[SCEV] Teach SCEV some axioms about non-wrapping arithmetic

Summary:
 - A s<  (A + C)<nsw> if C >  0
 - A s<= (A + C)<nsw> if C >= 0
 - (A + C)<nsw> s<  A if C <  0
 - (A + C)<nsw> s<= A if C <= 0

Right now `C` needs to be a constant, but we can later generalize it to
be a non-constant if needed.

Reviewers: atrick, hfinkel, reames, nlewycky

Subscribers: sanjoy, llvm-commits

Differential Revision: http://reviews.llvm.org/D13686

llvm-svn: 251050

1 files changed, 57 insertions, 2 deletions

diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index c5ca839e474..d30e982c8d5 100644
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -7162,6 +7162,60 @@ ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
   return false;
 }
 
+bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
+                                                    const SCEV *LHS,
+                                                    const SCEV *RHS) {
+
+  // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
+  // Return Y via OutY.
+  auto MatchBinaryAddToConst =
+      [this](const SCEV *Result, const SCEV *X, APInt &OutY,
+             SCEV::NoWrapFlags ExpectedFlags) {
+    const SCEV *NonConstOp, *ConstOp;
+    SCEV::NoWrapFlags FlagsPresent;
+
+    if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
+        !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
+      return false;
+
+    OutY = cast<SCEVConstant>(ConstOp)->getValue()->getValue();
+    return (FlagsPresent & ExpectedFlags) != 0;
+  };
+
+  APInt C;
+
+  switch (Pred) {
+  default:
+    break;
+
+  case ICmpInst::ICMP_SGE:
+    std::swap(LHS, RHS);
+  case ICmpInst::ICMP_SLE:
+    // X s<= (X + C)<nsw> if C >= 0
+    if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
+      return true;
+
+    // (X + C)<nsw> s<= X if C <= 0
+    if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
+        !C.isStrictlyPositive())
+      return true;
+
+  case ICmpInst::ICMP_SGT:
+    std::swap(LHS, RHS);
+  case ICmpInst::ICMP_SLT:
+    // X s< (X + C)<nsw> if C > 0
+    if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
+        C.isStrictlyPositive())
+      return true;
+
+    // (X + C)<nsw> s< X if C < 0
+    if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
+      return true;
+  }
+
+  return false;
+}
+
 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
                                                    const SCEV *LHS,
                                                    const SCEV *RHS) {
@@ -7811,8 +7865,9 @@ ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
   auto IsKnownPredicateFull =
       [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
     return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
-        IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
-        IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS);
+           IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
+           IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
+           isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
   };
 
   switch (Pred) {