rdx

A radix conversion module.

Implementation of

• How to convert an integer to a string in any base?
• How to find length of digits in an integer?

Installation

pip install rdx

Usage

This module provides the following functions:

• int_to_digits(n, b=10): Returns the digits of number n in base b.
• digits_to_int(d, b=10): Returns the number represented by the digits d in base b.

  >>> from rdx import *
  >>> int_to_digits(42, 2)
  [0, 1, 0, 1, 0, 1]
  >>> int_to_digits(42, 16)
  [10, 2]
  >>> digits_to_int([27, 1], 42)
  69
  

• int_to_len_digits(n, b=10): Returns the amount of digits the number n represented in base b needs.

  >>> int_to_len_digits(1024, 2)
  11
  

• digits_to_characters(d, alphabet=digits+ascii_letters): Converts integer digits d to characters of the given alphabet.
• characters_to_digits(s, alphabet=digits+ascii_letters): Converts characters s of the given alphabet to integer digits.

  >>> digits_to_characters([0, 1, 9, 10, 15, 16])
  ['0', '1', '9', 'a', 'f', 'g']
  >>> characters_to_digits(['0', '1', '9', 'a', 'f', 'g'])
  [0, 1, 9, 10, 15, 16]
  

• digits_to_string(d, alphabet=string.digits+string.ascii_letters): Converts integer digits d to a right-to-left string in the given alphabet.
• string_to_digits(s, alphabet=string.digits+string.ascii_letters): Converts a right-to-left string s in the given alphabet to integer digits.

  >>> digits_to_string([0, 0, 15])
  'f00'
  >>> string_to_digits('f12')
  [2, 1, 15]
  

Conventions

Data type

Currently digits or characters are returned as lists. In the future this will be switched to tuples as they are more similar to strings, and a digit representation is similar to a string.

Digit or character arguments should be provided in form of an iterable, not an iterator, as in most functions the will be iterated twice and an iterator will be exhausted after the first run.

Ordering

As a digit representation a list of integers is used, where every element represents a digit, all ordered in ascending positions. So the lowest digit at position with index 0, will be at position 0. But this also means, that when a list of digits is printed, it will be ordered left-to-right, opposed to the usual human-readable right-to-left. E.g. 12 (twelve) corresponds to [2, 1].

int_to_len_digits(n) vs len(int_to_digits(n))

len(int_to_digits(n)) is the naive and non-optimal approach. int_to_len_digits(n) calculates the number of digits intelligently as int(log(n, b))+1 as mentioned in the discussion. But to avoid errors due to math.log using floating point arithmetic sympy.log is used, adding a hefty overhead. A comparison for time critical applications: (integers with just 3s were choosen because random values introduce to much noise and because 100... seemed to risky for a systematic error and 33... lies exactly between those 100...s on a logarithmic scale)

TODO

• [ ] put digits in tuples instead of lists
• [ ] non-standard positional numeral systems
  • [ ] mixed radix
    • [ ] factorial
    • [ ] primorial
    • [ ] ...
  • [ ] negative base
  • [ ] complex base

License (MIT)

Copyright (c) 2023 Sebastian Gössl

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.