- Introduce Fourier-Motzkin variable elimination to eliminate a dimension from
a system of linear equalities/inequalities. Update isEmpty to use this.
Since FM is only exact on rational/real spaces, an emptiness check based on
this is guaranteed to be exact whenever it says the underlying set is empty;
if it says, it's not empty, there may still be no integer points in it.
Also, supports a version that computes "dark shadows".
- Test this by checking for "always false" conditionals in if statements.
- Unique IntegerSet's that are small (few constraints, few variables). This
basically means the canonical empty set and other small sets that are
likely commonly used get uniqued; allows checking for the canonical empty set
by pointer. IntegerSet::kUniquingThreshold gives the threshold constraint size
for uniqui'ing.
- rename simplify-affine-expr -> simplify-affine-structures
Other cleanup
- IntegerSet::numConstraints, AffineMap::numResults are no longer needed;
remove them.
- add copy assignment operators for AffineMap, IntegerSet.
- rename Invalid() -> Null() on AffineExpr, AffineMap, IntegerSet
- Misc cleanup for FlatAffineConstraints API
PiperOrigin-RevId: 218690456
This CL applies the same pattern as AffineMap to IntegerSet: a simple struct
that acts as the storage is allocated in the bump pointer. The IntegerSet is
immutable and accessed everywhere by value.
Note that unlike AffineMap, it is not possible to remove the MLIRContext
parameter when constructing an IntegerSet for now. One possible way to achieve
this would be to add an enum to distinguish between the mathematically empty
set, the universe set and other sets.
This is left for future discussion.
PiperOrigin-RevId: 216545361
Mehdi Amini