Infinity_codec/utils/arithmeticcoding.py at main · oys1124/Infinity_codec · GitHub

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# Reference arithmetic coding

# Copyright (c) Project Nayuki

# https://www.nayuki.io/page/reference-arithmetic-coding

# https://github.com/nayuki/Reference-arithmetic-coding

import numpy as np

import sys

python3 = sys.version_info.major >= 3

import time

# ---- Arithmetic coding core classes ----

# Provides the state and behaviors that arithmetic coding encoders and decoders share.

class ArithmeticCoderBase(object):

# Constructs an arithmetic coder, which initializes the code range.

def __init__(self, statesize):

# if statesize < 1:

# raise ValueError("State size out of range")

# -- Configuration fields --

# Number of bits for the 'low' and 'high' state variables. Must be at least 1.

# - Larger values are generally better - they allow a larger maximum frequency total (MAX_TOTAL),

# and they reduce the approximation error inherent in adapting fractions to integers;

# both effects reduce the data encoding loss and asymptotically approach the efficiency

# of arithmetic coding using exact fractions.

# - But larger state sizes increase the computation time for integer arithmetic,

# and compression gains beyond ~30 bits essentially zero in real-world applications.

# - Python has native bigint arithmetic, so there is no upper limit to the state size.

# For Java and C++ where using native machine-sized integers makes the most sense,

# they have a recommended value of STATE_SIZE=32 as the most versatile setting.

self.STATE_SIZE = statesize

# Maximum range (high+1-low) during coding (trivial), which is 2^STATE_SIZE = 1000...000.

self.MAX_RANGE = 1 << self.STATE_SIZE

# Minimum range (high+1-low) during coding (non-trivial), which is 0010...010.

self.MIN_RANGE = (self.MAX_RANGE >> 2) + 2

# Maximum allowed total from a frequency table at all times during coding. This differs from Java

# and C++ because Python's native bigint avoids constraining the size of intermediate computations.

self.MAX_TOTAL = self.MIN_RANGE

# Bit mask of STATE_SIZE ones, which is 0111...111.

self.MASK = self.MAX_RANGE - 1

# The top bit at width STATE_SIZE, which is 0100...000.

self.TOP_MASK = self.MAX_RANGE >> 1

# The second highest bit at width STATE_SIZE, which is 0010...000. This is zero when STATE_SIZE=1.

self.SECOND_MASK = self.TOP_MASK >> 1

# -- State fields --

# Low end of this arithmetic coder's current range. Conceptually has an infinite number of trailing 0s.

self.low = 0

# High end of this arithmetic coder's current range. Conceptually has an infinite number of trailing 1s.

self.high = self.MASK

# Updates the code range (low and high) of this arithmetic coder as a result

# of processing the given symbol with the given frequency table.

# Invariants that are true before and after encoding/decoding each symbol:

# - 0 <= low <= code <= high < 2^STATE_SIZE. ('code' exists only in the decoder.)

# Therefore these variables are unsigned integers of STATE_SIZE bits.

# - (low < 1/2 * 2^STATE_SIZE) && (high >= 1/2 * 2^STATE_SIZE).

# In other words, they are in different halves of the full range.

# - (low < 1/4 * 2^STATE_SIZE) || (high >= 3/4 * 2^STATE_SIZE).

# In other words, they are not both in the middle two quarters.

# - Let range = high - low + 1, then MAX_RANGE/4 < MIN_RANGE <= range

# <= MAX_RANGE = 2^STATE_SIZE. These invariants for 'range' essentially

# dictate the maximum total that the incoming frequency table can have.

def update(self, cumul, symbol):

# State check

#s = time.time()

low = self.low

high = self.high

# if low >= high or (low & self.MASK) != low or (high & self.MASK) != high:

# raise AssertionError("Low or high out of range")

range = high - low + 1

# if not (self.MIN_RANGE <= range <= self.MAX_RANGE):

# raise AssertionError("Range out of range")

# Frequency table values check

total = cumul[-1].item()

symlow = cumul[symbol].item()

symhigh = cumul[symbol+1].item()

# if symlow == symhigh:

# raise ValueError("Symbol has zero frequency")

# if total > self.MAX_TOTAL:

# raise ValueError("Cannot code symbol because total is too large")

# Update range

newlow = low + symlow * range // total

newhigh = low + symhigh * range // total - 1

self.low = newlow

self.high = newhigh

# While the highest bits are equal

#s1 = time.time()

