Define a new numerical base in python (new charset)

Question

I would like to know how to define a new numerical base in Python.

For example:

base dimension = 4
Charset = 'u', '$', '6', '}' (from the least important to the most)

I would like to know how to create and handle it, to be able to do simple arithmetic like:

$} + 6u * 6 = $$}
 7 +  8 * 2 =  23

I know I could use replace to replace u -> 0, $ -> 1 and so on, and use the int() function. However int() is not defined for base > 36, and I will have to handle these cases.

I know I could make my own function to convert them to base 10, do the math, and convert them back, but I would like to avoid that if possible.

the work in converting to and from base 10 would be less than the work in directly implementing the arithmetical operations in your new char sets — John Coleman, Oct 20 '15 at 15:28

score 1 · Answer 1 · answered Oct 20 '15 at 15:55

Rather than replace, you can use dictionaries to translate back and forth between the charset and regular ints, something like:

charset = 'u$6}'
b = len(charset) #base

vals = {c:i for i,c in enumerate(charset)}
digits = {vals[c]: c for c in vals} #inverse dictionary

def toInt(s):
    return sum(vals[c]*b**i for i,c in enumerate(reversed(s)))

def toNewBase(n):
    nums = [] if n > 0 else [0]
    while n > 0:
        n,r = divmod(n,b)
        nums.append(r)
    return ''.join(digits[i] for i in reversed(nums))

def add(s,t):
    return toNewBase(toInt(s) + toInt(t))

def subtract(s,t):
    return toNewBase(toInt(s) - toInt(t))

def multiply(s,t):
    return toNewBase(toInt(s) * toInt(t))

def divide(s,t):
    return toNewBase(toInt(s) // toInt(t))

typical output:

>>> add('$}',multiply('6u','6'))
'$$}'

score 1 · Answer 2 · answered Oct 20 '15 at 17:22

def str_base(number, base):
   # http://stackoverflow.com/a/24763277/3821804
   (d,m) = divmod(number,len(base))
   if d > 0:
      return str_base(d,base)+base[m]
   return base[m]



def charset(chars):
    class cls(int):
        __slots__ = ()

        def __new__(cls, src):
            if isinstance(src, str):
                return int.__new__(
                    cls,
                    ''.join(str(chars.index(i)) for i in src),
                    len(chars)
                )
            return int.__new__(cls, src)

        def __str__(self):
            return str_base(self, chars)

        def __repr__(self):
            return '%s(%r)' % (type(self).__name__, str(self))

    cls.__name__ = 'charset(%r)' % chars
    return cls

Usage:

test = charset('u$6}')
print(test( test('$}') + test('6u') * test('6') ) ) # => '$$}'

See it working online: http://rextester.com/WYSE48066

At the moment, I'm too tired to explain it.

Define a new numerical base in python (new charset)

2 Answers2

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