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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 coder/decoder |
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""" |
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from __future__ import ( |
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absolute_import, |
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division, |
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print_function, |
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unicode_literals, |
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) |
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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__ = ['Arithmetic', 'ac_decode', 'ac_encode', 'ac_train'] |
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class Arithmetic(object): |
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"""Arithmetic Coder. |
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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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""" |
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_probs = {} |
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def __init__(self, text=None): |
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"""Initialize arithmetic coder object. |
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Parameters |
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---------- |
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text : str |
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The training text |
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""" |
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if text is not None: |
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self.train(text) |
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def get_probs(self): |
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"""Return the probs dictionary. |
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Returns |
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------- |
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dict |
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The dictionary of probabilities |
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""" |
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return self._probs |
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def set_probs(self, probs): |
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"""Set the probs dictionary. |
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Parameters |
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---------- |
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probs : dict |
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The dictionary of probabilities |
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""" |
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self._probs = probs |
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def train(self, text): |
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r"""Generate a probability dict from the provided text. |
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Text to 0-order probability statistics as a dict |
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Parameters |
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---------- |
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text : str |
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The text data over which to calculate probability statistics. This |
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must not contain the NUL (0x00) character because that is used to |
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indicate the end of data. |
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Example |
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------- |
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>>> ac = Arithmetic() |
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>>> ac.train('the quick brown fox jumped over the lazy dog') |
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>>> ac.get_probs() |
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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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self._probs = {} |
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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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self._probs[char] = (prev, follow) |
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prev = follow |
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tot = tot + count |
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def encode(self, text): |
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"""Encode a text using arithmetic coding. |
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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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Parameters |
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---------- |
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text : str |
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A string to encode |
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Returns |
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------- |
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tuple |
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The arithmetically coded text |
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Example |
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------- |
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>>> ac = Arithmetic('the quick brown fox jumped over the lazy dog') |
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>>> ac.encode('align') |
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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 = self._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 decode(self, longval, nbits): |
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"""Decode the number to a string using the given statistics. |
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Parameters |
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---------- |
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longval : int |
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The first part of an encoded tuple from encode |
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nbits : int |
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The second part of an encoded tuple from encode |
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Returns |
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------- |
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str |
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The arithmetically decoded text |
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Example |
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------- |
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>>> ac = Arithmetic('the quick brown fox jumped over the lazy dog') |
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>>> ac.decode(16720586181, 34) |
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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) |
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for (char, (minval, maxval)) in self._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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def ac_train(text): |
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r"""Generate a probability dict from the provided text. |
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This is a wrapper for :py:meth:`Arithmetic.train`. |
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Parameters |
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---------- |
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text : str |
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The text data over which to calculate probability statistics. This must |
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not contain the NUL (0x00) character because that's used to indicate |
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the end of data. |
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Returns |
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------- |
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dict |
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A probability dict |
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Example |
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------- |
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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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return Arithmetic(text).get_probs() |
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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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This is a wrapper for :py:meth:`Arithmetic.encode`. |
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Parameters |
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---------- |
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text : str |
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A string to encode |
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probs : dict |
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A probability statistics dictionary generated by |
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:py:meth:`Arithmetic.train` |
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Returns |
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------- |
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315
|
|
|
tuple |
|
316
|
|
|
The arithmetically coded text |
|
317
|
|
|
|
|
318
|
|
|
Example |
|
319
|
|
|
------- |
|
320
|
|
|
>>> pr = ac_train('the quick brown fox jumped over the lazy dog') |
|
321
|
|
|
>>> ac_encode('align', pr) |
|
322
|
|
|
(16720586181, 34) |
|
323
|
|
|
|
|
324
|
|
|
""" |
|
325
|
1 |
|
coder = Arithmetic() |
|
326
|
1 |
|
coder.set_probs(probs) |
|
327
|
1 |
|
return coder.encode(text) |
|
328
|
|
|
|
|
329
|
|
|
|
|
330
|
1 |
|
def ac_decode(longval, nbits, probs): |
|
331
|
|
|
"""Decode the number to a string using the given statistics. |
|
332
|
|
|
|
|
333
|
|
|
This is a wrapper for :py:meth:`Arithmetic.decode`. |
|
334
|
|
|
|
|
335
|
|
|
Parameters |
|
336
|
|
|
---------- |
|
337
|
|
|
longval : int |
|
338
|
|
|
The first part of an encoded tuple from ac_encode |
|
339
|
|
|
nbits : int |
|
340
|
|
|
The second part of an encoded tuple from ac_encode |
|
341
|
|
|
probs : dict |
|
342
|
|
|
A probability statistics dictionary generated by |
|
343
|
|
|
:py:meth:`Arithmetic.train` |
|
344
|
|
|
|
|
345
|
|
|
Returns |
|
346
|
|
|
------- |
|
347
|
|
|
str |
|
348
|
|
|
The arithmetically decoded text |
|
349
|
|
|
|
|
350
|
|
|
Example |
|
351
|
|
|
------- |
|
352
|
|
|
>>> pr = ac_train('the quick brown fox jumped over the lazy dog') |
|
353
|
|
|
>>> ac_decode(16720586181, 34, pr) |
|
354
|
|
|
'align' |
|
355
|
|
|
|
|
356
|
|
|
""" |
|
357
|
1 |
|
coder = Arithmetic() |
|
358
|
1 |
|
coder.set_probs(probs) |
|
359
|
1 |
|
return coder.decode(longval, nbits) |
|
360
|
|
|
|
|
361
|
|
|
|
|
362
|
|
|
if __name__ == '__main__': |
|
363
|
|
|
import doctest |
|
364
|
|
|
|
|
365
|
|
|
doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE) |
|
366
|
|
|
|
chrislit /
abydos
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