import functools
import importlib
import sys
import types

import torch

from .allowed_functions import _disallowed_function_ids, is_user_defined_allowed

from .utils import hashable

from .variables import (
    SkipFilesVariable,
    TorchCtxManagerClassVariable,
    TorchInGraphFunctionVariable,
)


"""
Map of torch objects to their tracing rules (Dynamo variables).
* TorchVariable: The functions should be put into the FX graph or can be constant folded. E.g.,
  - torch.add: should be put into the FX graph.
  - torch.is_floating_point: constant folded.
* TorchCtxManagerClassVariable: The context manager classes are supported by Dynamo. E.g., torch.no_grad
* SkipFilesVariable: The objects should be skipped from tracing.
* UserFunctionVariable: The functions should be inlined.

We explicitly list torch objects which should be wrapped as TorchCtxManagerClassVariable.
The initial list comes from the heuristic in test/dynamo/test_trace_rules.py:generate_allow_list.

For developers: If you add/remove a torch level API, it may trigger failures from
test/dynamo/test_trace_rules.py:test_torch_name_rule_map. To fix the failures:
If you are adding a new torch level API or Dynamo implementation:
* Add the name with TorchCtxManagerClassVariable to this map
  if you are adding Dynamo implementation for that context manager.
* Remove the object name from test/dynamo/test_trace_rules.ignored_torch_name_rule_set if it's there.

If you are removing an existing torch level API:
* Remove the entry represented the API from this map or test/dynamo/test_trace_rules.ignored_torch_name_rule_set
  depends on where it is.

TODO: Add torch object names mapping to TorchVariable for in graph and constant fold functions.
TODO: We would consolidate the skipfiles.check rules into trace_rules.lookup later.
TODO: We would support explictly list objects treated as skip/inline after the skipfiles.check
and trace_rules.lookup consolidation is done. Then the explicit listing of skip/inline objects have
a higher priority, which can be used to override the skipfiles.check rules in some cases.
"""
manual_torch_name_rule_map = {
    "torch.profiler.profiler.profile": TorchCtxManagerClassVariable,
    "torch.autograd.profiler.profile": TorchCtxManagerClassVariable,
    "torch.autograd.profiler.record_function": TorchCtxManagerClassVariable,
    "torch.onnx.is_in_onnx_export": TorchInGraphFunctionVariable,
    "torch.onnx.operators.shape_as_tensor": TorchInGraphFunctionVariable,
    "torch.overrides.is_tensor_like": TorchInGraphFunctionVariable,
    "torch.jit.is_scripting": TorchInGraphFunctionVariable,
    "torch.jit.is_tracing": TorchInGraphFunctionVariable,
    "torch.jit.annotate": TorchInGraphFunctionVariable,
    "torch.distributed.is_available": TorchInGraphFunctionVariable,
    "torch.distributed.is_initialized": TorchInGraphFunctionVariable,
    "torch.distributed.get_rank": TorchInGraphFunctionVariable,
    "torch.distributed.get_world_size": TorchInGraphFunctionVariable,
    "torch.distributed._tensor.api.DTensor#from_local": TorchInGraphFunctionVariable,
    "torch.distributed.distributed_c10d._get_group_tag": TorchInGraphFunctionVariable,
    "torch.distributed.distributed_c10d.get_process_group_ranks": TorchInGraphFunctionVariable,
    "torch._utils.is_compiling": TorchInGraphFunctionVariable,
    "torch.overrides.get_default_nowrap_functions": TorchInGraphFunctionVariable,
    "torch.fx._symbolic_trace.is_fx_tracing": TorchInGraphFunctionVariable,
    "torch._dynamo.external_utils.is_compiling": TorchInGraphFunctionVariable,
    "torch.autograd.graph.disable_saved_tensors_hooks": TorchInGraphFunctionVariable,
    "torch.autograd._profiler_enabled": SkipFilesVariable,
    # We graph break on RNG state setters or getters like
    # `torch.get_rng_state` or `torch.set_rng_state`. These functions
    # are not aten operations and therefore they are completely ignored
    # by the AOT dispatcher. As a result, the AOT graph does not have
    # these setter or getter functions, producing an incorrect graph
    # when it comes to rng states.
    "torch.default_generator#get_state": SkipFilesVariable,
    "torch._C.Generator#get_state": SkipFilesVariable,
    "torch.get_rng_state": SkipFilesVariable,
    "torch.cuda.get_rng_state": SkipFilesVariable,
    "torch.default_generator#set_state": SkipFilesVariable,
    "torch._C.Generator#set_state": SkipFilesVariable,
    "torch.set_rng_state": SkipFilesVariable,
    "torch.cuda.set_rng_state": SkipFilesVariable,
    # https://github.com/pytorch/pytorch/issues/107187
    "torch.manual_seed": SkipFilesVariable,
    # https://github.com/pytorch/pytorch/issues/93501
    "torch.nn.utils.rnn.pack_padded_sequence": SkipFilesVariable,
    # https://github.com/pytorch/pytorch/issues/99569
    "torch.nn.Parameter": SkipFilesVariable,
    "torch._nested_tensor_from_mask": SkipFilesVariable,
    "torch._nested_from_padded": SkipFilesVariable,
}


# Dynamo implemented context managers
torch_ctx_manager_classes = {
    k: TorchCtxManagerClassVariable
    for k in [
        "torch._C.DisableTorchFunctionSubclass",
        "torch.amp.autocast_mode.autocast",
        "torch.autograd.grad_mode.enable_grad",
        "torch.autograd.grad_mode.inference_mode",
        "torch.autograd.grad_mode.no_grad",
        "torch.autograd.grad_mode.set_grad_enabled",
        "torch.cpu.amp.autocast_mode.autocast",
        "torch.cuda.amp.autocast_mode.autocast",
    ]
}


