Python：紧凑且可逆地将大整数编码为具有可变或固定长度的base64或base16

Question

我想将具有任意位数的无符号或有符号大整数紧凑地编码为 base64、base32 或 base16（十六进制）表示形式。输出最终将用作一个字符串，该字符串将用作文件名，但这应该不是重点。我用的是最新的 Python 3.

这可行，但远非紧凑：

>>> import base64, sys
>>> i: int = 2**62 - 3  # Can be signed or unsigned.
>>> b64: bytes =  base64.b64encode(str(i).encode()) # Not a compact encoding.
>>> len(b64), sys.getsizeof(b64)
(28, 61)

有一个 prior question，现已关闭，其答案严格关注低效表示。再次注意，我们不想在本练习中使用任何字符串或不必要的长字节序列。因此，这个问题不是那个问题的重复。

Answer 1

这个答案的部分原因是 Erik A. 的不同评论，例如 this answer. The integer is first compactly converted to bytes, following which the bytes are encoded to a variable base。

from typing import Callable, Optional
import base64

class IntBaseEncoder:
    """Reversibly encode an unsigned or signed integer into a customizable encoding of a variable or fixed length."""
    # Ref: 
    def __init__(self, encoding: str, *, bits: Optional[int] = None, signed: bool = False):
        """
        :param encoder: Name of encoding from base64 module, e.g. b64, urlsafe_b64, b32, b16, etc.
        :param bits: Max bit length of int which is to be encoded. If specified, the encoding is of a fixed length,
        otherwise of a variable length.
        :param signed: If True, integers are considered signed, otherwise unsigned.
        """
        self._decoder: Callable[[bytes], bytes] = getattr(base64, f'{encoding}decode')
        self._encoder: Callable[[bytes], bytes] = getattr(base64, f'{encoding}encode')
        self.signed: bool = signed
        self.bytes_length: Optional[int] = bits and self._bytes_length(2 ** bits - 1)

    def _bytes_length(self, i: int) -> int:
        return (i.bit_length() + 7 + self.signed) // 8

    def encode(self, i: int) -> bytes:
        length = self.bytes_length or self._bytes_length(i)
        i_bytes = i.to_bytes(length, byteorder='big', signed=self.signed)
        return self._encoder(i_bytes)

    def decode(self, b64: bytes) -> int:
        i_bytes = self._decoder(b64)
        return int.from_bytes(i_bytes, byteorder='big', signed=self.signed)

# Tests:
import unittest

class TestIntBaseEncoder(unittest.TestCase):

    ENCODINGS = ('b85', 'b64', 'urlsafe_b64', 'b32', 'b16')

    def test_unsigned_with_variable_length(self):
        for encoding in self.ENCODINGS:
            encoder = IntBaseEncoder(encoding)
            previous_length = 0
            for i in range(1234):
                encoded = encoder.encode(i)
                self.assertGreaterEqual(len(encoded), previous_length)
                self.assertEqual(i, encoder.decode(encoded))

    def test_signed_with_variable_length(self):
        for encoding in self.ENCODINGS:
            encoder = IntBaseEncoder(encoding, signed=True)
            previous_length = 0
            for i in range(-1234, 1234):
                encoded = encoder.encode(i)
                self.assertGreaterEqual(len(encoded), previous_length)
                self.assertEqual(i, encoder.decode(encoded))

    def test_unsigned_with_fixed_length(self):
        for encoding in self.ENCODINGS:
            for maxint in range(257):
                encoder = IntBaseEncoder(encoding, bits=maxint.bit_length())
                maxlen = len(encoder.encode(maxint))
                for i in range(maxint + 1):
                    encoded = encoder.encode(i)
                    self.assertEqual(len(encoded), maxlen)
                    self.assertEqual(i, encoder.decode(encoded))

    def test_signed_with_fixed_length(self):
        for encoding in self.ENCODINGS:
            for maxint in range(257):
                encoder = IntBaseEncoder(encoding, bits=maxint.bit_length(), signed=True)
                maxlen = len(encoder.encode(maxint))
                for i in range(-maxint, maxint + 1):
                    encoded = encoder.encode(i)
                    self.assertEqual(len(encoded), maxlen)
                    self.assertEqual(i, encoder.decode(encoded))

if __name__ == '__main__':
    unittest.main()

如果使用输出作为文件名，使用 'urlsafe_b64' 甚至 'b16' 编码初始化编码器是更安全的选择。

使用示例：

# Variable length encoding
>>> encoder = IntBaseEncoder('urlsafe_b64')
>>> encoder.encode(12345)
b'MDk='
>>> encoder.decode(_)
12345

# Fixed length encoding
>>> encoder = IntBaseEncoder('b16', bits=32)
>>> encoder.encode(12345)
b'00003039'
>>> encoder.encode(123456789)
b'075BCD15'
>>> encoder.decode(_)
123456789

# Signed
encoder = IntBaseEncoder('b32', signed=True)
encoder.encode(-12345)
b'Z7DQ===='
encoder.decode(_)
-12345

Answer 2

来自 this answer 的以下代码片段应该可以满足您的需求，并且没有依赖性：

def v2r(n, base): # value to representation
    """
    Convert a positive integer to its string representation in a custom base.
    
    :param n: the numeric value to be represented by the custom base
    :param base: the custom base defined as a string of characters, used as symbols of the base
    :returns: the string representation of natural number n in the custom base
    """
    if n == 0: return base[0]
    b = len(base)
    digits = ''
    while n > 0:
        digits = base[n % b] + digits
        n  = n // b
    return digits

它不直接执行典型的base64转换（虽然它可以用来获取它）但结果是相似的，因为它returns表示一个大整数（只有正数，但你可以轻松克服这种限制）在由自定义符号组成的自定义长度数字基础中。

一些例子比任何词都更能说明它的简单和通用用法：

# base64 filename-safe characters
# perform a base64 conversion if applied to multiples of 3-bytes chunks
>>> v2r(4276803,'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_')
'QUJD'

# hexadecimal base
>>> v2r(123456789,'0123456789ABCDEF')
'75BCD15'
>>> v2r(255,'0123456789ABCDEF')
'FF'

# custom base of 62 filename-safe characters
>>> v2r(123456789,'0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ')
'8m0Kx'

# custom base of 36 filename-safe lowercase characters for case insensitive file systems
>>> v2r(123456789,'0123456789abcdefghijklmnopqrstuvwxyz')
'21i3v9'

# binary conversion
>>> v2r(123456789,'01')
'111010110111100110100010101'
>>> v2r(255,'01')
'11111111'

Python：紧凑且可逆地将大整数编码为具有可变或固定长度的base64或base16

Python: Compactly and reversibly encode large integer as base64 or base16 having variable or fixed length

python

encoding

integer

filenames

memory-efficient