//  [python]
def compressed_allreduce(self, buffer_m: torch.tensor, worker_error, server_error, local_rank):

        # all_start_time = time.time()
        original_shape = buffer_m.size()
        if len(original_shape) > 1:
            buffer_m = torch.flatten(buffer_m)
        original_size = buffer_m.numel()
        worker_error_size = worker_error.numel()
        cupy.cuda.Device(local_rank).use()

        if original_size != worker_error_size:
            empty_tensor = torch.zeros(worker_error_size - original_size, device=buffer_m.device)
            buffer_m = torch.cat([buffer_m, empty_tensor])

        buffer_m.add_(worker_error)
        worker_scale = torch.linalg.norm(buffer_m) / np.sqrt(buffer_m.numel())
        worker_error.set_(buffer_m - worker_scale * buffer_m.sign().add_(1).bool().float().add_(-0.5).mul_(2.0))

        if self.bool_not_supported:
            cupy_sign_list_packed = self.compression_backend.compress_by_chunk(
                self.compression_backend.torch2cupy(buffer_m.sign_().add_(1).bool().to(dtype=torch.uint8)), self.size)
        else:
            cupy_sign_list_packed = self.compression_backend.compress_by_chunk(
                self.compression_backend.torch2cupy(buffer_m.sign_().add_(1).bool()), self.size)
        cupy_worker_scale = self.compression_backend.torch2cupy(worker_scale)

        cupy_recvbuf_sign = cupy.zeros([self.size, cupy_sign_list_packed[self.rank].size],
                                       dtype=cupy_sign_list_packed[0].dtype)
        # cupy_recvbuf_scale = cupy.zeros([self.size, 1], dtype=cupy_worker_scale.dtype)

        sign_list_packed = [
            self.compression_backend.cupy2torch(cupy_sign_list_packed[idx]) for idx in range(self.size)
        ]

        # worker_scale = self.compression_backend.cupy2torch(cupy_worker_scale)
        recvbuf_sign = self.compression_backend.cupy2torch(cupy_recvbuf_sign)
        #recvbuf_scale = self.compression_backend.cupy2torch(cupy_recvbuf_scale)
        recvbuf_scale = [
            torch.zeros(1, dtype=worker_scale.dtype, device=torch.device(get_accelerator().device_name(local_rank)))
            for i in range(self.size)
        ]

        # communication phase 1
        # gather_start = time.time()
        # Alltoall for sign
        dist.all_to_all_single(recvbuf_sign, torch.stack(sign_list_packed), group=self.world_group)
        # Allgather for scale
        dist.all_gather(recvbuf_scale, worker_scale, group=self.world_group)

        # gather_end = time.time()

        # cupy_sign_list_packed, sign_list_packed, cupy_worker_scale, worker_scale = None, None, None, None
        cupy_sign_list_packed = None

        cupy_recvbuf_sign = self.compression_backend.torch2cupy(recvbuf_sign)
        #cupy_recvbuf_scale = self.compression_backend.torch2cupy(torch.stack(recvbuf_scale))

        compensated_server_m = self.compression_backend.cupy2torch(
            (cupy.unpackbits(cupy_recvbuf_sign.flatten())).reshape(self.size, -1)).float().add_(-0.5).mul_(2.0).mul_(
                torch.stack(recvbuf_scale).mul_(1 / self.size)).sum(0)
        compensated_server_m.add_(server_error)
        server_scale = torch.linalg.norm(compensated_server_m) / np.sqrt(compensated_server_m.numel())
        server_error.set_(compensated_server_m -
                          server_scale * compensated_server_m.sign().add_(1).bool().float().add_(-0.5).mul_(2.0))

        # cupy_server_scale = self.compression_backend.torch2cupy(server_scale)

        if self.bool_not_supported:
            cupy_server_sign_packed = self.compression_backend.compress_by_chunk(
                self.compression_backend.torch2cupy(compensated_server_m.sign_().add_(1).bool().to(dtype=torch.uint8)),
                1)
        else:
            cupy_server_sign_packed = self.compression_backend.compress_by_chunk(
                self.compression_backend.torch2cupy(compensated_server_m.sign_().add_(1).bool()), 1)
        compensated_server_m = None

        cupy_recvbuf_sign_server = cupy.zeros([self.size, cupy_server_sign_packed[0].size],
                                              dtype=cupy_recvbuf_sign.dtype)
        # cupy_recvbuf_sign, recvbuf_sign = None, None
        cupy_recvbuf_sign = None

        server_sign_packed = [self.compression_backend.cupy2torch(cupy_server_sign_packed[0])]
        recvbuf_sign_server = [
            self.compression_backend.cupy2torch(cupy_recvbuf_sign_server[idx]) for idx in range(self.size)
        ]

        # server_scale = self.compression_backend.cupy2torch(cupy_server_scale)
        cupy_recvbuf_scale_server = cupy.zeros([self.size, 1], dtype=cupy_worker_scale.dtype)
        # cupy_recvbuf_scale, recvbuf_scale = None, None

        recvbuf_scale_server = [
            self.compression_backend.cupy2torch(cupy_recvbuf_scale_server[idx]) for idx in range(self.size)
        ]

        # Communication Phase 2
        dist.all_gather(recvbuf_sign_server, server_sign_packed[0], group=self.world_group)
        dist.all_gather(recvbuf_scale_server, server_scale, group=self.world_group)

        cupy_server_sign_packed = None

        # need to convert from a tensor list to a single tensor
        # dist.all_gather only provides a tensor list as the recv/output buffer
        recvbuf_sign_server = torch.stack(recvbuf_sign_server)

        cupy_recvbuf_sign_server = self.compression_backend.torch2cupy(recvbuf_sign_server)

        buffer_m.data.copy_(
            self.compression_backend.cupy2torch((cupy.unpackbits(cupy_recvbuf_sign_server.flatten())).reshape(
                self.size, -1)).float().add_(-0.5).mul_(2.0).mul_(
                    self.compression_backend.cupy2torch(cupy_recvbuf_scale_server)).flatten().data)
        if original_size != worker_error_size:
            buffer_m = buffer_m[0:original_size]
        if len(original_shape) > 1:
            buffer_m = buffer_m.reshape(original_shape)

        return buffer_m