[ScalarEvolution] Predicate implication from operations

This patch allows SCEV predicate analysis to prove implication of some expression predicates
from context predicates related to arguments of those expressions.
It introduces three new rules:

For addition:
  (A >X && B >= 0) || (B >= 0 && A > X) ===> (A + B) > X.

For division:
  (A > X) && (0 < B <= X + 1) ===> (A / B > 0).
  (A > X) && (-B <= X < 0) ===> (A / B >= 0).

Using these rules, SCEV is able to prove facts like "if X > 1 then X / 2 > 0".
They can also be combined with the same context, to prove more complex expressions like
"if X > 1 then X/2 + 1 > 1".

Diffirential Revision: https://reviews.llvm.org/D30887

Reviewed by: sanjoy

llvm-svn: 298481

0 files changed, 0 insertions, 0 deletions