base_decode and base_encode

from string import digits, ascii_uppercase, ascii_lowercase


# every character except the dash (-) is allowed as a digit
DIGITS = tuple(digits + ascii_uppercase + ascii_lowercase)
DIGITS_TO_DECIMAL = dict((c, i) for i, c in enumerate(DIGITS))
BASE = len(DIGITS)


def base_decode(string, base=BASE, digits_to_decimal=DIGITS_TO_DECIMAL):
    """
    Decodes a number with a custom base (in form of a string) to a decimal.

    By default the digits are 0-9, A-Z, a-z and thus the base is 62.
    You need to supply the base and a dictionary that maps every digit to a
    decimal.

    >>> base_decode('0')
    0
    >>> base_decode('z')
    61
    >>> base_decode('10')
    62
    >>> base_decode('-y')
    -60
    """
    factor = 1
    if string.startswith("-"):
        string = string[1:]
        factor = -1

    number = 0
    for c in string:
        number = number * base + digits_to_decimal[c]

    return factor * number


def base_encode(number, base=BASE, digits=DIGITS):
    """
    Encodes a decimal to a number with a custom base in form of a string.

    By default the digits are 0-9, A-Z, a-z and thus the base is 62.
    You need to supply the base and the digits.

    >>> base_encode(0)
    '0'
    >>> base_encode(61)
    'z'
    >>> base_encode(62)
    '10'
    >>> base_encode(-60)
    '-y'
    """
    if not number:
        return digits[0]

    prefix = ""
    if number < 0:
        prefix = "-"
        number = abs(number)

    string = ""
    while number:
        number, rem = divmod(number, base)
        string = digits[rem] + string

    return prefix + string