Module digint.digint

digint

Holds the main digitwise intiger classes digint module.

Classes

class ExtendedBasedIntiger (value: Union[int, str, Iterable[Union[int, str]]] = 0, base: int = 10, *, notation_format: Optional[NotationFormat] = NotationFormat(value_symbols=('0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'), undefined_symbol='?', positive_symbol='+', negative_symbol='-', radix_point_symbol='.', group_split_symbol=None, group_split_count=0, implicit_positive=True, implicit_negative=False))

ExtendedBasedIntiger

A mutable sequence type of intiger that has a explicitly set base, allowing for specific digit values to be get and set.

Supports any initger base starting at (and including) base 1. The base is presumed to be in the traditional place value format of value == d[x] * (base ** x) where value is the value the digit holds in the intiger, d is a single digit value form a sequence of digits, base is the base, and x is the specific index in question of the intiger.

However, base 1 produces inconsistencies with this specific format. Using this logic, one would also presume that the only digit in base 1 is 0 (or whatever relevant "naught" character would be used). This is why the extention of base 1 functionality is done in a child class of PositionalBasedIntiger.

Base 1, as implemented here, uses both the "naught" (with a value of 0) and "unity" (with a value of '1') digits, but in a tally system. This also means that the value of any given index of a digit means very little without the context of the rest of the defined digits as well. It is also implemented in such a way that the set digits will always be grouped together, ie. all "unity" digits will be grouped together, starting at the first digit and remaining completely set all the way to the digits index that matches the value of the number represented.

For these reason base 1 will have not functionality for functions that set or unset digits, as setting and unsetting digits are not relevant in unary. Attempting to do so will raise either a BaseInvalidOpperationError or a BaseValueError. Deleting digits are still possible, however.

Unary numbers are also fully compatible with negative values.

ex.

    1111111111 (base 1) == 10 (base 10)
    11111 (base 1) == 5 (base 10)
    111111 (base 1) == 11 (base 2)
    1101101 (base 1) == IMPOSSIBLE (the are unset digits in between the set digits)
      ^  ^
    000111000 (base 1) == IMPOSSIBLE (the first set digit is not the first digit in the number)
          ^^^

Effectively: base 1 (uniary) notation treates the value of the number as a sequence of a single type of digit that when counted add up to the value of the number.

NOTE: No functionality of any higher base is nor will modified in this class, making this class a superset of all proper positional based intiger notation formats and uniary.

Also supports customizable notation formats with the optional notation_format attribute, including unary.

Expand source code

class ExtendedBasedIntiger(PositionalBasedIntiger):
    """
    `ExtendedBasedIntiger`

    A mutable sequence type of intiger that has a explicitly set base,
    allowing for specific digit values to be get and set.

    Supports any initger base starting at (and including) base 1.
    The base is presumed to be in the traditional place value format of
    `value == d[x] * (base ** x)` where `value` is the value the digit holds in the intiger,
    `d` is a single digit value form a sequence of digits,
    `base` is the base,
    and `x` is the specific index in question of the intiger.

    However, base 1 produces inconsistencies with this specific format.
    Using this logic, one would also presume that the only digit in base 1 is `0`
    (or whatever relevant "naught" character would be used).
    This is why the extention of base 1 functionality is done in a child class of
    `PositionalBasedIntiger`.

    Base 1, as implemented here, uses both the "naught" (with a value of `0`)
    and "unity" (with a value of '1') digits, but in a tally system.
    This also means that the value of any given index of a digit means very
    little without the context of the rest of the defined digits as well.
    It is also implemented in such a way that the set digits will always be grouped together,
    ie. all "unity" digits will be grouped together,
    starting at the first digit and remaining completely set
    all the way to the digits index that matches the value of the number represented.

    For these reason base 1 will have not functionality for functions that set or unset digits,
    as setting and unsetting digits are not relevant in unary.
    Attempting to do so will raise either a `BaseInvalidOpperationError` or a `BaseValueError`.
    Deleting digits are still possible, however.

    Unary numbers are also fully compatible with negative values.

    ex.
    ```
        1111111111 (base 1) == 10 (base 10)
        11111 (base 1) == 5 (base 10)
        111111 (base 1) == 11 (base 2)
        1101101 (base 1) == IMPOSSIBLE (the are unset digits in between the set digits)
          ^  ^
        000111000 (base 1) == IMPOSSIBLE (the first set digit is not the first digit in the number)
              ^^^
    ```

    Effectively: base 1 (uniary) notation treates the value of the number as a
    sequence of a single type of digit that when counted add up to the value of the number.

    NOTE: No functionality of any higher base is nor will modified in this class,
    making this class a superset of all proper positional based intiger notation formats and uniary.

    Also supports customizable notation formats with the optional `notation_format` attribute,
    including unary.
    """
    @override
    def __init__(self,
                 value:Union[int, str, Iterable[Union[int, str]]] = 0,
                 base:int = 10,
                 *,
                 notation_format:Optional[NotationFormat] = DEFAULT_FORMAT
                 ):

        self.__base:int = 2
        super().__init__(0 if base == 1 else value, base, notation_format=notation_format)

        if base == 1:
            self.base = 1
            if isinstance(value, int):
                self.x = value
            elif isinstance(value, str):
                value = value.lstrip("0")
                if not all(c == "1" for c in value):
                    raise BaseValueError(f"{value} cannot be represented in base 1")
                self.x = len(value)

    @override
    def copy(self,
             value:Optional[Union[int, str]] = None,
             base:Optional[int] = None,
             notation_format_override:Optional[NotationFormat] = None
             ) -> 'ExtendedBasedIntiger':
        """
        `copy`

        Creates a shallow copy of this object.

        Keyword Arguments:
            `value` -- When not `None`, will overrides the `x` value of the copy.
            `base` -- When not `None`, will overrides the `base` of the copy.
            `notation_format_override` -- When not `None`,
                will overrides the `notation_format` of the copy.

        Returns:
            The copy of the object.
        """
        if notation_format_override is not None:
            notation_format_override = self.notation_format
        return ExtendedBasedIntiger(value if value is not None else self.x,
                                    base if base is not None else self.base,
                                    notation_format = notation_format_override
                                    )
    __copy__ = copy

    @override
    def __deepcopy__(self, _ = None) -> 'ExtendedBasedIntiger':
        return self.copy(None,
                         None,
                         None if self.notation_format is None else self.notation_format.copy()
                         )

    @property
    @override
    def base(self) -> int:
        """
        `base`

        The base of this number. Must be greater than 0.
        Base 1 is handled particularly differently than other bases.
        """
        return self.__base

    @base.setter
    @override
    def base(self, value:int):
        if value <= 0:
            raise BaseValueError()
        self.__base = value

    @override
    def _get_single_digit(self, index:int) -> int:
        if self.base == 1:
            index = absindex(index, self.digit_length())
            return 1 if index < abs(self.x) else 0
        else:
            return super()._get_single_digit(index)

    @override
    def _pop_first(self) -> int:
        if self.base == 1:
            self.x -= 1
            return 1
        else:
            return super()._pop_first()

    @override
    def _mask_value_continuous(self, dindex: int, count: int = 1) -> int:
        if count <= 0:
            raise IndexError("The length of a continuous mask must be at least 1")

        if self.base == 1:
            return min(abs(self.x) - dindex, count)
        else:
            return super()._mask_value_continuous(dindex, count)

    @override
    def notate(self, notation_format:Optional[NotationFormat] = None) -> str:
        if self.base >= 2:
            return super().notate(notation_format)

        if notation_format is None:
            notation_format = self.notation_format

        if notation_format is None:
            raise BaseInvalidOpperationError("No format set, cannot notate")

        relevant_sign = ""
        if self.x < 0 and not notation_format.implicit_negative:
            if notation_format.negative_symbol is None:
                raise ValueError("Explicit negative values require a negative symbol")
            else:
                relevant_sign = notation_format.negative_symbol
        elif self.x > 0 and not notation_format.implicit_positive:
            if notation_format.positive_symbol is None:
                raise ValueError("Explicit positive values require a positive symbol")
            else:
                relevant_sign = notation_format.positive_symbol

        if notation_format.unity is None:
            raise NotationError("Cannot notate base 1 without a digit for unity")
        return relevant_sign + ((notation_format.unity) * self.x)

