





from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def 		lowerCAmelCase_    (  __UpperCAmelCase:			str		,   __UpperCAmelCase:			complex		,   __UpperCAmelCase:			str = "x"		,   __UpperCAmelCase:			float = 10**-10		,   __UpperCAmelCase:			int = 1		,   )      ->	complex:
    UpperCamelCase__							:				Optional[int]          =      symbols(__UpperCAmelCase      )
    UpperCamelCase__							:				Dict          =      lambdify(__UpperCAmelCase		,   __UpperCAmelCase      )
    UpperCamelCase__							:				List[str]          =      lambdify(__UpperCAmelCase		,   diff(__UpperCAmelCase		,   __UpperCAmelCase      )      )

    UpperCamelCase__							:				int          =      starting_point

    while True:
        if diff_function(__UpperCAmelCase      ) != 0:
            UpperCamelCase__							:				Optional[int]          =      prev_guess - multiplicity * func(__UpperCAmelCase      ) / diff_function(
                __UpperCAmelCase      )
        else:
            raise ZeroDivisionError('''Could not find root'''      ) from None

        # Precision is checked by comparing the difference of consecutive guesses
        if abs(next_guess - prev_guess      ) < precision:
            return next_guess

        UpperCamelCase__							:				Tuple          =      next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(F'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')

  # Find root of polynomial
  # Find fourth Root of 5
  print(F'''The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}''')

  # Find value of e
  print(
      'The root of log(y) - 1 = 0 is ',
      F'''{newton_raphson("log(y) - 1", 2, variable="y")}''',
  )

  # Exponential Roots
  print(
      'The root of exp(x) - 1 = 0 is',
      F'''{newton_raphson("exp(x) - 1", 10, precision=0.005)}''',
  )

  # Find root of cos(x)
  print(F'''The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}''')








def 		lowerCAmelCase_    (  __UpperCAmelCase:			int      )      ->	int:
    if not isinstance(__UpperCAmelCase		,   __UpperCAmelCase      ) or number < 0:
        raise ValueError('''Input must be a non-negative integer'''      )

    UpperCamelCase__							:				Optional[Any]          =      0
    while number:
        # This way we arrive at next set bit (next 1) instead of looping
        # through each bit and checking for 1s hence the
        # loop won't run 32 times it will only run the number of `1` times
        number &= number - 1
        count += 1
    return count


if __name__ == "__main__":
  import doctest

  doctest.testmod()