# In graph functions (including constant folding) that are C bindings
torch_c_binding_in_graph_functions = {
    k: TorchInGraphFunctionVariable
    for k in [
        "math.acos",
        "math.acosh",
        "math.asin",
        "math.asinh",
        "math.atan",
        "math.atan2",
        "math.atanh",
        "math.ceil",
        "math.comb",
        "math.copysign",
        "math.cos",
        "math.cosh",
        "math.degrees",
        "math.dist",
        "math.erf",
        "math.erfc",
        "math.exp",
        "math.expm1",
        "math.fabs",
        "math.factorial",
        "math.floor",
        "math.fmod",
        "math.frexp",
        "math.fsum",
        "math.gamma",
        "math.gcd",
        "math.hypot",
        "math.isclose",
        "math.isfinite",
        "math.isinf",
        "math.isnan",
        "math.isqrt",
        "math.ldexp",
        "math.lgamma",
        "math.log",
        "math.log10",
        "math.log1p",
        "math.log2",
        "math.modf",
        "math.nextafter",
        "math.perm",
        "math.pow",
        "math.prod",
        "math.radians",
        "math.remainder",
        "math.sin",
        "math.sinh",
        "math.tan",
        "math.tanh",
        "math.trunc",
        "math.ulp",
        "torch._adaptive_avg_pool2d",
        "torch._adaptive_avg_pool3d",
        "torch._add_batch_dim",
        "torch._add_relu_",
        "torch._add_relu",
        "torch._addmm_activation",
        "torch._aminmax",
        "torch._amp_foreach_non_finite_check_and_unscale_",
        "torch._amp_update_scale_",
        "torch._assert_async",
        "torch._assert_tensor_metadata",
        "torch._batch_norm_impl_index",
        "torch._C._activate_cuda_trace",
        "torch._C._add_cached_tensor",
        "torch._C._add_docstr",
        "torch._C._are_functorch_transforms_active",
        "torch._C._autograd_init",
        "torch._C._awaitable_nowait",
        "torch._C._awaitable_wait",
        "torch._C._awaitable",
        "torch._C._backport_for_mobile_from_buffer_to_buffer",
        "torch._C._backport_for_mobile_from_buffer",
        "torch._C._backport_for_mobile_to_buffer",
        "torch._C._backport_for_mobile",
        "torch._C._broadcast_coalesced",
        "torch._C._broadcast_out",
        "torch._C._broadcast",
        "torch._C._c10d_init",
        "torch._C._calculate_package_version_based_on_upgraders",
        "torch._C._can_use_flash_attention",
        "torch._C._can_use_mem_efficient_attention",
        "torch._C._check_onnx_proto",
        "torch._C._check_sparse_tensor_invariants",
        "torch._C._collect_all",
        "torch._C._commit_update",
        "torch._C._compile_graph_to_code_table",
        "torch._C._construct_CUDA_Tensor_From_Storage_And_Metadata",
        "torch._C._construct_storage_from_data_pointer",
        "torch._C._conv_determine_backend_memory_format",
        "torch._C._cpu._is_cpu_support_vnni",
        "torch._C._crash_if_aten_asan",
        "torch._C._crash_if_csrc_asan",
        "torch._C._crash_if_csrc_ubsan",
        "torch._C._crash_if_debug_asserts_fail",
        "torch._C._crash_if_vptr_ubsan",
        "torch._C._create_function_from_graph",
        "torch._C._create_function_from_trace_with_dict",
        "torch._C._create_function_from_trace",
        "torch._C._create_graph_by_tracing",
        "torch._C._create_module_with_type",
        "torch._C._create_object_with_type",
        "torch._C._cuda_attach_out_of_memory_observer",
        "torch._C._cuda_beginAllocateCurrentStreamToPool",
        "torch._C._cuda_canDeviceAccessPeer",
        "torch._C._cuda_changeCurrentAllocator",
        "torch._C._cuda_checkPoolLiveAllocations",
        "torch._C._cuda_clearCublasWorkspaces",
        "torch._C._cuda_cudaCachingAllocator_raw_alloc",
        "torch._C._cuda_cudaCachingAllocator_raw_delete",
        "torch._C._cuda_cudaCachingAllocator_set_allocator_settings",
        "torch._C._cuda_cudaHostAllocator",
        "torch._C._cuda_customAllocator",
        "torch._C._cuda_emptyCache",
        "torch._C._cuda_endAllocateCurrentStreamToPool",
        "torch._C._cuda_exchangeDevice",
        "torch._C._cuda_get_conv_benchmark_empty_cache",
        "torch._C._cuda_get_cudnn_benchmark_limit",
        "torch._C._cuda_get_sync_debug_mode",
        "torch._C._cuda_getAllocator",
        "torch._C._cuda_getAllocatorBackend",
        "torch._C._cuda_getArchFlags",
        "torch._C._cuda_getCheckpointState",
        "torch._C._cuda_getCompiledVersion",
        "torch._C._cuda_getCurrentBlasHandle",
        "torch._C._cuda_getCurrentRawStream",
        "torch._C._cuda_getCurrentStream",
        "torch._C._cuda_getDefaultStream",
        "torch._C._cuda_getDevice",
        "torch._C._cuda_getDeviceCount",
        "torch._C._cuda_hasPrimaryContext",
        "torch._C._cuda_init",
        "torch._C._cuda_ipc_collect",
        "torch._C._cuda_isCurrentStreamCapturing",
        "torch._C._cuda_isHistoryEnabled",
        "torch._C._cuda_isInBadFork",
        "torch._C._cuda_jiterator_compile_and_launch_kernel",
        "torch._C._cuda_lock_mutex",
        "torch._C._cuda_maybeExchangeDevice",
        "torch._C._cuda_memorySnapshot",
        "torch._C._cuda_memoryStats",
        "torch._C._cuda_record_memory_history_legacy",
        "torch._C._cuda_record_memory_history",
        "torch._C._cuda_releasePool",
        "torch._C._cuda_resetAccumulatedMemoryStats",
        "torch._C._cuda_resetPeakMemoryStats",
        "torch._C._cuda_set_cudnn_benchmark_limit",
        "torch._C._cuda_set_sync_debug_mode",
        "torch._C._cuda_setCheckpointPoolState",
        "torch._C._cuda_setDevice",
        "torch._C._cuda_setMemoryFraction",
        "torch._C._cuda_setStream",
        "torch._C._cuda_sleep",
        "torch._C._cuda_synchronize",
        "torch._C._cuda_unlock_mutex",
        "torch._C._cudnn_set_conv_benchmark_empty_cache",
        "torch._C._cudnn.getCompileVersion",
        "torch._C._cudnn.getRuntimeVersion",
        "torch._C._cudnn.getVersionInt",
        "torch._C._current_autograd_node",
        "torch._C._current_graph_task_execution_order",
        "torch._C._current_graph_task_id",
        "torch._C._cxx_flags",
        "torch._C._debug_get_fusion_group_inlining",
        "torch._C._debug_only_are_vmap_fallback_warnings_enabled",
        "torch._C._debug_only_display_vmap_fallback_warnings",
        "torch._C._debug_set_autodiff_subgraph_inlining",
        "torch._C._debug_set_fusion_group_inlining",
        "torch._C._demangle",
        "torch._C._disabled_torch_dispatch_impl",
        "torch._C._disabled_torch_function_impl",
        "torch._C._dispatch_call_boxed",
        "torch._C._dispatch_check_all_invariants",
        "torch._C._dispatch_check_invariants",
        "torch._C._dispatch_dump_table",
        "torch._C._dispatch_dump",
        "torch._C._dispatch_find_dangling_impls",
        "torch._C._dispatch_find_schema_or_throw",
        "torch._C._dispatch_get_all_op_names",
        "torch._C._dispatch_get_backend_keyset_from_autograd",
        "torch._C._dispatch_get_registrations_for_dispatch_key",
        "torch._C._dispatch_has_backend_fallback",
        "torch._C._dispatch_has_computed_kernel_for_dispatch_key",
        "torch._C._dispatch_has_kernel_for_any_dispatch_key",
        "torch._C._dispatch_has_kernel_for_dispatch_key",
        "torch._C._dispatch_has_kernel",
        "torch._C._dispatch_is_alias_key",
        "torch._C._dispatch_is_included_in_alias",
        "torch._C._dispatch_is_main_interpreter",
        "torch._C._dispatch_isTensorSubclassLike",
        "torch._C._dispatch_key_for_device",
        "torch._C._dispatch_key_name",
        "torch._C._dispatch_key_parse",
        "torch._C._dispatch_key_set",
        "torch._C._dispatch_keys",
        "torch._C._dispatch_keyset_full_after",
        "torch._C._dispatch_keyset_full",
        "torch._C._dispatch_keyset_to_string",
        "torch._C._dispatch_library",
        "torch._C._dispatch_num_backends",
        "torch._C._dispatch_print_registrations_for_dispatch_key",
        "torch._C._dispatch_pystub",
        "torch._C._dispatch_set_report_error_callback",
        "torch._C._dispatch_tls_is_dispatch_key_excluded",
        "torch._C._dispatch_tls_is_dispatch_key_included",
        "torch._C._dispatch_tls_local_exclude_set",
        "torch._C._dispatch_tls_local_include_set",
        "torch._C._dispatch_tls_set_dispatch_key_excluded",
        "torch._C._dispatch_tls_set_dispatch_key_included",
        "torch._C._dist_autograd_init",
        "torch._C._dump_local_tls_set",
        "torch._C._dump_upgraders_map",
        "torch._C._enable_mobile_interface_call_export",
        "torch._C._enter_dual_level",
        "torch._C._error_if_any_worker_fails",
        "torch._C._exit_dual_level",
        "torch._C._export_operator_list",
        "torch._C._export_opnames",
        "torch._C._faulty_agent_init",
        "torch._C._fft.fft_fft",
        "torch._C._fft.fft_fft2",
        "torch._C._fft.fft_fftfreq",
        "torch._C._fft.fft_fftn",
        "torch._C._fft.fft_fftshift",
        "torch._C._fft.fft_hfft",
        "torch._C._fft.fft_hfft2",
        "torch._C._fft.fft_hfftn",
        "torch._C._fft.fft_ifft",
        "torch._C._fft.fft_ifft2",
        "torch._C._fft.fft_ifftn",
        "torch._C._fft.fft_ifftshift",
        "torch._C._fft.fft_ihfft",
        "torch._C._fft.fft_ihfft2",
        "torch._C._fft.fft_ihfftn",
        "torch._C._fft.fft_irfft",
        "torch._C._fft.fft_irfft2",
        "torch._C._fft.fft_irfftn",
        "torch._C._fft.fft_rfft",
        "torch._C._fft.fft_rfft2",
        "torch._C._fft.fft_rfftfreq",
        "torch._C._fft.fft_rfftn",
        "torch._C._free_And_Remove_DeleterFn",
        "torch._C._freeze_module",
        "torch._C._from_dlpack",
        "torch._C._functionality_to_backend_keys",
        "torch._C._functionalization_reapply_views_tls",
