# Path: diffprivlib/utils.py
# class Budget(tuple):
#     """Custom tuple subclass for privacy budgets of the form (epsilon, delta).
# 
#     The ``Budget`` class allows for correct comparison/ordering of privacy budget, ensuring that both epsilon and delta
#     satisfy the comparison (tuples are compared lexicographically).  Additionally, tuples are represented with added
#     verbosity, labelling epsilon and delta appropriately.
# 
#     Examples
#     --------
# 
#     >>> from diffprivlib.utils import Budget
#     >>> Budget(1, 0.5)
#     (epsilon=1, delta=0.5)
#     >>> Budget(2, 0) >= Budget(1, 0.5)
#     False
#     >>> (2, 0) >= (1, 0.5) # Tuples are compared with lexicographic ordering
#     True
# 
#     """
#     def __new__(cls, epsilon, delta):
#         from diffprivlib.validation import check_epsilon_delta
# 
#         check_epsilon_delta(epsilon, delta, allow_zero=True)
#         return tuple.__new__(cls, (epsilon, delta))
# 
#     def __gt__(self, other):
#         if self.__ge__(other) and not self.__eq__(other):
#             return True
#         return False
# 
#     def __ge__(self, other):
#         if self[0] >= other[0] and self[1] >= other[1]:
#             return True
#         return False
# 
#     def __lt__(self, other):
#         if self.__le__(other) and not self.__eq__(other):
#             return True
#         return False
# 
#     def __le__(self, other):
#         if self[0] <= other[0] and self[1] <= other[1]:
#             return True
#         return False
# 
#     def __repr__(self):
#         return f"(epsilon={self[0]}, delta={self[1]})"
# 
# class BudgetError(ValueError):
#     """Custom exception to capture the privacy budget being exceeded, typically controlled by a
#     :class:`.BudgetAccountant`.
# 
#     For example, this exception may be raised when the user:
# 
#         - Attempts to execute a query which would exceed the privacy budget of the accountant.
#         - Attempts to change the slack of the accountant in such a way that the existing budget spends would exceed the
#           accountant's budget.
# 
#     """
# 
# Path: diffprivlib/validation.py
# def check_epsilon_delta(epsilon, delta, allow_zero=False):
#     """Checks that epsilon and delta are valid values for differential privacy.  Throws an error if checks fail,
#     otherwise returns nothing.
# 
#     As well as the requirements of epsilon and delta separately, both cannot be simultaneously zero, unless
#     ``allow_zero`` is set to ``True``.
# 
#     Parameters
#     ----------
#     epsilon : float
#         Epsilon parameter for differential privacy.  Must be non-negative.
# 
#     delta : float
#         Delta parameter for differential privacy.  Must be on the unit interval, [0, 1].
# 
#     allow_zero : bool, default: False
#         Allow epsilon and delta both be zero.
# 
#     """
#     if not isinstance(epsilon, Real) or not isinstance(delta, Real):
#         raise TypeError("Epsilon and delta must be numeric")
# 
#     if epsilon < 0:
#         raise ValueError("Epsilon must be non-negative")
# 
#     if not 0 <= delta <= 1:
#         raise ValueError("Delta must be in [0, 1]")
# 
#     if not allow_zero and epsilon + delta == 0:
#         raise ValueError("Epsilon and Delta cannot both be zero")


from numbers import Integral
from diffprivlib.utils import Budget, BudgetError
from diffprivlib.validation import check_epsilon_delta
import numpy as np
            return Budget(total_epsilon_naive, total_delta)

        total_epsilon_drv = epsilon_exp_sum + np.sqrt(2 * epsilon_sq_sum * np.log(1 / slack))
        total_epsilon_kov = epsilon_exp_sum + np.sqrt(2 * epsilon_sq_sum *
                                                      np.log(np.exp(1) + np.sqrt(epsilon_sq_sum) / slack))

        return Budget(min(total_epsilon_naive, total_epsilon_drv, total_epsilon_kov), total_delta)

    def check(self, epsilon, delta):
        """Checks if the provided (epsilon,delta) can be spent without exceeding the accountant's budget ceiling.

        Parameters
        ----------
        epsilon : float
            Epsilon budget spend to check.

        delta : float
            Delta budget spend to check.

        Returns
        -------
        bool
            True if the budget can be spent, otherwise a :class:`.BudgetError` is raised.

        Raises
        ------
        BudgetError
            If the specified budget spend will result in the budget ceiling being exceeded.

