================
@@ -77,6 +77,177 @@ struct LLVMPointerPointerLikeModel
 };
 } // namespace
 
+/// Generate a name of a canonical loop nest of the format
+/// `<prefix>(_s<num>_r<num>)*` that describes its nesting inside parent
+/// operations (`_r<num>`) and that operation's region (`_s<num>`). The region
+/// number is omitted if the parent operation has just one region. If a loop
+/// nest just consists of canonical loops nested inside each other, also uses
+/// `d<num>` where <num> is the nesting depth of the loop.
+static std::string generateLoopNestingName(StringRef prefix,
+                                           CanonicalLoopOp op) {
+  struct Component {
+    // An region argument of an operation
+    Operation *parentOp;
+    size_t regionInOpIdx;
+    bool isOnlyRegionInOp;
+    bool skipRegion;
+
+    // An operation somewhere in a parent region
+    Operation *thisOp;
+    Region *parentRegion;
+    size_t opInRegionIdx;
+    bool isOnlyOpInRegion;
+    bool skipOp;
+    int depth = -1;
+  };
+  SmallVector<Component> components;
+
+  // Gather a list of parent regions and operations, and the position within
+  // their parent
+  Operation *o = op.getOperation();
+  while (o) {
+    if (o->hasTrait<mlir::OpTrait::IsIsolatedFromAbove>())
+      break;
+
+    // Operation within a region
+    Region *r = o->getParentRegion();
+    if (!r)
+      break;
+
+    llvm::ReversePostOrderTraversal<Block *> 
traversal(&r->getBlocks().front());
+    size_t idx = 0;
+    bool found = false;
+    size_t sequentialIdx = -1;
+    bool isOnlyLoop = true;
+    for (Block *b : traversal) {
+      for (Operation &op : *b) {
+        if (&op == o && !found) {
+          sequentialIdx = idx;
+          found = true;
+        }
+        if (op.getNumRegions()) {
+          idx += 1;
+          if (idx > 1)
+            isOnlyLoop = false;
+        }
+        if (found && !isOnlyLoop)
+          break;
+      }
+    }
+
+    Component &comp = components.emplace_back();
+    comp.thisOp = o;
+    comp.parentRegion = r;
+    comp.opInRegionIdx = sequentialIdx;
+    comp.isOnlyOpInRegion = isOnlyLoop;
+
+    // Region argument of an operation
+    Operation *parent = r->getParentOp();
+
+    comp.parentOp = parent;
+    comp.regionInOpIdx = 0;
+    comp.isOnlyRegionInOp = true;
+    if (parent && parent->getRegions().size() > 1) {
+      auto getRegionIndex = [](Operation *o, Region *r) {
+        for (auto [idx, region] : llvm::enumerate(o->getRegions())) {
+          if (&region == r)
+            return idx;
+        }
+        llvm_unreachable("Region not child of its parent operation");
+      };
+      comp.regionInOpIdx = getRegionIndex(parent, r);
+      comp.isOnlyRegionInOp = false;
+    }
+
+    if (!parent)
+      break;
+
+    // next parent
+    o = parent;
+  }
+
+  // Reorder components from outermost to innermost
+  std::reverse(components.begin(), components.end());
----------------
tblah wrote:

Unsure if it is worth doing given I wouldn't expect components to ever be that 
long, but the cost of this reversal could be avoided by just using backwards 
iterators in the following loops (where needed).

https://github.com/llvm/llvm-project/pull/159773
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