ref: 56cb5cf31fcff1d5dcdaa51b8b6c6603657d9c1a
parent: dffd9449b5cdf2833af293c8d18aedebb6eb8728
author: Jean-Marc Valin <[email protected]>
date: Fri Oct 17 17:27:21 EDT 2008
Multiply-free version of the range coder. Haven't yet decided which version to use.
--- /dev/null
+++ b/libcelt/mfrngdec.c
@@ -1,0 +1,278 @@
+#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 make sure the above conditional only triggers once, and 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){+ unsigned d;
+ /*Step 1: Compute the normalization factor for the frequency counts.*/
+ _this->nrm=EC_ILOG(_this->rng)-EC_ILOG(_ft);
+ _ft<<=_this->nrm;
+ d=_ft>_this->rng;
+ _ft>>=d;
+ _this->nrm-=d;
+ /*Step 2: invert the partition function.*/
+ d=_this->rng-_ft;
+ return EC_MAXI((int)(_this->dif>>1),(int)(_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){+ unsigned r;
+ unsigned s;
+ unsigned d;
+ /*Step 4: Evaluate the two partition function values.*/
+ _fl<<=_this->nrm;
+ _fh<<=_this->nrm;
+ _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<<3;
+ /*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
--- /dev/null
+++ b/libcelt/mfrngenc.c
@@ -1,0 +1,183 @@
+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#include "arch.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://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
+ }*/
+
+
+
+/*Outputs a symbol, with a carry bit.
+ If there is a potential to propagate 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 stream becomes
+ undecodable.
+ This gives a theoretical limit of a few billion symbols in a single packet on
+ 32-bit systems.
+ The alternative is to truncate the range in order to force a carry, but
+ requires similar carry tracking in the decoder, needlessly slowing it down.*/
+static void ec_enc_carry_out(ec_enc *_this,int _c){+ if(_c!=EC_SYM_MAX){+ /*No further carry propagation 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 inline 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;
+ unsigned d;
+ int nrm;
+ /*Step 1: we want ft in the range of [rng/2,rng).
+ The high-order bits of the rng and ft are computed via a logarithm.
+ This could also be done on some architectures with some custom assembly,
+ which would provide even more speed.*/
+ nrm=EC_ILOG(_this->rng)-EC_ILOG(_ft);
+ /*Having the same high order bit may be too much.
+ We may need to shift one less to ensure that ft is actually in the proper
+ range.*/
+ _ft<<=nrm;
+ d=_ft>_this->rng;
+ _ft>>=d;
+ nrm-=d;
+ /*We then scale everything by the computed power of 2.*/
+ _fl<<=nrm;
+ _fh<<=nrm;
+ /*Step 2: compute the two values of the partition function.
+ d is the splitting point of the interval [0,ft).*/
+ d=_this->rng-_ft;
+ r=_fh+EC_MINI(_fh,d);
+ s=_fl+EC_MINI(_fl,d);
+ /*Step 3: Update the end-point and range of the interval.*/
+ _this->low+=s;
+ _this->rng=r-s;
+ /*Step 4: Normalize the interval.*/
+ ec_enc_normalize(_this);
+}
+
+void ec_encode_bin(ec_enc *_this,unsigned _fl,unsigned _fh,unsigned bits){+ ec_encode(_this, _fl, _fh, 1U<<bits);
+}
+
+long ec_enc_tell(ec_enc *_this,int _b){+ ec_uint32 r;
+ int l;
+ long nbits;
+ nbits=ec_byte_bytes(_this->buf)+(_this->rem>=0)+_this->ext<<3;
+ /*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;
+}
+
+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){+ ec_uint32 end;
+ end=EC_CODE_TOP;
+ /*Ensure that the end value is in the range.*/
+ if(end-_this->low>=_this->rng){+ ec_uint32 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 flush it into the output buffer.*/
+ if(_this->rem>0||_this->ext>0){+ ec_enc_carry_out(_this,0);
+ _this->rem=-1;
+ }
+}