    @overload
    @override
    def set_digit(self, index:int, value:Union[int,str]): ...
    @overload
    @override
    def set_digit(self, index:Union[slice,range,Iterable[int]], value:Iterable[Union[int,str]]): ...
    @override # noqa:301
    def set_digit(self,
                  index:Union[int,slice,range,Iterable[int]],
                  value:Union[int,str,Iterable[Union[int,str]]]
                  ):
        if self.base == 1:
            raise BaseInvalidOpperationError("Digits cannot be set in base 1")
        super().set_digit(index, value) # type:ignore[reportCallIssue]

    @override
    def unset_digit(self, index:Union[int,slice,range,Iterable[int]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("Cannot unset digits in base 1")
        return super().unset_digit(index)

    # NOTE: just like python handles it in bit_length, a value of 0 will always have no digits
    @override
    def digit_length(self) -> int:
        if self.base == 1:
            return abs(self.x)
        return super().digit_length()

    @override
    def insert(self, index:int, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError(f"Cannot insert digits into a base {self.base} number")
        super().insert(index, value)

    @override
    def pop(self, index:int = -1) -> int:
        if self.base == 1:
            index = absindex(index, self.digit_length())
            self.x -= 1
            return 1
        else:
            return super().pop(index)

    # returns the count of non-zero (non-unset) digits
    @override
    def digit_count(self) -> int:
        if self.base == 1:
            return abs(self.x)
        return super().digit_count()

    @override
    def digit_shift_left(self, amount:int = 1):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be shifted")
        super().digit_shift_left(amount)

    @override
    def digit_shift_right(self, amount:int = 1):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be shifted")
        super().digit_shift_right(amount)

    @override
    def rstrip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be stripped")
        super().rstrip(value)

    @override
    def lstrip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be stripped")
        super().lstrip(value)

    @override
    def strip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be stripped")
        super().strip(value)

    @override
    def contains(self, value:Union[int, str]) -> bool:
        if self.base == 1:
            value = self._ensure_unnotated(value)
            return (value == 1 and self.x != 0) or (value == 0 and self.x == 0)
        return super().contains(value)

Ancestors

• PositionalBasedIntiger
• ExtendedUserInt
• UserInt
• typing.SupportsInt
• typing.SupportsFloat
• typing.SupportsAbs
• typing.SupportsComplex
• typing.SupportsRound
• typing.SupportsIndex
• typing.Protocol
• typing.Generic
• collections.abc.Hashable
• collections.abc.MutableSequence
• collections.abc.Sequence
• collections.abc.Reversible
• collections.abc.Collection
• collections.abc.Sized
• collections.abc.Iterable
• collections.abc.Container

Instance variables

prop base : int

base

The base of this number. Must be greater than 0. Base 1 is handled particularly differently than other bases.

Expand source code

@property
@override
def base(self) -> int:
    """
    `base`

    The base of this number. Must be greater than 0.
    Base 1 is handled particularly differently than other bases.
    """
    return self.__base

Methods

def contains(self, value: Union[int, str]) ‑> bool

contains

Returns true if the digit value appears anywhere in this digit sequence. This will not include leading 0s, but will return true if the tested digit value is 0 and this intiger's value is also 0.

Arguments

value – The value to check for.

def copy(self, value: Union[int, str, ForwardRef(None)] = None, base: Optional[int] = None, notation_format_override: Optional[NotationFormat] = None) ‑> ExtendedBasedIntiger

copy

Creates a shallow copy of this object.

Keyword Arguments: value – When not None, will overrides the x value of the copy. base – When not None, will overrides the base of the copy. notation_format_override – When not None, will overrides the notation_format of the copy.

Returns

The copy of the object.

def digit_count(self) ‑> int

digit_count

Similar to bit_count, but relitive to the current base. Not to be confused with digit_length.

Returns

The amount of non-zero (non-unset) digits in the value.

def digit_length(self) ‑> int

digit_length

Similar to bit_length, but relitive to the current base. Not to be confused with digit_count.

Returns

The minimum necessary about of digits needed to display the number in full.

def digit_shift_left(self, amount: int = 1)

digit_shift_left

Similar to a binary shift left, shifts the value left according to the set base.

Arguments

amount – The amount to shift left. Will shift right when negative.

def digit_shift_right(self, amount: int = 1)

digit_shift_right

Similar to a binary shift right, shifts the value right according to the set base.

Arguments

amount – The amount to shift right. Will shift left when negative.

def insert(self, index: int, value: Union[int, str, Iterable[Union[int, str]]])

insert

Inserts the given value (or values, following the order in which they are supplied) before the given index. When given multiple values, each value will be inserted before the given index in order.

Arguments

index – The index (or indexes) to be inserted before. value – The value (or values) to insert.

def lstrip(self, value: Union[int, str, Iterable[Union[int, str]]])

rstrip

Removes the given digit (or digits) from the left hand (greatest place value) spot. Works similarly to str.lstrip, except for the fact that when value is a single string (not a iterable of strings) it will be treated as a single digit instead of a iterable of digits. This will not strip any leading 0 digit values, as these are already not notated by default nor would effect the digit length of this intiger.

Arguments

value – The value (or iterable of values) to strip. Can be either a intiger digit value, or a string corelating to a single digit.

def notate(self, notation_format: Optional[NotationFormat] = None) ‑> str

notate Notates the intiger, using the given notation format if possible, or the notation_format set in the object's attributes if the paramater is not set.

Keyword Arguments: notation_format – A notation format to use over the one set in self.notation_format, if not None.

Raises

NotationError

Raised when both the argument and attribute notation_format are None; or when other errors are raised during notation.

Returns

The final notation of the intiger.

def pop(self, index: int = -1) ‑> int

pop

Gets the value at the given index while popping it.

Keyword Arguments: index – The target index to pop. Defaults to -1.

Returns

The value at the given index before removal.

def rstrip(self, value: Union[int, str, Iterable[Union[int, str]]])

rstrip

Removes the given digit (or digits) from the right hand (units) spot. Works similarly to str.rstrip, except for the fact that when value is a single string (not a iterable of strings) it will be treated as a single digit instead of a iterable of digits.

Arguments

value – The value (or iterable of values) to strip. Can be either a intiger digit value, or a string corelating to a single digit.

def set_digit(self, index: Union[int, slice, range, Iterable[int]], value: Union[int, str, Iterable[Union[int, str]]])

set_digit

Sets the digit (or digits) at the given index (or indexes) to the given value (or values). With multiple indexes and, there must be a matching quantity of values to set at those indexes.

Arguments

index – The index (or indexes) to set. value – The value (or values) to set the index (or indexes) to.

Raises

ValueError: Raised when the given value is out of bounds of the current base.

def strip(self, value: Union[int, str, Iterable[Union[int, str]]])

rstrip

Removes the given digit (or digits) from both sides. Works similarly to str.strip, except for the fact that when value is a single string (not a iterable of strings) it will be treated as a single digit instead of a iterable of digits. This will not strip any leading 0 digit values, as these are already not notated by default nor would effect the digit length of this intiger.

Arguments

value – The value (or iterable of values) to strip. Can be either a intiger digit value, or a string corelating to a single digit.

def unset_digit(self, index: Union[int, slice, range, Iterable[int]])

unset_digit

Unsets (set to 0) the value at the given index (or indexes).

Arguments

index – The index (or indexes) digit to be unset.

class digitint (value: Union[int, str, Iterable[Union[int, str]]] = 0, base: int = 10, *, notation_format: Optional[NotationFormat] = NotationFormat(value_symbols=('0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'), undefined_symbol='?', positive_symbol='+', negative_symbol='-', radix_point_symbol='.', group_split_symbol=None, group_split_count=0, implicit_positive=True, implicit_negative=False))

ExtendedBasedIntiger

A mutable sequence type of intiger that has a explicitly set base, allowing for specific digit values to be get and set.

Supports any initger base starting at (and including) base 1. The base is presumed to be in the traditional place value format of value == d[x] * (base ** x) where value is the value the digit holds in the intiger, d is a single digit value form a sequence of digits, base is the base, and x is the specific index in question of the intiger.

