[mlir][SCF] ValueBoundsConstraintSet: Support preliminary support for branches

This commit adds support for `scf.if` to `ValueBoundsConstraintSet`.

Example:
```
%0 = scf.if ... -> index {
  scf.yield %a : index
} else {
  scf.yield %b : index
}
```

The following constraints hold for %0:
* %0 >= min(%a, %b)
* %0 <= max(%a, %b)

Such constraints cannot be added to the constraint set; min/max is not supported by `IntegerRelation`. However, if we know which one of %a and %b is larger, we can add constraints for %0. E.g., if %a <= %b:
* %0 >= %a
* %0 <= %b

This commit required a few minor changes to the `ValueBoundsConstraintSet` infrastructure, so that values can be compared while we are still in the process of traversing the IR/adding constraints.

Author: matthias-springer

mlir/include/mlir/Interfaces/ValueBoundsOpInterface.h

@@ -203,6 +203,26 @@ class ValueBoundsConstraintSet
                        std::optional<int64_t> dim1 = std::nullopt,
                        std::optional<int64_t> dim2 = std::nullopt);
 
+  /// Traverse the IR starting from the given value/dim and populate constraints
+  /// as long as the stop condition holds. Also process all values/dims that are
+  /// already on the worklist.
+  void populateConstraints(Value value, std::optional<int64_t> dim);
+
+  /// Comparison operator for `ValueBoundsConstraintSet::compare`.
+  enum ComparisonOperator { LT, LE, EQ, GT, GE };
+
+  /// Try to prove that, based on the current state of this constraint set
+  /// (i.e., without analyzing additional IR or adding new constraints), the
+  /// "lhs" value/dim is LE/LT/EQ/GT/GE than the "rhs" value/dim.
+  ///
+  /// Return "true" if the specified relation between the two values/dims was
+  /// proven to hold. Return "false" if the specified relation could not be
+  /// proven. This could be because the specified relation does in fact not hold
+  /// or because there is not enough information in the constraint set. In other
+  /// words, if we do not know for sure, this function returns "false".
+  bool compare(Value lhs, std::optional<int64_t> lhsDim, ComparisonOperator cmp,
+               Value rhs, std::optional<int64_t> rhsDim);
+
   /// Compute whether the given values/dimensions are equal. Return "failure" if
   /// equality could not be determined.
   ///
@@ -274,13 +294,13 @@ class ValueBoundsConstraintSet
 
   ValueBoundsConstraintSet(MLIRContext *ctx, StopConditionFn stopCondition);
 
-  /// Populates the constraint set for a value/map without actually computing
-  /// the bound. Returns the position for the value/map (via the return value
-  /// and `posOut` output parameter).
-  int64_t populateConstraintsSet(Value value,
-                                 std::optional<int64_t> dim = std::nullopt);
-  int64_t populateConstraintsSet(AffineMap map, ValueDimList mapOperands,
-                                 int64_t *posOut = nullptr);
+  /// Given an affine map with a single result (and map operands), add a new
+  /// column to the constraint set that represents the result of the map.
+  /// Traverse additional IR starting from the map operands as needed (as long
+  /// as the stop condition is not satisfied). Also process all values/dims that
+  /// are already on the worklist. Return the position of the newly added
+  /// column.
+  int64_t populateConstraints(AffineMap map, ValueDimList mapOperands);
 
   /// Iteratively process all elements on the worklist until an index-typed
   /// value or shaped value meets `stopCondition`. Such values are not processed
@@ -295,14 +315,19 @@ class ValueBoundsConstraintSet
   /// value/dimension exists in the constraint set.
   int64_t getPos(Value value, std::optional<int64_t> dim = std::nullopt) const;
 