        "torch._C._fuse_to_static_module",
        "torch._C._gather_out",
        "torch._C._gather",
        "torch._C._generate_upgraders_graph",
        "torch._C._get_autograd_fallback_mode",
        "torch._C._get_backcompat_broadcast_warn",
        "torch._C._get_backcompat_keepdim_warn",
        "torch._C._get_caught_jit_exception_class_name",
        "torch._C._get_caught_jit_exception_original_msg",
        "torch._C._get_constant_bool_symnode",
        "torch._C._get_cpp_backtrace",
        "torch._C._get_cpu_capability",
        "torch._C._get_cublas_allow_bf16_reduced_precision_reduction",
        "torch._C._get_cublas_allow_fp16_reduced_precision_reduction",
        "torch._C._get_cublas_allow_tf32",
        "torch._C._get_cudnn_allow_tf32",
        "torch._C._get_cudnn_benchmark",
        "torch._C._get_cudnn_deterministic",
        "torch._C._get_cudnn_enabled",
        "torch._C._get_custom_class_python_wrapper",
        "torch._C._get_default_device",
        "torch._C._get_deterministic_algorithms_warn_only",
        "torch._C._get_deterministic_algorithms",
        "torch._C._get_deterministic_fill_uninitialized_memory",
        "torch._C._get_dispatch_mode",
        "torch._C._get_dispatch_stack_at",
        "torch._C._get_file_format",
        "torch._C._get_flash_sdp_enabled",
        "torch._C._get_float32_matmul_precision",
        "torch._C._get_function_stack_at",
        "torch._C._get_graph_executor_optimize",
        "torch._C._get_linalg_preferred_backend",
        "torch._C._get_math_sdp_enabled",
        "torch._C._get_max_operator_version",
        "torch._C._get_mem_efficient_sdp_enabled",
        "torch._C._get_mkldnn_enabled",
        "torch._C._get_mobile_model_contained_types_from_buffer",
        "torch._C._get_mobile_model_contained_types",
        "torch._C._get_model_bytecode_version_from_buffer",
        "torch._C._get_model_bytecode_version",
        "torch._C._get_model_extra_files_from_buffer",
        "torch._C._get_model_extra_files",
        "torch._C._get_model_ops_and_info_from_buffer",
        "torch._C._get_model_ops_and_info",
        "torch._C._get_module_info_from_flatbuffer",
        "torch._C._get_obj_in_tls",
        "torch._C._get_operation_overload",
        "torch._C._get_operator_version_map",
        "torch._C._get_privateuse1_backend_name",
        "torch._C._get_qengine",
        "torch._C._get_schema",
        "torch._C._get_singleton_int",
        "torch._C._get_tensor_metadata",
        "torch._C._get_tracing_state",
        "torch._C._get_upgrader_ranges",
        "torch._C._get_upgraders_entry_map",
        "torch._C._get_upgraders_map_size",
        "torch._C._get_value_trace",
        "torch._C._get_version_calculator_flag",
        "torch._C._get_warnAlways",
        "torch._C._graph_pool_handle",
        "torch._C._group_tensors_by_device_and_dtype",
        "torch._C._hack_do_not_use_clone_module_with_class",
        "torch._C._has_distributed",
        "torch._C._has_Standard_Deleter",
        "torch._C._has_storage",
        "torch._C._has_tensorexpr_cpp_tests",
        "torch._C._run_tensorexpr_cpp_tests",
        "torch._C._has_torch_function_unary",
        "torch._C._has_torch_function_variadic",
        "torch._C._has_torch_function",
        "torch._C._import_ir_module_from_package",
        "torch._C._increment_version",
        "torch._C._infer_size",
        "torch._C._init_names",
        "torch._C._initExtension",
        "torch._C._is_alias_of",
        "torch._C._is_any_autocast_enabled",
        "torch._C._is_cached_tensor",
        "torch._C._is_fwd_grad_enabled",
        "torch._C._is_key_in_tls",
        "torch._C._is_multithreading_enabled",
        "torch._C._is_torch_function_enabled",
        "torch._C._is_torch_function_mode_enabled",
        "torch._C._is_tracing",
        "torch._C._is_view_replay_enabled",
        "torch._C._is_xnnpack_enabled",
        "torch._C._itt.is_available",
        "torch._C._itt.mark",
        "torch._C._itt.rangePop",
        "torch._C._itt.rangePush",
        "torch._C._ivalue_debug_python_object",
        "torch._C._ivalue_tags_match",
        "torch._C._jit_assert_is_instance",
        "torch._C._jit_can_fuse_on_cpu_legacy",
        "torch._C._jit_can_fuse_on_cpu",
        "torch._C._jit_can_fuse_on_gpu",
        "torch._C._jit_cat_wo_conditionals",
        "torch._C._jit_check_alias_annotation",
        "torch._C._jit_clear_class_registry",
        "torch._C._jit_debug_fuser_num_cached_kernel_specs",
        "torch._C._jit_debug_module_iterators",
        "torch._C._jit_decay_packed_param_input_types",
        "torch._C._jit_decomposition_graph_for_node",
        "torch._C._jit_differentiate",
        "torch._C._jit_erase_non_input_shape_information",
        "torch._C._jit_flatten",
        "torch._C._jit_fuser_get_fused_kernel_code",
        "torch._C._jit_get_all_schemas",
        "torch._C._jit_get_custom_class_schemas",
        "torch._C._jit_get_emit_hooks",
        "torch._C._jit_get_inline_everything_mode",
        "torch._C._jit_get_logging_option",
        "torch._C._jit_get_num_profiled_runs",
        "torch._C._jit_get_operation",
        "torch._C._jit_get_schemas_for_operator",
        "torch._C._jit_get_te_cuda_pointwise_block_count",
        "torch._C._jit_get_te_cuda_pointwise_block_size",
        "torch._C._jit_get_te_cuda_pointwise_loop_levels",
        "torch._C._jit_get_te_generate_block_code",
        "torch._C._jit_get_te_must_use_llvm_cpu",
        "torch._C._jit_get_tracer_state_warn",
        "torch._C._jit_has_cpp_tests",
        "torch._C._jit_init",
        "torch._C._jit_interpret_graph",
        "torch._C._jit_is_onnx_log_enabled",
        "torch._C._jit_is_script_object",
        "torch._C._jit_llga_enabled",
        "torch._C._jit_nvfuser_can_be_enabled",
        "torch._C._jit_nvfuser_clear_comparison_callback",
        "torch._C._jit_nvfuser_enabled",
        "torch._C._jit_nvfuser_horizontal_mode",
        "torch._C._jit_nvfuser_set_comparison_callback",
        "torch._C._jit_nvfuser_single_node_mode",
        "torch._C._jit_object_is_non_holding",
        "torch._C._jit_onnx_convert_pattern_from_subblock",
        "torch._C._jit_onnx_create_full_scope_name",
        "torch._C._jit_onnx_list_model_parameters",
        "torch._C._jit_onnx_log",
        "torch._C._jit_opt_conditionals",
        "torch._C._jit_override_can_fuse_on_cpu_legacy",
        "torch._C._jit_override_can_fuse_on_cpu",
        "torch._C._jit_override_can_fuse_on_gpu",
        "torch._C._jit_pass_autocast",
        "torch._C._jit_pass_batch_mm",
        "torch._C._jit_pass_canonicalize_graph_fuser_ops",
        "torch._C._jit_pass_canonicalize",
        "torch._C._jit_pass_complete_shape_analysis",
        "torch._C._jit_pass_concat_frozen_linear",
        "torch._C._jit_pass_constant_loop_unrolling",
        "torch._C._jit_pass_constant_pooling",
        "torch._C._jit_pass_constant_propagation_immutable_types",
        "torch._C._jit_pass_constant_propagation",
        "torch._C._jit_pass_convert_frozen_ops_to_mkldnn",
        "torch._C._jit_pass_create_autodiff_subgraphs",
        "torch._C._jit_pass_create_functional_graphs",
        "torch._C._jit_pass_cse",
        "torch._C._jit_pass_custom_pattern_based_rewrite_graph",
        "torch._C._jit_pass_custom_pattern_based_rewrite",
        "torch._C._jit_pass_dbr_quant_remove_redundant_aliases",
        "torch._C._jit_pass_dce_allow_deleting_nodes_with_side_effects",
        "torch._C._jit_pass_dce",
        "torch._C._jit_pass_decompose_ops",
        "torch._C._jit_pass_dedup_module_uses",
        "torch._C._jit_pass_erase_number_types",
        "torch._C._jit_pass_erase_shape_information",
        "torch._C._jit_pass_filter_non_tensor_arguments",
        "torch._C._jit_pass_fixup_onnx_controlflow_node",
        "torch._C._jit_pass_fold_convbn",
        "torch._C._jit_pass_fold_frozen_conv_add_or_sub",
        "torch._C._jit_pass_fold_frozen_conv_bn",
        "torch._C._jit_pass_fold_frozen_conv_mul_or_div",
        "torch._C._jit_pass_fold_frozen_linear_bn",
        "torch._C._jit_pass_fold_prepacking_ops",
        "torch._C._jit_pass_functional_to_inplace_activation",
        "torch._C._jit_pass_fuse_add_relu",
        "torch._C._jit_pass_fuse_addmm",
        "torch._C._jit_pass_fuse_clamp_w_prepacked_linear_conv",
        "torch._C._jit_pass_fuse_frozen_conv_add_relu",
        "torch._C._jit_pass_fuse_linear",
        "torch._C._jit_pass_fuse_quantized_add_relu",
        "torch._C._jit_pass_fuse_tensorexprs",
        "torch._C._jit_pass_fuse",
        "torch._C._jit_pass_inline_fork_wait",
        "torch._C._jit_pass_inline_functional_graphs",
        "torch._C._jit_pass_inline",
        "torch._C._jit_pass_inplace_to_functional_activation",
        "torch._C._jit_pass_insert_observer_method_for_ondevice_ptq",
        "torch._C._jit_pass_insert_observers",
        "torch._C._jit_pass_insert_prepack_unpack",
        "torch._C._jit_pass_insert_prepacked_ops",
        "torch._C._jit_pass_insert_quant_dequant_for_ondevice_ptq",
        "torch._C._jit_pass_insert_quant_dequant",
        "torch._C._jit_pass_integer_value_refinement",
        "torch._C._jit_pass_lint",
        "torch._C._jit_pass_loop_unrolling",
        "torch._C._jit_pass_lower_all_tuples",
        "torch._C._jit_pass_lower_graph",
        "torch._C._jit_pass_metal_fold_prepacking_ops",
        "torch._C._jit_pass_metal_fuse_clamp_w_prepacked_conv",
        "torch._C._jit_pass_metal_insert_prepacked_ops",
        "torch._C._jit_pass_metal_optimize_for_mobile",
        "torch._C._jit_pass_onnx_assign_output_shape",
        "torch._C._jit_pass_onnx_assign_scoped_names_for_node_and_value",
        "torch._C._jit_pass_onnx_autograd_function_process",
        "torch._C._jit_pass_onnx_block",
        "torch._C._jit_pass_onnx_cast_all_constant_to_floating",
        "torch._C._jit_pass_onnx_clear_scope_records",