However, base 1 produces inconsistencies with this specific format. Using this logic, one would also presume that the only digit in base 1 is 0 (or whatever relevant "naught" character would be used). This is why the extention of base 1 functionality is done in a child class of PositionalBasedIntiger.

Base 1, as implemented here, uses both the "naught" (with a value of 0) and "unity" (with a value of '1') digits, but in a tally system. This also means that the value of any given index of a digit means very little without the context of the rest of the defined digits as well. It is also implemented in such a way that the set digits will always be grouped together, ie. all "unity" digits will be grouped together, starting at the first digit and remaining completely set all the way to the digits index that matches the value of the number represented.

For these reason base 1 will have not functionality for functions that set or unset digits, as setting and unsetting digits are not relevant in unary. Attempting to do so will raise either a BaseInvalidOpperationError or a BaseValueError. Deleting digits are still possible, however.

Unary numbers are also fully compatible with negative values.

ex.

    1111111111 (base 1) == 10 (base 10)
    11111 (base 1) == 5 (base 10)
    111111 (base 1) == 11 (base 2)
    1101101 (base 1) == IMPOSSIBLE (the are unset digits in between the set digits)
      ^  ^
    000111000 (base 1) == IMPOSSIBLE (the first set digit is not the first digit in the number)
          ^^^

Effectively: base 1 (uniary) notation treates the value of the number as a sequence of a single type of digit that when counted add up to the value of the number.

NOTE: No functionality of any higher base is nor will modified in this class, making this class a superset of all proper positional based intiger notation formats and uniary.

Also supports customizable notation formats with the optional notation_format attribute, including unary.

Expand source code

class ExtendedBasedIntiger(PositionalBasedIntiger):
    """
    `ExtendedBasedIntiger`

    A mutable sequence type of intiger that has a explicitly set base,
    allowing for specific digit values to be get and set.

    Supports any initger base starting at (and including) base 1.
    The base is presumed to be in the traditional place value format of
    `value == d[x] * (base ** x)` where `value` is the value the digit holds in the intiger,
    `d` is a single digit value form a sequence of digits,
    `base` is the base,
    and `x` is the specific index in question of the intiger.

    However, base 1 produces inconsistencies with this specific format.
    Using this logic, one would also presume that the only digit in base 1 is `0`
    (or whatever relevant "naught" character would be used).
    This is why the extention of base 1 functionality is done in a child class of
    `PositionalBasedIntiger`.

    Base 1, as implemented here, uses both the "naught" (with a value of `0`)
    and "unity" (with a value of '1') digits, but in a tally system.
    This also means that the value of any given index of a digit means very
    little without the context of the rest of the defined digits as well.
    It is also implemented in such a way that the set digits will always be grouped together,
    ie. all "unity" digits will be grouped together,
    starting at the first digit and remaining completely set
    all the way to the digits index that matches the value of the number represented.

    For these reason base 1 will have not functionality for functions that set or unset digits,
    as setting and unsetting digits are not relevant in unary.
    Attempting to do so will raise either a `BaseInvalidOpperationError` or a `BaseValueError`.
    Deleting digits are still possible, however.

    Unary numbers are also fully compatible with negative values.

    ex.
    ```
        1111111111 (base 1) == 10 (base 10)
        11111 (base 1) == 5 (base 10)
        111111 (base 1) == 11 (base 2)
        1101101 (base 1) == IMPOSSIBLE (the are unset digits in between the set digits)
          ^  ^
        000111000 (base 1) == IMPOSSIBLE (the first set digit is not the first digit in the number)
              ^^^
    ```

    Effectively: base 1 (uniary) notation treates the value of the number as a
    sequence of a single type of digit that when counted add up to the value of the number.

    NOTE: No functionality of any higher base is nor will modified in this class,
    making this class a superset of all proper positional based intiger notation formats and uniary.

    Also supports customizable notation formats with the optional `notation_format` attribute,
    including unary.
    """
    @override
    def __init__(self,
                 value:Union[int, str, Iterable[Union[int, str]]] = 0,
                 base:int = 10,
                 *,
                 notation_format:Optional[NotationFormat] = DEFAULT_FORMAT
                 ):

        self.__base:int = 2
        super().__init__(0 if base == 1 else value, base, notation_format=notation_format)

        if base == 1:
            self.base = 1
            if isinstance(value, int):
                self.x = value
            elif isinstance(value, str):
                value = value.lstrip("0")
                if not all(c == "1" for c in value):
                    raise BaseValueError(f"{value} cannot be represented in base 1")
                self.x = len(value)

    @override
    def copy(self,
             value:Optional[Union[int, str]] = None,
             base:Optional[int] = None,
             notation_format_override:Optional[NotationFormat] = None
             ) -> 'ExtendedBasedIntiger':
        """
        `copy`

        Creates a shallow copy of this object.

        Keyword Arguments:
            `value` -- When not `None`, will overrides the `x` value of the copy.
            `base` -- When not `None`, will overrides the `base` of the copy.
            `notation_format_override` -- When not `None`,
                will overrides the `notation_format` of the copy.

        Returns:
            The copy of the object.
        """
        if notation_format_override is not None:
            notation_format_override = self.notation_format
        return ExtendedBasedIntiger(value if value is not None else self.x,
                                    base if base is not None else self.base,
                                    notation_format = notation_format_override
                                    )
    __copy__ = copy

    @override
    def __deepcopy__(self, _ = None) -> 'ExtendedBasedIntiger':
        return self.copy(None,
                         None,
                         None if self.notation_format is None else self.notation_format.copy()
                         )

    @property
    @override
    def base(self) -> int:
        """
        `base`

        The base of this number. Must be greater than 0.
        Base 1 is handled particularly differently than other bases.
        """
        return self.__base

    @base.setter
    @override
    def base(self, value:int):
        if value <= 0:
            raise BaseValueError()
        self.__base = value

    @override
    def _get_single_digit(self, index:int) -> int:
        if self.base == 1:
            index = absindex(index, self.digit_length())
            return 1 if index < abs(self.x) else 0
        else:
            return super()._get_single_digit(index)

    @override
    def _pop_first(self) -> int:
        if self.base == 1:
            self.x -= 1
            return 1
        else:
            return super()._pop_first()

    @override
    def _mask_value_continuous(self, dindex: int, count: int = 1) -> int:
        if count <= 0:
            raise IndexError("The length of a continuous mask must be at least 1")

        if self.base == 1:
            return min(abs(self.x) - dindex, count)
        else:
            return super()._mask_value_continuous(dindex, count)

    @override
    def notate(self, notation_format:Optional[NotationFormat] = None) -> str:
        if self.base >= 2:
            return super().notate(notation_format)

        if notation_format is None:
            notation_format = self.notation_format

        if notation_format is None:
            raise BaseInvalidOpperationError("No format set, cannot notate")

        relevant_sign = ""
        if self.x < 0 and not notation_format.implicit_negative:
            if notation_format.negative_symbol is None:
                raise ValueError("Explicit negative values require a negative symbol")
            else:
                relevant_sign = notation_format.negative_symbol
        elif self.x > 0 and not notation_format.implicit_positive:
            if notation_format.positive_symbol is None:
                raise ValueError("Explicit positive values require a positive symbol")
            else:
                relevant_sign = notation_format.positive_symbol

        if notation_format.unity is None:
            raise NotationError("Cannot notate base 1 without a digit for unity")
        return relevant_sign + ((notation_format.unity) * self.x)

    @overload
    @override
    def set_digit(self, index:int, value:Union[int,str]): ...
    @overload
    @override
    def set_digit(self, index:Union[slice,range,Iterable[int]], value:Iterable[Union[int,str]]): ...
    @override # noqa:301
    def set_digit(self,
                  index:Union[int,slice,range,Iterable[int]],
                  value:Union[int,str,Iterable[Union[int,str]]]
                  ):
        if self.base == 1:
            raise BaseInvalidOpperationError("Digits cannot be set in base 1")
        super().set_digit(index, value) # type:ignore[reportCallIssue]

