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# $Id$
# Author: Adam Turner.
# Copyright: This module is placed in the public domain
# or under the `Zero Clause BSD licence`_,
# whichever is more permissive.
#
# .. _Zero Clause BSD licence: https://opensource.org/license/0BSD
"""Conversion between integers and roman numerals."""
from __future__ import annotations
import sys
TYPE_CHECKING = False
if TYPE_CHECKING:
from typing import Final, final
from docutils.utils._typing import Self
else:
from docutils.utils._typing import final
__all__: Final = (
'MAX',
'MIN',
'InvalidRomanNumeralError',
'OutOfRangeError',
'RomanNumeral',
)
MIN: Final = 1
"""The value of the smallest well-formed roman numeral."""
# Note that 4,999 (MMMMCMXCIX) breaks one of the rules of Roman numerals,
# that the same character may not appear more than thrice consecutively,
# meaning the largest 'well-formed' Roman numeral is 3,999 (MMMCMXCIX).
# We use 4,999 for backwards compatibility reasons.
MAX: Final = 4_999
"""The value of the largest well-formed roman numeral."""
@final
class OutOfRangeError(TypeError):
"""Number out of range (must be between 1 and 4,999)."""
@final
class InvalidRomanNumeralError(ValueError):
"""Not a valid Roman numeral."""
def __init__(self, value: str, *args: object) -> None:
msg = f'Invalid Roman numeral: {value}'
super().__init__(msg, *args)
@final
class RomanNumeral:
"""A Roman numeral.
Only values between 1 and 4,999 are valid.
Stores the value internally as an ``int``.
>>> answer = RomanNumeral(42)
>>> print(answer.to_uppercase())
XLII
"""
__slots__ = ('_value',)
_value: int
def __init__(self, value: int, /) -> None:
if not isinstance(value, int):
value_qualname = type(value).__qualname__
msg = f'RomanNumeral: an integer is required, not {value_qualname!r}' # NoQA: E501
raise TypeError(msg)
if value < MIN or value > MAX:
msg = f'Number out of range (must be between 1 and 4,999). Got {value}.' # NoQA: E501
raise OutOfRangeError(msg)
super().__setattr__('_value', value)
def __int__(self) -> int:
"""Return the integer value of this numeral."""
return self._value
def __str__(self) -> str:
"""Return the well-formed (uppercase) string for this numeral."""
return self.to_uppercase()
def __repr__(self) -> str:
"""Return the string representation of this numeral."""
return f'{self.__class__.__name__}({self._value!r})'
def __eq__(self, other: object) -> bool:
"""Return self == other."""
if isinstance(other, RomanNumeral):
return self._value == other._value
return NotImplemented
def __lt__(self, other: object) -> bool:
"""Return self < other."""
if isinstance(other, RomanNumeral):
return self._value < other._value
return NotImplemented
def __hash__(self) -> int:
"""Return the hashed value of this numeral."""
return hash(self._value)
def __setattr__(self, key: str, value: object) -> None:
"""Implement setattr(self, name, value)."""
if key == '_value':
msg = f'Cannot set the {key!r} attribute.'
raise AttributeError(msg)
super().__setattr__(key, value)
def to_uppercase(self) -> str:
"""Convert a ``RomanNumeral`` to an uppercase string.
>>> answer = RomanNumeral(42)
>>> assert answer.to_uppercase() == 'XLII'
"""
out: list[str] = []
n = self._value
for value, name, _ in _ROMAN_NUMERAL_PREFIXES:
while n >= value:
n -= value
out.append(name)
return ''.join(out)
def to_lowercase(self) -> str:
"""Convert a ``RomanNumeral`` to a lowercase string.
>>> answer = RomanNumeral(42)
>>> assert answer.to_lowercase() == 'xlii'
"""
out: list[str] = []
n = self._value
for value, _, name in _ROMAN_NUMERAL_PREFIXES:
while n >= value:
n -= value
out.append(name)
return ''.join(out)
@classmethod
def from_string(cls, string: str, /) -> Self:
"""Create a ``RomanNumeral`` from a well-formed string representation.