        "torch._C._jit_pass_onnx_constant_fold",
        "torch._C._jit_pass_onnx_deduplicate_initializers",
        "torch._C._jit_pass_onnx_eliminate_unused_items",
        "torch._C._jit_pass_onnx_eval_peephole",
        "torch._C._jit_pass_onnx_function_extraction",
        "torch._C._jit_pass_onnx_function_substitution",
        "torch._C._jit_pass_onnx_graph_shape_type_inference",
        "torch._C._jit_pass_onnx_lint",
        "torch._C._jit_pass_onnx_node_shape_type_inference",
        "torch._C._jit_pass_onnx_peephole",
        "torch._C._jit_pass_onnx_preprocess_caffe2",
        "torch._C._jit_pass_onnx_preprocess",
        "torch._C._jit_pass_onnx_quantization_insert_permutes",
        "torch._C._jit_pass_onnx_remove_inplace_ops_for_onnx",
        "torch._C._jit_pass_onnx_remove_print",
        "torch._C._jit_pass_onnx_scalar_type_analysis",
        "torch._C._jit_pass_onnx_set_dynamic_input_shape",
        "torch._C._jit_pass_onnx_track_scope_attributes",
        "torch._C._jit_pass_onnx_unpack_quantized_weights",
        "torch._C._jit_pass_onnx",
        "torch._C._jit_pass_optimize_for_inference",
        "torch._C._jit_pass_optimize_for_mobile",
        "torch._C._jit_pass_optimize_frozen_graph",
        "torch._C._jit_pass_pattern_based_rewrite",
        "torch._C._jit_pass_peephole_list_idioms",
        "torch._C._jit_pass_peephole",
        "torch._C._jit_pass_prepare_division_for_onnx",
        "torch._C._jit_pass_propagate_device",
        "torch._C._jit_pass_propagate_dtype",
        "torch._C._jit_pass_propagate_shapes_on_graph_and_build_compute",
        "torch._C._jit_pass_propagate_shapes_on_graph",
        "torch._C._jit_pass_quant_finalize_for_ondevice_ptq",
        "torch._C._jit_pass_quant_finalize",
        "torch._C._jit_pass_quant_fusion",
        "torch._C._jit_pass_refine_integer_values",
        "torch._C._jit_pass_refine_tuple_types",
        "torch._C._jit_pass_remove_dropout",
        "torch._C._jit_pass_remove_expands",
        "torch._C._jit_pass_remove_inplace_ops",
        "torch._C._jit_pass_remove_mutation",
        "torch._C._jit_pass_replace_old_ops_with_upgraders",
        "torch._C._jit_pass_replicate_dequantize",
        "torch._C._jit_pass_run_decompositions",
        "torch._C._jit_pass_specialize_autogradzero",
        "torch._C._jit_pass_swap_functional_linear",
        "torch._C._jit_pass_transform_conv1d_to_conv2d",
        "torch._C._jit_pass_transpose_frozen_linear",
        "torch._C._jit_pass_vulkan_fold_prepacking_ops",
        "torch._C._jit_pass_vulkan_fuse_clamp_w_prepacked_conv",
        "torch._C._jit_pass_vulkan_insert_prepacked_ops",
        "torch._C._jit_pass_vulkan_optimize_for_mobile",
        "torch._C._jit_register_decomposition_for_schema",
        "torch._C._jit_register_shape_compute_graph_for_node",
        "torch._C._jit_resolve_packet",
        "torch._C._jit_run_cpp_tests",
        "torch._C._jit_script_class_compile",
        "torch._C._jit_script_compile_overload",
        "torch._C._jit_script_compile",
        "torch._C._jit_script_interface_compile",
        "torch._C._jit_set_autocast_mode",
        "torch._C._jit_set_bailout_depth",
        "torch._C._jit_set_emit_hooks",
        "torch._C._jit_set_fusion_strategy",
        "torch._C._jit_set_inline_everything_mode",
        "torch._C._jit_set_llga_enabled",
        "torch._C._jit_set_logging_option",
        "torch._C._jit_set_logging_stream",
        "torch._C._jit_set_num_profiled_runs",
        "torch._C._jit_set_nvfuser_enabled",
        "torch._C._jit_set_nvfuser_guard_mode",
        "torch._C._jit_set_nvfuser_horizontal_mode",
        "torch._C._jit_set_nvfuser_single_node_mode",
        "torch._C._jit_set_nvfuser_skip_node_kind",
        "torch._C._jit_set_onnx_log_enabled",
        "torch._C._jit_set_onnx_log_output_stream",
        "torch._C._jit_set_profiling_executor",
        "torch._C._jit_set_profiling_mode",
        "torch._C._jit_set_symbolic_shapes_test_mode",
        "torch._C._jit_set_te_cuda_pointwise_block_count",
        "torch._C._jit_set_te_cuda_pointwise_block_size",
        "torch._C._jit_set_te_cuda_pointwise_loop_levels",
        "torch._C._jit_set_te_generate_block_code",
        "torch._C._jit_set_te_must_use_llvm_cpu",
        "torch._C._jit_set_texpr_dynamic_shape_enabled",
        "torch._C._jit_set_texpr_fuser_enabled",
        "torch._C._jit_set_texpr_reductions_enabled",
        "torch._C._jit_set_tracer_state_warn",
        "torch._C._jit_set_utf8_decoding_ignore",
        "torch._C._jit_shape_compute_graph_for_node",
        "torch._C._jit_symbolic_shapes_test_mode_enabled",
        "torch._C._jit_texpr_dynamic_shape_enabled",
        "torch._C._jit_texpr_fallback_allowed",
        "torch._C._jit_texpr_fuser_enabled",
        "torch._C._jit_texpr_reductions_enabled",
        "torch._C._jit_texpr_set_fallback_allowed",
        "torch._C._jit_to_backend_selective",
        "torch._C._jit_to_backend",
        "torch._C._jit_to_static_module",
        "torch._C._jit_trace_graph",
        "torch._C._jit_trace_module",
        "torch._C._jit_tree_views.FalseLiteral",
        "torch._C._jit_tree_views.NoneLiteral",
        "torch._C._jit_tree_views.TrueLiteral",
        "torch._C._jit_try_infer_type",
        "torch._C._jit_unflatten",
        "torch._C._last_executed_optimized_graph",
        "torch._C._len_torch_dispatch_stack",
        "torch._C._len_torch_function_stack",
        "torch._C._linalg.linalg_cholesky_ex",
        "torch._C._linalg.linalg_cholesky",
        "torch._C._linalg.linalg_cond",
        "torch._C._linalg.linalg_cross",
        "torch._C._linalg.linalg_det",
        "torch._C._linalg.linalg_diagonal",
        "torch._C._linalg.linalg_eig",
        "torch._C._linalg.linalg_eigh",
        "torch._C._linalg.linalg_eigvals",
        "torch._C._linalg.linalg_eigvalsh",
        "torch._C._linalg.linalg_householder_product",
        "torch._C._linalg.linalg_inv_ex",
        "torch._C._linalg.linalg_inv",
        "torch._C._linalg.linalg_ldl_factor_ex",
        "torch._C._linalg.linalg_ldl_factor",
        "torch._C._linalg.linalg_ldl_solve",
        "torch._C._linalg.linalg_lstsq",
        "torch._C._linalg.linalg_lu_factor_ex",
        "torch._C._linalg.linalg_lu_factor",
        "torch._C._linalg.linalg_lu_solve",
        "torch._C._linalg.linalg_lu",
        "torch._C._linalg.linalg_matmul",
        "torch._C._linalg.linalg_matrix_exp",
        "torch._C._linalg.linalg_matrix_norm",
        "torch._C._linalg.linalg_matrix_power",
        "torch._C._linalg.linalg_matrix_rank",
        "torch._C._linalg.linalg_multi_dot",
        "torch._C._linalg.linalg_norm",
        "torch._C._linalg.linalg_pinv",
        "torch._C._linalg.linalg_qr",
        "torch._C._linalg.linalg_slogdet",
        "torch._C._linalg.linalg_solve_ex",
        "torch._C._linalg.linalg_solve_triangular",
        "torch._C._linalg.linalg_solve",
        "torch._C._linalg.linalg_svd",
        "torch._C._linalg.linalg_svdvals",
        "torch._C._linalg.linalg_tensorinv",
        "torch._C._linalg.linalg_tensorsolve",
        "torch._C._linalg.linalg_vander",
        "torch._C._linalg.linalg_vecdot",
        "torch._C._linalg.linalg_vector_norm",
        "torch._C._llvm_enabled",
        "torch._C._load_for_lite_interpreter_from_buffer",
        "torch._C._load_for_lite_interpreter",
        "torch._C._load_jit_module_from_bytes",
        "torch._C._load_jit_module_from_file",
        "torch._C._load_mobile_module_from_bytes",
        "torch._C._load_mobile_module_from_file",
        "torch._C._log_api_usage_metadata",
        "torch._C._log_api_usage_once",
        "torch._C._logging_set_logger",
        "torch._C._meta_in_tls_dispatch_include",
        "torch._C._mps_acquireEvent",
        "torch._C._mps_currentAllocatedMemory",
        "torch._C._mps_deviceSynchronize",
        "torch._C._mps_driverAllocatedMemory",
        "torch._C._mps_elapsedTimeOfEvents",
        "torch._C._mps_emptyCache",
        "torch._C._mps_get_default_generator",
        "torch._C._mps_is_available",
        "torch._C._mps_is_in_bad_fork",
        "torch._C._mps_is_on_macos_13_or_newer",
        "torch._C._mps_profilerStartTrace",
        "torch._C._mps_profilerStopTrace",
        "torch._C._mps_queryEvent",
        "torch._C._mps_recordEvent",
        "torch._C._mps_releaseEvent",
        "torch._C._mps_setMemoryFraction",
        "torch._C._mps_synchronizeEvent",
        "torch._C._mps_waitForEvent",
        "torch._C._multiprocessing_init",
        "torch._C._nccl_all_gather",
        "torch._C._nccl_all_reduce",
        "torch._C._nccl_broadcast",
        "torch._C._nccl_init_rank",
        "torch._C._nccl_reduce_scatter",
        "torch._C._nccl_reduce",
        "torch._C._nccl_unique_id",
        "torch._C._nccl_version_suffix",
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        "torch._C._nested.nested_tensor",
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        "torch._C._new_symbolic_shape_symbol",
        "torch._C._nn_module_to_mobile",
        "torch._C._nn._conv_depthwise2d",
        "torch._C._nn._pad_circular",
        "torch._C._nn._pad_enum",
        "torch._C._nn._parse_to",
        "torch._C._nn._test_ambiguous_defaults",
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        "torch._C._nn._test_string_default",
        "torch._C._nn._test_warn_in_autograd",
        "torch._C._nn._upsample_bicubic2d_aa",
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        "torch._C._nn.adaptive_avg_pool2d",
        "torch._C._nn.adaptive_avg_pool3d",
        "torch._C._nn.adaptive_max_pool2d",
        "torch._C._nn.adaptive_max_pool3d",
        "torch._C._nn.avg_pool2d",
        "torch._C._nn.avg_pool3d",
        "torch._C._nn.binary_cross_entropy",
        "torch._C._nn.col2im",
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        "torch._C._nn.cross_entropy_loss",