    @override
    def unset_digit(self, index:Union[int,slice,range,Iterable[int]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("Cannot unset digits in base 1")
        return super().unset_digit(index)

    # NOTE: just like python handles it in bit_length, a value of 0 will always have no digits
    @override
    def digit_length(self) -> int:
        if self.base == 1:
            return abs(self.x)
        return super().digit_length()

    @override
    def insert(self, index:int, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError(f"Cannot insert digits into a base {self.base} number")
        super().insert(index, value)

    @override
    def pop(self, index:int = -1) -> int:
        if self.base == 1:
            index = absindex(index, self.digit_length())
            self.x -= 1
            return 1
        else:
            return super().pop(index)

    # returns the count of non-zero (non-unset) digits
    @override
    def digit_count(self) -> int:
        if self.base == 1:
            return abs(self.x)
        return super().digit_count()

    @override
    def digit_shift_left(self, amount:int = 1):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be shifted")
        super().digit_shift_left(amount)

    @override
    def digit_shift_right(self, amount:int = 1):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be shifted")
        super().digit_shift_right(amount)

    @override
    def rstrip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be stripped")
        super().rstrip(value)

    @override
    def lstrip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be stripped")
        super().lstrip(value)

    @override
    def strip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        if self.base == 1:
            raise BaseInvalidOpperationError("This base cannot be stripped")
        super().strip(value)

    @override
    def contains(self, value:Union[int, str]) -> bool:
        if self.base == 1:
            value = self._ensure_unnotated(value)
            return (value == 1 and self.x != 0) or (value == 0 and self.x == 0)
        return super().contains(value)

Ancestors

• PositionalBasedIntiger
• ExtendedUserInt
• UserInt
• typing.SupportsInt
• typing.SupportsFloat
• typing.SupportsAbs
• typing.SupportsComplex
• typing.SupportsRound
• typing.SupportsIndex
• typing.Protocol
• typing.Generic
• collections.abc.Hashable
• collections.abc.MutableSequence
• collections.abc.Sequence
• collections.abc.Reversible
• collections.abc.Collection
• collections.abc.Sized
• collections.abc.Iterable
• collections.abc.Container

Instance variables

prop base : int

base

The base of this number. Must be greater than 0. Base 1 is handled particularly differently than other bases.

Expand source code

@property
@override
def base(self) -> int:
    """
    `base`

    The base of this number. Must be greater than 0.
    Base 1 is handled particularly differently than other bases.
    """
    return self.__base

prop limit_high : Optional[int]

Inherited from: PositionalBasedIntiger.limit_high

limit_high …

prop limit_low : Optional[int]

Inherited from: PositionalBasedIntiger.limit_low

limit_low …

var on_changed

Inherited from: PositionalBasedIntiger.on_changed

on_changed …

prop radix : int

Inherited from: PositionalBasedIntiger.radix

radix …

prop sign : int

Inherited from: PositionalBasedIntiger.sign

sign …

prop x : int

Inherited from: PositionalBasedIntiger.x

x …

Methods

def bit_count(self) ‑> int

Inherited from: PositionalBasedIntiger.bit_count

bit_count …

def bit_length(self) ‑> int

Inherited from: PositionalBasedIntiger.bit_length

bit_count …

def contains(self, value: Union[int, str]) ‑> bool

Inherited from: PositionalBasedIntiger.contains

contains …

def copy(self, value: Union[int, str, ForwardRef(None)] = None, base: Optional[int] = None, notation_format_override: Optional[NotationFormat] = None) ‑> ExtendedBasedIntiger

copy

Creates a shallow copy of this object.

Keyword Arguments: value – When not None, will overrides the x value of the copy. base – When not None, will overrides the base of the copy. notation_format_override – When not None, will overrides the notation_format of the copy.

Returns

The copy of the object.

def delete_digit(self, index: Union[int, slice, range, Iterable[int]])

Inherited from: PositionalBasedIntiger.delete_digit

delete_digit …

def digit_count(self) ‑> int

Inherited from: PositionalBasedIntiger.digit_count

digit_count …

def digit_length(self) ‑> int

Inherited from: PositionalBasedIntiger.digit_length

digit_length …

def digit_rotate_left(self, amount: int = 1)

Inherited from: PositionalBasedIntiger.digit_rotate_left

digit_rotate_left …

def digit_rotate_right(self, amount: int = 1)

Inherited from: PositionalBasedIntiger.digit_rotate_right

digit_rotate_right …

def digit_shift_left(self, amount: int = 1)

Inherited from: PositionalBasedIntiger.digit_shift_left

digit_shift_left …

def digit_shift_right(self, amount: int = 1)

Inherited from: PositionalBasedIntiger.digit_shift_right

digit_shift_right …

def fixed_sign_and(self, value: int) ‑> int

Inherited from: PositionalBasedIntiger.fixed_sign_and

fixed_sign_and …

def fixed_sign_invert(self) ‑> int

Inherited from: PositionalBasedIntiger.fixed_sign_invert

fixed_sign_invert …

def fixed_sign_or(self, value: int) ‑> int

Inherited from: PositionalBasedIntiger.fixed_sign_or

fixed_sign_or …

def fixed_sign_xor(self, value: int) ‑> int

Inherited from: PositionalBasedIntiger.fixed_sign_xor

fixed_sign_xor …

def get_digit(self, index: Union[int, slice, range, Iterable[int]]) ‑> Union[int, List[int]]

Inherited from: PositionalBasedIntiger.get_digit

get_digit …

def insert(self, index: int, value: Union[int, str, Iterable[Union[int, str]]])

Inherited from: PositionalBasedIntiger.insert

insert …

def is_integer(self) ‑> bool

Inherited from: PositionalBasedIntiger.is_integer

is_integer …

def iter_digits(self, at_least: int = 0) ‑> Iterator[int]

Inherited from: PositionalBasedIntiger.iter_digits

iter_digits Returns an iterable that iterates through the digit values of the integer, starting at the units spot. Will iterate 0 when all other …

def iter_symbols(self, at_least: int = 1) ‑> Iterator[str]

Inherited from: PositionalBasedIntiger.iter_symbols

iter_symbols …

def lstrip(self, value: Union[int, str, Iterable[Union[int, str]]])

Inherited from: PositionalBasedIntiger.lstrip

rstrip …

def mask(self, index: Union[int, slice, range, Iterable[int]]) ‑> int

Inherited from: PositionalBasedIntiger.mask

mask …

def notate(self, notation_format: Optional[NotationFormat] = None) ‑> str

Inherited from: PositionalBasedIntiger.notate

notate Notates the intiger, using the given notation format if possible, or the notation_format set in the object's attributes if the paramater is …

def pop(self, index: int = -1) ‑> int

Inherited from: PositionalBasedIntiger.pop

pop …

def reversed_iter_digits(self, at_least: int = 0) ‑> Iterator[int]

Inherited from: PositionalBasedIntiger.reversed_iter_digits

reversed_iter_digits Returns an iterable that iterates through the digit values of the integer, ending at the units spot. Will iterate 0 when all …

def reversed_iter_symbols(self, at_least: int = 1) ‑> Iterator[str]

Inherited from: PositionalBasedIntiger.reversed_iter_symbols

reversed_iter_symbols …

def rstrip(self, value: Union[int, str, Iterable[Union[int, str]]])

Inherited from: PositionalBasedIntiger.rstrip

rstrip …

def set_digit(self, index: Union[int, slice, range, Iterable[int]], value: Union[int, str, Iterable[Union[int, str]]])

Inherited from: PositionalBasedIntiger.set_digit

set_digit …

def strip(self, value: Union[int, str, Iterable[Union[int, str]]])

Inherited from: PositionalBasedIntiger.strip

rstrip …

def to_bytes(self, length: , byteorder: Literal['little', 'big'], *, signed: bool = False) ‑> bytes

Inherited from: PositionalBasedIntiger.to_bytes

to_bytes …

def unset_digit(self, index: Union[int, slice, range, Iterable[int]])

Inherited from: PositionalBasedIntiger.unset_digit

unset_digit …

class PositionalBasedIntiger (value: Union[int, str, Iterable[Union[int, str]], bytes, bytearray, memoryview] = 0, base: int = 10, *, notation_format: Optional[NotationFormat] = NotationFormat(value_symbols=('0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'), undefined_symbol='?', positive_symbol='+', negative_symbol='-', radix_point_symbol='.', group_split_symbol=None, group_split_count=0, implicit_positive=True, implicit_negative=False))

PositionalBasedIntiger

A mutable sequence type of intiger that has a explicitly set base, allowing for specific digit values to be get and set.

