



"""simple docstring"""
SCREAMING_SNAKE_CASE_				= """0.18.2"""

from .configuration_utils import ConfigMixin
from .utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_onnx_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    logging,
)


try:
					if not is_onnx_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_onnx_objects import *  # noqa F403
else:
					from .pipelines import OnnxRuntimeModel

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_pt_objects import *  # noqa F403
else:
					from .models import (
					    AutoencoderKL,
					    ControlNetModel,
					    ModelMixin,
					    PriorTransformer,
					    TaFilmDecoder,
					    TransformeraDModel,
					    UNetaDModel,
					    UNetaDConditionModel,
					    UNetaDModel,
					    UNetaDConditionModel,
					    VQModel,
					)
					from .optimization import (
					    get_constant_schedule,
					    get_constant_schedule_with_warmup,
					    get_cosine_schedule_with_warmup,
					    get_cosine_with_hard_restarts_schedule_with_warmup,
					    get_linear_schedule_with_warmup,
					    get_polynomial_decay_schedule_with_warmup,
					    get_scheduler,
					)
					from .pipelines import (
					    AudioPipelineOutput,
					    ConsistencyModelPipeline,
					    DanceDiffusionPipeline,
					    DDIMPipeline,
					    DDPMPipeline,
					    DiffusionPipeline,
					    DiTPipeline,
					    ImagePipelineOutput,
					    KarrasVePipeline,
					    LDMPipeline,
					    LDMSuperResolutionPipeline,
					    PNDMPipeline,
					    RePaintPipeline,
					    ScoreSdeVePipeline,
					)
					from .schedulers import (
					    CMStochasticIterativeScheduler,
					    DDIMInverseScheduler,
					    DDIMParallelScheduler,
					    DDIMScheduler,
					    DDPMParallelScheduler,
					    DDPMScheduler,
					    DEISMultistepScheduler,
					    DPMSolverMultistepInverseScheduler,
					    DPMSolverMultistepScheduler,
					    DPMSolverSinglestepScheduler,
					    EulerAncestralDiscreteScheduler,
					    EulerDiscreteScheduler,
					    HeunDiscreteScheduler,
					    IPNDMScheduler,
					    KarrasVeScheduler,
					    KDPMaAncestralDiscreteScheduler,
					    KDPMaDiscreteScheduler,
					    PNDMScheduler,
					    RePaintScheduler,
					    SchedulerMixin,
					    ScoreSdeVeScheduler,
					    UnCLIPScheduler,
					    UniPCMultistepScheduler,
					    VQDiffusionScheduler,
					)
					from .training_utils import EMAModel

try:
					if not (is_torch_available() and is_scipy_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
					from .schedulers import LMSDiscreteScheduler

try:
					if not (is_torch_available() and is_torchsde_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
					from .schedulers import DPMSolverSDEScheduler