        "torch._C._nn.elu_",
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        "torch._C._nn.fractional_max_pool2d",
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        "torch._C._nn.gelu_",
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        "torch._C._nn.leaky_relu_",
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        "torch._C._nn.linear",
        "torch._C._nn.log_sigmoid",
        "torch._C._nn.max_pool2d_with_indices",
        "torch._C._nn.max_pool3d_with_indices",
        "torch._C._nn.max_unpool2d",
        "torch._C._nn.max_unpool3d",
        "torch._C._nn.mish_",
        "torch._C._nn.mish",
        "torch._C._nn.mkldnn_linear",
        "torch._C._nn.mkldnn_reorder_conv2d_weight",
        "torch._C._nn.mkldnn_reorder_conv3d_weight",
        "torch._C._nn.mse_loss",
        "torch._C._nn.multi_margin_loss",
        "torch._C._nn.multilabel_margin_loss",
        "torch._C._nn.nll_loss_nd",
        "torch._C._nn.nll_loss",
        "torch._C._nn.nll_loss2d",
        "torch._C._nn.one_hot",
        "torch._C._nn.pad_sequence",
        "torch._C._nn.pad",
        "torch._C._nn.reflection_pad1d",
        "torch._C._nn.reflection_pad2d",
        "torch._C._nn.reflection_pad3d",
        "torch._C._nn.relu6_",
        "torch._C._nn.relu6",
        "torch._C._nn.replication_pad1d",
        "torch._C._nn.replication_pad2d",
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        "torch._C._nn.rrelu_with_noise_",
        "torch._C._nn.rrelu_with_noise",
        "torch._C._nn.scaled_dot_product_attention",
        "torch._C._nn.silu_",
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        "torch._C._nn.slow_conv_dilated2d",
        "torch._C._nn.slow_conv_dilated3d",
        "torch._C._nn.slow_conv_transpose2d",
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        "torch._C._nn.slow_conv3d",
        "torch._C._nn.smooth_l1_loss",
        "torch._C._nn.soft_margin_loss",
        "torch._C._nn.softplus",
        "torch._C._nn.softshrink",
        "torch._C._nn.thnn_conv2d",
        "torch._C._nn.unflatten_dense_tensors",
        "torch._C._nn.upsample_bicubic2d",
        "torch._C._nn.upsample_bilinear2d",
        "torch._C._nn.upsample_linear1d",
        "torch._C._nn.upsample_nearest1d",
        "torch._C._nn.upsample_nearest2d",
        "torch._C._nn.upsample_nearest3d",
        "torch._C._nn.upsample_trilinear3d",
        "torch._C._non_sym_sizes",
        "torch._C._overlaps",
        "torch._C._parallel_info",
        "torch._C._parse_dispatch_key",
        "torch._C._parse_source_def",
        "torch._C._pop_torch_dispatch_stack",
        "torch._C._pop_torch_function_stack",
        "torch._C._propagate_and_assign_input_shapes",
        "torch._C._propagate_shapes",
        "torch._C._propagate_xla_data",
        "torch._C._push_on_torch_dispatch_stack",
        "torch._C._push_on_torch_function_stack",
        "torch._C._quantize_ondevice_ptq_dynamic",
        "torch._C._register_py_class_for_device",
        "torch._C._remove_cached_tensor",
        "torch._C._remove_worker_pids",
        "torch._C._rename_privateuse1_backend",
        "torch._C._replace_",
        "torch._C._replace_overloaded_method_decl",
        "torch._C._resolve_type_from_object",
        "torch._C._resolve_type",
        "torch._C._rocm_is_backward_pass",
        "torch._C._rpc_init",
        "torch._C._run_emit_module_hook",
        "torch._C._save_jit_module_to_bytes",
        "torch._C._save_jit_module",
        "torch._C._save_mobile_module_to_bytes",
        "torch._C._save_mobile_module",
        "torch._C._save_parameters",
        "torch._C._scatter_out",
        "torch._C._scatter",
        "torch._C._select_conv_backend",
        "torch._C._set_autograd_fallback_mode",
        "torch._C._set_backcompat_broadcast_warn",
        "torch._C._set_backcompat_keepdim_warn",
        "torch._C._set_cached_tensors_enabled",
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        "torch._C._set_conj",
        "torch._C._set_cublas_allow_bf16_reduced_precision_reduction",
        "torch._C._set_cublas_allow_fp16_reduced_precision_reduction",
        "torch._C._set_cublas_allow_tf32",
        "torch._C._set_cudnn_allow_tf32",
        "torch._C._set_cudnn_benchmark",
        "torch._C._set_cudnn_deterministic",
        "torch._C._set_cudnn_enabled",
        "torch._C._set_default_dtype",
        "torch._C._set_default_mobile_cpu_allocator",
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        "torch.atan_",
        "torch.atan",
        "torch.atan2",
        "torch.atanh_",
        "torch.atanh",
        "torch.avg_pool1d",
        "torch.baddbmm",
        "torch.bartlett_window",
        "torch.batch_norm_backward_elemt",
        "torch.batch_norm_backward_reduce",
        "torch.batch_norm_elemt",
        "torch.batch_norm_gather_stats_with_counts",
        "torch.batch_norm_gather_stats",
        "torch.batch_norm_stats",
        "torch.batch_norm_update_stats",
        "torch.batch_norm",
        "torch.bernoulli",
        "torch.bilinear",
        "torch.binary_cross_entropy_with_logits",
        "torch.bincount",
        "torch.binomial",
        "torch.bitwise_and",
        "torch.bitwise_left_shift",
        "torch.bitwise_not",
        "torch.bitwise_or",
        "torch.bitwise_right_shift",
        "torch.bitwise_xor",
        "torch.blackman_window",
        "torch.bmm",
        "torch.broadcast_to",
        "torch.bucketize",
        "torch.can_cast",
        "torch.cat",
        "torch.ccol_indices_copy",
        "torch.ceil_",
        "torch.ceil",
        "torch.celu_",
        "torch.celu",
        "torch.channel_shuffle",
        "torch.cholesky_inverse",
        "torch.cholesky_solve",
        "torch.cholesky",
        "torch.choose_qparams_optimized",
        "torch.chunk",
        "torch.clamp_",
        "torch.clamp_max_",
        "torch.clamp_max",
        "torch.clamp_min_",
        "torch.clamp_min",
        "torch.clamp",
        "torch.clip_",
        "torch.clip",
        "torch.clone",
        "torch.col_indices_copy",
        "torch.column_stack",
        "torch.combinations",
        "torch.complex",
        "torch.concat",
        "torch.concatenate",
        "torch.conj_physical_",
        "torch.conj_physical",
        "torch.conj",
        "torch.constant_pad_nd",
        "torch.conv_tbc",
        "torch.conv_transpose1d",
        "torch.conv_transpose2d",
        "torch.conv_transpose3d",
        "torch.conv1d",
        "torch.conv2d",
        "torch.conv3d",
        "torch.convolution",
        "torch.copysign",
        "torch.corrcoef",
        "torch.cos_",
        "torch.cos",
        "torch.cosh_",
        "torch.cosh",
        "torch.cosine_embedding_loss",
        "torch.cosine_similarity",
        "torch.count_nonzero",
        "torch.cov",
        "torch.cross",
        "torch.crow_indices_copy",
        "torch.ctc_loss",
        "torch.cuda._get_device_properties",
        "torch.cudnn_affine_grid_generator",
        "torch.cudnn_batch_norm",
        "torch.cudnn_convolution_add_relu",
        "torch.cudnn_convolution_relu",
        "torch.cudnn_convolution_transpose",
        "torch.cudnn_convolution",
        "torch.cudnn_grid_sampler",
        "torch.cudnn_is_acceptable",
        "torch.cummax",
        "torch.cummin",
        "torch.cumprod",
        "torch.cumsum",
        "torch.cumulative_trapezoid",
        "torch.deg2rad_",
        "torch.deg2rad",
        "torch.dequantize",
        "torch.det",
        "torch.detach_",
        "torch.detach_copy",
        "torch.detach",
        "torch.diag_embed",
        "torch.diag",
        "torch.diagflat",
        "torch.diagonal_copy",
        "torch.diagonal_scatter",
        "torch.diagonal",
        "torch.diff",
        "torch.digamma",
        "torch.dist",
        "torch.div",
        "torch.divide",
        "torch.dot",
        "torch.dropout_",
        "torch.dropout",
        "torch.dsmm",
        "torch.dsplit",
        "torch.dstack",
        "torch.embedding_bag",
        "torch.embedding_renorm_",
        "torch.embedding",
        "torch.empty_like",
        "torch.empty_permuted",
        "torch.empty_quantized",
        "torch.empty_strided",
        "torch.empty",
        "torch.eq",
        "torch.equal",
        "torch.erf_",
        "torch.erf",
        "torch.erfc_",
        "torch.erfc",
        "torch.erfinv",
        "torch.exp_",
        "torch.exp",
        "torch.exp2_",
        "torch.exp2",
        "torch.expand_copy",
        "torch.expm1_",
        "torch.expm1",
        "torch.eye",
        "torch.fake_quantize_per_channel_affine",
        "torch.fake_quantize_per_tensor_affine",
        "torch.fbgemm_linear_fp16_weight_fp32_activation",
        "torch.fbgemm_linear_fp16_weight",
        "torch.fbgemm_linear_int8_weight_fp32_activation",
        "torch.fbgemm_linear_int8_weight",
        "torch.fbgemm_linear_quantize_weight",
        "torch.fbgemm_pack_gemm_matrix_fp16",
        "torch.fbgemm_pack_quantized_matrix",
        "torch.feature_alpha_dropout_",
        "torch.feature_alpha_dropout",
        "torch.feature_dropout_",
        "torch.feature_dropout",
        "torch.fill_",
        "torch.fill",
        "torch.fix_",
        "torch.fix",
        "torch.flatten",
        "torch.flip",
        "torch.fliplr",
        "torch.flipud",
        "torch.float_power",
        "torch.floor_",
        "torch.floor_divide",
        "torch.floor",
        "torch.fmax",
        "torch.fmin",
        "torch.fmod",
        "torch.frac_",
        "torch.frac",
        "torch.frexp",
        "torch.frobenius_norm",
        "torch.from_file",
        "torch.from_numpy",
        "torch.frombuffer",
        "torch.full_like",
        "torch.full",
        "torch.fused_moving_avg_obs_fake_quant",
        "torch.gather",
        "torch.gcd_",
        "torch.gcd",
        "torch.ge",
        "torch.geqrf",