Supports any initger base starting at binary (base 2). These bases are presumed to be in the traditional place value format of value == d[x] * (base ** x) where value is the value the digit holds in the intiger, d is a single digit value form a sequence of digits, base is the base, and x is the specific index in question of the intiger.

Supports many operators and methods that built in integers suport, casting the type back into a default intiger type when possible.

Also supports customizable notation formats with the optional notation_format attribute.

Expand source code

class PositionalBasedIntiger(*tuple(__POSITIONAL_BASED_INT_BASES)):
    """
    `PositionalBasedIntiger`

    A mutable sequence type of intiger that has a explicitly set base,
    allowing for specific digit values to be get and set.

    Supports any initger base starting at binary (base 2).
    These bases are presumed to be in the traditional place value format of
    `value == d[x] * (base ** x)` where `value` is the value the digit holds in the intiger,
    `d` is a single digit value form a sequence of digits,
    `base` is the base,
    and `x` is the specific index in question of the intiger.

    Supports many operators and methods that built in integers suport,
    casting the type back into a default intiger type when possible.

    Also supports customizable notation formats with the optional `notation_format` attribute.
    """

    def __init__(self,
                 value:Union[int, str, Iterable[Union[int, str]], bytes, bytearray, memoryview] = 0,
                 base:int = 10,
                 *,
                 notation_format:Optional[NotationFormat] = DEFAULT_FORMAT
                 ):

        super().__init__(0)
        self.__base:int = 2

        self.x = 0
        self.base = base
        self.notation_format:Optional[NotationFormat] = notation_format
        if isinstance(value, int):
            self.x = value
        elif isinstance(value, str):
            self.x = int(value, base)
        else:
            for digit_value in value:
                digit_value = self._ensure_unnotated(digit_value)
                if digit_value >= base:
                    raise ValueError(f"Digit of value {digit_value} isn't possible in base {base}")
                self.x = (self.x * base) + digit_value

    def copy(self,
             value:Optional[Union[int, str]] = None,
             base:Optional[int] = None,
             notation_format_override:Optional[NotationFormat] = None
             ) -> 'PositionalBasedIntiger':
        """
        `copy`

        Creates a shallow copy of this object.

        Keyword Arguments:
            value -- When not `None`, will overrides the `x` value of the copy.
            base -- When not `None`, will overrides the `base` of the copy.
            notation_format_override -- When not `None`,
                will overrides the `notation_format` of the copy.

        Returns:
            The copy of the object.
        """
        if notation_format_override is not None:
            notation_format_override = self.notation_format
        return PositionalBasedIntiger(value if value is not None else self.x,
                                      base if base is not None else self.base,
                                      notation_format = notation_format_override
                                      )
    __copy__ = copy

    def __deepcopy__(self, _ = None) -> 'PositionalBasedIntiger':
        return self.copy(None,
                         None,
                         None if self.notation_format is None else self.notation_format.copy()
                         )

    @property
    def base(self) -> int:
        """
        `base`

        The base of the intiger.
        Must be at or above 2, as this class does not support any non-standard bases.
        """
        return self.__base

    @base.setter
    def base(self, value:int):
        if value < 2:
            raise ValueError("Invalid base", value)
        self.__base = value

    @property
    def radix(self) -> int:
        """
        radix

        Returns:
            The absolute value of the base.
            Will always return `base` when used in a `PositionalBasedIntiger`,
            but may differ when using with a extended type.
        """
        return abs(self.base)

    def _ensure_notated(self, value:Union[int,str]) -> str:
        if self.notation_format is None:
            raise NotationError("Cannot reference a symbol without a notation format")

        if isinstance(value, str):
            return value
        else:
            dig = self.notation_format.get_digit(value)
            if dig is None:
                raise NotationError(f"Could not find digit for {value} in current notation format")
            return dig

    def _ensure_unnotated(self, value:Union[int,str]) -> int:
        if self.notation_format is None:
            raise NotationError("Cannot reference a symbol without a notation format")

        if isinstance(value, int):
            return value

        v = self.notation_format.get_value(value)
        if v is None:
            raise NotationError(f"Given symbol '{value}' not found in current notation format")
        return v

    def _get_single_digit(self, index:int) -> int:
        index = absindex(index, self.digit_length())
        if self.base == 2:
            return (abs(self.x) >> index) % (0b1 << 1)
        else:
            return (abs(self.x) // (self.base ** index)) % self.base

    # this pops the digit in the units spot,
    # effectively shifts left once while returning units shifted out
    # slightly faster than the arbitrary pop method
    def _pop_first(self) -> int:
        dm = divmod(self.x, self.base)
        self.x = dm[0]
        return dm[1]

    # this pushes a value into the units place
    # effectively shifts right while appending a new value to the units
    # slightly faster than the arbitrary insert method
    def _prepend(self, value:Union[int,str]):
        value = self._ensure_unnotated(value)

        if value < 0 or value >= self.base:
            raise ValueError("Digit value out of bounds of base")

        if self.sign == -1:
            value *= -1

        self.x = (self.x * self.base) + value

    # effectively, this returns a continuous sequence
    # form the intiger with its place value still intact
    def _mask_value_continuous(self, dindex:int, count:int = 1) -> int:
        if count <= 0:
            raise IndexError("The length of a continuous mask must be at least 1")

        dindex = absindex(dindex, self.digit_length())

        if self.base == 2: # binary optimisable
            return abs(self.x) & (((0b1 << (count - 1)) - 1) << dindex)
        else:
            pv1 = self.base ** dindex
            pv2 = pv1 * (self.base ** count) # aka ```self.base ** (dindex + count)```
            return (abs(self.x) % pv2) - (abs(self.x) % pv1)

    def iter_digits(self, at_least:int = 0) -> Iterator[int]:
        """
        `iter_digits`
        Returns an iterable that iterates through the digit values of the integer,
        starting at the units spot.
        Will iterate 0 when all other digits are already iterated.

        Keyword Arguments:
            `at_least` -- Ensures that at least the given amount of digits are iterated, if above 1.

        Returns:
            An iterator that returns the digit values, starting at the units spot.

        Yields:
            The digits of the intiger, starting at the units spot.
        """
        indexes = range(max(self.digit_length(), at_least))
        return (self._get_single_digit(i) for i in indexes)
    __iter__ = iter_digits

    def reversed_iter_digits(self, at_least:int = 0) -> Iterator[int]:
        """
        `reversed_iter_digits`
        Returns an iterable that iterates through the digit values of the integer,
        ending at the units spot.
        Will iterate 0 when all other digits are already iterated.

        Keyword Arguments:
            `at_least` -- Ensures that at least the given amount of digits are iterated, if above 1.

        Returns:
            An iterator that returns the digit values, ending at the units spot.

        Yields:
            The digits of the intiger, ending at the units spot.
        """
        indexes = range(max(self.digit_length(), at_least)-1, -1, -1)
        return (self._get_single_digit(i) for i in indexes)
    __reverse__ = reversed_iter_digits

    def __bytes__(self):
        return bytes(self.iter_digits(0))

    def iter_symbols(self, at_least:int = 1) -> Iterator[str]:
        """
        `iter_symbols`

        Iterate the digit symbols starting at the units spot.
        When intending to use iteration for notation,
        it's suggested to use `reversed_iter_symbols` to avoid odering errors.

        Keyword Arguments:
            `at_least` -- ensures that at least the given amount of symbols are returned.
                Defaults to 1.

        Returns:
            An iterator of symbols.

        Yields:
            Digit symdols, starting at the units spot.
        """
        return (self._ensure_notated(x) for x in self.iter_digits(at_least))

    def reversed_iter_symbols(self, at_least:int = 1) -> Iterator[str]:
        """
        `reversed_iter_symbols`

        Iterate the digit symbols ending at the units spot.
        Intending to be used for notation purposes, as the ordering for string notation is correct.

