#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "arch.h"
#include "entdec.h"
#include "mfrngcod.h"
/*A multiply-free range decoder.
This is an entropy decoder based upon \cite{Mar79}, which is itself a
rediscovery of the FIFO arithmetic code introduced by \cite{Pas76}.
It is very similar to arithmetic encoding, except that encoding is done with
digits in any base, instead of with bits, and so it is faster when using
larger bases (i.e.: a byte).
The author claims an average waste of $\frac{1}{2}\log_b(2b)$ bits, where $b$
is the base, longer than the theoretical optimum, but to my knowledge there
is no published justification for this claim.
This only seems true when using near-infinite precision arithmetic so that
the process is carried out with no rounding errors.
IBM (the author's employer) never sought to patent the idea, and to my
knowledge the algorithm is unencumbered by any patents, though its
performance is very competitive with proprietary arithmetic coding.
The two are based on very similar ideas, however.
An excellent description of implementation details is available at
http://www.arturocampos.com/ac_range.html
A recent work \cite{MNW98} which proposes several changes to arithmetic
encoding for efficiency actually re-discovers many of the principles
behind range encoding, and presents a good theoretical analysis of them.
The coder is made multiply-free by replacing the standard multiply/divide
used to partition the current interval according to the total frequency
count.
The new partition function scales the count so that it differs from the size
of the interval by no more than a factor of two and then assigns each symbol
one or two code words in the interval.
For details see \cite{SM98}.
This coder also handles the end of the stream in a slightly more graceful
fashion than most arithmetic or range coders.
Once the final symbol has been encoded, the coder selects the code word with
the shortest number of bits that still falls within the final interval.
This method is not novel.
Here, by the length of the code word, we refer to the number of bits until
its final 1.
Any trailing zeros may be discarded, since the encoder, once it runs out of
input, will pad its buffer with zeros.
But this means that no encoded stream would ever have any zero bytes at the
end.
Since there are some coded representations we cannot produce, it implies that
there is still some redundancy in the stream.
In this case, we can pick a special byte value, RSV1, and should the stream
end in a sequence of zeros, followed by the RSV1 byte, we can code the
zeros, and discard the RSV1 byte.
The decoder, knowing that the encoder would never produce a sequence of zeros
at the end, would then know to add in the RSV1 byte if it observed it.
Now, the encoder would never produce a stream that ended in a sequence of
zeros followed by a RSV1 byte.
So, if the stream ends in a non-empty sequence of zeros, followed by any
positive number of RSV1 bytes, the last RSV1 byte is discarded.
The decoder, if it encounters a stream that ends in non-empty sequence of
zeros followed by any non-negative number of RSV1 bytes, adds an additional
RSV1 byte to the stream.
With this strategy, every possible sequence of input bytes is transformed to
one that could actually be produced by the encoder.
The only question is what non-zero value to use for RSV1.
We select 0x80, since it has the nice property of producing the shortest
possible byte streams when using our strategy for selecting a number within
the final interval to encode.
Clearly if the shortest possible code word that falls within the interval has
its last one bit as the most significant bit of the final byte, and the
previous bytes were a non-empty sequence of zeros followed by a non-negative
number of 0x80 bytes, then the last byte would be discarded.
If the shortest code word is not so formed, then no other code word in the
interval would result in any more bytes being discarded.
Any longer code word would have an additional one bit somewhere, and so would
require at a minimum that that byte would be coded.
If the shortest code word has a 1 before the final one that is preventing the
stream from ending in a non-empty sequence of zeros followed by a
non-negative number of 0x80's, then there is no code word of the same length
which contains that bit as a zero.
If there were, then we could simply leave that bit a 1, and drop all the bits
after it without leaving the interval, thus producing a shorter code word.
In this case, RSV1 can only drop 1 bit off the final stream.
Other choices could lead to savings of up to 8 bits for particular streams,
but this would produce the odd situation that a stream with more non-zero
bits is actually encoded in fewer bytes.
@PHDTHESIS{Pas76,
author="Richard Clark Pasco",
title="Source coding algorithms for fast data compression",
school="Dept. of Electrical Engineering, Stanford University",
address="Stanford, CA",
month=May,
year=1976
}
@INPROCEEDINGS{Mar79,
author="Martin, G.N.N.",
title="Range encoding: an algorithm for removing redundancy from a digitised
message",
booktitle="Video & Data Recording Conference",
year=1979,
address="Southampton",
month=Jul
}
@ARTICLE{MNW98,
author="Alistair Moffat and Radford Neal and Ian H. Witten",
title="Arithmetic Coding Revisited",
journal="{ACM} Transactions on Information Systems",
year=1998,
volume=16,
number=3,
pages="256--294",
month=Jul,
URL="http://www.stanford.edu/class/ee398/handouts/papers/Moffat98ArithmCoding.pdf"
}
@INPROCEEDINGS{SM98,
author="Lang Stuiver and Alistair Moffat",
title="Piecewise Integer Mapping for Arithmetic Coding",
booktitle="Proceedings of the {IEEE} Data Compression Conference",
pages="1--10",
address="Snowbird, UT",
month="Mar./Apr.",
year=1998
}*/
/*Gets the next byte of input.
