




import colorsys

from PIL import Image  # type: ignore







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      int      )     ->       float:





				"""simple docstring"""


				__lowerCamelCase		       =    x
				__lowerCamelCase		       =    y
				for step in range(UpperCamelCase__      ):  # noqa: B007
								__lowerCamelCase		       =    a * a - b * b + x
								__lowerCamelCase		       =    2 * a * b + y
								__lowerCamelCase		       =    a_new

								# divergence happens for all complex number with an absolute value
								# greater than 4
								if a * a + b * b > 4:
												break
				return step / (max_step - 1)







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       tuple:





				"""simple docstring"""


				if distance == 1:
								return (0, 0, 0)
				else:
								return (255, 255, 255)







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       tuple:





				"""simple docstring"""


				if distance == 1:
								return (0, 0, 0)
				else:
								return tuple(round(i * 255      ) for i in colorsys.hsv_to_rgb(UpperCamelCase__ ,     1 ,     1      )      )







def 			lowerCamelCase_		(       UpperCamelCase__				:      int = 800 ,     UpperCamelCase__				:      int = 600 ,     UpperCamelCase__				:      float = -0.6 ,     UpperCamelCase__				:      float = 0 ,     UpperCamelCase__				:      float = 3.2 ,     UpperCamelCase__				:      int = 50 ,     UpperCamelCase__				:      bool = True ,     )     ->       Image.Image:





				"""simple docstring"""


				__lowerCamelCase		       =    Image.new('RGB' ,     (image_width, image_height)      )
				__lowerCamelCase		       =    img.load()

				# loop through the image-coordinates
				for image_x in range(UpperCamelCase__      ):
								for image_y in range(UpperCamelCase__      ):
												# determine the figure-coordinates based on the image-coordinates
												__lowerCamelCase		       =    figure_width / image_width * image_height
												__lowerCamelCase		       =    figure_center_x + (image_x / image_width - 0.5) * figure_width
												__lowerCamelCase		       =    figure_center_y + (image_y / image_height - 0.5) * figure_height

												__lowerCamelCase		       =    get_distance(UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__      )

												# color the corresponding pixel based on the selected coloring-function
												if use_distance_color_coding:
																__lowerCamelCase		       =    get_color_coded_rgb(UpperCamelCase__      )
												else:
																__lowerCamelCase		       =    get_black_and_white_rgb(UpperCamelCase__      )

				return img


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# colored version, full figure
					__A        =    get_image()

					# uncomment for colored version, different section, zoomed in
					# img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
					# figure_width = 0.8)

					# uncomment for black and white version, full figure
					# img = get_image(use_distance_color_coding = False)

					# uncomment to save the image
					# img.save("mandelbrot.png")

					img.show()






from .constants import (
    MODEL_NAME,
    OPTIMIZER_NAME,
    RNG_STATE_NAME,
    SAFE_WEIGHTS_INDEX_NAME,
    SAFE_WEIGHTS_NAME,
    SCALER_NAME,
    SCHEDULER_NAME,
    TORCH_LAUNCH_PARAMS,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
)
from .dataclasses import (
    BnbQuantizationConfig,
    ComputeEnvironment,
    CustomDtype,
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    DynamoBackend,
    FPaRecipeKwargs,
    FullyShardedDataParallelPlugin,
    GradientAccumulationPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    KwargsHandler,
    LoggerType,
    MegatronLMPlugin,
    PrecisionType,
    ProjectConfiguration,
    RNGType,
    SageMakerDistributedType,
    TensorInformation,
    TorchDynamoPlugin,
)
from .environment import get_int_from_env, parse_choice_from_env, parse_flag_from_env
from .imports import (
    get_ccl_version,
    is_abit_bnb_available,
    is_abit_bnb_available,
    is_aim_available,
    is_bfaa_available,
    is_bnb_available,
    is_botoa_available,
    is_ccl_available,
    is_comet_ml_available,
    is_datasets_available,
    is_deepspeed_available,
    is_fpa_available,
    is_ipex_available,
    is_megatron_lm_available,
    is_mlflow_available,
    is_mps_available,
    is_npu_available,
    is_rich_available,
    is_safetensors_available,
    is_sagemaker_available,
    is_tensorboard_available,
    is_tpu_available,
    is_transformers_available,
    is_wandb_available,
    is_xpu_available,
)
from .modeling import (
    check_device_map,
    check_tied_parameters_in_config,
    check_tied_parameters_on_same_device,
    compute_module_sizes,
    convert_file_size_to_int,
    dtype_byte_size,
    find_tied_parameters,
    get_balanced_memory,
    get_max_layer_size,
    get_max_memory,
    get_mixed_precision_context_manager,
    id_tensor_storage,
    infer_auto_device_map,
    load_checkpoint_in_model,
    load_offloaded_weights,
    load_state_dict,
    named_module_tensors,
    retie_parameters,
    set_module_tensor_to_device,
    shard_checkpoint,
)
from .offload import (
    OffloadedWeightsLoader,
    PrefixedDataset,
    extract_submodules_state_dict,
    load_offloaded_weight,
    offload_state_dict,
    offload_weight,
    save_offload_index,
)
from .operations import (
    broadcast,
    broadcast_object_list,
    concatenate,
    convert_outputs_to_fpaa,
    convert_to_fpaa,
    find_batch_size,
    find_device,
    gather,
    gather_object,
    get_data_structure,
    honor_type,
    initialize_tensors,
    is_namedtuple,
    is_tensor_information,
    is_torch_tensor,
    listify,
    pad_across_processes,
    recursively_apply,
    reduce,
    send_to_device,
    slice_tensors,
)
from .versions import compare_versions, is_torch_version


if is_deepspeed_available():
    from .deepspeed import (
        DeepSpeedEngineWrapper,
        DeepSpeedOptimizerWrapper,
        DeepSpeedSchedulerWrapper,
        DummyOptim,
        DummyScheduler,
        HfDeepSpeedConfig,
    )

from .bnb import has_abit_bnb_layers, load_and_quantize_model
from .fsdp_utils import load_fsdp_model, load_fsdp_optimizer, save_fsdp_model, save_fsdp_optimizer
from .launch import (
    PrepareForLaunch,
    _filter_args,
    prepare_deepspeed_cmd_env,
    prepare_multi_gpu_env,
    prepare_sagemager_args_inputs,
    prepare_simple_launcher_cmd_env,
    prepare_tpu,
)
from .megatron_lm import (
    AbstractTrainStep,
    BertTrainStep,
    GPTTrainStep,
    MegatronEngine,
    MegatronLMDummyDataLoader,
    MegatronLMDummyScheduler,
    MegatronLMOptimizerWrapper,
    MegatronLMSchedulerWrapper,
    TaTrainStep,
    avg_losses_across_data_parallel_group,
    gather_across_data_parallel_groups,
)
from .megatron_lm import initialize as megatron_lm_initialize
from .megatron_lm import prepare_data_loader as megatron_lm_prepare_data_loader
from .megatron_lm import prepare_model as megatron_lm_prepare_model
from .megatron_lm import prepare_optimizer as megatron_lm_prepare_optimizer
from .megatron_lm import prepare_scheduler as megatron_lm_prepare_scheduler
from .memory import find_executable_batch_size, release_memory
from .other import (
    extract_model_from_parallel,
    get_pretty_name,
    is_port_in_use,
    merge_dicts,
    patch_environment,
    save,
    wait_for_everyone,
    write_basic_config,
)
from .random import set_seed, synchronize_rng_state, synchronize_rng_states
from .torch_xla import install_xla
from .tqdm import tqdm
from .transformer_engine import convert_model, has_transformer_engine_layers


