Commits on Aug 19, 2016

1. Simplify bounds checks for multi-dimensional array accesses …

   This simplifies the array bounds check code that is emitted for
   multi-dimensional array accesses that use "regular" indexing, i.e.
   accesses of the form `A[i1,i2,...,iN]` to some `N`-dimensional array
   `A`.
   
   For example, with this change, the access `A[i,j,k]` to an array
   with the three dimensions `m`, `n` and `o` now leads to bounds checks
   that correspond to the following pseudo code:
   
   ```
   if (i >= m)
     out_of_bounds_error();
   else if (j >= n)
     out_of_bounds_error();
   else if (k >= o)
     out_of_bounds_error();
   ```
   
   So far, the following more complicated bounds checks would have been
   emitted:
   
   ```
   if (i >= m)
     out_of_bounds_error();
   else if (j >= n)
     out_of_bounds_error();
   else if (((k * n + j) * m + i) >= m * n * o)
     out_of_bounds_error();
   ```
   
   Julia also allows one-dimensional and "partial" linear indexing
   (see JuliaLang#14770), i.e. the number of indices used to access an array does
   not have to match the actual number of dimensions of the accessed array.
   For this case we still have use this old scheme.
   
   One motivation for this change was the following: expressions like
   `((k * n + j) * m + i)` are non-affine and Polly would not be able
   to analyze them. This change therefore also facilitates Polly's bounds
   check elimination logic, which would hoist such checks out of loops
   or may remove them entirely where possible.

   

   MatthiasJReisinger committed Aug 19, 2016
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