+  /// Return an affine expression that represents column `pos` in the constraint
+  /// set.
+  AffineExpr getPosExpr(int64_t pos);
+
   /// Insert a value/dimension into the constraint set. If `isSymbol` is set to
   /// "false", a dimension is added. The value/dimension is added to the
-  /// worklist.
+  /// worklist if `addToWorklist` is set.
   ///
   /// Note: There are certain affine restrictions wrt. dimensions. E.g., they
   /// cannot be multiplied. Furthermore, bounds can only be queried for
   /// dimensions but not for symbols.
-  int64_t insert(Value value, std::optional<int64_t> dim, bool isSymbol = true);
+  int64_t insert(Value value, std::optional<int64_t> dim, bool isSymbol = true,
+                 bool addToWorklist = true);
 
   /// Insert an anonymous column into the constraint set. The column is not
   /// bound to any value/dimension. If `isSymbol` is set to "false", a dimension

mlir/lib/Dialect/SCF/IR/ValueBoundsOpInterfaceImpl.cpp

@@ -111,6 +111,66 @@ struct ForOpInterface
   }
 };
 
+struct IfOpInterface
+    : public ValueBoundsOpInterface::ExternalModel<IfOpInterface, IfOp> {
+
+  static void populateBounds(scf::IfOp ifOp, Value value,
+                             std::optional<int64_t> dim,
+                             ValueBoundsConstraintSet &cstr) {
+    unsigned int resultNum = cast<OpResult>(value).getResultNumber();
+    Value thenValue = ifOp.thenYield().getResults()[resultNum];
+    Value elseValue = ifOp.elseYield().getResults()[resultNum];
+
+    // Populate constraints for the yielded value (and all values on the
+    // backward slice, as long as the current stop condition is not satisfied).
+    cstr.populateConstraints(thenValue, dim);
+    cstr.populateConstraints(elseValue, dim);
+    auto boundsBuilder = cstr.bound(value);
+    if (dim)
+      boundsBuilder[*dim];
+
+    // Compare yielded values.
+    // If thenValue <= elseValue:
+    // * result <= elseValue
+    // * result >= thenValue
+    if (cstr.compare(thenValue, dim,
+                     ValueBoundsConstraintSet::ComparisonOperator::LE,
+                     elseValue, dim)) {
+      if (dim) {
+        cstr.bound(value)[*dim] >= cstr.getExpr(thenValue, dim);
+        cstr.bound(value)[*dim] <= cstr.getExpr(elseValue, dim);
+      } else {
+        cstr.bound(value) >= thenValue;
+        cstr.bound(value) <= elseValue;
+      }
+    }
+    // If elseValue <= thenValue:
+    // * result <= thenValue
+    // * result >= elseValue
+    if (cstr.compare(elseValue, dim,
+                     ValueBoundsConstraintSet::ComparisonOperator::LE,
+                     thenValue, dim)) {
+      if (dim) {
+        cstr.bound(value)[*dim] >= cstr.getExpr(elseValue, dim);
+        cstr.bound(value)[*dim] <= cstr.getExpr(thenValue, dim);
+      } else {
+        cstr.bound(value) >= elseValue;
+        cstr.bound(value) <= thenValue;
+      }
+    }
+  }
+
+  void populateBoundsForIndexValue(Operation *op, Value value,
+                                   ValueBoundsConstraintSet &cstr) const {
+    populateBounds(cast<IfOp>(op), value, /*dim=*/std::nullopt, cstr);
+  }
+
+  void populateBoundsForShapedValueDim(Operation *op, Value value, int64_t dim,
+                                       ValueBoundsConstraintSet &cstr) const {
+    populateBounds(cast<IfOp>(op), value, dim, cstr);
+  }
+};
+
 } // namespace
 } // namespace scf
 } // namespace mlir
@@ -119,5 +179,6 @@ void mlir::scf::registerValueBoundsOpInterfaceExternalModels(
     DialectRegistry &registry) {
   registry.addExtension(+[](MLIRContext *ctx, scf::SCFDialect *dialect) {
     scf::ForOp::attachInterface<scf::ForOpInterface>(*ctx);
+    scf::IfOp::attachInterface<scf::IfOpInterface>(*ctx);
   });
 }

