diff --git a/mlir/include/mlir/Analysis/AffineStructures.h b/mlir/include/mlir/Analysis/AffineStructures.h
--- a/mlir/include/mlir/Analysis/AffineStructures.h
+++ b/mlir/include/mlir/Analysis/AffineStructures.h
@@ -592,6 +592,20 @@
   FlatAffineValueConstraints(ArrayRef<const AffineValueMap *> avmRef,
                              IntegerSet set);
 
+  // Construct a hyperrectangular constraint set from ValueRanges that represent
+  // induction variables, lower and upper bounds. `ivs`, `lbs` and `ubs` are
+  // expected to match one to one. The order of variables and constraints is:
+  //
+  // ivs | lbs | ubs | eq/ineq
+  // ----+-----+-----+---------
+  //   1   -1     0      >= 0
+  // ----+-----+-----+---------
+  //  -1    0     1      >= 0
+  //
+  // All dimensions as set as DimId.
+  static FlatAffineValueConstraints
+  getHyperrectangular(ValueRange ivs, ValueRange lbs, ValueRange ubs);
+
   /// Return the kind of this FlatAffineConstraints.
   Kind getKind() const override { return Kind::FlatAffineValueConstraints; }
 
diff --git a/mlir/lib/Analysis/AffineStructures.cpp b/mlir/lib/Analysis/AffineStructures.cpp
--- a/mlir/lib/Analysis/AffineStructures.cpp
+++ b/mlir/lib/Analysis/AffineStructures.cpp
@@ -189,6 +189,48 @@
   values.resize(numIds, None);
 }
 
+// Construct a hyperrectangular constraint set from ValueRanges that represent
+// induction variables, lower and upper bounds. `ivs`, `lbs` and `ubs` are
+// expected to match one to one. The order of variables and constraints is:
+//
+// ivs | lbs | ubs | eq/ineq
+// ----+-----+-----+---------
+//   1   -1     0      >= 0
+// ----+-----+-----+---------
+//  -1    0     1      >= 0
+//
+// All dimensions as set as DimId.
+FlatAffineValueConstraints
+FlatAffineValueConstraints::getHyperrectangular(ValueRange ivs, ValueRange lbs,
+                                                ValueRange ubs) {
+  FlatAffineValueConstraints res;
+  unsigned nIvs = ivs.size();
+  assert(nIvs == lbs.size() && "expected as many lower bounds as ivs");
+  assert(nIvs == ubs.size() && "expected as many upper bounds as ivs");
+
+  if (nIvs == 0)
+    return res;
+
+  res.appendDimId(ivs);
+  unsigned lbsStart = res.appendDimId(lbs);
+  unsigned ubsStart = res.appendDimId(ubs);
+
+  MLIRContext *ctx = ivs.front().getContext();
+  for (int ivIdx = 0, e = nIvs; ivIdx < e; ++ivIdx) {
+    // iv - lb >= 0
+    AffineMap lb = AffineMap::get(/*dimCount=*/3 * nIvs, /*symbolCount=*/0,
+                                  getAffineDimExpr(lbsStart + ivIdx, ctx));
+    if (failed(res.addBound(BoundType::LB, ivIdx, lb)))
+      llvm_unreachable("Unexpected FlatAffineValueConstraints creation error");
+    // -iv + ub >= 0
+    AffineMap ub = AffineMap::get(/*dimCount=*/3 * nIvs, /*symbolCount=*/0,
+                                  getAffineDimExpr(ubsStart + ivIdx, ctx));
+    if (failed(res.addBound(BoundType::UB, ivIdx, ub)))
+      llvm_unreachable("Unexpected FlatAffineValueConstraints creation error");
+  }
+  return res;
+}
+
 void FlatAffineConstraints::reset(unsigned numReservedInequalities,
                                   unsigned numReservedEqualities,
                                   unsigned newNumReservedCols,
diff --git a/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp b/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/HoistPadding.cpp
@@ -189,43 +189,6 @@
   valid = true;
 }
 
-/// Given a set of loops, assumed to be scf::ForOp, create a constraint set
-/// containing the inequalities `iv - lb >= 0` and `-iv + ub - 1 >= 0` for each
-/// loop. The order of the constraints follows:
-///
-///  ivs | lbs | ubs | eq/ineq
-///  ----+-----+-----+---------
-///   1    -1     0      >= 0
-///  ----+-----+-----+---------
-///  -1    0      1      >= 0
-///
-static FlatAffineValueConstraints
-initLoopIvsAndBounds(ArrayRef<scf::ForOp> loops) {
-  FlatAffineValueConstraints constraints;
-  // Append dims for all ivs, lbs, ubs: the order is important.
-  for (scf::ForOp op : loops)
-    constraints.appendDimId(op.getInductionVar());
-  for (scf::ForOp op : loops)
-    constraints.appendDimId(op.lowerBound());
-  for (scf::ForOp op : loops)
-    constraints.appendDimId(op.upperBound());
-  int numLoops = loops.size();
-  for (int ivIdx = 0, e = numLoops; ivIdx < e; ++ivIdx) {
-    // iv - lb >= 0
-    SmallVector<int64_t, 8> ineqLb(constraints.getNumCols(), 0);
-    ineqLb[ivIdx] = 1;
-    ineqLb[ivIdx + numLoops] = -1;
-    // -iv + ub >= 0
-    SmallVector<int64_t, 8> ineqUb(constraints.getNumCols(), 0);
-    ineqUb[ivIdx] = -1;
-    ineqUb[ivIdx + 2 * numLoops] = 1;
-    ineqUb[constraints.getNumCols() - 1] = -1;
-    constraints.addInequality(ineqLb);
-    constraints.addInequality(ineqUb);
-  }
-  return constraints;
-}
-
 static bool isDefinedOutsideOrConstant(scf::ForOp outer, Value v) {
   return outer.isDefinedOutsideOfLoop(v) || v.getDefiningOp<ConstantOp>();
 }
@@ -317,8 +280,16 @@
 // `backwardSlice`.
 FailureOr<SmallVector<Value>>
 HoistingAnalysis::getPackedTensorSizes(ImplicitLocOpBuilder &b) {
-  FlatAffineValueConstraints constraints =
-      initLoopIvsAndBounds(packingLoops.getArrayRef());
+  // Create the base affine constaints for the packedLoops.
+  auto constraints = FlatAffineValueConstraints::getHyperrectangular(
+      llvm::to_vector<8>(llvm::map_range(
+          packingLoops, [](scf::ForOp op) { return op.getInductionVar(); })),
+      llvm::to_vector<8>(llvm::map_range(
+          packingLoops, [](scf::ForOp op) { return op.lowerBound(); })),
+      llvm::to_vector<8>(llvm::map_range(
+          packingLoops, [](scf::ForOp op) { return op.upperBound(); })));
+
+  // Iteratively try to fold the upper bounds into the constraints set.
   if (failed(foldUpperBoundsIntoConstraintsSet(
           constraints, outermostEnclosingForOp, packingLoops.getArrayRef())))
     return failure();