        "torch.ger",
        "torch.get_device",
        "torch.gradient",
        "torch.greater_equal",
        "torch.greater",
        "torch.grid_sampler_2d",
        "torch.grid_sampler_3d",
        "torch.grid_sampler",
        "torch.group_norm",
        "torch.gru_cell",
        "torch.gru",
        "torch.gt",
        "torch.hamming_window",
        "torch.hann_window",
        "torch.hardshrink",
        "torch.heaviside",
        "torch.hinge_embedding_loss",
        "torch.histc",
        "torch.histogram",
        "torch.histogramdd",
        "torch.hsmm",
        "torch.hsplit",
        "torch.hspmm",
        "torch.hstack",
        "torch.hypot",
        "torch.i0_",
        "torch.i0",
        "torch.igamma",
        "torch.igammac",
        "torch.imag",
        "torch.index_add",
        "torch.index_copy",
        "torch.index_fill",
        "torch.index_put_",
        "torch.index_put",
        "torch.index_reduce",
        "torch.index_select",
        "torch.indices_copy",
        "torch.inner",
        "torch.instance_norm",
        "torch.int_repr",
        "torch.inverse",
        "torch.is_complex",
        "torch.is_conj",
        "torch.is_distributed",
        "torch.is_floating_point",
        "torch.is_inference",
        "torch.is_neg",
        "torch.is_nonzero",
        "torch.is_same_size",
        "torch.is_signed",
        "torch.is_vulkan_available",
        "torch.isclose",
        "torch.isfinite",
        "torch.isin",
        "torch.isinf",
        "torch.isnan",
        "torch.isneginf",
        "torch.isposinf",
        "torch.isreal",
        "torch.istft",
        "torch.kaiser_window",
        "torch.kl_div",
        "torch.kron",
        "torch.kthvalue",
        "torch.layer_norm",
        "torch.lcm_",
        "torch.lcm",
        "torch.ldexp_",
        "torch.ldexp",
        "torch.le",
        "torch.lerp",
        "torch.less_equal",
        "torch.less",
        "torch.lgamma",
        "torch.linspace",
        "torch.log_",
        "torch.log_softmax",
        "torch.log",
        "torch.log10_",
        "torch.log10",
        "torch.log1p_",
        "torch.log1p",
        "torch.log2_",
        "torch.log2",
        "torch.logaddexp",
        "torch.logaddexp2",
        "torch.logcumsumexp",
        "torch.logdet",
        "torch.logical_and",
        "torch.logical_not",
        "torch.logical_or",
        "torch.logical_xor",
        "torch.logit_",
        "torch.logit",
        "torch.logspace",
        "torch.logsumexp",
        "torch.lstm_cell",
        "torch.lstm",
        "torch.lt",
        "torch.lu_solve",
        "torch.lu_unpack",
        "torch.margin_ranking_loss",
        "torch.masked_fill",
        "torch.masked_scatter",
        "torch.masked_select",
        "torch.matmul",
        "torch.matrix_exp",
        "torch.matrix_power",
        "torch.max_pool1d_with_indices",
        "torch.max_pool1d",
        "torch.max_pool2d",
        "torch.max_pool3d",
        "torch.max",
        "torch.maximum",
        "torch.mean",
        "torch.median",
        "torch.min",
        "torch.minimum",
        "torch.miopen_batch_norm",
        "torch.miopen_convolution_add_relu",
        "torch.miopen_convolution_relu",
        "torch.miopen_convolution_transpose",
        "torch.miopen_convolution",
        "torch.miopen_depthwise_convolution",
        "torch.miopen_rnn",
        "torch.mkldnn_adaptive_avg_pool2d",
        "torch.mkldnn_convolution",
        "torch.mkldnn_linear_backward_weights",
        "torch.mkldnn_max_pool2d",
        "torch.mkldnn_max_pool3d",
        "torch.mkldnn_rnn_layer",
        "torch.mm",
        "torch.mode",
        "torch.moveaxis",
        "torch.movedim",
        "torch.msort",
        "torch.mul",
        "torch.multinomial",
        "torch.multiply",
        "torch.mv",
        "torch.mvlgamma",
        "torch.nan_to_num_",
        "torch.nan_to_num",
        "torch.nanmean",
        "torch.nanmedian",
        "torch.nanquantile",
        "torch.nansum",
        "torch.narrow_copy",
        "torch.narrow",
        "torch.native_batch_norm",
        "torch.native_channel_shuffle",
        "torch.native_dropout",
        "torch.native_group_norm",
        "torch.native_layer_norm",
        "torch.native_norm",
        "torch.ne",
        "torch.neg_",
        "torch.neg",
        "torch.negative_",
        "torch.negative",
        "torch.nextafter",
        "torch.nonzero_static",
        "torch.nonzero",
        "torch.norm_except_dim",
        "torch.normal",
        "torch.not_equal",
        "torch.nuclear_norm",
        "torch.numel",
        "torch.obj",
        "torch.ones_like",
        "torch.ones",
        "torch.orgqr",
        "torch.ormqr",
        "torch.outer",
        "torch.pairwise_distance",
        "torch.pdist",
        "torch.permute_copy",
        "torch.permute",
        "torch.pinverse",
        "torch.pixel_shuffle",
        "torch.pixel_unshuffle",
        "torch.poisson_nll_loss",
        "torch.poisson",
        "torch.polar",
        "torch.polygamma",
        "torch.positive",
        "torch.pow",
        "torch.prelu",
        "torch.prod",
        "torch.promote_types",
        "torch.put",
        "torch.q_per_channel_axis",
        "torch.q_per_channel_scales",
        "torch.q_per_channel_zero_points",
        "torch.q_scale",
        "torch.q_zero_point",
        "torch.qr",
        "torch.quantile",
        "torch.quantize_per_channel",
        "torch.quantize_per_tensor_dynamic",
        "torch.quantize_per_tensor",
        "torch.quantized_batch_norm",
        "torch.quantized_gru_cell",
        "torch.quantized_lstm_cell",
        "torch.quantized_max_pool1d",
        "torch.quantized_max_pool2d",
        "torch.quantized_max_pool3d",
        "torch.quantized_rnn_relu_cell",
        "torch.quantized_rnn_tanh_cell",
        "torch.rad2deg_",
        "torch.rad2deg",
        "torch.rand_like",
        "torch.rand",
        "torch.randint_like",
        "torch.randint",
        "torch.randn_like",
        "torch.randn",
        "torch.randperm",
        "torch.range",
        "torch.ravel",
        "torch.real",
        "torch.reciprocal_",
        "torch.reciprocal",
        "torch.relu_",
        "torch.relu",
        "torch.remainder",
        "torch.renorm",
        "torch.repeat_interleave",
        "torch.reshape",
        "torch.resize_as_",
        "torch.resize_as_sparse_",
        "torch.resolve_conj",
        "torch.resolve_neg",
        "torch.result_type",
        "torch.rnn_relu_cell",
        "torch.rnn_relu",
        "torch.rnn_tanh_cell",
        "torch.rnn_tanh",
        "torch.roll",
        "torch.rot90",
        "torch.round_",
        "torch.round",
        "torch.row_indices_copy",
        "torch.row_stack",
        "torch.rrelu_",
        "torch.rrelu",
        "torch.rsqrt_",
        "torch.rsqrt",
        "torch.rsub",
        "torch.saddmm",
        "torch.scalar_tensor",
        "torch.scatter_add",
        "torch.scatter_reduce",
        "torch.scatter",
        "torch.searchsorted",
        "torch.segment_reduce",
        "torch.select_copy",
        "torch.select_scatter",
        "torch.select",
        "torch.selu_",
        "torch.selu",
        "torch.sgn",
        "torch.sigmoid_",
        "torch.sigmoid",
        "torch.sign",
        "torch.signal.windows.windows.sqrt",
        "torch.signbit",
        "torch.sin_",
        "torch.sin",
        "torch.sinc_",
        "torch.sinc",
        "torch.sinh_",
        "torch.sinh",
        "torch.slice_copy",
        "torch.slice_scatter",
        "torch.slogdet",
        "torch.smm",
        "torch.softmax",
        "torch.sort",
        "torch.sparse_bsc_tensor",
        "torch.sparse_bsr_tensor",
        "torch.sparse_compressed_tensor",
        "torch.sparse_coo_tensor",
        "torch.sparse_csc_tensor",
        "torch.sparse_csr_tensor",
        "torch.split_copy",
        "torch.split_with_sizes_copy",
        "torch.split_with_sizes",
        "torch.spmm",
        "torch.sqrt_",
        "torch.sqrt",
        "torch.square_",
        "torch.square",
        "torch.squeeze_copy",
        "torch.squeeze",
        "torch.sspaddmm",
        "torch.stack",
        "torch.std_mean",
        "torch.std",
        "torch.sub",
        "torch.subtract",
        "torch.sum",
        "torch.svd",
        "torch.swapaxes",
        "torch.swapdims",
        "torch.sym_constrain_range_for_size",
        "torch.sym_constrain_range",
        "torch.t_copy",
        "torch.t",
        "torch.take_along_dim",
        "torch.take",
        "torch.tan_",
        "torch.tan",
        "torch.tanh_",
        "torch.tanh",
        "torch.tensor_split",
        "torch.tensor",
        "torch.threshold_",
        "torch.threshold",
        "torch.tile",
        "torch.topk",
        "torch.trace",
        "torch.transpose_copy",
        "torch.transpose",
        "torch.trapezoid",
        "torch.trapz",
        "torch.triangular_solve",
        "torch.tril_indices",
        "torch.tril",
        "torch.triplet_margin_loss",
        "torch.triu_indices",
        "torch.triu",
        "torch.true_divide",
        "torch.trunc_",
        "torch.trunc",
        "torch.unbind_copy",
        "torch.unbind",
        "torch.unflatten",
        "torch.unfold_copy",
        "torch.unsafe_chunk",
        "torch.unsafe_split_with_sizes",
        "torch.unsafe_split",
        "torch.unsqueeze_copy",
        "torch.unsqueeze",
        "torch.values_copy",
        "torch.vander",
        "torch.var_mean",
        "torch.var",
        "torch.vdot",
        "torch.view_as_complex_copy",
        "torch.view_as_complex",
        "torch.view_as_real_copy",
        "torch.view_as_real",
        "torch.view_copy",
        "torch.vsplit",
        "torch.vstack",
        "torch.where",
        "torch.xlogy_",
        "torch.xlogy",
        "torch.zero_",
        "torch.zeros",
    ]
}