try:
					if not (is_torch_available() and is_transformers_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
					from .pipelines import (
					    AltDiffusionImgaImgPipeline,
					    AltDiffusionPipeline,
					    AudioLDMPipeline,
					    CycleDiffusionPipeline,
					    IFImgaImgPipeline,
					    IFImgaImgSuperResolutionPipeline,
					    IFInpaintingPipeline,
					    IFInpaintingSuperResolutionPipeline,
					    IFPipeline,
					    IFSuperResolutionPipeline,
					    ImageTextPipelineOutput,
					    KandinskyImgaImgPipeline,
					    KandinskyInpaintPipeline,
					    KandinskyPipeline,
					    KandinskyPriorPipeline,
					    KandinskyVaaControlnetImgaImgPipeline,
					    KandinskyVaaControlnetPipeline,
					    KandinskyVaaImgaImgPipeline,
					    KandinskyVaaInpaintPipeline,
					    KandinskyVaaPipeline,
					    KandinskyVaaPriorEmbaEmbPipeline,
					    KandinskyVaaPriorPipeline,
					    LDMTextToImagePipeline,
					    PaintByExamplePipeline,
					    SemanticStableDiffusionPipeline,
					    ShapEImgaImgPipeline,
					    ShapEPipeline,
					    StableDiffusionAttendAndExcitePipeline,
					    StableDiffusionControlNetImgaImgPipeline,
					    StableDiffusionControlNetInpaintPipeline,
					    StableDiffusionControlNetPipeline,
					    StableDiffusionDepthaImgPipeline,
					    StableDiffusionDiffEditPipeline,
					    StableDiffusionImageVariationPipeline,
					    StableDiffusionImgaImgPipeline,
					    StableDiffusionInpaintPipeline,
					    StableDiffusionInpaintPipelineLegacy,
					    StableDiffusionInstructPixaPixPipeline,
					    StableDiffusionLatentUpscalePipeline,
					    StableDiffusionLDMaDPipeline,
					    StableDiffusionModelEditingPipeline,
					    StableDiffusionPanoramaPipeline,
					    StableDiffusionParadigmsPipeline,
					    StableDiffusionPipeline,
					    StableDiffusionPipelineSafe,
					    StableDiffusionPixaPixZeroPipeline,
					    StableDiffusionSAGPipeline,
					    StableDiffusionUpscalePipeline,
					    StableUnCLIPImgaImgPipeline,
					    StableUnCLIPPipeline,
					    TextToVideoSDPipeline,
					    TextToVideoZeroPipeline,
					    UnCLIPImageVariationPipeline,
					    UnCLIPPipeline,
					    UniDiffuserModel,
					    UniDiffuserPipeline,
					    UniDiffuserTextDecoder,
					    VersatileDiffusionDualGuidedPipeline,
					    VersatileDiffusionImageVariationPipeline,
					    VersatileDiffusionPipeline,
					    VersatileDiffusionTextToImagePipeline,
					    VideoToVideoSDPipeline,
					    VQDiffusionPipeline,
					)

try:
					if not (is_torch_available() and is_transformers_available() and is_invisible_watermark_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_transformers_and_invisible_watermark_objects import *  # noqa F403
else:
					from .pipelines import StableDiffusionXLImgaImgPipeline, StableDiffusionXLPipeline

try:
					if not (is_torch_available() and is_transformers_available() and is_k_diffusion_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_transformers_and_k_diffusion_objects import *  # noqa F403
else:
					from .pipelines import StableDiffusionKDiffusionPipeline

try:
					if not (is_torch_available() and is_transformers_available() and is_onnx_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_transformers_and_onnx_objects import *  # noqa F403
else:
					from .pipelines import (
					    OnnxStableDiffusionImgaImgPipeline,
					    OnnxStableDiffusionInpaintPipeline,
					    OnnxStableDiffusionInpaintPipelineLegacy,
					    OnnxStableDiffusionPipeline,
					    OnnxStableDiffusionUpscalePipeline,
					    StableDiffusionOnnxPipeline,
					)

try:
					if not (is_torch_available() and is_librosa_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_torch_and_librosa_objects import *  # noqa F403
else:
					from .pipelines import AudioDiffusionPipeline, Mel

try:
					if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
					from .pipelines import SpectrogramDiffusionPipeline

try:
					if not is_flax_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_flax_objects import *  # noqa F403
else:
					from .models.controlnet_flax import FlaxControlNetModel
					from .models.modeling_flax_utils import FlaxModelMixin
					from .models.unet_ad_condition_flax import FlaxUNetaDConditionModel
					from .models.vae_flax import FlaxAutoencoderKL
					from .pipelines import FlaxDiffusionPipeline
					from .schedulers import (
					    FlaxDDIMScheduler,
					    FlaxDDPMScheduler,
					    FlaxDPMSolverMultistepScheduler,
					    FlaxKarrasVeScheduler,
					    FlaxLMSDiscreteScheduler,
					    FlaxPNDMScheduler,
					    FlaxSchedulerMixin,
					    FlaxScoreSdeVeScheduler,
					)


try:
					if not (is_flax_available() and is_transformers_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_flax_and_transformers_objects import *  # noqa F403
else:
					from .pipelines import (
					    FlaxStableDiffusionControlNetPipeline,
					    FlaxStableDiffusionImgaImgPipeline,
					    FlaxStableDiffusionInpaintPipeline,
					    FlaxStableDiffusionPipeline,
					)

try:
					if not (is_note_seq_available()):
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					from .utils.dummy_note_seq_objects import *  # noqa F403
else:
					from .pipelines import MidiProcessor




