Python elegant inverse function of int(string,base)

digit_to_char could be implemented like this:

def digit_to_char(digit):
    return (string.digits + string.lowercase)[digit]

review this.

def int2str(num, base=16, sbl=None):
    if not sbl:
        sbl = '0123456789abcdefghijklmnopqrstuvwxyz'
    if len(sbl) < 2:
        raise ValueError, 'size of symbols should be >= 2'
    if base < 2 or base > len(sbl):
        raise ValueError, 'base must be in range 2-%d' % (len(sbl))

    neg = False
    if num < 0:
        neg = True
        num = -num

    num, rem = divmod(num, base)
    ret = ''
    while num:
        ret = sbl[rem] + ret
        num, rem = divmod(num, base)
    ret = ('-' if neg else '') + sbl[rem] + ret

    return ret

Maybe this shouldn’t be an answer, but it could be helpful for some: the built-in format function does convert numbers to string in a few bases:

>>> format(255, 'b') # base 2
'11111111'
>>> format(255, 'd') # base 10
'255'
>>> format(255, 'o') # base 8
'377'
>>> format(255, 'x') # base 16
'ff'

If you use Numpy, there is numpy.base_repr.

You can read the code under numpy/core/numeric.py. Short and elegant

The above answers are really nice. It helped me a lot to prototype an algortithm I had to implement in C

I’d like to come up with a little change (I used) to convert decimal to a base of symbolspace

I also ignored negativ values just for shortness and the fact that’s mathematical incorrect
–> other rules for modular arithmetics
–> other math if you use binary, oct or hex –> diff in unsigned & signed values

def str_base(number, base):
   (d,m) = divmod(number,len(base))
   if d > 0:
      return str_base(d,base)+base[m]
   return base[m]

that lead’s to following output

>>> str_base(13,'01')
'1101'
>>> str_base(255,'01')
'11111111'
>>> str_base(255,'01234567')
'377'
>>> str_base(255,'0123456789')
'255'
>>> str_base(255,'0123456789abcdef')
'ff'
>>> str_base(1399871903,'_helowrd')
'hello_world'

if you want to padd with the propper zero symbol you can use

symbol_space = 'abcdest'

>>> str_base(734,symbol_space).rjust(0,symbol_space[0])
'catt'
>>> str_base(734,symbol_space).rjust(6,symbol_space[0])
'aacatt'

Here’s my solution:

def int2base(a, base, numerals="0123456789abcdefghijklmnopqrstuvwxyz"):
     baseit = lambda a=a, b=base: (not a) and numerals[0] or baseit(a-a%b,b*base)+numerals[a%b%(base-1) or (a%b) and (base-1)]
     return baseit()

Explanation

In any base, every number is equal to a1+a2*base**2+a3*base**3.... The “mission” is to find all a’s.

For every N=1,2,3..., the code is isolating the aN*base**N by “mouduling” by b for b=base**(N+1) which slice all a’s bigger than N, and slicing all the a’s that their serial is smaller than N by decreasing a every time the function is called by the current aN*base**N.

Base%(base-1)==1 therefore base**p%(base-1)==1 and therefore q*base^p%(base-1)==q with only one exception when q=base-1 which returns 0.
To fix that, in case it returns 0, the function is checking is it 0 from the beginning.

Advantages

In this sample, there is only one multiplication (instead of division) and some instances of modulus which take relatively small amounts of time.

I had once written my own function with the same goal but is now embarrassingly complicated.

from math import log, ceil, floor
from collections import deque
from itertools import repeat
from string import uppercase, digits
import re

__alphanumerals = (digits + uppercase)

class InvalidBaseError(ValueError): pass
class FloatConvertError(ValueError): pass
class IncorrectBaseError(ValueError): pass

def getbase(number, base=2, frombase = 10):
    if not frombase == 10:
        number = getvalue(number, frombase)
        #getvalue is also a personal function to replicate int(number, base)

    if 1 >= base or base >= len(__alphanumerals) or not floor(base) == base:
        raise InvalidBaseError("Invalid value: {} entered as base to convert
          to. n{}".format(base,
        "Assert that the base to convert to is a decimal integer."))

