Moving to non-multiply-free entropy coder

libentcode/Makefile.am

@@ -2,7 +2,7 @@ INCLUDES =
 METASOURCES = AUTO
 lib_LTLIBRARIES = libentcode.la
 libentcode_la_SOURCES = bitrdec.c bitree.c bitrenc.c ecintrin.h entcode.c \
-	entdec.c entenc.c laplace.c mfrngdec.c mfrngenc.c probdec.c probenc.c probmod.c
+	entdec.c entenc.c laplace.c rangedec.c rangeenc.c probdec.c probenc.c probmod.c
 bin_PROGRAMS = ectest
 ectest_SOURCES = ectest.c
 ectest_LDADD = $(top_builddir)/libentcode/libentcode.la

libentcode/rangedec.c

+#include <stddef.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="Sorce 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://dev.acm.org/pubs/citations/journals/tois/1998-16-3/p256-moffat/"
+  }
+  @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){
+    unsigned char *buf;
+    long           bytes;
+    bytes=ec_byte_bytes(_this->buf);
+    buf=ec_byte_get_buffer(_this->buf);
+    /*Breaking abstraction: don't do this at home, kids.*/
+    if(_this->buf->storage==bytes){
+      ec_byte_adv1(_this->buf);
+      if(bytes>0){
+        unsigned char *p;
+        p=buf+bytes;
+        /*If we end in a string of 0 or more EC_FOF_RSV1 bytes preceded by a
+           zero, return an extra EC_FOF_RSV1 byte.*/
+        do p--;
+        while(p>buf&&p[0]==EC_FOF_RSV1);
+        if(!p[0])return EC_FOF_RSV1;
+      }
+    }
+    return 0;
+  }
+  else return ret;
+}
+
+/*Normalizes the contents of low and rng so that rng is contained in the
+   high-order symbol of low.*/
+static 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->rng-(_this->rem>>EC_SYM_BITS-EC_CODE_EXTRA);
+  /*Normalize the interval.*/
+  ec_dec_normalize(_this);
+}
+
+
+unsigned ec_decode(ec_dec *_this,unsigned _ft){
+  unsigned s;
+  _this->nrm=_this->rng/_ft;
+  s=(unsigned)((_this->dif-1)/_this->nrm);
+  return _ft-EC_MINI(s+1,_ft);
+}
+
+void ec_dec_update(ec_dec *_this,unsigned _fl,unsigned _fh,unsigned _ft){
+  ec_uint32 s;
+  s=_this->nrm*(_ft-_fh);
+  _this->dif-=s;
+  _this->rng=_fl>0?_this->nrm*(_fh-_fl):_this->rng-s;
+  ec_dec_normalize(_this);
+}
+
+#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

libentcode/rangeenc.c

+#include <stddef.h>
+#include "entenc.h"
+#include "mfrngcod.h"
+
+
+
+/*A multiply-free range encoder.
+  See mfrngdec.c and the references for implementation details
+   \cite{Mar79,MNW98,SM98}.
+
+  @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://dev.acm.org/pubs/citations/journals/tois/1998-16-3/p256-moffat/"
+  }
+  @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
+  }*/
+
+
+
+/*Outputs a symbol, with a carry bit.
+  If there is a potential to propogate a carry over several symbols, they are
+   buffered until it can be determined whether or not an actual carry will
+   occur.
+  If the counter for the buffered symbols overflows, then the range is
+   truncated to force a carry to occur, towards whichever side maximizes the
+   remaining range.*/
+static void ec_enc_carry_out(ec_enc *_this,int _c){
+  if(_c!=EC_SYM_MAX){
+    /*No further carry propogation possible, flush buffer.*/
+    int carry;
+    carry=_c>>EC_SYM_BITS;
+    /*Don't output a byte on the first write.
+      This compare should be taken care of by branch-prediction thereafter.*/
+    if(_this->rem>=0)ec_byte_write1(_this->buf,_this->rem+carry);
+    if(_this->ext>0){
+      unsigned sym;
+      sym=EC_SYM_MAX+carry&EC_SYM_MAX;
+      do ec_byte_write1(_this->buf,sym);
+      while(--(_this->ext)>0);
+    }
+    _this->rem=_c&EC_SYM_MAX;
+  }
+  else _this->ext++;
+}
+
+static void ec_enc_normalize(ec_enc *_this){
+  /*If the range is too small, output some bits and rescale it.*/
+  while(_this->rng<=EC_CODE_BOT){
+    ec_enc_carry_out(_this,(int)(_this->low>>EC_CODE_SHIFT));
+    /*Move the next-to-high-order symbol into the high-order position.*/
+    _this->low=_this->low<<EC_SYM_BITS&EC_CODE_TOP-1;
+    _this->rng<<=EC_SYM_BITS;
+  }
+}
+
+void ec_enc_init(ec_enc *_this,ec_byte_buffer *_buf){
+  _this->buf=_buf;
+  _this->rem=-1;
+  _this->ext=0;
+  _this->low=0;
+  _this->rng=EC_CODE_TOP;
+}
+
+void ec_encode(ec_enc *_this,unsigned _fl,unsigned _fh,unsigned _ft){
+  unsigned r;
+  unsigned s;
+  r=_this->rng/_ft;
+  if(_fl>0){
+    s=r*(_ft-_fl);
+    _this->low+=_this->rng-s;
+    _this->rng=r*(_fh-_fl);
+  }
+  else _this->rng-=r*(_ft-_fh);
+  ec_enc_normalize(_this);
+}
+
+void ec_enc_done(ec_enc *_this){
+  /*We compute the integer in the current interval that has the largest number
+     of trailing zeros, and write that to the stream.
+    This is guaranteed to yield the smallest possible encoding.*/
+  if(_this->low){
+    unsigned end;
+    end=EC_CODE_TOP;
+    /*Ensure that the end value is in the range.*/
+    if(end-_this->low>=_this->rng){
+      unsigned msk;
+      msk=EC_CODE_TOP-1;
+      do{
+        msk>>=1;
+        end=(_this->low+msk)&~msk|msk+1;
+      }
+      while(end-_this->low>=_this->rng);
+    }
+    /*The remaining output is the next free end.*/
+    while(end){
+      ec_enc_carry_out(_this,end>>EC_CODE_SHIFT);
+      end=end<<EC_SYM_BITS&EC_CODE_TOP-1;
+    }
+  }
+  /*If we have a buffered byte...*/
+  if(_this->rem>=0){
+    unsigned char *p;
+    unsigned char *buf;
+    /*Flush it into the output buffer.*/
+    ec_enc_carry_out(_this,0);
+    /*We may be able to drop some redundant bytes from the end.*/
+    buf=ec_byte_get_buffer(_this->buf);
+    p=buf+ec_byte_bytes(_this->buf)-1;
+    /*Strip trailing zeros.*/
+    while(p>=buf&&!p[0])p--;
+    /*Strip one trailing EC_FOF_RSV1 byte if the buffer ends in a string of
+       consecutive EC_FOF_RSV1 bytes preceded by one (or more) zeros.*/
+    if(p>buf&&p[0]==EC_FOF_RSV1){
+      unsigned char *q;
+      q=p;
+      do q--;
+      while(q>buf&&q[0]==EC_FOF_RSV1);
+      if(!q[0])p--;
+    }
+    ec_byte_writetrunc(_this->buf,p+1-buf);
+  }
+}