"""simple docstring"""
def        lowerCAmelCase_						(							SCREAMING_SNAKE_CASE__, SCREAMING_SNAKE_CASE__ = False	)			->      bool:
		if n == 2:
				return True
		if not n % 2 or n < 2:
				return False
		if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
				return False
		if n > 3_317_044_064_679_887_385_961_981 and not allow_probable:
				raise ValueError(
				    "Warning: upper bound of deterministic test is exceeded. "
				    "Pass allow_probable=True to allow probabilistic test. "
				    "A return value of True indicates a probable prime."	)
		# array bounds provided by analysis
		a_     :      Optional[Any] 						=     [
		    2_047,
		    1_373_653,
		    25_326_001,
		    3_215_031_751,
		    2_152_302_898_747,
		    3_474_749_660_383,
		    341_550_071_728_321,
		    1,
		    3_825_123_056_546_413_051,
		    1,
		    1,
		    318_665_857_834_031_151_167_461,
		    3_317_044_064_679_887_385_961_981,
		]

		a_     :      Optional[int] 						=     [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
		for idx, _p in enumerate(SCREAMING_SNAKE_CASE__, 1	):
				if n < _p:
						# then we have our last prime to check
						a_     :      List[Any] 						=     primes[:idx]
						break
		a_						,				a_     :      Tuple 						=     n - 1, 0
		# break up n -1 into a power of 2 (s) and
		# remaining odd component
		# essentially, solve for d * 2 ** s == n - 1
		while d % 2 == 0:
				d //= 2
				s += 1
		for prime in plist:
				a_     :      str 						=     False
				for r in range(SCREAMING_SNAKE_CASE__	):
						a_     :      List[str] 						=     pow(SCREAMING_SNAKE_CASE__, d * 2**r, SCREAMING_SNAKE_CASE__	)
						# see article for analysis explanation for m
						if (r == 0 and m == 1) or ((m + 1) % n == 0):
								a_     :      List[Any] 						=     True
								# this loop will not determine compositeness
								break
				if pr:
						continue
				# if pr is False, then the above loop never evaluated to true,
				# and the n MUST be composite
				return False
		return True



def        lowerCAmelCase_						(							)			->      None:
		assert not miller_rabin(561	)
		assert miller_rabin(563	)
		# 2047

		assert not miller_rabin(838_201	)
		assert miller_rabin(838_207	)
		# 1_373_653

		assert not miller_rabin(17_316_001	)
		assert miller_rabin(17_316_017	)
		# 25_326_001

		assert not miller_rabin(3_078_386_641	)
		assert miller_rabin(3_078_386_653	)
		# 3_215_031_751

		assert not miller_rabin(1_713_045_574_801	)
		assert miller_rabin(1_713_045_574_819	)
		# 2_152_302_898_747

		assert not miller_rabin(2_779_799_728_307	)
		assert miller_rabin(2_779_799_728_327	)
		# 3_474_749_660_383

		assert not miller_rabin(113_850_023_909_441	)
		assert miller_rabin(113_850_023_909_527	)
		# 341_550_071_728_321

		assert not miller_rabin(1_275_041_018_848_804_351	)
		assert miller_rabin(1_275_041_018_848_804_391	)
		# 3_825_123_056_546_413_051

		assert not miller_rabin(79_666_464_458_507_787_791_867	)
		assert miller_rabin(79_666_464_458_507_787_791_951	)
		# 318_665_857_834_031_151_167_461

		assert not miller_rabin(552_840_677_446_647_897_660_333	)
		assert miller_rabin(552_840_677_446_647_897_660_359	)
		# 3_317_044_064_679_887_385_961_981
		# upper limit for probabilistic test


if __name__ == "__main__":
					test_miller_rabin()