[SCEV] Prove implications of different type via truncation

When we need to prove implication of expressions of different type width,
the default strategy is to widen everything to wider type and prove in this
type. This does not interact well with AddRecs with negative steps and
unsigned predicates: such AddRec will likely not have a `nuw` flag, and its
`zext` to wider type will not be an AddRec. In contraty, `trunc` of an AddRec
in some cases can easily be proved to be an `AddRec` too.

This patch introduces an alternative way to handling implications of different
type widths. If we can prove that wider type values actually fit in the narrow type,
we truncate them and prove the implication in narrow type.

Differential Revision: https://reviews.llvm.org/D89548
Reviewed By: fhahn

Author: Max Kazantsev

llvm/lib/Analysis/ScalarEvolution.cpp

@@ -9699,6 +9699,25 @@ bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
   // Balance the types.
   if (getTypeSizeInBits(LHS->getType()) <
       getTypeSizeInBits(FoundLHS->getType())) {
+    // For unsigned and equality predicates, try to prove that both found
+    // operands fit into narrow unsigned range. If so, try to prove facts in
+    // narrow types.
+    if (!CmpInst::isSigned(FoundPred)) {
+      auto *NarrowType = LHS->getType();
+      auto *WideType = FoundLHS->getType();
+      auto BitWidth = getTypeSizeInBits(NarrowType);
+      const SCEV *MaxValue = getZeroExtendExpr(
+          getConstant(APInt::getMaxValue(BitWidth)), WideType);
+      if (isKnownPredicate(ICmpInst::ICMP_ULE, FoundLHS, MaxValue) &&
+          isKnownPredicate(ICmpInst::ICMP_ULE, FoundRHS, MaxValue)) {
+        const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType);
+        const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType);
+        if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, TruncFoundLHS,
+                                       TruncFoundRHS, Context))
+          return true;
+      }
+    }
+
     if (CmpInst::isSigned(Pred)) {
       LHS = getSignExtendExpr(LHS, FoundLHS->getType());
       RHS = getSignExtendExpr(RHS, FoundLHS->getType());

llvm/test/Analysis/ScalarEvolution/srem.ll

@@ -29,7 +29,7 @@ define dso_local void @_Z4loopi(i32 %width) local_unnamed_addr #0 {
 ; CHECK-NEXT:    %add = add nsw i32 %2, %call
 ; CHECK-NEXT:    --> (%2 + %call) U: full-set S: full-set Exits: <<Unknown>> LoopDispositions: { %for.cond: Variant }
 ; CHECK-NEXT:    %inc = add nsw i32 %i.0, 1
-; CHECK-NEXT:    --> {1,+,1}<nuw><%for.cond> U: [1,0) S: [1,0) Exits: (1 + %width) LoopDispositions: { %for.cond: Computable }
+; CHECK-NEXT:    --> {1,+,1}<nuw><%for.cond> U: full-set S: full-set Exits: (1 + %width) LoopDispositions: { %for.cond: Computable }
 ; CHECK-NEXT:  Determining loop execution counts for: @_Z4loopi
 ; CHECK-NEXT:  Loop %for.cond: backedge-taken count is %width
 ; CHECK-NEXT:  Loop %for.cond: max backedge-taken count is -1

llvm/unittests/Analysis/ScalarEvolutionTest.cpp

@@ -1316,4 +1316,45 @@ TEST_F(ScalarEvolutionsTest, UnsignedIsImpliedViaOperations) {
   });
 }
 
+TEST_F(ScalarEvolutionsTest, ProveImplicationViaNarrowing) {
+  LLVMContext C;
+  SMDiagnostic Err;
+  std::unique_ptr<Module> M = parseAssemblyString(
+      "define i32 @foo(i32 %start, i32* %q) { "
+      "entry: "
+      "  %wide.start = zext i32 %start to i64 "
+      "  br label %loop "
+      "loop: "
+      "  %wide.iv = phi i64 [%wide.start, %entry], [%wide.iv.next, %backedge] "
+      "  %iv = phi i32 [%start, %entry], [%iv.next, %backedge] "
+      "  %cond = icmp eq i64 %wide.iv, 0 "
+      "  br i1 %cond, label %exit, label %backedge "
+      "backedge: "
+      "  %iv.next = add i32 %iv, -1 "
+      "  %index = zext i32 %iv.next to i64 "
+      "  %load.addr = getelementptr i32, i32* %q, i64 %index "
+      "  %stop = load i32, i32* %load.addr "
+      "  %loop.cond = icmp eq i32 %stop, 0 "
+      "  %wide.iv.next = add nsw i64 %wide.iv, -1 "
+      "  br i1 %loop.cond, label %loop, label %failure "
+      "exit: "
+      "  ret i32 0 "
+      "failure: "
+      "  unreachable "
+      "} ",
+      Err, C);
+
+  ASSERT_TRUE(M && "Could not parse module?");
+  ASSERT_TRUE(!verifyModule(*M) && "Must have been well formed!");
+
+  runWithSE(*M, "foo", [](Function &F, LoopInfo &LI, ScalarEvolution &SE) {
+    auto *IV = SE.getSCEV(getInstructionByName(F, "iv"));
+    auto *Zero = SE.getZero(IV->getType());
+    auto *Backedge = getInstructionByName(F, "iv.next")->getParent();
+    ASSERT_TRUE(Backedge);
+    EXPECT_TRUE(SE.isBasicBlockEntryGuardedByCond(Backedge, ICmpInst::ICMP_UGT,
+                                                  IV, Zero));
+  });
+}
+
 }  // end namespace llvm