mlir/lib/Dialect/Vector/IR/ScalableValueBoundsConstraintSet.cpp

@@ -59,20 +59,24 @@ ScalableValueBoundsConstraintSet::computeScalableBound(
   ScalableValueBoundsConstraintSet scalableCstr(
       value.getContext(), stopCondition ? stopCondition : defaultStopCondition,
       vscaleMin, vscaleMax);
-  int64_t pos = scalableCstr.populateConstraintsSet(value, dim);
+  int64_t pos = scalableCstr.insert(value, dim, /*isSymbol=*/false);
+  scalableCstr.processWorklist();
 
-  // Project out all variables apart from vscale.
-  // This should result in constraints in terms of vscale only.
+  // Project out all columns apart from vscale and the starting point
+  // (value/dim). This should result in constraints in terms of vscale only.
   auto projectOutFn = [&](ValueDim p) {
-    return p.first != scalableCstr.getVscaleValue();
+    bool isStartingPoint =
+        p.first == value &&
+        p.second == dim.value_or(ValueBoundsConstraintSet::kIndexValue);
+    return p.first != scalableCstr.getVscaleValue() && !isStartingPoint;
   };
   scalableCstr.projectOut(projectOutFn);
 
   assert(scalableCstr.cstr.getNumDimAndSymbolVars() ==
              scalableCstr.positionToValueDim.size() &&
          "inconsistent mapping state");
 
-  // Check that the only symbols left are vscale.
+  // Check that the only columns left are vscale and the starting point.
   for (int64_t i = 0; i < scalableCstr.cstr.getNumDimAndSymbolVars(); ++i) {
     if (i == pos)
       continue;

mlir/lib/Interfaces/ValueBoundsOpInterface.cpp

@@ -110,25 +110,47 @@ AffineExpr ValueBoundsConstraintSet::getExpr(Value value,
   assertValidValueDim(value, dim);
 #endif // NDEBUG
 
+  // Check if the value/dim is statically known. In that case, an affine
+  // constant expression should be returned. This allows us to support
+  // multiplications with constants. (Multiplications of two columns in the
+  // constraint set is not supported.)
+  std::optional<int64_t> constSize = std::nullopt;
   auto shapedType = dyn_cast<ShapedType>(value.getType());
   if (shapedType) {
-    // Static dimension: return constant directly.
     if (shapedType.hasRank() && !shapedType.isDynamicDim(*dim))
-      return builder.getAffineConstantExpr(shapedType.getDimSize(*dim));
-  } else {
-    // Constant index value: return directly.
-    if (auto constInt = ::getConstantIntValue(value))
-      return builder.getAffineConstantExpr(*constInt);
+      constSize = shapedType.getDimSize(*dim);
+  } else if (auto constInt = ::getConstantIntValue(value)) {
+    constSize = *constInt;
   }
 
-  // Dynamic value: add to constraint set.
+  // If the value/dim is already mapped, return the corresponding expression
+  // directly.
   ValueDim valueDim = std::make_pair(value, dim.value_or(kIndexValue));
-  if (!valueDimToPosition.contains(valueDim))
-    (void)insert(value, dim);
-  int64_t pos = getPos(value, dim);
-  return pos < cstr.getNumDimVars()
-             ? builder.getAffineDimExpr(pos)
-             : builder.getAffineSymbolExpr(pos - cstr.getNumDimVars());
+  if (valueDimToPosition.contains(valueDim)) {
+    // If it is a constant, return an affine constant expression. Otherwise,
+    // return an affine expression that represents the respective column in the
+    // constraint set.
+    if (constSize)
+      return builder.getAffineConstantExpr(*constSize);
+    return getPosExpr(getPos(value, dim));
+  }
+
+  if (constSize) {
+    // Constant index value/dim: add column to the constraint set, add EQ bound
+    // and return an affine constant expression without pushing the newly added
+    // column to the worklist.
+    (void)insert(value, dim, /*isSymbol=*/true, /*addToWorklist=*/false);
+    if (shapedType)
+      bound(value)[*dim] == *constSize;
+    else
+      bound(value) == *constSize;
+    return builder.getAffineConstantExpr(*constSize);
+  }
+
+  // Dynamic value/dim: insert column to the constraint set and put it on the
+  // worklist. Return an affine expression that represents the newly inserted
+  // column in the constraint set.
+  return getPosExpr(insert(value, dim, /*isSymbol=*/true));
 }
 