After all the bytes in the current packet have been consumed, and the extra
end code returned if needed, this function will continue to return zero each
time it is called.
Return: The next byte of input.*/
static int ec_dec_in(ec_dec *_this){
int ret;
ret=ec_byte_read1(_this->buf);
if(ret<0){
ret=0;
/*Needed to keep oc_dec_tell() operating correctly.*/
ec_byte_adv1(_this->buf);
}
return ret;
}
/*Normalizes the contents of dif and rng so that rng lies entirely in the
high-order symbol.*/
static inline void ec_dec_normalize(ec_dec *_this){
/*If the range is too small, rescale it and input some bits.*/
while(_this->rng<=EC_CODE_BOT){
int sym;
_this->rng<<=EC_SYM_BITS;
/*Use up the remaining bits from our last symbol.*/
sym=_this->rem<rem=ec_dec_in(_this);
/*Take the rest of the bits we need from this new symbol.*/
sym|=_this->rem>>EC_SYM_BITS-EC_CODE_EXTRA;
_this->dif=(_this->dif<dif>EC_CODE_TOP)_this->dif-=EC_CODE_TOP;*/
_this->dif^=_this->dif&_this->dif-1&EC_CODE_TOP;
}
}
void ec_dec_init(ec_dec *_this,ec_byte_buffer *_buf){
_this->buf=_buf;
_this->rem=ec_dec_in(_this);
_this->rng=1U<dif=_this->rem>>EC_SYM_BITS-EC_CODE_EXTRA;
/*Normalize the interval.*/
ec_dec_normalize(_this);
}
unsigned ec_decode(ec_dec *_this,unsigned _ft){
ec_uint32 ft;
ec_uint32 d;
unsigned e;
/*Step 1: Compute the normalization factor for the frequency counts.*/
_this->nrm=EC_ILOG(_this->rng)-EC_ILOG(_ft);
ft=(ec_uint32)_ft<<_this->nrm;
e=ft>_this->rng;
ft>>=e;
_this->nrm-=e;
/*Step 2: invert the partition function.*/
d=_this->rng-ft;
return EC_MAXI((ec_int32)(_this->dif>>1),(ec_int32)(_this->dif-d))>>
_this->nrm;
/*Step 3: The caller locates the range [fl,fh) containing the return value
and calls ec_dec_update().*/
}
unsigned ec_decode_bin(ec_dec *_this,unsigned bits){
return ec_decode(_this, 1U<nrm;
fh=(ec_uint32)_fh<<_this->nrm;
ft=(ec_uint32)_ft<<_this->nrm;
d=_this->rng-ft;
r=fh+EC_MINI(fh,d);
s=fl+EC_MINI(fl,d);
/*Step 5: Update the interval.*/
_this->rng=r-s;
_this->dif-=s;
/*Step 6: Normalize the interval.*/
ec_dec_normalize(_this);
}
long ec_dec_tell(ec_dec *_this,int _b){
ec_uint32 r;
int l;
long nbits;
nbits=(ec_byte_bytes(_this->buf)-(EC_CODE_BITS+EC_SYM_BITS-1)/EC_SYM_BITS)*
EC_SYM_BITS;
/*To handle the non-integral number of bits still left in the encoder state,
we compute the number of bits of low that must be encoded to ensure that
the value is inside the range for any possible subsequent bits.
Note that this is subtly different than the actual value we would end the
stream with, which tries to make as many of the trailing bits zeros as
possible.*/
nbits+=EC_CODE_BITS;
nbits<<=_b;
l=EC_ILOG(_this->rng);
r=_this->rng>>l-16;
while(_b-->0){
int b;
r=r*r>>15;
b=(int)(r>>16);
l=l<<1|b;
r>>=b;
}
return nbits-l;
}
#if 0
int ec_dec_done(ec_dec *_this){
unsigned low;
int ret;
/*Check to make sure we've used all the input bytes.
This ensures that no more ones would ever be inserted into the decoder.*/
if(_this->buf->ptr-ec_byte_get_buffer(_this->buf)<=
ec_byte_bytes(_this->buf)){
return 0;
}
/*We compute the smallest finitely odd fraction that fits inside the current
range, and write that to the stream.
This is guaranteed to yield the smallest possible encoding.*/
/*TODO: Fix this line, as it is wrong.
It doesn't seem worth being able to make this check to do an extra
subtraction for every symbol decoded.*/
low=/*What we want: _this->top-_this->rng; What we have:*/_this->dif
if(low){
unsigned end;
end=EC_CODE_TOP;
/*Ensure that the next free end is in the range.*/
if(end-low>=_this->rng){
unsigned msk;
msk=EC_CODE_TOP-1;
do{
msk>>=1;
end=low+msk&~msk|msk+1;
}
while(end-low>=_this->rng);
}
/*The remaining input should have been the next free end.*/
return end-low!=_this->dif;
}
return 1;
}
#endif