[SCEV] Clarify behavior around max backedge taken count

This change makes the split between the "exact" backedge taken count
and the "maximum" backedge taken count a bit more obvious.  Both of
these are upper bounds on the number of times the loop header
executes (since SCEV does not account for most kinds of abnormal
control flow), but the latter is guaranteed to be a constant.

There were a few places where the max backedge taken count *was* a
non-constant; I've changed those to compute constants instead.

At this point, I'm not sure if the constant max backedge count can be
computed by calling `getUnsignedRange(Exact).getUnsignedMax()` without
losing precision.  If it can, we can simplify even further by making
`getMaxBackedgeTakenCount` a thin wrapper around
`getBackedgeTakenCount` and `getUnsignedRange`.

llvm-svn: 303497

Author: sanjoy

llvm/include/llvm/Analysis/ScalarEvolution.h

@@ -656,10 +656,12 @@ class ScalarEvolution {
     /// Test whether this BackedgeTakenInfo contains complete information.
     bool hasFullInfo() const { return isComplete(); }
 
-    /// Return an expression indicating the exact backedge-taken count of the
-    /// loop if it is known or SCEVCouldNotCompute otherwise. This is the
-    /// number of times the loop header can be guaranteed to execute, minus
-    /// one.
+    /// Return an expression indicating the exact *backedge-taken*
+    /// count of the loop if it is known or SCEVCouldNotCompute
+    /// otherwise.  If execution makes it to the backedge on every
+    /// iteration (i.e. there are no abnormal exists like exception
+    /// throws and thread exits) then this is the number of times the
+    /// loop header will execute minus one.
     ///
     /// If the SCEV predicate associated with the answer can be different
     /// from AlwaysTrue, we must add a (non null) Predicates argument.
@@ -1398,11 +1400,11 @@ class ScalarEvolution {
   const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
 
   /// If the specified loop has a predictable backedge-taken count, return it,
-  /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
-  /// is the number of times the loop header will be branched to from within
-  /// the loop. This is one less than the trip count of the loop, since it
-  /// doesn't count the first iteration, when the header is branched to from
-  /// outside the loop.
+  /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
+  /// the number of times the loop header will be branched to from within the
+  /// loop, assuming there are no abnormal exists like exception throws. This is
+  /// one less than the trip count of the loop, since it doesn't count the first
+  /// iteration, when the header is branched to from outside the loop.
   ///
   /// Note that it is not valid to call this method on a loop without a
   /// loop-invariant backedge-taken count (see
@@ -1417,8 +1419,10 @@ class ScalarEvolution {
   const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
                                               SCEVUnionPredicate &Predicates);
 
-  /// Similar to getBackedgeTakenCount, except return the least SCEV value
-  /// that is known never to be less than the actual backedge taken count.
+  /// When successful, this returns a SCEVConstant that is greater than or equal
+  /// to (i.e. a "conservative over-approximation") of the value returend by
+  /// getBackedgeTakenCount.  If such a value cannot be computed, it returns the
+  /// SCEVCouldNotCompute object.
   const SCEV *getMaxBackedgeTakenCount(const Loop *L);
 
   /// Return true if the backedge taken count is either the value returned by

llvm/lib/Analysis/ScalarEvolution.cpp

@@ -5947,6 +5947,8 @@ ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
   if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
     return SE->getCouldNotCompute();
 
+  assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) &&
+         "No point in having a non-constant max backedge taken count!");
   return getMax();
 }
 
@@ -5972,7 +5974,11 @@ bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
 }
 
 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
-    : ExactNotTaken(E), MaxNotTaken(E), MaxOrZero(false) {}
+    : ExactNotTaken(E), MaxNotTaken(E), MaxOrZero(false) {
+  assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
+          isa<SCEVConstant>(MaxNotTaken)) &&
+         "No point in having a non-constant max backedge taken count!");
+}
 
 ScalarEvolution::ExitLimit::ExitLimit(
     const SCEV *E, const SCEV *M, bool MaxOrZero,
@@ -5981,6 +5987,9 @@ ScalarEvolution::ExitLimit::ExitLimit(
   assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
           !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
          "Exact is not allowed to be less precise than Max");
+  assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
+          isa<SCEVConstant>(MaxNotTaken)) &&
+         "No point in having a non-constant max backedge taken count!");
   for (auto *PredSet : PredSetList)
     for (auto *P : *PredSet)
       addPredicate(P);
@@ -5989,11 +5998,19 @@ ScalarEvolution::ExitLimit::ExitLimit(
 ScalarEvolution::ExitLimit::ExitLimit(
     const SCEV *E, const SCEV *M, bool MaxOrZero,
     const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
-    : ExitLimit(E, M, MaxOrZero, {&PredSet}) {}
+    : ExitLimit(E, M, MaxOrZero, {&PredSet}) {
+  assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
+          isa<SCEVConstant>(MaxNotTaken)) &&
+         "No point in having a non-constant max backedge taken count!");
+}
 
 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
                                       bool MaxOrZero)
-    : ExitLimit(E, M, MaxOrZero, None) {}
+    : ExitLimit(E, M, MaxOrZero, None) {
+  assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
+          isa<SCEVConstant>(MaxNotTaken)) &&
+         "No point in having a non-constant max backedge taken count!");
+}
 
