
'''simple docstring'''
from math import factorial






class    UpperCAmelCase_				:





 def __init__(    self ,       lowercase_ ,       lowercase_):
     snake_case_ :    Optional[Any]     			=						real
     if isinstance(__a ,       __a):
         snake_case_ :    Tuple     			=						[1] * rank
     else:
         snake_case_ :    Any     			=						rank





 def __repr__(    self):
     return (
         F'{self.real}+'
         F'{"+".join(str(__a)+"E"+str(n+1)for n,dual in enumerate(self.duals))}'
     )





 def        snake_case__		(    self):
     snake_case_ :    Tuple     			=						self.duals.copy()
     while cur[-1] == 0:
         cur.pop(-1)
     return Dual(self.real ,       __a)





 def __add__(    self ,       lowercase_):
     if not isinstance(__a ,       __a):
         return Dual(self.real + other ,       self.duals)
     snake_case_ :    Optional[Any]     			=						self.duals.copy()
     snake_case_ :    Any     			=						other.duals.copy()
     if len(__a) > len(__a):
         o_dual.extend([1] * (len(__a) - len(__a)))
     elif len(__a) < len(__a):
         s_dual.extend([1] * (len(__a) - len(__a)))
     snake_case_ :    Optional[Any]     			=						[]
     for i in range(len(__a)):
         new_duals.append(s_dual[i] + o_dual[i])
     return Dual(self.real + other.real ,       __a)

 UpperCAmelCase_		    =						__add__





 def __sub__(    self ,       lowercase_):
     return self + other * -1





 def __mul__(    self ,       lowercase_):
     if not isinstance(__a ,       __a):
         snake_case_ :    Tuple     			=						[]
         for i in self.duals:
             new_duals.append(i * other)
         return Dual(self.real * other ,       __a)
     snake_case_ :    Any     			=						[0] * (len(self.duals) + len(other.duals) + 1)
     for i, item in enumerate(self.duals):
         for j, jtem in enumerate(other.duals):
             new_duals[i + j + 1] += item * jtem
     for k in range(len(self.duals)):
         new_duals[k] += self.duals[k] * other.real
     for index in range(len(other.duals)):
         new_duals[index] += other.duals[index] * self.real
     return Dual(self.real * other.real ,       __a)

 UpperCAmelCase_		    =						__mul__





 def __truediv__(    self ,       lowercase_):
     if not isinstance(__a ,       __a):
         snake_case_ :    List[str]     			=						[]
         for i in self.duals:
             new_duals.append(i / other)
         return Dual(self.real / other ,       __a)
     raise ValueError





 def __floordiv__(    self ,       lowercase_):
     if not isinstance(__a ,       __a):
         snake_case_ :    List[Any]     			=						[]
         for i in self.duals:
             new_duals.append(i // other)
         return Dual(self.real // other ,       __a)
     raise ValueError





 def __pow__(    self ,       lowercase_):
     if n < 0 or isinstance(__a ,       __a):
         raise ValueError("power must be a positive integer")
     if n == 0:
         return 1
     if n == 1:
         return self
     snake_case_ :    int     			=						self
     for _ in range(n - 1):
         x *= self
     return x


def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ):
    """simple docstring"""






    if not callable(UpperCamelCase__       ):
        raise ValueError("differentiate() requires a function as input for func"       )
    if not isinstance(UpperCamelCase__,		(float, int)       ):
        raise ValueError("differentiate() requires a float as input for position"       )
    if not isinstance(UpperCamelCase__,		UpperCamelCase__       ):
        raise ValueError("differentiate() requires an int as input for order"       )
    snake_case_ :    Union[str, Any]     			=						Dual(UpperCamelCase__,		1       )
    snake_case_ :    int     			=						func(UpperCamelCase__       )
    if order == 0:
        return result.real
    return result.duals[order - 1] * factorial(UpperCamelCase__       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE       ):
      """simple docstring"""






      return y**2 * y**4


  print(differentiate(f, 9, 2))






'''simple docstring'''
import contextlib
from multiprocessing import Pool, RLock

from tqdm.auto import tqdm

from ..utils import experimental, logging


a_											=						logging.get_logger(__name__)






class    UpperCAmelCase_				:
 UpperCAmelCase_		    =						None


@experimental
def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ):
    """simple docstring"""






    if ParallelBackendConfig.backend_name is None:
        return _map_with_multiprocessing_pool(
            __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       )

    return _map_with_joblib(__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       )

def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ):
    """simple docstring"""






    snake_case_ :    str     			=						num_proc if num_proc <= len(__SCREAMING_SNAKE_CASE       ) else len(__SCREAMING_SNAKE_CASE       )
    snake_case_ :    Optional[int]     			=						[]  # We organize the splits ourselve (contiguous splits)
    for index in range(__SCREAMING_SNAKE_CASE       ):
        snake_case_ :    List[str]     			=						len(__SCREAMING_SNAKE_CASE       ) // num_proc
        snake_case_ :    Optional[Any]     			=						len(__SCREAMING_SNAKE_CASE       ) % num_proc
        snake_case_ :    Optional[Any]     			=						div * index + min(__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       )
        snake_case_ :    Union[str, Any]     			=						start + div + (1 if index < mod else 0)
        split_kwds.append((function, iterable[start:end], types, index, disable_tqdm, desc)       )

    if len(__SCREAMING_SNAKE_CASE       ) != sum(len(i[1]       ) for i in split_kwds       ):
        raise ValueError(
            f'Error dividing inputs iterable among processes. '
            f'Total number of objects {len(__SCREAMING_SNAKE_CASE       )}, '
            f'length: {sum(len(i[1]       ) for i in split_kwds       )}'       )

    logger.info(
        f'Spawning {num_proc} processes for {len(__SCREAMING_SNAKE_CASE       )} objects in slices of {[len(i[1]       ) for i in split_kwds]}'       )
    snake_case_			, snake_case_ :    Tuple     			=						None, None
    if not disable_tqdm:
        snake_case_			, snake_case_ :    int     			=						(RLock(),), tqdm.set_lock
    with Pool(__SCREAMING_SNAKE_CASE,		initargs=__SCREAMING_SNAKE_CASE,		initializer=__SCREAMING_SNAKE_CASE       ) as pool:
        snake_case_ :    Union[str, Any]     			=						pool.map(__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       )
    logger.info(f'Finished {num_proc} processes'       )
    snake_case_ :    str     			=						[obj for proc_res in mapped for obj in proc_res]
    logger.info(f'Unpacked {len(__SCREAMING_SNAKE_CASE       )} objects'       )

    return mapped

def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE       ):
    """simple docstring"""






    import joblib

    with joblib.parallel_backend(ParallelBackendConfig.backend_name,		n_jobs=__SCREAMING_SNAKE_CASE       ):
        return joblib.Parallel()(
            joblib.delayed(__SCREAMING_SNAKE_CASE       )((function, obj, types, None, True, None)       ) for obj in iterable       )


@experimental
@contextlib.contextmanager
def 						UpperCamelCase_     (	__SCREAMING_SNAKE_CASE       ):
    """simple docstring"""






    snake_case_ :    Union[str, Any]     			=						backend_name

    if backend_name == "spark":
        from joblibspark import register_spark

        register_spark()

        # TODO: call create_cache_and_write_probe if "download" in steps
        # TODO: raise NotImplementedError when Dataset.map etc is called

    try:
        yield
    finally:
        snake_case_ :    Any     			=						None




