- 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 AffineExpr to AffineMap: a simple struct
that acts as the storage is allocated in the bump pointer. The AffineMap is
immutable and accessed everywhere by value.
PiperOrigin-RevId: 216445930
Uday Bondhugula