/* Copyright (c) 2001-2008 Timothy B. Terriberry
Copyright (c) 2008-2009 Xiph.Org Foundation */
/*
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
documentation and/or other materials provided with the distribution.
- 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,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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 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.
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"
}*/
/*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->nbits_total+=EC_SYM_BITS;
_this->rng<<=EC_SYM_BITS;
/*Use up the remaining bits from our last symbol.*/
sym=_this->rem;
/*Read the next value from the input.*/
_this->rem=ec_byte_read(_this->buf);
/*Take the rest of the bits we need from this new symbol.*/
sym=(sym<rem)>>EC_SYM_BITS-EC_CODE_EXTRA;
/*And subtract them from dif, capped to be less than EC_CODE_TOP.*/
_this->dif=(_this->dif<buf=_buf;
_this->rem=ec_byte_read(_buf);
_this->rng=1U<dif=_this->rng-1-(_this->rem>>EC_SYM_BITS-EC_CODE_EXTRA);
/*Normalize the interval.*/
ec_dec_normalize(_this);
_this->end_window=0;
_this->nend_bits=0;
/*This is the offset from which ec_enc_tell() will subtract partial bits.
This must be after the initial ec_dec_normalize(), or you will have to
compensate for the bits that are read there.*/
_this->nbits_total=EC_CODE_BITS+1;
_this->error=0;
}
unsigned ec_decode(ec_dec *_this,unsigned _ft){
unsigned s;
_this->nrm=_this->rng/_ft;
s=(unsigned)(_this->dif/_this->nrm);
return _ft-EC_MINI(s+1,_ft);
}
unsigned ec_decode_bin(ec_dec *_this,unsigned _bits){
unsigned s;
_this->nrm=_this->rng>>_bits;
s=(unsigned)(_this->dif/_this->nrm);
return (1<<_bits)-EC_MINI(s+1,1<<_bits);
}
void ec_dec_update(ec_dec *_this,unsigned _fl,unsigned _fh,unsigned _ft){
ec_uint32 s;
s=IMUL32(_this->nrm,_ft-_fh);
_this->dif-=s;
_this->rng=_fl>0?IMUL32(_this->nrm,_fh-_fl):_this->rng-s;
ec_dec_normalize(_this);
}
/*The probability of having a "one" is given in 1/65536.*/
int ec_dec_bit_prob(ec_dec *_this,unsigned _prob){
ec_uint32 r;
ec_uint32 d;
ec_uint32 s;
int val;
r=_this->rng;
d=_this->dif;
s=(r>>16)*_prob;
val=d~~dif=d-s;
_this->rng=val?s:r-s;
ec_dec_normalize(_this);
return val;
}
/*The probability of having a "one" is 1/(1<<_logp).*/
int ec_dec_bit_logp(ec_dec *_this,unsigned _logp){
ec_uint32 r;
ec_uint32 d;
ec_uint32 s;
int val;
r=_this->rng;
d=_this->dif;
s=r>>_logp;
val=d~~~~dif=d-s;
_this->rng=val?s:r-s;
ec_dec_normalize(_this);
return val;
}
int ec_dec_icdf(ec_dec *_this,const unsigned char *_icdf,unsigned _ftb){
ec_uint32 r;
ec_uint32 d;
ec_uint32 s;
ec_uint32 t;
int val;
s=_this->rng;
d=_this->dif;
r=s>>_ftb;
val=0;
do{
t=s;
s=IMUL32(r,_icdf[val++]);
}
while(d~~~~dif=d-s;
_this->rng=t-s;
ec_dec_normalize(_this);
return val-1;
}
ec_uint32 ec_dec_bits(ec_dec *_this,unsigned _bits){
ec_window window;
int available;
ec_uint32 ret;
window=_this->end_window;
available=_this->nend_bits;
if(available<_bits){
do{
window|=(ec_window)ec_byte_read_from_end(_this->buf)<>=_bits;
available-=_bits;
_this->end_window=window;
_this->nend_bits=available;
_this->nbits_total+=_bits;
return ret;
}
ec_uint32 ec_dec_tell(ec_dec *_this,int _b){
ec_uint32 nbits;
ec_uint32 r;
int l;
/*To handle the non-integral number of bits still left in the decoder state,
we compute the worst-case number of bits of low that must be encoded to
ensure that the value is inside the range for any possible subsequent
bits.
The computation here is independent of low itself (the decoder does not
even track that value), even though the real number of bits used after
ec_enc_done() may be 1 smaller if rng is a power of two and the
corresponding trailing bits of low are all zeros.
If we did try to track that special case, then coding a value with a
probability of 1/(1<nbits_total<<_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;
}
~~