        """

# Path: diffprivlib/utils.py
# class Budget(tuple):
#     """Custom tuple subclass for privacy budgets of the form (epsilon, delta).
# 
#     The ``Budget`` class allows for correct comparison/ordering of privacy budget, ensuring that both epsilon and delta
#     satisfy the comparison (tuples are compared lexicographically).  Additionally, tuples are represented with added
#     verbosity, labelling epsilon and delta appropriately.
# 
#     Examples
#     --------
# 
#     >>> from diffprivlib.utils import Budget
#     >>> Budget(1, 0.5)
#     (epsilon=1, delta=0.5)
#     >>> Budget(2, 0) >= Budget(1, 0.5)
#     False
#     >>> (2, 0) >= (1, 0.5) # Tuples are compared with lexicographic ordering
#     True
# 
#     """
#     def __new__(cls, epsilon, delta):
#         from diffprivlib.validation import check_epsilon_delta
# 
#         check_epsilon_delta(epsilon, delta, allow_zero=True)
#         return tuple.__new__(cls, (epsilon, delta))
# 
#     def __gt__(self, other):
#         if self.__ge__(other) and not self.__eq__(other):
#             return True
#         return False
# 
#     def __ge__(self, other):
#         if self[0] >= other[0] and self[1] >= other[1]:
#             return True
#         return False
# 
#     def __lt__(self, other):
#         if self.__le__(other) and not self.__eq__(other):
#             return True
#         return False
# 
#     def __le__(self, other):
#         if self[0] <= other[0] and self[1] <= other[1]:
#             return True
#         return False
# 
#     def __repr__(self):
#         return f"(epsilon={self[0]}, delta={self[1]})"
# 
# class BudgetError(ValueError):
#     """Custom exception to capture the privacy budget being exceeded, typically controlled by a
#     :class:`.BudgetAccountant`.
# 
#     For example, this exception may be raised when the user:
# 
#         - Attempts to execute a query which would exceed the privacy budget of the accountant.
#         - Attempts to change the slack of the accountant in such a way that the existing budget spends would exceed the
#           accountant's budget.
# 
#     """
# 
# Path: diffprivlib/validation.py
# def check_epsilon_delta(epsilon, delta, allow_zero=False):
#     """Checks that epsilon and delta are valid values for differential privacy.  Throws an error if checks fail,
#     otherwise returns nothing.
# 
#     As well as the requirements of epsilon and delta separately, both cannot be simultaneously zero, unless
#     ``allow_zero`` is set to ``True``.
# 
#     Parameters
#     ----------
#     epsilon : float
#         Epsilon parameter for differential privacy.  Must be non-negative.
# 
#     delta : float
#         Delta parameter for differential privacy.  Must be on the unit interval, [0, 1].
# 
#     allow_zero : bool, default: False
#         Allow epsilon and delta both be zero.
# 
#     """
#     if not isinstance(epsilon, Real) or not isinstance(delta, Real):
#         raise TypeError("Epsilon and delta must be numeric")
# 
#     if epsilon < 0:
#         raise ValueError("Epsilon must be non-negative")
# 
#     if not 0 <= delta <= 1:
#         raise ValueError("Delta must be in [0, 1]")
# 
#     if not allow_zero and epsilon + delta == 0:
#         raise ValueError("Epsilon and Delta cannot both be zero")


# Path: diffprivlib/accountant.py
from numbers import Integral
from diffprivlib.utils import Budget, BudgetError
from diffprivlib.validation import check_epsilon_delta
import numpy as np

            return Budget(total_epsilon_naive, total_delta)

        total_epsilon_drv = epsilon_exp_sum + np.sqrt(2 * epsilon_sq_sum * np.log(1 / slack))
        total_epsilon_kov = epsilon_exp_sum + np.sqrt(2 * epsilon_sq_sum *
                                                      np.log(np.exp(1) + np.sqrt(epsilon_sq_sum) / slack))

        return Budget(min(total_epsilon_naive, total_epsilon_drv, total_epsilon_kov), total_delta)

    def check(self, epsilon, delta):
        """Checks if the provided (epsilon,delta) can be spent without exceeding the accountant's budget ceiling.

        Parameters
        ----------
        epsilon : float
            Epsilon budget spend to check.

        delta : float
            Delta budget spend to check.

        Returns
        -------
        bool
            True if the budget can be spent, otherwise a :class:`.BudgetError` is raised.

        Raises
        ------
        BudgetError
            If the specified budget spend will result in the budget ceiling being exceeded.

        """

        check_epsilon_delta(epsilon, delta)