[SCEV] make SCEV smarter about proving no-wrap.

Summary:
Teach SCEV to prove no overflow for an add recurrence by proving
something about the range of another add recurrence a loop-invariant
distance away from it.

Reviewers: atrick, hfinkel

Subscribers: llvm-commits

Differential Revision: http://reviews.llvm.org/D7980

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@231305 91177308-0d34-0410-b5e6-96231b3b80d8

include/llvm/Analysis/ScalarEvolution.h

@@ -561,6 +561,15 @@ namespace llvm {
     /// pointer.
     bool checkValidity(const SCEV *S) const;
 
+    // Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be equal
+    // to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}.  This is equivalent to
+    // proving no signed (resp. unsigned) wrap in {`Start`,+,`Step`} if
+    // `ExtendOpTy` is `SCEVSignExtendExpr` (resp. `SCEVZeroExtendExpr`).
+    //
+    template<typename ExtendOpTy>
+    bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
+                                   const Loop *L);
+
   public:
     static char ID; // Pass identification, replacement for typeid
     ScalarEvolution();