Remove multiplier-free version since we don't need it
This commit is contained in:
Jean-Marc Valin
parent
e4475871fb
commit
c35883d74b
2 changed files with 0 additions and 446 deletions
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@ -1,271 +0,0 @@
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#include <stddef.h>
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#include "entdec.h"
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#include "mfrngcod.h"
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/*A multiply-free range decoder.
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This is an entropy decoder based upon \cite{Mar79}, which is itself a
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rediscovery of the FIFO arithmetic code introduced by \cite{Pas76}.
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It is very similar to arithmetic encoding, except that encoding is done with
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digits in any base, instead of with bits, and so it is faster when using
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larger bases (i.e.: a byte).
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The author claims an average waste of $\frac{1}{2}\log_b(2b)$ bits, where $b$
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is the base, longer than the theoretical optimum, but to my knowledge there
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is no published justification for this claim.
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This only seems true when using near-infinite precision arithmetic so that
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the process is carried out with no rounding errors.
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IBM (the author's employer) never sought to patent the idea, and to my
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knowledge the algorithm is unencumbered by any patents, though its
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performance is very competitive with proprietary arithmetic coding.
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The two are based on very similar ideas, however.
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An excellent description of implementation details is available at
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http://www.arturocampos.com/ac_range.html
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A recent work \cite{MNW98} which proposes several changes to arithmetic
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encoding for efficiency actually re-discovers many of the principles
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behind range encoding, and presents a good theoretical analysis of them.
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The coder is made multiply-free by replacing the standard multiply/divide
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used to partition the current interval according to the total frequency
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count.
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The new partition function scales the count so that it differs from the size
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of the interval by no more than a factor of two and then assigns each symbol
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one or two code words in the interval.
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For details see \cite{SM98}.
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This coder also handles the end of the stream in a slightly more graceful
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fashion than most arithmetic or range coders.
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Once the final symbol has been encoded, the coder selects the code word with
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the shortest number of bits that still falls within the final interval.
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This method is not novel.
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Here, by the length of the code word, we refer to the number of bits until
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its final 1.
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Any trailing zeros may be discarded, since the encoder, once it runs out of
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input, will pad its buffer with zeros.
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But this means that no encoded stream would ever have any zero bytes at the
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end.
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Since there are some coded representations we cannot produce, it implies that
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there is still some redundancy in the stream.
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In this case, we can pick a special byte value, RSV1, and should the stream
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end in a sequence of zeros, followed by the RSV1 byte, we can code the
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zeros, and discard the RSV1 byte.
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The decoder, knowing that the encoder would never produce a sequence of zeros
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at the end, would then know to add in the RSV1 byte if it observed it.
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Now, the encoder would never produce a stream that ended in a sequence of
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zeros followed by a RSV1 byte.
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So, if the stream ends in a non-empty sequence of zeros, followed by any
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positive number of RSV1 bytes, the last RSV1 byte is discarded.
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The decoder, if it encounters a stream that ends in non-empty sequence of
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zeros followed by any non-negative number of RSV1 bytes, adds an additional
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RSV1 byte to the stream.
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With this strategy, every possible sequence of input bytes is transformed to
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one that could actually be produced by the encoder.
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The only question is what non-zero value to use for RSV1.
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We select 0x80, since it has the nice property of producing the shortest
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possible byte streams when using our strategy for selecting a number within
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the final interval to encode.
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Clearly if the shortest possible code word that falls within the interval has
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its last one bit as the most significant bit of the final byte, and the
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previous bytes were a non-empty sequence of zeros followed by a non-negative
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number of 0x80 bytes, then the last byte would be discarded.
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If the shortest code word is not so formed, then no other code word in the
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interval would result in any more bytes being discarded.
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Any longer code word would have an additional one bit somewhere, and so would
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require at a minimum that that byte would be coded.
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If the shortest code word has a 1 before the final one that is preventing the
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stream from ending in a non-empty sequence of zeros followed by a
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non-negative number of 0x80's, then there is no code word of the same length
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which contains that bit as a zero.
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If there were, then we could simply leave that bit a 1, and drop all the bits
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after it without leaving the interval, thus producing a shorter code word.
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In this case, RSV1 can only drop 1 bit off the final stream.
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Other choices could lead to savings of up to 8 bits for particular streams,
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but this would produce the odd situation that a stream with more non-zero
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bits is actually encoded in fewer bytes.
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@PHDTHESIS{Pas76,
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author="Richard Clark Pasco",
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title="Source coding algorithms for fast data compression",
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school="Dept. of Electrical Engineering, Stanford University",
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address="Stanford, CA",
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month=May,
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year=1976
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}
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@INPROCEEDINGS{Mar79,
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author="Martin, G.N.N.",
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title="Range encoding: an algorithm for removing redundancy from a digitised
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message",
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booktitle="Video & Data Recording Conference",
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year=1979,
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address="Southampton",
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month=Jul
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}
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@ARTICLE{MNW98,
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author="Alistair Moffat and Radford Neal and Ian H. Witten",
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title="Arithmetic Coding Revisited",
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journal="{ACM} Transactions on Information Systems",
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year=1998,
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volume=16,
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number=3,
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pages="256--294",
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month=Jul,
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URL="http://www.stanford.edu/class/ee398/handouts/papers/Moffat98ArithmCoding.pdf"
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}
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@INPROCEEDINGS{SM98,
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author="Lang Stuiver and Alistair Moffat",
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title="Piecewise Integer Mapping for Arithmetic Coding",
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booktitle="Proceedings of the {IEEE} Data Compression Conference",
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pages="1--10",
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address="Snowbird, UT",
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month="Mar./Apr.",
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year=1998
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}*/
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/*Gets the next byte of input.
