[Backend] Use post-order traversal for liveness numbering (#1027)

Also add tests for `tt.trans`.

lib/Analysis/Alias.cpp

@@ -25,13 +25,14 @@ ChangeResult SharedMemoryAliasAnalysis::visitOperation(
   if (maybeSharedAllocationOp(op)) {
     // These ops may allocate a new shared memory buffer.
     auto result = op->getResult(0);
-    // FIXME(Keren): extract and insert are always alias for now
+    // XXX(Keren): the following ops are always aliasing for now
     if (isa<tensor::ExtractSliceOp, triton::TransOp>(op)) {
       // extract_slice %src
+      // trans %src
       aliasInfo = AliasInfo(operands[0]->getValue());
       pessimistic = false;
-    } else if (isa<tensor::InsertSliceOp>(op) ||
-               isa<triton::gpu::InsertSliceAsyncOp>(op)) {
+    } else if (isa<tensor::InsertSliceOp, triton::gpu::InsertSliceAsyncOp>(
+                   op)) {
       // insert_slice_async %src, %dst, %index
       // insert_slice %src into %dst[%offsets]
       aliasInfo = AliasInfo(operands[1]->getValue());

lib/Analysis/Allocation.cpp

@@ -298,10 +298,24 @@ private:
 
   /// Resolves liveness of all values involved under the root operation.
   void resolveLiveness() {
-    // In the SCF dialect, we always have a sequentially nested structure of
-    // blocks
+    // Assign an ID to each operation using post-order traversal.
+    // To achieve the correct liveness range, the parent operation's ID
+    // should be greater than each of its child operation's ID .
+    // Example:
+    //     ...
+    //     %5 = triton.convert_layout %4
+    //     %6 = scf.for ... iter_args(%arg0 = %0) -> (i32) {
+    //       %2 = triton.convert_layout %5
+    //       ...
+    //       scf.yield %arg0
+    //     }
+    // For example, %5 is defined in the parent region and used in
+    // the child region, and is not passed as a block argument.
+    // %6 should should have an ID greater than its child operations,
+    // otherwise %5 liveness range ends before the child operation's liveness
+    // range ends.
     DenseMap<Operation *, size_t> operationId;
-    operation->walk<WalkOrder::PreOrder>(
+    operation->walk<WalkOrder::PostOrder>(
         [&](Operation *op) { operationId[op] = operationId.size(); });
 
     // Analyze liveness of explicit buffers