#print("update1", s1-s)

while ((self.low ^ self.high) & self.TOP_MASK) == 0:

self.shift()

self.low = (self.low << 1) & self.MASK

self.high = ((self.high << 1) & self.MASK) | 1

# While the second highest bit of low is 1 and the second highest bit of high is 0

#s2 = time.time()

#print("update2", s2-s1)

while (self.low & ~self.high & self.SECOND_MASK) != 0:

self.underflow()

self.low = (self.low << 1) & (self.MASK >> 1)

self.high = ((self.high << 1) & (self.MASK >> 1)) | self.TOP_MASK | 1

#s3 = time.time()

#print("update3", s3-s2)

# Called to handle the situation when the top bit of 'low' and 'high' are equal.

def shift(self):

raise NotImplementedError()

# Called to handle the situation when low=01(...) and high=10(...).

def underflow(self):

raise NotImplementedError()

# Encodes symbols and writes to an arithmetic-coded bit stream.

class ArithmeticEncoder(ArithmeticCoderBase):

# Constructs an arithmetic coding encoder based on the given bit output stream.

def __init__(self, statesize, bitout):

super(ArithmeticEncoder, self).__init__(statesize)

# The underlying bit output stream.

self.output = bitout

# Number of saved underflow bits. This value can grow without bound.

self.num_underflow = 0

# Encodes the given symbol based on the given frequency table.

# This updates this arithmetic coder's state and may write out some bits.

def write(self, cumul, symbol):

# if not isinstance(freqs, CheckedFrequencyTable):

# freqs = CheckedFrequencyTable(freqs)

#s = time.time()

self.update(cumul, symbol)

#print('update', time.time()-s)

# Terminates the arithmetic coding by flushing any buffered bits, so that the output can be decoded properly.

# It is important that this method must be called at the end of the each encoding process.

# Note that this method merely writes data to the underlying output stream but does not close it.

def finish(self):

#s = time.time()

self.output.write(1)

#print('finish', time.time()-s)

def shift(self):

#s = time.time()

bit = self.low >> (self.STATE_SIZE - 1)

self.output.write(bit)

# Write out the saved underflow bits

#s1 = time.time()

#print('shift1', s1-s)

for _ in range(self.num_underflow):

self.output.write(bit ^ 1)

self.num_underflow = 0

#print('shift2', time.time()-s1)

def underflow(self):

self.num_underflow += 1

# Reads from an arithmetic-coded bit stream and decodes symbols.

class ArithmeticDecoder(ArithmeticCoderBase):

# Constructs an arithmetic coding decoder based on the

# given bit input stream, and fills the code bits.

def __init__(self, statesize, bitin):

super(ArithmeticDecoder, self).__init__(statesize)

# The underlying bit input stream.

self.input = bitin

# The current raw code bits being buffered, which is always in the range [low, high].

self.code = 0

for _ in range(self.STATE_SIZE):

self.code = self.code << 1 | self.read_code_bit()

# Decodes the next symbol based on the given frequency table and returns it.

# Also updates this arithmetic coder's state and may read in some bits.

def read(self, cumul, alphabet_size):

# if not isinstance(freqs, CheckedFrequencyTable):

# freqs = CheckedFrequencyTable(freqs)

# Translate from coding range scale to frequency table scale

total = cumul[-1].item()

# if total > self.MAX_TOTAL:

# raise ValueError("Cannot decode symbol because total is too large")

range = self.high - self.low + 1

offset = self.code - self.low

value = ((offset + 1) * total - 1) // range

# assert value * range // total <= offset

# assert 0 <= value < total

# A kind of binary search. Find highest symbol such that freqs.get_low(symbol) <= value.

start = 0

end = alphabet_size

while end - start > 1:

middle = (start + end) >> 1

if cumul[middle] > value:

end = middle

else:

start = middle

# assert start + 1 == end

symbol = start

# assert freqs.get_low(symbol) * range // total <= offset < freqs.get_high(symbol) * range // total

self.update(cumul, symbol)

# if not (self.low <= self.code <= self.high):

# raise AssertionError("Code out of range")

return symbol

def shift(self):

self.code = ((self.code << 1) & self.MASK) | self.read_code_bit()

def underflow(self):

self.code = (self.code & self.TOP_MASK) | ((self.code << 1) & (self.MASK >> 1)) | self.read_code_bit()

# Returns the next bit (0 or 1) from the input stream. The end

# of stream is treated as an infinite number of trailing zeros.

def read_code_bit(self):

temp = self.input.read()

if temp == -1:

temp = 0

return temp

class BitCollector:

"""