        Keyword Arguments:
            `at_least` -- ensures that at least the given amount of symbols are returned.
                Defaults to 1.

        Returns:
            An iterator of symbols.

        Yields:
            Digit symdols, ending at the units spot.
        """
        return (self._ensure_notated(x) for x in self.reversed_iter_digits(at_least))

    def notate(self, notation_format:Optional[NotationFormat] = None) -> str:
        """
        `notate`
        Notates the intiger, using the given notation format if possible,
        or the `notation_format` set in the object's attributes if the paramater is not set.

        Keyword Arguments:
            notation_format -- A notation format to use
                over the one set in `self.notation_format`, if not `None`.

        Raises:
            NotationError: Raised when both the argument and attribute `notation_format` are `None`;
                or when other errors are raised during notation.

        Returns:
            The final notation of the intiger.
        """
        if notation_format is None:
            notation_format = self.notation_format

        if notation_format is None:
            raise NotationError("No format set, cannot notate")

        relevant_sign = ""
        if self.x < 0 and not notation_format.implicit_negative:
            if notation_format.negative_symbol is None:
                raise NotationError("Explicit negative values require a negative symbol")
            else:
                relevant_sign = notation_format.negative_symbol
        elif self.x > 0 and not notation_format.implicit_positive:
            if notation_format.positive_symbol is None:
                raise NotationError("Explicit positive values require a positive symbol")
            else:
                relevant_sign = notation_format.positive_symbol

        group_joint = ""
        if notation_format.group_split_symbol is not None:
            group_joint = notation_format.group_split_symbol
        group_count = notation_format.group_split_count

        if group_joint != "" and group_count > 0:
            groups = list(self.iter_symbols())
            group_indexes = range(0, self.digit_length(), group_count)
            groups = [''.join(groups[i:i+group_count])[::-1] for i in group_indexes]
            groups = groups[::-1]
        else:
            groups = self.reversed_iter_symbols()

        return relevant_sign + group_joint.join(groups)
    __str__ = notate
    __repr__ = notate

    @overload
    def get_digit(self, index:int) -> int: ...
    @overload
    def get_digit(self, index:Union[slice,range,Iterable[int]]) -> List[int]: ...
    def get_digit(self, # noqa:301
                  index:Union[int,slice,range,Iterable[int]]
                  ) -> Union[int,List[int]]:
        """
        `get_digit`

        Gets the specific digit's (or digits's) value at the specific index (or indexes).

        Arguments:
            `index` -- The index (or indexes) in question.

        Returns:
            The value (or values, contained in a `List`) found at the index.
        """
        if isinstance(index, int):
            return self._get_single_digit(index)

        if isinstance(index, slice):
            index = slice_to_range(index, self.digit_length())

        return list(self._get_single_digit(absindex(i, self.digit_length())) for i in index)
    __getitem__ = get_digit

    @overload
    def set_digit(self, index:int, value:Union[int,str]): ...
    @overload
    def set_digit(self, index:Union[slice,range,Iterable[int]], value:Iterable[Union[int,str]]): ...
    def set_digit(self, # noqa:301
                  index:Union[int,slice,range,Iterable[int]],
                  value:Union[int,str,Iterable[Union[int,str]]]
                  ):
        """
        `set_digit`

        Sets the digit (or digits) at the given index (or indexes) to the given value (or values).
        With multiple indexes and,
        there must be a matching quantity of values to set at those indexes.

        Arguments:
            `index` -- The index (or indexes) to set.
            `value` -- The value (or values) to set the index (or indexes) to.

        Raises:
            `ValueError`: Raised when the given value is out of bounds of the current `base`.
        """
        if isinstance(value, Iterable):
            value = (self._ensure_unnotated(v) for v in value)
        else:
            value = self._ensure_unnotated(value)

        if isinstance(value, int):
            value = [value]
        else:
            value = cast(List[int], list(value))

        if isinstance(index, int):
            index = (index, )
        elif isinstance(index, slice):
            index = slice_to_range(index, self.digit_length())

        sign = self.sign
        self.x = abs(self.x)

        for i, v in zip(index, value):
            if v < 0 or v >= self.base:
                raise ValueError("Digit value out of bounds of base")
            i = absindex(i, self.digit_length())
            if self.base == 2: # binary optimisable
                if v == 1:
                    self.x |= (0b1 << i)
                else:
                    self.x &= ~(0b1 << i)
            else:
                pv = self.base ** i
                mask = self._mask_value_continuous(i)
                self.x = (self.x - mask) + (v * pv)

        if sign != 0:
            self.x *= sign
    __setitem__ = set_digit

    def delete_digit(self, index:Union[int,slice,range,Iterable[int]]):
        """
        `delete_digit`

        Removes the value at the given index (or indexes).

        Arguments:
            `index` -- The index (or indexes) digit to be removed.
        """

        if isinstance(index, slice):
            index = slice_to_range(index, self.digit_length())

        if isinstance(index, int):
            index = (index, )

        for i in sorted(index, reverse=True):
            self.pop(i)
    __delitem__ = delete_digit

    def unset_digit(self, index:Union[int,slice,range,Iterable[int]]):
        """
        `unset_digit`

        Unsets (set to 0) the value at the given index (or indexes).

        Arguments:
            `index` -- The index (or indexes) digit to be unset.
        """
        if isinstance(index, slice):
            index = slice_to_range(index, self.digit_length())

        if isinstance(index, int):
            index = (index, )

        sign = self.sign
        self.x = abs(self.x)

        if self.base == 2: # binary optimization
            for i in index:
                i = absindex(i, self.digit_length())
                self.x = (self.x >> 1) << 1
        else:
            for i in index:
                i = absindex(i, self.digit_length())
                self.x -= self._mask_value_continuous(i)

        if sign != 0:
            self.x *= sign

    # NOTE: just like python handles it in bit_length, a value of 0 will always have no digits
    def digit_length(self) -> int:
        """
        `digit_length`

        Similar to `bit_length`, but relitive to the current `base`.
        Not to be confused with `digit_count`.

        Returns:
            The minimum necessary about of digits needed to display the number in full.
        """
        if self.x == 0:
            return 0

        if self.base == 2:
            return abs(self.x).bit_length()
        else:
            c = 0
            v = abs(self.x)
            while v != 0:
                c += 1
                v //= self.base
            return c
    __len__ = digit_length

    def insert(self, index:int, value:Union[int,str,Iterable[Union[int,str]]]):
        """
        `insert`

        Inserts the given value (or values, following the order in which they are supplied)
        before the given index.
        When given multiple values, each value will be inserted before the given index in order.

        Arguments:
            `index` -- The index (or indexes) to be inserted before.
            `value` -- The value (or values) to insert.
        """

        # not the current length, but the length this will have after the insert
        index = absindex(index, self.digit_length() + 1)

        if isinstance(value, Iterable):
            value = (self._ensure_unnotated(v) for v in value)
        else:
            value = self._ensure_unnotated(value)

        if isinstance(value, int):
            value = (value, )

        for v in value:
            if v < 0 or v >= self.base:
                raise ValueError("Digit value out of bounds of base")

            restore_sign = self.sign
            self.x = abs(self.x)

            if index == 0:
                self._prepend(v)
                continue

            high = self.copy()
            high.unset_digit(slice(0, index))

            if high.x != 0:
                self.x -= high.x
                high.x *= high.base
                self.x += high.x

            v = self.copy(v)
            v.x *= (v.base ** (index))
            self.x += v.x

            self.x *= restore_sign

    def pop(self, index:int = -1) -> int:
        """
        `pop`

        Gets the value at the given index while popping it.

        Keyword Arguments:
            index -- The target index to pop. Defaults to -1.

        Returns:
            The value at the given index before removal.
        """
        index = absindex(index, self.digit_length())

        if index == 0:
            return self._pop_first()

        popped = self._get_single_digit(index)
        high = self.copy()

        self.unset_digit(range(index, len(self)))
        high.unset_digit(range(0, index+1))

        if int(high) != 0:
            high.x //= high.base
            self.x += int(high)

        return popped

    def digit_count(self) -> int:
        """
        `digit_count`

        Similar to `bit_count`, but relitive to the current `base`.
        Not to be confused with `digit_length`.