if sys.version_info >= (3, 9):
    torch_c_binding_in_graph_functions["math.lcm"] = TorchInGraphFunctionVariable
if sys.version_info >= (3, 11):
    torch_c_binding_in_graph_functions["math.exp2"] = TorchInGraphFunctionVariable
    torch_c_binding_in_graph_functions["math.cbrt"] = TorchInGraphFunctionVariable


# In graph functions (including constant folding) that are not C bindings
torch_non_c_binding_in_graph_functions = {
    k: TorchInGraphFunctionVariable
    for k in [
        "torch.__future__.get_overwrite_module_params_on_conversion",
        "torch.__future__.set_overwrite_module_params_on_conversion",
        "torch.__getattr__",
        "torch._assert",
        "torch._check_index",
        "torch._check_is_size",
        "torch._check_not_implemented",
        "torch._check_tensor_all_with",
        "torch._check_tensor_all",
        "torch._check_type",
        "torch._check_value",
        "torch._check_with",
        "torch._check",
        "torch._compile._disable_dynamo",
        "torch._constrain_as_size",
        "torch._constrain_as_value",
        "torch._functorch.apis.chunk_vmap",
        "torch._functorch.autograd_function.custom_function_call_functionalize",
        "torch._functorch.autograd_function.custom_function_call_grad",
        "torch._functorch.autograd_function.custom_function_call_vmap_generate_rule",
        "torch._functorch.autograd_function.custom_function_call_vmap",
        "torch._functorch.autograd_function.generate_single_level_function",
        "torch._functorch.autograd_function.get_tangents_in_dims",
        "torch._functorch.autograd_function.has_overriden_vmap_rule",
        "torch._functorch.autograd_function.reductify_leaf",
        "torch._functorch.autograd_function.reductify",
        "torch._functorch.autograd_function.validate_vmap_returns_tuple_of_two_elements",
        "torch._functorch.autograd_function.vmapify_autograd_function",
        "torch._functorch.autograd_function.wrap_outputs_maintaining_identity",
        "torch._functorch.batch_norm_replacement.batch_norm_without_running_stats",
        "torch._functorch.batch_norm_replacement.replace_all_batch_norm_modules_",
        "torch._functorch.deprecated.combine_state_for_ensemble",
        "torch._functorch.deprecated.functionalize",
        "torch._functorch.deprecated.get_warning",
        "torch._functorch.deprecated.grad_and_value",
        "torch._functorch.deprecated.hessian",
        "torch._functorch.deprecated.jacfwd",
        "torch._functorch.deprecated.jacrev",
        "torch._functorch.deprecated.jvp",
        "torch._functorch.deprecated.make_functional_with_buffers",
        "torch._functorch.deprecated.make_functional",
        "torch._functorch.deprecated.setup_docs",
        "torch._functorch.deprecated.vjp",
        "torch._functorch.deprecated.warn_deprecated",
        "torch._functorch.eager_transforms._any_differentiable",
        "torch._functorch.eager_transforms._as_tuple",
        "torch._functorch.eager_transforms._autograd_grad",
        "torch._functorch.eager_transforms._check_unique_non_empty",
        "torch._functorch.eager_transforms._chunked_standard_basis_for_",
        "torch._functorch.eager_transforms._construct_standard_basis_for",
        "torch._functorch.eager_transforms._create_differentiable",
        "torch._functorch.eager_transforms._is_differentiable",
        "torch._functorch.eager_transforms._jvp_with_argnums",
        "torch._functorch.eager_transforms._maybe_unwrap_functional_tensor",
        "torch._functorch.eager_transforms._maybe_wrap_functional_tensor",
        "torch._functorch.eager_transforms._replace_args",
        "torch._functorch.eager_transforms._safe_zero_index",
        "torch._functorch.eager_transforms._slice_argnums",
        "torch._functorch.eager_transforms._undo_create_differentiable",
        "torch._functorch.eager_transforms._unwrap_all_tensors_from_functional",
        "torch._functorch.eager_transforms._validate_and_wrap_argnum",
        "torch._functorch.eager_transforms._validate_and_wrap_argnums",
        "torch._functorch.eager_transforms._vjp_with_argnums",
        "torch._functorch.eager_transforms._wrap_all_tensors_to_functional",
        "torch._functorch.eager_transforms._wrap_all_tensors",
        "torch._functorch.eager_transforms._wrap_tensor_for_grad",
        "torch._functorch.eager_transforms.assert_flat_tuple_of_tensors",
        "torch._functorch.eager_transforms.assert_non_empty_list_of_tensors",
        "torch._functorch.eager_transforms.assert_non_empty_tensor_output",
        "torch._functorch.eager_transforms.assert_output_is_tensor_or_tensors",
        "torch._functorch.eager_transforms.enable_inplace_requires_grad",
        "torch._functorch.eager_transforms.error_if_complex",
        "torch._functorch.eager_transforms.functionalize",
        "torch._functorch.eager_transforms.grad_and_value",
        "torch._functorch.eager_transforms.grad_impl",
        "torch._functorch.eager_transforms.hessian",
        "torch._functorch.eager_transforms.jacfwd",
        "torch._functorch.eager_transforms.jacrev",
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        "torch.nn.functional._mha_shape_check",
        "torch.nn.functional._no_grad_embedding_renorm_",
        "torch.nn.functional._none_or_dtype",
        "torch.nn.functional._threshold",
        "torch.nn.functional._unpool_output_size",
        "torch.nn.functional._verify_batch_size",
        "torch.nn.functional._verify_spatial_size",
        "torch.nn.functional.adaptive_avg_pool2d",
        "torch.nn.functional.adaptive_avg_pool3d",
        "torch.nn.functional.adaptive_max_pool1d_with_indices",
        "torch.nn.functional.adaptive_max_pool1d",
        "torch.nn.functional.adaptive_max_pool2d_with_indices",
        "torch.nn.functional.adaptive_max_pool2d",
        "torch.nn.functional.adaptive_max_pool3d_with_indices",
        "torch.nn.functional.adaptive_max_pool3d",
        "torch.nn.functional.affine_grid",
        "torch.nn.functional.alpha_dropout",
        "torch.nn.functional.assert_int_or_pair",
        "torch.nn.functional.batch_norm",
        "torch.nn.functional.binary_cross_entropy_with_logits",
        "torch.nn.functional.binary_cross_entropy",
        "torch.nn.functional.celu",
        "torch.nn.functional.cosine_embedding_loss",
        "torch.nn.functional.cross_entropy",
        "torch.nn.functional.ctc_loss",
        "torch.nn.functional.dropout",
        "torch.nn.functional.dropout1d",
        "torch.nn.functional.dropout2d",
        "torch.nn.functional.dropout3d",
        "torch.nn.functional.elu",
        "torch.nn.functional.embedding_bag",
        "torch.nn.functional.embedding",
        "torch.nn.functional.feature_alpha_dropout",
        "torch.nn.functional.fold",
        "torch.nn.functional.fractional_max_pool2d_with_indices",
        "torch.nn.functional.fractional_max_pool2d",
        "torch.nn.functional.fractional_max_pool3d_with_indices",
        "torch.nn.functional.fractional_max_pool3d",
        "torch.nn.functional.gaussian_nll_loss",
        "torch.nn.functional.glu",
        "torch.nn.functional.grid_sample",
        "torch.nn.functional.group_norm",
        "torch.nn.functional.gumbel_softmax",
        "torch.nn.functional.hardsigmoid",
        "torch.nn.functional.hardswish",
        "torch.nn.functional.hardtanh",
        "torch.nn.functional.hinge_embedding_loss",
        "torch.nn.functional.huber_loss",
        "torch.nn.functional.instance_norm",
        "torch.nn.functional.interpolate",
        "torch.nn.functional.kl_div",
        "torch.nn.functional.l1_loss",
        "torch.nn.functional.layer_norm",
        "torch.nn.functional.leaky_relu",
        "torch.nn.functional.local_response_norm",
        "torch.nn.functional.log_softmax",
        "torch.nn.functional.lp_pool1d",
        "torch.nn.functional.lp_pool2d",
        "torch.nn.functional.margin_ranking_loss",
        "torch.nn.functional.max_pool1d_with_indices",
        "torch.nn.functional.max_pool1d",
        "torch.nn.functional.max_pool2d_with_indices",
        "torch.nn.functional.max_pool2d",
        "torch.nn.functional.max_pool3d_with_indices",
        "torch.nn.functional.max_pool3d",
        "torch.nn.functional.max_unpool1d",
        "torch.nn.functional.max_unpool2d",
        "torch.nn.functional.max_unpool3d",
        "torch.nn.functional.mish",
        "torch.nn.functional.mse_loss",
        "torch.nn.functional.multi_head_attention_forward",
        "torch.nn.functional.multi_margin_loss",
        "torch.nn.functional.multilabel_margin_loss",
        "torch.nn.functional.multilabel_soft_margin_loss",
        "torch.nn.functional.nll_loss",
        "torch.nn.functional.normalize",
        "torch.nn.functional.poisson_nll_loss",
        "torch.nn.functional.relu",
        "torch.nn.functional.relu6",
        "torch.nn.functional.rrelu",
        "torch.nn.functional.selu",
        "torch.nn.functional.sigmoid",
        "torch.nn.functional.silu",
        "torch.nn.functional.smooth_l1_loss",
        "torch.nn.functional.soft_margin_loss",
        "torch.nn.functional.softmax",
        "torch.nn.functional.softmin",
        "torch.nn.functional.softsign",
        "torch.nn.functional.tanh",
        "torch.nn.functional.tanhshrink",
        "torch.nn.functional.triplet_margin_loss",
        "torch.nn.functional.unfold",
        "torch.nn.functional.upsample_bilinear",
        "torch.nn.functional.upsample_nearest",
        "torch.nn.functional.upsample",
        "torch.nn.grad._pair",
        "torch.nn.grad._single",
        "torch.nn.grad._triple",
        "torch.nn.grad.conv1d_input",
        "torch.nn.grad.conv1d_weight",
        "torch.nn.grad.conv2d_input",
        "torch.nn.grad.conv2d_weight",
        "torch.nn.grad.conv3d_input",
        "torch.nn.grad.conv3d_weight",
        "torch.nn.modules.activation._arg_requires_grad",
        "torch.nn.modules.activation._check_arg_device",
        "torch.nn.modules.activation._is_make_fx_tracing",
        "torch.nn.modules.container._addindent",
        "torch.nn.modules.transformer._detect_is_causal_mask",
        "torch.nn.modules.transformer._generate_square_subsequent_mask",
        "torch.nn.modules.transformer._get_activation_fn",
        "torch.nn.modules.transformer._get_clones",
        "torch.nn.modules.transformer._get_seq_len",
        "torch.nn.modules.utils._list_with_default",
        "torch.nn.modules.utils._ntuple",
        "torch.nn.modules.utils._quadruple",
        "torch.nn.modules.utils._reverse_repeat_tuple",
        "torch.nn.modules.utils.consume_prefix_in_state_dict_if_present",
        "torch.nn.parameter.is_lazy",
        "torch.norm",
        "torch.quantization.default_eval_fn",
        "torch.random._seed_custom_device",
        "torch.random.fork_rng",
        "torch.random.initial_seed",
        "torch.random.seed",
        "torch.return_types.pytree_register_structseq",
        "torch.set_default_device",
        "torch.set_default_dtype",
        "torch.set_default_tensor_type",
        "torch.set_deterministic_debug_mode",
        "torch.set_float32_matmul_precision",
        "torch.set_warn_always",
        "torch.signal.windows.windows._add_docstr",
        "torch.signal.windows.windows._window_function_checks",
        "torch.signal.windows.windows.bartlett",
        "torch.signal.windows.windows.blackman",
        "torch.signal.windows.windows.cosine",
        "torch.signal.windows.windows.exponential",
        "torch.signal.windows.windows.gaussian",
        "torch.signal.windows.windows.general_cosine",
        "torch.signal.windows.windows.general_hamming",
        "torch.signal.windows.windows.hamming",
        "torch.signal.windows.windows.hann",
        "torch.signal.windows.windows.kaiser",
        "torch.signal.windows.windows.merge_dicts",
        "torch.signal.windows.windows.nuttall",
        "torch.signal.windows.windows.parse_kwargs",
        "torch.sparse.as_sparse_gradcheck",
        "torch.sparse.semi_structured.to_sparse_semi_structured",
        "torch.sparse.sum",
        "torch.split",
        "torch.stft",
        "torch.sym_float",
        "torch.sym_int",
        "torch.sym_ite",
        "torch.sym_max",
        "torch.sym_min",
        "torch.sym_not",
        "torch.tensordot",
        "torch.typename",
        "torch.unique_consecutive",
        "torch.use_deterministic_algorithms",
    ]
}