    if isinstance(number, str):
        try:
            number = atof(number)
        except ValueError:
            #The first check of whether the base is 10 would have already corrected the number
            raise IncorrectBaseError("Incorrect base passed as base of number -> number: {} base: {}".format(number, frombase))
    #^ v was supporting float numbers incase number was the return of another operation
    if number > floor(number):
        raise FloatConvertError("The number to be converted must not be a float. {}".format(number))

    isNegative = False
    if number < 0:
        isNegative = True
        number = abs(number)

    logarithm = log(number, base) if number else 0 #get around number being zero easily

    ceiling = int(logarithm) + 1

    structure = deque(repeat(0, ceiling), maxlen = ceiling)

    while number:
        if number >= (base ** int(logarithm)):
            acceptable_digit = int(number / (base ** floor(logarithm)))
            structure.append(acceptable_digit if acceptable_digit < 10 else     __alphanumerals[acceptable_digit])
            number -= acceptable_digit * (base ** floor(logarithm))
        else:
            structure.append(0)

        logarithm -= 1

    while structure[0] == 0:
        #the result needs trailing zeros
        structure.rotate(-1)

    return ("-" if isNegative and number else "") + reduce(lambda a, b: a + b, map(lambda a: str(a), structure))

I think though that the function strbase should only support bases >= 2 and <= 36 to prevent conflict with other tools in python such as int.
Also, I think that only one case of alphabets should be used preferably uppercase again to prevent conflict with other functions like int since it will consider both “a” and “A” to be 10.

from string import uppercase

dig_to_chr = lambda num: str(num) if num < 10 else uppercase[num - 10]

def strbase(number, base):
    if not 2 <= base <= 36:
        raise ValueError("Base to convert to must be >= 2 and <= 36")

    if number < 0:
        return "-" + strbase(-number, base)

    d, m = divmod(number, base)
    if d:
        return strbase(d, base) + dig_to_chr(m)

    return dig_to_chr(m)

Looks like this might be my time to shine. Believe it or not, the following is some ported and modified Scratch code I wrote nearly three years ago to see just how quickly I could convert from denary to hexadecimal.

Simply put, it works by first taking an integer, base, and an optional accompanying string of numerals, then calculating each digit of the converted integer beginning with the least significant.

def int2base(num, base, abc="0123456789abcdefghijklmnopqrstuvwxyz"):
  if num < 0:
    return '-' + int2base(-num, base, abc)

  output = abc[num % base] # rightmost digit

  while num >= base:
    num //= base # move to next digit to the left
    output = abc[num % base] + output # this digit

  return output

On my own PC, this code was able to complete 10 million iterations using the input range, 0-9999, and base, 36, in consistently below 5 seconds. Using the same test, I have found this to be at least 4 seconds faster than any other answer so far.

>>> timeit.timeit(lambda: [int2base(n, 36) for n in range(10000)], number=1000)
4.883068453882515

numpy.base_repr is a quite good solution, however, in some cases, we want a fixed-length string with leading zeros.

def base_repr(x: int, base: int, length: int):
    from numpy import base_repr
    from math import log, ceil
    s = base_repr(x, base, length - ceil(log(x, base)))
    return s

Here is a recursive function:

def encode(nIn, nBase):
   n = nIn // nBase
   s = '0123456789abcdefghijklmnopqrstuvwxyz'[nIn % nBase]
   return encode(n, nBase) + s if n > 0 else s

n = 1577858399
s = encode(n, 36)
print(s == 'q3ezbz')

To summarise, what I could find at Stackoverflow, the shortest way is something as follows:

base = lambda integer, b,  
  numerals='0123456789abcdefghijklmnopqrstuvwxyz': 
  numerals[0] if integer == 0 
  else 
  base(integer // b, b, numerals).lstrip(numerals[0]) 
  + numerals[integer % b]

>>> base(983779, 36)
>>> l337

But you have to pay for brevity — no error checking and also recursion overflow is possible.

P.S.: In the iPython interpreter, remove the line breaks that were added for clarity here. These may, however, remain in place in a Python script file.