        Returns:
            The amount of non-zero (non-unset) digits in the value.
        """
        if self.x == 0:
            return 0

        if self.base == 2:
            return abs(self.x).bit_count()
        else:
            c = 0
            v = abs(self.x)
            while v != 0:
                if v % self.base != 0:
                    c += 1
                v //= self.base
            return c

    # gets the specified digits with their place value as an int
    # a higher level implementation of the concept of bit masking done with binary numbers
    def mask(self, index:Union[int,slice,range,Iterable[int]]) -> int:
        """
        `mask`

        Similar to the concept of a 'bit mask', but on a arbitrary base.
        Returns a value with all digits unset except for the given index (or indexes).

        Arguments:
            index -- The index (or indexes) to mask the digits of.

        Returns:
            The value with all digits unset except for the given index (or indexes).
        """
        if isinstance(index, int):
            return self._mask_value_continuous(index)

        slices = []

        if isinstance(index, slice) and index.step == 1:
            slices = [index]
        else:
            if isinstance(index, slice):
                index = slice_to_range(index, self.digit_length())
            slices = iter_to_slices(cast(Iterable[int], index), self.digit_length())

        return sum(self._mask_value_continuous(s.start, s.stop - s.start) for s in slices)

    def digit_shift_left(self, amount:int = 1):
        """
        `digit_shift_left`

        Similar to a binary shift left, shifts the value left according to the set base.

        Arguments:
            amount -- The amount to shift left. Will shift right when negative.
        """
        if amount < 0:
            self.digit_shift_right(-amount)
            return

        if self.base == 2:
            self.x = (abs(self.x) << amount) * self.sign
        else:
            self.x *= (self.base**amount)

    def digit_shift_right(self, amount:int = 1):
        """
        `digit_shift_right`

        Similar to a binary shift right, shifts the value right according to the set base.

        Arguments:
            amount -- The amount to shift right. Will shift left when negative.
        """
        if amount < 0:
            self.digit_shift_left(-amount)
            return

        if self.base == 2:
            self.x = (abs(self.x) >> amount) * self.sign
        else:
            self.x //= (self.base**amount)

    def digit_rotate_left(self, amount:int = 1):
        """
        `digit_rotate_left`

        Similar to a binary rotate left, rotates the value left according to the set base.
        This will pop the digit at the largest signifiant place value and inserts
        it at the smallest place value spot.

        Arguments:
            amount -- The amount to rotate left. Will rotate right when negative.
        """

        if amount < 0:
            self.digit_rotate_right(-amount)

        for _ in range(amount):
            popped = self.pop(-1)
            self.digit_shift_left(1)
            self.x += popped

    def digit_rotate_right(self, amount:int = 1):
        """
        `digit_rotate_right`

        Similar to a binary rotate right, rotates the value right according to the set base.
        This will pop the digit at the smallest signifiant place value and inserts
        it at the largest place value spot.

        Arguments:
            amount -- The amount to rotate right. Will rotate left when negative.
        """

        if amount < 0:
            self.digit_rotate_left(-amount)

        for _ in range(amount):
            popped = self.pop(0)
            self.digit_shift_right(1)
            self.append(popped)

    def rstrip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        """
        `rstrip`

        Removes the given digit (or digits) from the right hand (units) spot.
        Works similarly to ``str.rstrip``,
        except for the fact that when ``value`` is a single string
        (**not** a iterable of strings)
        it will be treated as a single digit instead of a iterable of digits.

        Arguments:
            value -- The value (or iterable of values) to strip.
                Can be either a intiger digit value, or a string corelating to a single digit.
        """

        if isinstance(value, Iterable):
            value = tuple(self._ensure_unnotated(v) for v in value)
        else:
            value = (self._ensure_unnotated(value), )

        if len(value) == 0:
            return

        while self.x != 0 and self._get_single_digit(0) in value:
            self._pop_first()

    def lstrip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        """
        `rstrip`

        Removes the given digit (or digits) from the left hand (greatest place value) spot.
        Works similarly to ``str.lstrip``,
        except for the fact that when ``value`` is a single string
        (**not** a iterable of strings)
        it will be treated as a single digit instead of a iterable of digits.
        This will not strip any leading `0` digit values,
        as these are already not notated by default
        nor would effect the digit length of this intiger.

        Arguments:
            value -- The value (or iterable of values) to strip.
                Can be either a intiger digit value, or a string corelating to a single digit.
        """
        if isinstance(value, Iterable):
            value = [self._ensure_unnotated(v) for v in value]
        else:
            value = [self._ensure_unnotated(value)]

        value.remove(0)

        if len(value) == 0:
            return

        while self.x != 0 and self._get_single_digit(-1) in value:
            self.pop(-1)

    def strip(self, value:Union[int,str,Iterable[Union[int,str]]]):
        """
        `rstrip`

        Removes the given digit (or digits) from both sides.
        Works similarly to ``str.strip``,
        except for the fact that when ``value`` is a single string
        (**not** a iterable of strings)
        it will be treated as a single digit instead of a iterable of digits.
        This will not strip any leading `0` digit values,
        as these are already not notated by default
        nor would effect the digit length of this intiger.

        Arguments:
            value -- The value (or iterable of values) to strip.
                Can be either a intiger digit value, or a string corelating to a single digit.
        """
        self.rstrip(value)
        self.lstrip(value)

    def contains(self, value:Union[int, str]) -> bool:
        """
        `contains`

        Returns true if the digit value appears anywhere in this digit sequence.
        This will not include leading 0s,
        but will return true if the tested digit value is `0` and this intiger's value is also 0.

        Arguments:
            value -- The value to check for.
        """
        value = self._ensure_unnotated(value)

        if self.x == 0:
            return value == 0

        working_value = abs(self.x)
        while working_value > 0:
            if self.base == 2:
                if working_value & 0b1 == value:
                    return True
                working_value >>= 1
            else:
                if working_value % self.base == value:
                    return True
                working_value //= self.base
        return False
    __contains__ = contains

Ancestors

• ExtendedUserInt
• UserInt
• typing.SupportsInt
• typing.SupportsFloat
• typing.SupportsAbs
• typing.SupportsComplex
• typing.SupportsRound
• typing.SupportsIndex
• typing.Protocol
• typing.Generic
• collections.abc.Hashable
• collections.abc.MutableSequence
• collections.abc.Sequence
• collections.abc.Reversible
• collections.abc.Collection
• collections.abc.Sized
• collections.abc.Iterable
• collections.abc.Container

Subclasses

• ExtendedBasedIntiger

Instance variables

prop base : int

base

The base of the intiger. Must be at or above 2, as this class does not support any non-standard bases.

Expand source code

@property
def base(self) -> int:
    """
    `base`

    The base of the intiger.
    Must be at or above 2, as this class does not support any non-standard bases.
    """
    return self.__base

prop limit_high : Optional[int]

Inherited from: ExtendedUserInt.limit_high

limit_high …

prop limit_low : Optional[int]

Inherited from: ExtendedUserInt.limit_low

limit_low …

var on_changed

Inherited from: ExtendedUserInt.on_changed

on_changed …

prop radix : int

radix

Returns

The absolute value of the base. Will always return base when used in a PositionalBasedIntiger, but may differ when using with a extended type.

Expand source code

@property
def radix(self) -> int:
    """
    radix

    Returns:
        The absolute value of the base.
        Will always return `base` when used in a `PositionalBasedIntiger`,
        but may differ when using with a extended type.
    """
    return abs(self.base)

prop sign : int

Inherited from: ExtendedUserInt.sign

sign …

prop x : int

Inherited from: ExtendedUserInt.x

x …

Methods

def bit_count(self) ‑> int

Inherited from: ExtendedUserInt.bit_count

bit_count …

def bit_length(self) ‑> int

Inherited from: ExtendedUserInt.bit_length

bit_count …

def contains(self, value: Union[int, str]) ‑> bool

contains

Returns true if the digit value appears anywhere in this digit sequence. This will not include leading 0s, but will return true if the tested digit value is 0 and this intiger's value is also 0.