torch_name_rule_map = {
    **manual_torch_name_rule_map,
    **torch_ctx_manager_classes,
    **torch_c_binding_in_graph_functions,
    **torch_non_c_binding_in_graph_functions,
}

"""
Generate the torch object - Dynamo tracing rule (the wrapping variable) map.
"""


@functools.lru_cache(None)
def get_torch_obj_rule_map():
    d = dict()
    for k, v in torch_name_rule_map.items():
        obj = load_object(k)
        if obj is not None:
            d[obj] = v
    return d


def _load_obj_from_str(fully_qualified_name):
    module, obj_name = fully_qualified_name.rsplit(".", maxsplit=1)
    return getattr(importlib.import_module(module), obj_name)


"""
Load string represented torch objects.
"""


def load_object(name):
    try:
        x = name.split("#")
        if len(x) == 2:
            obj = _load_obj_from_str(x[0])
            val = getattr(obj, x[1])
        else:
            assert len(x) == 1, f"Invalid obj name {name}"
            val = _load_obj_from_str(x[0])
        if hasattr(val, "__wrapped__"):
            val = val.__wrapped__
    except (AttributeError, ModuleNotFoundError):
        val = None
    return val


"""
Get all torch.Tensor methods which are allowed to be in graph functions.
"""


@functools.lru_cache(None)
def get_tensor_method():
    s = set()
    for name in dir(torch.Tensor):
        method = getattr(torch.Tensor, name)
        if isinstance(
            method, (types.MethodDescriptorType, types.WrapperDescriptorType)
        ):
            s.add(method)
    return frozenset(s)


"""
Return if a torch object is ATen op or torch.Tensor method.
"""


def is_aten_op_or_tensor_method(obj):
    return obj in get_tensor_method() or isinstance(
        obj,
        (torch._ops.OpOverloadPacket, torch._ops.OpOverload),
    )


"""
Main entry point for looking up the trace rule (the Dynamo variable) for a given object.
E.g, the lookup result of `torch.amp.autocast_mode.autocast` is `TorchCtxManagerClassVariable`.
"""


def lookup(obj):
    if not hashable(obj):
        return None
    # Custom allow/disallow in graph takes precedence over the `torch_name_rule_map`.
    if id(obj) in _disallowed_function_ids:
        return None
    if is_user_defined_allowed(obj):
        return TorchInGraphFunctionVariable
    if hasattr(obj, "__wrapped__"):
        # TODO: Weird case, should not unwrap if it's wrapped as _VariableFunctionsClass.
        if not (
            hasattr(obj, "__qualname__")
            and str(obj.__qualname__).startswith("_VariableFunctionsClass")
        ):
            obj = obj.__wrapped__
    rule = get_torch_obj_rule_map().get(obj, None)
    if rule is None and is_aten_op_or_tensor_method(obj):
        return TorchInGraphFunctionVariable
    else:
        return rule
