[MLIR] Simplify semi-affine expressions

Simplify semi-affine expression for the operations like ceildiv,
floordiv and modulo by any given symbol by checking divisibilty by that
symbol.

Some properties used in simplification are:

1) Commutative property of the floordiv and ceildiv:
((expr1 floordiv expr2) floordiv expr3 ) = ((expr1 floordiv expr3) floordiv expr2)
((expr1 ceildiv expr2) ceildiv expr3 ) = ((expr1 ceildiv expr3) ceildiv expr2)

While simplification if operations are different no simplification is
possible as there is no property that simplify expressions like these:
((expr1 ceildiv expr2) floordiv expr3) or  ((expr1 floordiv expr2)
ceildiv expr3).

2) If both expr1 and expr2 are divisible by the expr3 then:
(expr1 % expr2) / expr3 = ((expr1 / expr3) % (expr2 / expr3))
where / is divide symbol.

3) If expr1 is divisible by expr2 then expr1 % expr2 = 0.

Signed-off-by: Yash Jain <yash.jain@polymagelabs.com>

Differential Revision: https://reviews.llvm.org/D84920

0 files changed, 0 insertions, 0 deletions