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Re: Linear time baseconversion

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From Ian Kelly <ian.g.kelly@gmail.com>
Date Tue, 30 Jun 2015 09:45:05 -0600
Subject Re: Linear time baseconversion
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On Tue, Jun 30, 2015 at 9:40 AM, Ian Kelly <ian.g.kelly@gmail.com> wrote:
> On Tue, Jun 30, 2015 at 3:07 AM, Christian Gollwitzer <auriocus@gmx.de> wrote:
>> Am 30.06.15 um 10:52 schrieb jonas.thornvall@gmail.com:
>>>
>>> It still bug out on very big numbers if base outside integer scope.
>>> I am very keen on suggestions regarding the logic to make it faster.
>>
>>
>> Concerning the algorithmic complexity, it can't be faster than square time
>> in the number of digits N. Baseconversion needs to do a sequence of division
>> operations, where every operation gves you one digit in the new base. The
>> number of digits in the new base is proportional to the number of digits in
>> the old base (the ratio is log b1/log b2). Therefore it will be O(N^2).
>
> I don't think that's true. Here's a linear hexadecimal to binary function:
>
>>>> def hextobin(value):
> ...     digits = {'0': '0000', '1': '0001', '2': '0010', '3': '0011',
> ...         '4': '0100', '5': '0101', '6': '0110', '7': '0111',
> ...         '8': '1000', '9': '1001', 'A': '1010', 'B': '1011',
> ...         'C': '1100', 'D': '1101', 'E': '1110', 'F': '1111'}
> ...     return ''.join(digits[d.upper()] for d in value)
> ...
>>>> hextobin('3f')
> '00111111'
>
> I believe this approach can be extended to arbitrary bases with some
> effort, although for converting arbitrary base b1 to b2, you would
> need up to b2 different mappings if b1 and b2 are relatively prime.

Actually, I think you need up to b1 * b2 mappings, as you're
effectively building a state machine with b1 * b2 states. The mappings
can be pre-computed, however, so actually running the state machine
would then just be a linear algorithm.

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Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-29 15:39 -0700
  Re: Linear time baseconversion Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-29 16:56 -0600
  Re: Linear time baseconversion Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-29 17:10 -0600
    Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-29 16:23 -0700
    Re: Linear time baseconversion Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-06-30 01:09 +0100
      Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 01:52 -0700
        Re: Linear time baseconversion Christian Gollwitzer <auriocus@gmx.de> - 2015-06-30 11:07 +0200
          Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 02:20 -0700
          Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 02:34 -0700
            Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 02:43 -0700
              Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 06:22 -0700
                Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 07:13 -0700
                Re: Linear time baseconversion Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-30 09:29 -0600
          Re: Linear time baseconversion Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-30 09:45 -0600
          Re: Linear time baseconversion Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-30 09:40 -0600
            Re: Linear time baseconversion Christian Gollwitzer <auriocus@gmx.de> - 2015-07-01 00:22 +0200
          Re: Linear time baseconversion Chris Angelico <rosuav@gmail.com> - 2015-07-01 02:10 +1000
          Re: Linear time baseconversion Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-30 10:34 -0600
            Re: Linear time baseconversion Christian Gollwitzer <auriocus@gmx.de> - 2015-07-01 00:27 +0200
    Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-29 23:49 -0700
  Re: Linear time baseconversion Michael Torrie <torriem@gmail.com> - 2015-06-30 10:12 -0600
    Re: Linear time baseconversion jonas.thornvall@gmail.com - 2015-06-30 09:24 -0700
      Re: Linear time baseconversion Michael Torrie <torriem@gmail.com> - 2015-06-30 13:55 -0600

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