/* (C) 2001-2008 Timothy B. Terriberry
(C) 2008 Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
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- Neither the name of the Xiph.org Foundation nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#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}.
End of stream is handled by writing out the smallest number of bits that
ensures that the stream will be correctly decoded regardless of the value of
any subsequent bits.
ec_dec_tell() can be used to determine how many bits were needed to decode
all the symbols thus far; other data can be packed in the remaining bits of
the input buffer.
@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);
_this->end_bits_left=0;
_this->nb_end_bits=0;
}
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){
#if 0
return ec_decode(_this, 1U<nb_end_bits += bits;
while (bits>=_this->end_bits_left)
{
value |= _this->end_byte>>(8-_this->end_bits_left)<end_bits_left;
bits -= _this->end_bits_left;
_this->end_byte=ec_byte_look_at_end(_this->buf);
_this->end_bits_left = 8;
}
value |= ((_this->end_byte>>(8-_this->end_bits_left))&((1<end_bits_left -= bits;
return value;
#endif
}
void ec_dec_update(ec_dec *_this,unsigned _fl,unsigned _fh,unsigned _ft){
ec_uint32 fl;
ec_uint32 fh;
ec_uint32 ft;
ec_uint32 r;
ec_uint32 s;
ec_uint32 d;
/*Step 4: Evaluate the two partition function values.*/
fl=(ec_uint32)_fl<<_this->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 decoder 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.*/
nbits+=EC_CODE_BITS+1+_this->nb_end_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;
}