 AffineExpr ValueBoundsConstraintSet::getExpr(OpFoldResult ofr) {
@@ -145,7 +167,7 @@ AffineExpr ValueBoundsConstraintSet::getExpr(int64_t constant) {
 
 int64_t ValueBoundsConstraintSet::insert(Value value,
                                          std::optional<int64_t> dim,
-                                         bool isSymbol) {
+                                         bool isSymbol, bool addToWorklist) {
 #ifndef NDEBUG
   assertValidValueDim(value, dim);
 #endif // NDEBUG
@@ -160,7 +182,12 @@ int64_t ValueBoundsConstraintSet::insert(Value value,
     if (positionToValueDim[i].has_value())
       valueDimToPosition[*positionToValueDim[i]] = i;
 
-  worklist.push(pos);
+  if (addToWorklist) {
+    LLVM_DEBUG(llvm::dbgs() << "Push to worklist: " << value
+                            << " (dim: " << dim.value_or(kIndexValue) << ")\n");
+    worklist.push(pos);
+  }
+
   return pos;
 }
 
@@ -190,6 +217,13 @@ int64_t ValueBoundsConstraintSet::getPos(Value value,
   return it->second;
 }
 
+AffineExpr ValueBoundsConstraintSet::getPosExpr(int64_t pos) {
+  assert(pos >= 0 && pos < cstr.getNumDimAndSymbolVars() && "invalid position");
+  return pos < cstr.getNumDimVars()
+             ? builder.getAffineDimExpr(pos)
+             : builder.getAffineSymbolExpr(pos - cstr.getNumDimVars());
+}
+
 static Operation *getOwnerOfValue(Value value) {
   if (auto bbArg = dyn_cast<BlockArgument>(value))
     return bbArg.getOwner()->getParentOp();
@@ -492,15 +526,16 @@ FailureOr<int64_t> ValueBoundsConstraintSet::computeConstantBound(
 
   // Default stop condition if none was specified: Keep adding constraints until
   // a bound could be computed.
-  int64_t pos;
+  int64_t pos = 0;
   auto defaultStopCondition = [&](Value v, std::optional<int64_t> dim,
                                   ValueBoundsConstraintSet &cstr) {
     return cstr.cstr.getConstantBound64(type, pos).has_value();
   };
 
   ValueBoundsConstraintSet cstr(
       map.getContext(), stopCondition ? stopCondition : defaultStopCondition);
-  cstr.populateConstraintsSet(map, operands, &pos);
+  pos = cstr.populateConstraints(map, operands);
+  assert(pos == 0 && "expected `map` is the first column");
 
   // Compute constant bound for `valueDim`.
   int64_t ubAdjustment = closedUB ? 0 : 1;
@@ -509,29 +544,28 @@ FailureOr<int64_t> ValueBoundsConstraintSet::computeConstantBound(
   return failure();
 }
 
-int64_t
-ValueBoundsConstraintSet::populateConstraintsSet(Value value,
-                                                 std::optional<int64_t> dim) {
+void ValueBoundsConstraintSet::populateConstraints(Value value,
+                                                   std::optional<int64_t> dim) {
 #ifndef NDEBUG
   assertValidValueDim(value, dim);
 #endif // NDEBUG
 
