diff --git a/advanced_source/cpp_extension.rst b/advanced_source/cpp_extension.rst
index 6db82bc7711..e0e7a034267 100644
--- a/advanced_source/cpp_extension.rst
+++ b/advanced_source/cpp_extension.rst
@@ -946,7 +946,8 @@ without having to convert to a single pointer:
 Accessor objects have a relatively high level interface, with ``.size()`` and
 ``.stride()`` methods and multi-dimensional indexing. The ``.accessor<>``
 interface is designed to access data efficiently on cpu tensor. The equivalent
-for cuda tensors is the ``packed_accessor<>``, which produces a Packed Accessor.
+for cuda tensors are ``packed_accessor64<>`` and ``packed_accessor32<>``, which
+produce Packed Accessors with either 64-bit or 32-bit integer indexing.
 
 The fundamental difference with Accessor is that a Packed Accessor copies size
 and stride data inside of its structure instead of pointing to it. It allows us
@@ -957,20 +958,20 @@ We can design a function that takes Packed Accessors instead of pointers.
 .. code-block:: cpp
 
   __global__ void lltm_cuda_forward_kernel(
-      const torch::PackedTensorAccessor<scalar_t,3,torch::RestrictPtrTraits,size_t> gates,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> old_cell,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> new_h,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> new_cell,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> input_gate,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> output_gate,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> candidate_cell)
+      const torch::PackedTensorAccessor32<scalar_t,3,torch::RestrictPtrTraits> gates,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> old_cell,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> new_h,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> new_cell,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> input_gate,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> output_gate,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> candidate_cell)
 
 Let's decompose the template used here. the first two arguments ``scalar_t`` and
 ``2`` are the same as regular Accessor. The argument
 ``torch::RestrictPtrTraits`` indicates that the ``__restrict__`` keyword must be
-used. Finally, the argument ``size_t`` indicates that sizes and strides must be
-stored in a ``size_t`` integer. This is important as by default ``int64_t`` is
-used and can make the kernel slower.
+used. Note also that we've used the ``PackedAccessor32`` variant which store the
+sizes and strides in an ``int32_t``. This is important as using the 64-bit
+variant (``PackedAccessor64``) can make the kernel slower.
 
 The function declaration becomes
 
@@ -978,13 +979,13 @@ The function declaration becomes
 
   template <typename scalar_t>
   __global__ void lltm_cuda_forward_kernel(
-      const torch::PackedTensorAccessor<scalar_t,3,torch::RestrictPtrTraits,size_t> gates,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> old_cell,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> new_h,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> new_cell,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> input_gate,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> output_gate,
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> candidate_cell) {
+      const torch::PackedTensorAccessor32<scalar_t,3,torch::RestrictPtrTraits> gates,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> old_cell,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> new_h,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> new_cell,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> input_gate,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> output_gate,
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> candidate_cell) {
     //batch index
     const int n = blockIdx.y;
     // column index
@@ -1000,7 +1001,7 @@ The function declaration becomes
   }
 
 The implementation is much more readable! This function is then called by
-creating Packed Accessors with the ``.packed_accessor<>`` method within the
+creating Packed Accessors with the ``.packed_accessor32<>`` method within the
 host function.
 
 .. code-block:: cpp
@@ -1029,13 +1030,13 @@ host function.
 
     AT_DISPATCH_FLOATING_TYPES(gates.type(), "lltm_forward_cuda", ([&] {
       lltm_cuda_forward_kernel<scalar_t><<<blocks, threads>>>(
-          gates.packed_accessor<scalar_t,3,torch::RestrictPtrTraits,size_t>(),
-          old_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          new_h.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          new_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          input_gate.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          output_gate.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          candidate_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>());
+          gates.packed_accessor32<scalar_t,3,torch::RestrictPtrTraits>(),
+          old_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          new_h.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          new_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          input_gate.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          output_gate.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          candidate_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>());
     }));
 
     return {new_h, new_cell, input_gate, output_gate, candidate_cell, X, gates};
@@ -1048,15 +1049,15 @@ on it:
 
   template <typename scalar_t>
   __global__ void lltm_cuda_backward_kernel(
-      torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> d_old_cell,
-      torch::PackedTensorAccessor<scalar_t,3,torch::RestrictPtrTraits,size_t> d_gates,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> grad_h,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> grad_cell,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> new_cell,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> input_gate,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> output_gate,
-      const torch::PackedTensorAccessor<scalar_t,2,torch::RestrictPtrTraits,size_t> candidate_cell,
-      const torch::PackedTensorAccessor<scalar_t,3,torch::RestrictPtrTraits,size_t> gate_weights) {
+      torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> d_old_cell,
+      torch::PackedTensorAccessor32<scalar_t,3,torch::RestrictPtrTraits> d_gates,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> grad_h,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> grad_cell,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> new_cell,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> input_gate,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> output_gate,
+      const torch::PackedTensorAccessor32<scalar_t,2,torch::RestrictPtrTraits> candidate_cell,
+      const torch::PackedTensorAccessor32<scalar_t,3,torch::RestrictPtrTraits> gate_weights) {
     //batch index
     const int n = blockIdx.y;
     // column index
@@ -1102,15 +1103,15 @@ on it:
 
     AT_DISPATCH_FLOATING_TYPES(X.type(), "lltm_forward_cuda", ([&] {
       lltm_cuda_backward_kernel<scalar_t><<<blocks, threads>>>(
-          d_old_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          d_gates.packed_accessor<scalar_t,3,torch::RestrictPtrTraits,size_t>(),
-          grad_h.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          grad_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          new_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          input_gate.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          output_gate.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          candidate_cell.packed_accessor<scalar_t,2,torch::RestrictPtrTraits,size_t>(),
-          gates.packed_accessor<scalar_t,3,torch::RestrictPtrTraits,size_t>());
+          d_old_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          d_gates.packed_accessor32<scalar_t,3,torch::RestrictPtrTraits>(),
+          grad_h.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          grad_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          new_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          input_gate.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          output_gate.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          candidate_cell.packed_accessor32<scalar_t,2,torch::RestrictPtrTraits>(),
+          gates.packed_accessor32<scalar_t,3,torch::RestrictPtrTraits>());
     }));
 
     auto d_gate_weights = d_gates.reshape({batch_size, 3*state_size});