diff --git a/cpp/src/join/conditional_join_kernels.cuh b/cpp/src/join/conditional_join_kernels.cuh
index dc455ad9cef..f665aba698f 100644
--- a/cpp/src/join/conditional_join_kernels.cuh
+++ b/cpp/src/join/conditional_join_kernels.cuh
@@ -67,23 +67,25 @@ __global__ void compute_conditional_join_output_size(
     &intermediate_storage[threadIdx.x * device_expression_data.num_intermediates];
 
   std::size_t thread_counter{0};
-  cudf::size_type const start_idx      = threadIdx.x + blockIdx.x * block_size;
-  cudf::size_type const stride         = block_size * gridDim.x;
-  cudf::size_type const left_num_rows  = left_table.num_rows();
-  cudf::size_type const right_num_rows = right_table.num_rows();
-  auto const outer_num_rows            = (swap_tables ? right_num_rows : left_num_rows);
-  auto const inner_num_rows            = (swap_tables ? left_num_rows : right_num_rows);
+  auto const start_idx = cudf::detail::grid_1d::global_thread_id();
+  auto const stride    = cudf::detail::grid_1d::grid_stride();
+
+  cudf::thread_index_type const left_num_rows  = left_table.num_rows();
+  cudf::thread_index_type const right_num_rows = right_table.num_rows();
+  auto const outer_num_rows                    = (swap_tables ? right_num_rows : left_num_rows);
+  auto const inner_num_rows                    = (swap_tables ? left_num_rows : right_num_rows);
 
   auto evaluator = cudf::ast::detail::expression_evaluator<has_nulls>(
     left_table, right_table, device_expression_data);
 
-  for (cudf::size_type outer_row_index = start_idx; outer_row_index < outer_num_rows;
+  for (cudf::thread_index_type outer_row_index = start_idx; outer_row_index < outer_num_rows;
        outer_row_index += stride) {
     bool found_match = false;
-    for (cudf::size_type inner_row_index = 0; inner_row_index < inner_num_rows; inner_row_index++) {
-      auto output_dest           = cudf::ast::detail::value_expression_result<bool, has_nulls>();
-      auto const left_row_index  = swap_tables ? inner_row_index : outer_row_index;
-      auto const right_row_index = swap_tables ? outer_row_index : inner_row_index;
+    for (cudf::thread_index_type inner_row_index = 0; inner_row_index < inner_num_rows;
+         ++inner_row_index) {
+      auto output_dest = cudf::ast::detail::value_expression_result<bool, has_nulls>();
+      cudf::size_type const left_row_index  = swap_tables ? inner_row_index : outer_row_index;
+      cudf::size_type const right_row_index = swap_tables ? outer_row_index : inner_row_index;
       evaluator.evaluate(
         output_dest, left_row_index, right_row_index, 0, thread_intermediate_storage);
       if (output_dest.is_valid() && output_dest.value()) {
@@ -161,18 +163,18 @@ __global__ void conditional_join(table_device_view left_table,
   auto thread_intermediate_storage =
     &intermediate_storage[threadIdx.x * device_expression_data.num_intermediates];
 
-  int const warp_id                    = threadIdx.x / detail::warp_size;
-  int const lane_id                    = threadIdx.x % detail::warp_size;
-  cudf::size_type const left_num_rows  = left_table.num_rows();
-  cudf::size_type const right_num_rows = right_table.num_rows();
-  auto const outer_num_rows            = (swap_tables ? right_num_rows : left_num_rows);
-  auto const inner_num_rows            = (swap_tables ? left_num_rows : right_num_rows);
+  int const warp_id                            = threadIdx.x / detail::warp_size;
+  int const lane_id                            = threadIdx.x % detail::warp_size;
+  cudf::thread_index_type const left_num_rows  = left_table.num_rows();
+  cudf::thread_index_type const right_num_rows = right_table.num_rows();
+  cudf::thread_index_type const outer_num_rows = (swap_tables ? right_num_rows : left_num_rows);
+  cudf::thread_index_type const inner_num_rows = (swap_tables ? left_num_rows : right_num_rows);
 
   if (0 == lane_id) { current_idx_shared[warp_id] = 0; }
 
   __syncwarp();
 
-  cudf::size_type outer_row_index = threadIdx.x + blockIdx.x * block_size;
+  auto outer_row_index = cudf::detail::grid_1d::global_thread_id();
 
   unsigned int const activemask = __ballot_sync(0xffff'ffffu, outer_row_index < outer_num_rows);
 
@@ -181,7 +183,8 @@ __global__ void conditional_join(table_device_view left_table,
 
   if (outer_row_index < outer_num_rows) {
     bool found_match = false;
-    for (size_type inner_row_index(0); inner_row_index < inner_num_rows; ++inner_row_index) {
+    for (thread_index_type inner_row_index(0); inner_row_index < inner_num_rows;
+         ++inner_row_index) {
       auto output_dest           = cudf::ast::detail::value_expression_result<bool, has_nulls>();
       auto const left_row_index  = swap_tables ? inner_row_index : outer_row_index;
       auto const right_row_index = swap_tables ? outer_row_index : inner_row_index;