-  AffineMap map =
-      AffineMap::get(/*dimCount=*/1, /*symbolCount=*/0,
-                     Builder(value.getContext()).getAffineDimExpr(0));
-  return populateConstraintsSet(map, {{value, dim}});
+  // `getExpr` pushes the value/dim onto the worklist (unless it was already
+  // analyzed).
+  (void)getExpr(value, dim);
+  // Process all values/dims on the worklist. This may traverse and analyze
+  // additional IR, depending the current stop function.
+  processWorklist();
 }
 
-int64_t ValueBoundsConstraintSet::populateConstraintsSet(AffineMap map,
-                                                         ValueDimList operands,
-                                                         int64_t *posOut) {
+int64_t ValueBoundsConstraintSet::populateConstraints(AffineMap map,
+                                                      ValueDimList operands) {
   assert(map.getNumResults() == 1 && "expected affine map with one result");
   int64_t pos = insert(/*isSymbol=*/false);
-  if (posOut)
-    *posOut = pos;
 
   // Add map and operands to the constraint set. Dimensions are converted to
-  // symbols. All operands are added to the worklist.
+  // symbols. All operands are added to the worklist (unless they were already
+  // processed).
   auto mapper = [&](std::pair<Value, std::optional<int64_t>> v) {
     return getExpr(v.first, v.second);
   };
@@ -566,6 +600,55 @@ ValueBoundsConstraintSet::computeConstantDelta(Value value1, Value value2,
                               {{value1, dim1}, {value2, dim2}});
 }
 
+bool ValueBoundsConstraintSet::compare(Value lhs, std::optional<int64_t> lhsDim,
+                                       ComparisonOperator cmp, Value rhs,
+                                       std::optional<int64_t> rhsDim) {
+  // This function returns "true" if "lhs CMP rhs" is proven to hold.
+  //
+  // Example for ComparisonOperator::LE and index-typed values: We would like to
+  // prove that lhs <= rhs. Proof by contradiction: add the inverse
+  // relation (lhs > rhs) to the constraint set and check if the resulting
+  // constraint set is "empty" (i.e. has no solution). In that case,
+  // lhs > rhs must be incorrect and we can deduce that lhs <= rhs holds.
+
+  // We cannot prove anything if the constraint set is already empty.
+  if (cstr.isEmpty()) {
+    LLVM_DEBUG(
+        llvm::dbgs()
+        << "cannot compare value/dims: constraint system is already empty");
+    return false;
+  }
+
+  // EQ can be expressed as LE and GE.
+  if (cmp == EQ)
+    return compare(lhs, lhsDim, ComparisonOperator::LE, rhs, rhsDim) &&
+           compare(lhs, lhsDim, ComparisonOperator::GE, rhs, rhsDim);
+
+  // Construct inequality. For the above example: lhs > rhs.
+  // `IntegerRelation` inequalities are expressed in the "flattened" form and
+  // with ">= 0". I.e., lhs - rhs - 1 >= 0.
+  SmallVector<int64_t> eq(cstr.getNumDimAndSymbolVars() + 1, 0);
+  if (cmp == LT || cmp == LE) {
+    ++eq[getPos(lhs, lhsDim)];
+    --eq[getPos(rhs, rhsDim)];
+  } else if (cmp == GT || cmp == GE) {
+    --eq[getPos(lhs, lhsDim)];
+    ++eq[getPos(rhs, rhsDim)];
+  } else {
+    llvm_unreachable("unsupported comparison operator");
+  }
+  if (cmp == LE || cmp == GE)
+    eq[cstr.getNumDimAndSymbolVars()] -= 1;
+
+  // Add inequality to the constraint set and check if it made the constraint
+  // set empty.
+  int64_t ineqPos = cstr.getNumInequalities();
+  cstr.addInequality(eq);
+  bool isEmpty = cstr.isEmpty();
+  cstr.removeInequality(ineqPos);
+  return isEmpty;
+}
+
 FailureOr<bool>
 ValueBoundsConstraintSet::areEqual(Value value1, Value value2,
                                    std::optional<int64_t> dim1,