一个伪输出流，它不写入文件，而是将所有比特收集到一个列表中。

"""

def __init__(self):

self.bits = []

def write(self, bit):

# 每当编码器尝试“写入”一个比特时，我们将其添加到列表中。

self.bits.append(bit)

def get_bits(self):

# 一个方便的方法来获取最终的比特列表。

return self.bits

class BitListReader:

"""

一个伪输入流，它从一个比特列表而不是文件中读取数据。

"""

def __init__(self, bits_list: list):

self.bits = bits_list

self.index = 0 # 追踪当前读取到哪个位置

def read(self):

# 检查是否已经读完列表中的所有比特

if self.index >= len(self.bits):

return -1 # 表示流的末尾 (End of Stream)

# 获取当前位置的比特

bit = self.bits[self.index]

# 将索引向后移动一位

self.index += 1

return bit

def get_consumed_bits_count(self):

"""返回已经从流中读取的比特总数。"""

return self.index

class BitOutputStream:

"""A simple bit-level output stream."""

def __init__(self, file):

self.file = file

self.buffer = 0

self.bit_count = 0

def write(self, bit):

if bit not in (0, 1):

raise ValueError("Bit must be 0 or 1")

self.buffer = (self.buffer << 1) | bit

self.bit_count += 1

if self.bit_count == 8:

self.file.write(bytes([self.buffer]))

self.buffer = 0

self.bit_count = 0

def flush(self):

"""

将缓冲区中剩余的比特写入文件 (用0填充到整字节)，但不关闭文件。

这是解决问题的关键。

"""

if self.bit_count > 0:

# 用0向左移位，填充剩余的比特位

self.buffer <<= (8 - self.bit_count)

self.file.write(bytes([self.buffer]))

self.buffer = 0

self.bit_count = 0

def close(self):

"""刷新缓冲区并关闭底层文件。"""

self.flush()

self.file.close()

class BitInputStream:

"""A simple bit-level input stream."""

def __init__(self, file):

self.file = file

self.buffer = 0

self.bit_count = 0

def read(self):

if self.bit_count == 0:

byte_data = self.file.read(1)

if not byte_data:

return -1 # End of stream

self.buffer = byte_data[0]

self.bit_count = 8

# Read the most significant bit from the buffer

bit = (self.buffer >> (self.bit_count - 1)) & 1

self.bit_count -= 1

return bit

def close(self):

self.file.close()

def probabilities_to_cumul(p0, total_freq=2**16):

"""

将符号0的概率转换为算术编码器所需的累积频率表。

Args:

p0 (float): 符号0出现的概率 (0.0 to 1.0).

total_freq (int): 用于模拟概率的整数总频率。

Returns:

numpy.ndarray: 累积频率表 (cumul)。

"""

# 确保概率在有效范围内

p0 = max(0.0, min(1.0, p0))

# 计算频率，并确保每个符号的频率至少为1

freq_0 = max(1, int(round(p0 * total_freq)))

freq_1 = max(1, int(round((1.0 - p0) * total_freq)))

# 重新计算总和

current_total = freq_0 + freq_1

# 创建累积频率表 [0, freq_0, freq_0 + freq_1]

cumul = np.array([0, freq_0, current_total], dtype=np.uint64)

return cumul

def compress_to_bit_list(bit_source, probabilities_of_zero):

"""

将源比特流压缩成一个精确的比特列表。

"""

bit_collector = BitCollector()

encoder = ArithmeticEncoder(statesize=32, bitout=bit_collector)

for i, bit in enumerate(bit_source):

p0 = probabilities_of_zero[i]

cumul = probabilities_to_cumul(p0) # probabilities_to_cumul 来自之前的答案

encoder.write(cumul, bit)

encoder.finish()

return bit_collector.get_bits()

def decompress_from_bit_list(exact_bit_list, num_bits, probabilities_of_zero):

"""

从一个精确的比特列表中解压缩出原始符号。

"""

# 使用 BitListReader 将我们的列表包装成解码器可以使用的输入流

bit_reader = BitListReader(exact_bit_list)

decoder = ArithmeticDecoder(statesize=32, bitin=bit_reader)

decoded_bits = []

alphabet_size = 2

for i in range(num_bits):

# 解码时必须使用与编码时完全相同的概率序列

p0 = probabilities_of_zero[i]

cumul = probabilities_to_cumul(p0)

bit = decoder.read(cumul, alphabet_size)

decoded_bits.append(bit)

return decoded_bits

Infinity_codec/utils/arithmeticcoding.py at main · oys1124/Infinity_codec · GitHub

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