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# -*- coding: utf-8 -*- |
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# Copyright 2014-2018 by Christopher C. Little. |
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# This file is part of Abydos. |
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# |
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# Abydos is free software: you can redistribute it and/or modify |
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# it under the terms of the GNU General Public License as published by |
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# the Free Software Foundation, either version 3 of the License, or |
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# (at your option) any later version. |
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# |
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# Abydos is distributed in the hope that it will be useful, |
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# but WITHOUT ANY WARRANTY; without even the implied warranty of |
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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# GNU General Public License for more details. |
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# |
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# You should have received a copy of the GNU General Public License |
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# along with Abydos. If not, see <http://www.gnu.org/licenses/>. |
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"""abydos.compression._arithmetic. |
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arithmetic coding functions |
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""" |
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from __future__ import division, unicode_literals |
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from collections import Counter |
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from fractions import Fraction |
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from six import PY3, text_type |
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if PY3: |
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long = int |
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__all__ = ['ac_decode', 'ac_encode', 'ac_train'] |
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def ac_train(text): |
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r"""Generate a probability dict from the provided text. |
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Text -> 0-order probability statistics as a dict |
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This is based on Andrew Dalke's public domain implementation |
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:cite:`Dalke:2005`. It has been ported to use the fractions.Fraction class. |
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:param str text: The text data over which to calculate probability |
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statistics. This must not contain the NUL (0x00) character because |
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that's used to indicate the end of data. |
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:returns: a probability dict |
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:rtype: dict |
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>>> ac_train('the quick brown fox jumped over the lazy dog') |
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{' ': (Fraction(0, 1), Fraction(8, 45)), |
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'o': (Fraction(8, 45), Fraction(4, 15)), |
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'e': (Fraction(4, 15), Fraction(16, 45)), |
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'u': (Fraction(16, 45), Fraction(2, 5)), |
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't': (Fraction(2, 5), Fraction(4, 9)), |
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'r': (Fraction(4, 9), Fraction(22, 45)), |
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'h': (Fraction(22, 45), Fraction(8, 15)), |
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'd': (Fraction(8, 15), Fraction(26, 45)), |
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'z': (Fraction(26, 45), Fraction(3, 5)), |
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'y': (Fraction(3, 5), Fraction(28, 45)), |
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'x': (Fraction(28, 45), Fraction(29, 45)), |
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'w': (Fraction(29, 45), Fraction(2, 3)), |
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'v': (Fraction(2, 3), Fraction(31, 45)), |
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'q': (Fraction(31, 45), Fraction(32, 45)), |
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'p': (Fraction(32, 45), Fraction(11, 15)), |
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'n': (Fraction(11, 15), Fraction(34, 45)), |
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'm': (Fraction(34, 45), Fraction(7, 9)), |
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'l': (Fraction(7, 9), Fraction(4, 5)), |
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'k': (Fraction(4, 5), Fraction(37, 45)), |
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'j': (Fraction(37, 45), Fraction(38, 45)), |
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'i': (Fraction(38, 45), Fraction(13, 15)), |
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'g': (Fraction(13, 15), Fraction(8, 9)), |
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'f': (Fraction(8, 9), Fraction(41, 45)), |
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'c': (Fraction(41, 45), Fraction(14, 15)), |
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'b': (Fraction(14, 15), Fraction(43, 45)), |
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'a': (Fraction(43, 45), Fraction(44, 45)), |
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'\x00': (Fraction(44, 45), Fraction(1, 1))} |
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""" |
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text = text_type(text) |
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if '\x00' in text: |
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text = text.replace('\x00', ' ') |
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counts = Counter(text) |
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counts['\x00'] = 1 |
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tot_letters = sum(counts.values()) |
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tot = 0 |
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prob_range = {} |
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prev = Fraction(0) |
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for char, count in sorted( |
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counts.items(), key=lambda x: (x[1], x[0]), reverse=True |
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): |
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follow = Fraction(tot + count, tot_letters) |
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prob_range[char] = (prev, follow) |
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prev = follow |
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tot = tot + count |
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# assert tot == tot_letters |
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return prob_range |
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def ac_encode(text, probs): |
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"""Encode a text using arithmetic coding with the provided probabilities. |
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Text and the 0-order probability statistics -> longval, nbits |
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The encoded number is Fraction(longval, 2**nbits) |
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This is based on Andrew Dalke's public domain implementation |
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:cite:`Dalke:2005`. It has been ported to use the fractions.Fraction class. |
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:param str text: A string to encode |
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:param dict probs: A probability statistics dictionary generated by |
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ac_train |
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:returns: The arithmetically coded text |
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:rtype: tuple |
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>>> pr = ac_train('the quick brown fox jumped over the lazy dog') |
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>>> ac_encode('align', pr) |
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(16720586181, 34) |
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""" |
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text = text_type(text) |
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if '\x00' in text: |
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text = text.replace('\x00', ' ') |
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minval = Fraction(0) |
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maxval = Fraction(1) |
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for char in text + '\x00': |
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prob_range = probs[char] |
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delta = maxval - minval |
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maxval = minval + prob_range[1] * delta |
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minval = minval + prob_range[0] * delta |
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# I tried without the /2 just to check. Doesn't work. |
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# Keep scaling up until the error range is >= 1. That |
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# gives me the minimum number of bits needed to resolve |
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# down to the end-of-data character. |
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delta = (maxval - minval) / 2 |
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nbits = long(0) |
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while delta < 1: |
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nbits += 1 |
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delta *= 2 |
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# The below condition shouldn't ever be false |
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if nbits == 0: # pragma: no cover |
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return 0, 0 |
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# using -1 instead of /2 |
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avg = (maxval + minval) * 2 ** (nbits - 1) |
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# Could return a rational instead ... |
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# the division truncation is deliberate |
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return avg.numerator // avg.denominator, nbits |
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def ac_decode(longval, nbits, probs): |
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"""Decode the number to a string using the given statistics. |
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This is based on Andrew Dalke's public domain implementation |
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:cite:`Dalke:2005`. It has been ported to use the fractions.Fraction class. |
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:param int longval: The first part of an encoded tuple from ac_encode |
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:param int nbits: The second part of an encoded tuple from ac_encode |
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:param dict probs: A probability statistics dictionary generated by |
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ac_train |
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:returns: The arithmetically decoded text |
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:rtype: str |
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>>> pr = ac_train('the quick brown fox jumped over the lazy dog') |
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>>> ac_decode(16720586181, 34, pr) |
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'align' |
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""" |
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val = Fraction(longval, long(1) << nbits) |
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letters = [] |
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probs_items = [ |
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(char, minval, maxval) for (char, (minval, maxval)) in probs.items() |
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] |
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char = '\x00' |
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while True: |
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for (char, minval, maxval) in probs_items: # noqa: B007 |
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if minval <= val < maxval: |
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break |
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if char == '\x00': |
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break |
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letters.append(char) |
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delta = maxval - minval |
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val = (val - minval) / delta |
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return ''.join(letters) |
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if __name__ == '__main__': |
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import doctest |
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doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE) |
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chrislit /
abydos
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