size for X_batch and y_batch. 
However, since the parfor body is anyway recompiled on parfor entry, we can 
improve upon this as follows:

* Leverage known constants and index ranges to perform a limit analysis for 
linear functions in indexing expressions. For example, the above expression for 
beg and end would simplify to {{(j-1) * 32 + 1}} and  {{beg + batch_size -1}}.
* Better handling of linear functions in right indexing HOPs - this would allow 
us to determine batch_size as the number of rows in the output.

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