Arguments

value – The value to check for.

def copy(self, value: Union[int, str, ForwardRef(None)] = None, base: Optional[int] = None, notation_format_override: Optional[NotationFormat] = None) ‑> PositionalBasedIntiger

copy

Creates a shallow copy of this object.

Keyword Arguments: value – When not None, will overrides the x value of the copy. base – When not None, will overrides the base of the copy. notation_format_override – When not None, will overrides the notation_format of the copy.

Returns

The copy of the object.

def delete_digit(self, index: Union[int, slice, range, Iterable[int]])

delete_digit

Removes the value at the given index (or indexes).

Arguments

index – The index (or indexes) digit to be removed.

def digit_count(self) ‑> int

digit_count

Similar to bit_count, but relitive to the current base. Not to be confused with digit_length.

Returns

The amount of non-zero (non-unset) digits in the value.

def digit_length(self) ‑> int

digit_length

Similar to bit_length, but relitive to the current base. Not to be confused with digit_count.

Returns

The minimum necessary about of digits needed to display the number in full.

def digit_rotate_left(self, amount: int = 1)

digit_rotate_left

Similar to a binary rotate left, rotates the value left according to the set base. This will pop the digit at the largest signifiant place value and inserts it at the smallest place value spot.

Arguments

amount – The amount to rotate left. Will rotate right when negative.

def digit_rotate_right(self, amount: int = 1)

digit_rotate_right

Similar to a binary rotate right, rotates the value right according to the set base. This will pop the digit at the smallest signifiant place value and inserts it at the largest place value spot.

Arguments

amount – The amount to rotate right. Will rotate left when negative.

def digit_shift_left(self, amount: int = 1)

digit_shift_left

Similar to a binary shift left, shifts the value left according to the set base.

Arguments

amount – The amount to shift left. Will shift right when negative.

def digit_shift_right(self, amount: int = 1)

digit_shift_right

Similar to a binary shift right, shifts the value right according to the set base.

Arguments

amount – The amount to shift right. Will shift left when negative.

def fixed_sign_and(self, value: int) ‑> int

Inherited from: ExtendedUserInt.fixed_sign_and

fixed_sign_and …

def fixed_sign_invert(self) ‑> int

Inherited from: ExtendedUserInt.fixed_sign_invert

fixed_sign_invert …

def fixed_sign_or(self, value: int) ‑> int

Inherited from: ExtendedUserInt.fixed_sign_or

fixed_sign_or …

def fixed_sign_xor(self, value: int) ‑> int

Inherited from: ExtendedUserInt.fixed_sign_xor

fixed_sign_xor …

def get_digit(self, index: Union[int, slice, range, Iterable[int]]) ‑> Union[int, List[int]]

get_digit

Gets the specific digit's (or digits's) value at the specific index (or indexes).

Arguments

index – The index (or indexes) in question.

Returns

The value (or values, contained in a List) found at the index.

def insert(self, index: int, value: Union[int, str, Iterable[Union[int, str]]])

insert

Inserts the given value (or values, following the order in which they are supplied) before the given index. When given multiple values, each value will be inserted before the given index in order.

Arguments

index – The index (or indexes) to be inserted before. value – The value (or values) to insert.

def is_integer(self) ‑> bool

Inherited from: ExtendedUserInt.is_integer

is_integer …

def iter_digits(self, at_least: int = 0) ‑> Iterator[int]

iter_digits Returns an iterable that iterates through the digit values of the integer, starting at the units spot. Will iterate 0 when all other digits are already iterated.

Keyword Arguments: at_least – Ensures that at least the given amount of digits are iterated, if above 1.

Returns

An iterator that returns the digit values, starting at the units spot.

Yields

The digits of the intiger, starting at the units spot.

def iter_symbols(self, at_least: int = 1) ‑> Iterator[str]

iter_symbols

Iterate the digit symbols starting at the units spot. When intending to use iteration for notation, it's suggested to use reversed_iter_symbols to avoid odering errors.

Keyword Arguments: at_least – ensures that at least the given amount of symbols are returned. Defaults to 1.

Returns

An iterator of symbols.

Yields

Digit symdols, starting at the units spot.

def lstrip(self, value: Union[int, str, Iterable[Union[int, str]]])

rstrip

Removes the given digit (or digits) from the left hand (greatest place value) spot. Works similarly to str.lstrip, except for the fact that when value is a single string (not a iterable of strings) it will be treated as a single digit instead of a iterable of digits. This will not strip any leading 0 digit values, as these are already not notated by default nor would effect the digit length of this intiger.

Arguments

value – The value (or iterable of values) to strip. Can be either a intiger digit value, or a string corelating to a single digit.

def mask(self, index: Union[int, slice, range, Iterable[int]]) ‑> int

mask

Similar to the concept of a 'bit mask', but on a arbitrary base. Returns a value with all digits unset except for the given index (or indexes).

Arguments

index – The index (or indexes) to mask the digits of.

Returns

The value with all digits unset except for the given index (or indexes).

def notate(self, notation_format: Optional[NotationFormat] = None) ‑> str

notate Notates the intiger, using the given notation format if possible, or the notation_format set in the object's attributes if the paramater is not set.

Keyword Arguments: notation_format – A notation format to use over the one set in self.notation_format, if not None.

Raises

NotationError

Raised when both the argument and attribute notation_format are None; or when other errors are raised during notation.

Returns

The final notation of the intiger.

def pop(self, index: int = -1) ‑> int

pop

Gets the value at the given index while popping it.

Keyword Arguments: index – The target index to pop. Defaults to -1.

Returns

The value at the given index before removal.

def reversed_iter_digits(self, at_least: int = 0) ‑> Iterator[int]

reversed_iter_digits Returns an iterable that iterates through the digit values of the integer, ending at the units spot. Will iterate 0 when all other digits are already iterated.

Keyword Arguments: at_least – Ensures that at least the given amount of digits are iterated, if above 1.

Returns

An iterator that returns the digit values, ending at the units spot.

Yields

The digits of the intiger, ending at the units spot.

def reversed_iter_symbols(self, at_least: int = 1) ‑> Iterator[str]

reversed_iter_symbols

Iterate the digit symbols ending at the units spot. Intending to be used for notation purposes, as the ordering for string notation is correct.

Keyword Arguments: at_least – ensures that at least the given amount of symbols are returned. Defaults to 1.

Returns

An iterator of symbols.

Yields

Digit symdols, ending at the units spot.

def rstrip(self, value: Union[int, str, Iterable[Union[int, str]]])

rstrip

Removes the given digit (or digits) from the right hand (units) spot. Works similarly to str.rstrip, except for the fact that when value is a single string (not a iterable of strings) it will be treated as a single digit instead of a iterable of digits.

Arguments

value – The value (or iterable of values) to strip. Can be either a intiger digit value, or a string corelating to a single digit.

def set_digit(self, index: Union[int, slice, range, Iterable[int]], value: Union[int, str, Iterable[Union[int, str]]])

set_digit

Sets the digit (or digits) at the given index (or indexes) to the given value (or values). With multiple indexes and, there must be a matching quantity of values to set at those indexes.

Arguments

index – The index (or indexes) to set. value – The value (or values) to set the index (or indexes) to.

Raises

ValueError: Raised when the given value is out of bounds of the current base.

def strip(self, value: Union[int, str, Iterable[Union[int, str]]])

rstrip

Removes the given digit (or digits) from both sides. Works similarly to str.strip, except for the fact that when value is a single string (not a iterable of strings) it will be treated as a single digit instead of a iterable of digits. This will not strip any leading 0 digit values, as these are already not notated by default nor would effect the digit length of this intiger.

Arguments

value – The value (or iterable of values) to strip. Can be either a intiger digit value, or a string corelating to a single digit.

def to_bytes(self, length: , byteorder: Literal['little', 'big'], *, signed: bool = False) ‑> bytes

Inherited from: ExtendedUserInt.to_bytes

to_bytes …

def unset_digit(self, index: Union[int, slice, range, Iterable[int]])

unset_digit

Unsets (set to 0) the value at the given index (or indexes).

Arguments

index – The index (or indexes) digit to be unset.