# 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
            Total delta spend remaining for `k` queries.

        """
        if not isinstance(k, Integral):
            raise TypeError(f"k must be integer-valued, got {type(k)}.")
        if k < 1:
            raise ValueError(f"k must be at least 1, got {k}.")

        _, spent_delta = self.total()
        delta = 1 - ((1 - self.delta) / (1 - spent_delta)) ** (1 / k) if spent_delta < 1.0 else 1.0
        # delta = 1 - np.exp((np.log(1 - self.delta) - np.log(1 - spent_delta)) / k)

        lower = 0
        upper = self.epsilon
        old_interval_size = (upper - lower) * 2

        while old_interval_size > upper - lower:
            old_interval_size = upper - lower
            mid = (upper + lower) / 2

            spent_budget = self.spent_budget + [(mid, 0)] * k
            x_0, _ = self.total(spent_budget=spent_budget)

            if x_0 >= self.epsilon:
                upper = mid
            if x_0 <= self.epsilon:
                lower = mid

        epsilon = (upper + lower) / 2


# 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

            Total delta spend remaining for `k` queries.

        """
        if not isinstance(k, Integral):
            raise TypeError(f"k must be integer-valued, got {type(k)}.")
        if k < 1:
            raise ValueError(f"k must be at least 1, got {k}.")

        _, spent_delta = self.total()
        delta = 1 - ((1 - self.delta) / (1 - spent_delta)) ** (1 / k) if spent_delta < 1.0 else 1.0
        # delta = 1 - np.exp((np.log(1 - self.delta) - np.log(1 - spent_delta)) / k)

        lower = 0
        upper = self.epsilon
        old_interval_size = (upper - lower) * 2

        while old_interval_size > upper - lower:
            old_interval_size = upper - lower
            mid = (upper + lower) / 2

            spent_budget = self.spent_budget + [(mid, 0)] * k
            x_0, _ = self.total(spent_budget=spent_budget)

            if x_0 >= self.epsilon:
                upper = mid
            if x_0 <= self.epsilon:
                lower = mid

        epsilon = (upper + lower) / 2


        return Budget(epsilon, delta)