# "number-in-base" ``oneliner''

Bengt Richter bokr at oz.net
Sat Oct 30 05:35:58 CEST 2004

```On Fri, 29 Oct 2004 23:58:47 +0200, aleaxit at yahoo.com (Alex Martelli) wrote:

>I hesitate a bit to post this, but... on the Italian Python NG, somebody
>was asking whether there was any way to convert an integer number x into
>a string which represents it in an arbitrary base N (given a sequence
>with a len of N that gives the digits to use) as "a single expression".
>
>I haven't found a really general way, much less a clear one, but, the
>best I have so far is...:
>
>def number_in_base(x, N, digits, maxlen=99):
>    return '-'[x>=0:] + (
>        (x and ''.join([digits[k%N] for i in range(maxlen)
>                        for k in [abs(x)//N**i] if k>0])[::-1]
>        ) or digits[0])
>
>Besides the lack of clarity, the obvious defect of this approach is that
>darned 'maxlen' parameter -- but then, since I can have only a 'for',
>not a 'while', in a list comprehension or generator expression, and I
>don't think recursion qualifies as 'a single expression'...:-(
>
>Anyway, improvements and suggestions welcome, thanks!
>
Maybe something useful in this? Not very tested (and not terribly clear either ;-)

>>> def number_in_base(x, N, digits):
...     return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in iter(
...                 lambda qr=[abs(x),0]:qr[0] and (
...                     qr.__setslice__(0,2,divmod(qr[0],N)) or digits[qr[1]])
...                 , 0)][::-1])
...
>>> number_in_base( 126 ,2,'0123456789ABCDEF')
'1111110'
>>> number_in_base( 126 ,8,'0123456789ABCDEF')
'176'
>>> number_in_base( 126 ,16,'0123456789ABCDEF')
'7E'
>>> number_in_base( 1   ,16,'0123456789ABCDEF')
'1'
>>> number_in_base( 0   ,16,'0123456789ABCDEF')
'0'
>>> number_in_base(-126 ,16,'0123456789ABCDEF')
'-7E'
>>> number_in_base(-126 ,2,'0123456789ABCDEF')
'-1111110'

Even less tested, and using a list subtype with overridden next to do the same:

>>> def number_in_base(x, N, digits):
...     return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in type('',(list,),{
...                 '__iter__':lambda s:s, 'next':lambda s:(
...                     s[0] is 0 and iter([]).next() or
...                     s.__setslice__(0,2,divmod(s[0],N)) or digits[s[1]])
...                 })([abs(x),0])][::-1])
...
>>> number_in_base(-126, 8, '01234567')
'-176'
>>> number_in_base(-126, 2, '01')
'-1111110'
>>> number_in_base(126, 2, '01')
'1111110'
>>> number_in_base( 0 , 2, '01')
'0'
>>> number_in_base( 1 , 2, '01')
'1'

;-)

Regards,
Bengt Richter

```