Returns ``RomanNumeral`` or raises ``InvalidRomanNumeralError``.
>>> answer = RomanNumeral.from_string('XLII')
>>> assert int(answer) == 42
"""
# Not an empty string.
if not string or not isinstance(string, str):
raise InvalidRomanNumeralError(string)
# ASCII-only uppercase string.
if string.isascii() and string.isupper():
chars = string.encode('ascii')
elif string.isascii() and string.islower():
chars = string.upper().encode('ascii')
else:
# Either Non-ASCII or mixed-case ASCII.
raise InvalidRomanNumeralError(string)
# ASCII-only uppercase string only containing I, V, X, L, C, D, M.
if not frozenset(b'IVXLCDM').issuperset(chars):
raise InvalidRomanNumeralError(string)
result: int = 0
idx: int = 0
# Thousands: between 0 and 4 "M" characters at the start
for _ in range(4):
if chars[idx:idx + 1] == b'M':
result += 1000
idx += 1
else:
break
if len(chars) == idx:
return cls(result)
# Hundreds: 900 ("CM"), 400 ("CD"), 0-300 (0 to 3 "C" chars),
# or 500-800 ("D", followed by 0 to 3 "C" chars)
if chars[idx:idx + 2] == b'CM':
result += 900
idx += 2
elif chars[idx:idx + 2] == b'CD':
result += 400
idx += 2
else:
if chars[idx:idx + 1] == b'D':
result += 500
idx += 1
for _ in range(3):
if chars[idx:idx + 1] == b'C':
result += 100
idx += 1
else:
break
if len(chars) == idx:
return cls(result)
# Tens: 90 ("XC"), 40 ("XL"), 0-30 (0 to 3 "X" chars),
# or 50-80 ("L", followed by 0 to 3 "X" chars)
if chars[idx:idx + 2] == b'XC':
result += 90
idx += 2
elif chars[idx:idx + 2] == b'XL':
result += 40
idx += 2
else:
if chars[idx:idx + 1] == b'L':
result += 50
idx += 1
for _ in range(3):
if chars[idx:idx + 1] == b'X':
result += 10
idx += 1
else:
break
if len(chars) == idx:
return cls(result)
# Ones: 9 ("IX"), 4 ("IV"), 0-3 (0 to 3 "I" chars),
# or 5-8 ("V", followed by 0 to 3 "I" chars)
if chars[idx:idx + 2] == b'IX':
result += 9
idx += 2
elif chars[idx:idx + 2] == b'IV':
result += 4
idx += 2
else:
if chars[idx:idx + 1] == b'V':
result += 5
idx += 1
for _ in range(3):
if chars[idx:idx + 1] == b'I':
result += 1
idx += 1
else:
break
if len(chars) == idx:
return cls(result)
raise InvalidRomanNumeralError(string)
_ROMAN_NUMERAL_PREFIXES: Final = [
(1000, sys.intern('M'), sys.intern('m')),
(900, sys.intern('CM'), sys.intern('cm')),
(500, sys.intern('D'), sys.intern('d')),
(400, sys.intern('CD'), sys.intern('cd')),
(100, sys.intern('C'), sys.intern('c')),
(90, sys.intern('XC'), sys.intern('xc')),
(50, sys.intern('L'), sys.intern('l')),
(40, sys.intern('XL'), sys.intern('xl')),
(10, sys.intern('X'), sys.intern('x')),
(9, sys.intern('IX'), sys.intern('ix')),
(5, sys.intern('V'), sys.intern('v')),
(4, sys.intern('IV'), sys.intern('iv')),
(1, sys.intern('I'), sys.intern('i')),
]
"""Numeral value, uppercase character, and lowercase character."""
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