def build_model_gbuf_param_range_map(cls, model, dtype, gbuf_world_range):
        """
        Build mapping from param reference to grad buffer shard ranges.

        This method builds a mapping from parameter references to grad
        buffer shard ranges, specific to each data-parallel (DP) rank's
        set of 'owned' parameters. Each grad buffer (padded to be an even
        multiple of DP-world-size) is conceptually divided into DP-world-size
        contiguous regions, where each DP rank 'owns' a contiguous regions.
        Ownership in this sense means DP rank is responsible for reducing
        the relevant subset of grads, and updating the relevant subset of
        params.

        This conceptual partitioning of the grad buffer does NOT respect
        parameter boundaries, and as such it is assumed that each created
        range references a shard (or subset) of the full parameter. It is
        easiest to think of each DP rank as operating (i.e., reducing,
        gathering) purely on views into the grad buffer, for all model-to-
        main & main-to-model operations.

        This method creates three ranges:
        - The param's range within the entire grad buffer (i.e., world index).
        - The param's range within the DP rank's local view of the grad buffer.
        - The param's range within itself (i.e., its shard).
        """

        # Param range map.
        param_world_index_map = model._grad_buffer_param_index_map[dtype]
        param_range_map = {}
        for param, param_world_indexes in param_world_index_map.items():

            # Param range.
            param_world_start, param_world_end = param_world_indexes
            param_local_start = max(
                0,
                param_world_start - gbuf_world_range.start)
            param_local_end = min(
                gbuf_world_range.size,
                param_world_end - gbuf_world_range.start)

            # Add param, if within local gbuf range.
            if param_local_end > param_local_start:
                param_local_range = Range(param_local_start, param_local_end)
                param_world_range = param_local_range.normalize(
                    param_local_start + gbuf_world_range.start)
                sub_param_start = max(0, gbuf_world_range.start-param_world_start)
                sub_param_range = param_local_range.normalize(sub_param_start)
                param_range_map[param] = {
                    "gbuf_world" : param_world_range,
                    "gbuf_local" : param_local_range,
                    "param" : sub_param_range,
                }

        return param_range_map

        Build mapping from param reference to grad buffer shard ranges.

        This method builds a mapping from parameter references to grad
        buffer shard ranges, specific to each data-parallel (DP) rank's
        set of 'owned' parameters. Each grad buffer (padded to be an even
        multiple of DP-world-size) is conceptually divided into DP-world-size
        contiguous regions, where each DP rank 'owns' a contiguous regions.
        Ownership in this sense means DP rank is responsible for reducing
        the relevant subset of grads, and updating the relevant subset of
        params.

        This conceptual partitioning of the grad buffer does NOT respect
        parameter boundaries, and as such it is assumed that each created
        range references a shard (or subset) of the full parameter. It is
        easiest to think of each DP rank as operating (i.e., reducing,
        gathering) purely on views into the grad buffer, for all model-to-
        main & main-to-model operations.

        This method creates three ranges:
        - The param's range within the entire grad buffer (i.e., world index).
        - The param's range within the DP rank's local view of the grad buffer.
        - The param's range within itself (i.e., its shard).
        
training/DeepSpeed-Domino/domino/optimizer/distrib_optimizer.py