 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
 /// computable exit into a persistent ExitNotTakenInfo array.
@@ -6018,6 +6035,8 @@ ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
 
         return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate));
       });
+  assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) &&
+         "No point in having a non-constant max backedge taken count!");
 }
 
 /// Invalidate this result and free the ExitNotTakenInfo array.
@@ -6279,7 +6298,7 @@ ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
       // to not.
       if (isa<SCEVCouldNotCompute>(MaxBECount) &&
           !isa<SCEVCouldNotCompute>(BECount))
-        MaxBECount = BECount;
+        MaxBECount = getConstant(getUnsignedRange(BECount).getUnsignedMax());
 
       return ExitLimit(BECount, MaxBECount, false,
                        {&EL0.Predicates, &EL1.Predicates});
@@ -7583,13 +7602,20 @@ ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
       loopHasNoAbnormalExits(AddRec->getLoop())) {
     const SCEV *Exact =
         getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
-    return ExitLimit(Exact, Exact, false, Predicates);
+    const SCEV *Max =
+        Exact == getCouldNotCompute()
+            ? Exact
+            : getConstant(getUnsignedRange(Exact).getUnsignedMax());
+    return ExitLimit(Exact, Max, false, Predicates);
   }
 
   // Solve the general equation.
-  const SCEV *E = SolveLinEquationWithOverflow(
-      StepC->getAPInt(), getNegativeSCEV(Start), *this);
-  return ExitLimit(E, E, false, Predicates);
+  const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
+                                               getNegativeSCEV(Start), *this);
+  const SCEV *M = E == getCouldNotCompute()
+                      ? E
+                      : getConstant(getUnsignedRange(E).getUnsignedMax());
+  return ExitLimit(E, M, false, Predicates);
 }
 
 ScalarEvolution::ExitLimit
@@ -9218,8 +9244,9 @@ ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
                                 getConstant(StrideForMaxBECount), false);
   }
 
-  if (isa<SCEVCouldNotCompute>(MaxBECount))
-    MaxBECount = BECount;
+  if (isa<SCEVCouldNotCompute>(MaxBECount) &&
+      !isa<SCEVCouldNotCompute>(BECount))
+    MaxBECount = getConstant(getUnsignedRange(BECount).getUnsignedMax());
 
   return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
 }

llvm/test/Analysis/ScalarEvolution/nsw.ll

@@ -102,7 +102,7 @@ for.body.i.i:                                     ; preds = %entry, %for.body.i.
   %cmp.i.i = icmp eq i32* %ptrincdec.i.i, %end
   br i1 %cmp.i.i, label %_ZSt4fillIPiiEvT_S1_RKT0_.exit, label %for.body.i.i
 ; CHECK: Loop %for.body.i.i: backedge-taken count is ((-4 + (-1 * %begin) + %end) /u 4)
-; CHECK: Loop %for.body.i.i: max backedge-taken count is ((-4 + (-1 * %begin) + %end) /u 4)
+; CHECK: Loop %for.body.i.i: max backedge-taken count is 4611686018427387903
 _ZSt4fillIPiiEvT_S1_RKT0_.exit:                   ; preds = %for.body.i.i, %entry
   ret void
 }

llvm/test/Analysis/ScalarEvolution/trip-count-pow2.ll

@@ -14,7 +14,7 @@ exit:
 
 ; CHECK-LABEL: @test1
 ; CHECK: Loop %loop: backedge-taken count is ((-32 + (96 * %n)) /u 32)
-; CHECK: Loop %loop: max backedge-taken count is ((-32 + (96 * %n)) /u 32)
+; CHECK: Loop %loop: max backedge-taken count is 134217727
 }
 
 ; PR19183
@@ -32,7 +32,7 @@ exit:
 
 ; CHECK-LABEL: @test2
 ; CHECK: Loop %loop: backedge-taken count is ((-32 + (32 * (%n /u 32))) /u 32)
-; CHECK: Loop %loop: max backedge-taken count is ((-32 + (32 * (%n /u 32))) /u 32)
+; CHECK: Loop %loop: max backedge-taken count is 134217727
 }
 
 define void @test3(i32 %n) {
@@ -49,7 +49,7 @@ exit:
 
 ; CHECK-LABEL: @test3
 ; CHECK: Loop %loop: backedge-taken count is ((-32 + (32 * %n)) /u 32)
-; CHECK: Loop %loop: max backedge-taken count is ((-32 + (32 * %n)) /u 32)
+; CHECK: Loop %loop: max backedge-taken count is 134217727
 }
 
 define void @test4(i32 %n) {
@@ -66,7 +66,7 @@ exit:
 
 ; CHECK-LABEL: @test4
 ; CHECK: Loop %loop: backedge-taken count is ((-4 + (-1431655764 * %n)) /u 4)
-; CHECK: Loop %loop: max backedge-taken count is ((-4 + (-1431655764 * %n)) /u 4)
+; CHECK: Loop %loop: max backedge-taken count is 1073741823
 }
 
 define void @test5(i32 %n) {
@@ -83,5 +83,5 @@ exit:
 
 ; CHECK-LABEL: @test5
 ; CHECK: Loop %loop: backedge-taken count is ((-4 + (4 * %n)) /u 4)
-; CHECK: Loop %loop: max backedge-taken count is ((-4 + (4 * %n)) /u 4)
+; CHECK: Loop %loop: max backedge-taken count is 1073741823
 }