opus/libcelt/mfrngdec.c

/* (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
   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 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<<EC_CODE_EXTRA&EC_SYM_MAX;
    /*Read the next value from the input.*/
    _this->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<<EC_SYM_BITS)+sym&EC_CODE_MASK;
    /*dif can never be larger than EC_CODE_TOP.
      This is equivalent to the slightly more readable:
      if(_this->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<<EC_CODE_EXTRA;
  _this->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<<bits);
}

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 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