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After all the bytes in the current packet have been consumed, and the extra
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end code returned if needed, this function will continue to return zero each
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time it is called.
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Return: The next byte of input.*/
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static int ec_dec_in(ec_dec *_this){
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int ret;
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ret=ec_byte_read1(_this->buf);
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if(ret<0){
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ret=0;
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/*Needed to make sure the above conditional only triggers once, and to keep
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oc_dec_tell() operating correctly.*/
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ec_byte_adv1(_this->buf);
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}
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return ret;
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}
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/*Normalizes the contents of dif and rng so that rng lies entirely in the
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high-order symbol.*/
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static void ec_dec_normalize(ec_dec *_this){
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/*If the range is too small, rescale it and input some bits.*/
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while(_this->rng<=EC_CODE_BOT){
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int sym;
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_this->rng<<=EC_SYM_BITS;
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/*Use up the remaining bits from our last symbol.*/
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sym=_this->rem<<EC_CODE_EXTRA&EC_SYM_MAX;
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/*Read the next value from the input.*/
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_this->rem=ec_dec_in(_this);
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/*Take the rest of the bits we need from this new symbol.*/
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sym|=_this->rem>>EC_SYM_BITS-EC_CODE_EXTRA;
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_this->dif=(_this->dif<<EC_SYM_BITS)+sym&EC_CODE_MASK;
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/*dif can never be larger than EC_CODE_TOP.
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This is equivalent to the slightly more readable:
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if(_this->dif>EC_CODE_TOP)_this->dif-=EC_CODE_TOP;*/
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_this->dif^=_this->dif&_this->dif-1&EC_CODE_TOP;
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}
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}
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void ec_dec_init(ec_dec *_this,ec_byte_buffer *_buf){
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_this->buf=_buf;
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_this->rem=ec_dec_in(_this);
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_this->rng=1U<<EC_CODE_EXTRA;
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_this->dif=_this->rem>>EC_SYM_BITS-EC_CODE_EXTRA;
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/*Normalize the interval.*/
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ec_dec_normalize(_this);
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}
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unsigned ec_decode(ec_dec *_this,unsigned _ft){
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unsigned d;
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/*Step 1: Compute the normalization factor for the frequency counts.*/
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_this->nrm=EC_ILOG(_this->rng)-EC_ILOG(_ft);
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_ft<<=_this->nrm;
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d=_ft>_this->rng;
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_ft>>=d;
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_this->nrm-=d;
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/*Step 2: invert the partition function.*/
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d=_this->rng-_ft;
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return EC_MAXI((int)(_this->dif>>1),(int)(_this->dif-d))>>_this->nrm;
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/*Step 3: The caller locates the range [fl,fh) containing the return value
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and calls ec_dec_update().*/
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}
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void ec_dec_update(ec_dec *_this,unsigned _fl,unsigned _fh,unsigned _ft){
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unsigned r;
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unsigned s;
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unsigned d;
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/*Step 4: Evaluate the two partition function values.*/
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_fl<<=_this->nrm;
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_fh<<=_this->nrm;
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_ft<<=_this->nrm;
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d=_this->rng-_ft;
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r=_fh+EC_MINI(_fh,d);
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s=_fl+EC_MINI(_fl,d);
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/*Step 5: Update the interval.*/
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_this->rng=r-s;
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_this->dif-=s;
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/*Step 6: Normalize the interval.*/
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ec_dec_normalize(_this);
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}
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long ec_dec_tell(ec_dec *_this,int _b){
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ec_uint32 r;
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int l;
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long nbits;
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nbits=ec_byte_bytes(_this->buf)-(EC_CODE_BITS+EC_SYM_BITS-1)/EC_SYM_BITS<<3;
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/*To handle the non-integral number of bits still left in the encoder state,
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we compute the number of bits of low that must be encoded to ensure that
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the value is inside the range for any possible subsequent bits.
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Note that this is subtly different than the actual value we would end the
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stream with, which tries to make as many of the trailing bits zeros as
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possible.*/
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nbits+=EC_CODE_BITS;
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nbits<<=_b;
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l=EC_ILOG(_this->rng);
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r=_this->rng>>l-16;
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while(_b-->0){
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int b;
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r=r*r>>15;
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b=(int)(r>>16);
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l=l<<1|b;
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r>>=b;
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}
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return nbits-l;
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}
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#if 0
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int ec_dec_done(ec_dec *_this){
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unsigned low;
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int ret;
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/*Check to make sure we've used all the input bytes.
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This ensures that no more ones would ever be inserted into the decoder.*/
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if(_this->buf->ptr-ec_byte_get_buffer(_this->buf)<=
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ec_byte_bytes(_this->buf)){
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return 0;
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}
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/*We compute the smallest finitely odd fraction that fits inside the current
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range, and write that to the stream.
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This is guaranteed to yield the smallest possible encoding.*/
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/*TODO: Fix this line, as it is wrong.
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It doesn't seem worth being able to make this check to do an extra
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subtraction for every symbol decoded.*/
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low=/*What we want: _this->top-_this->rng; What we have:*/_this->dif
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if(low){
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unsigned end;
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end=EC_CODE_TOP;
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/*Ensure that the next free end is in the range.*/
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if(end-low>=_this->rng){
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unsigned msk;
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msk=EC_CODE_TOP-1;
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do{
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msk>>=1;
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end=low+msk&~msk|msk+1;
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}
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while(end-low>=_this->rng);
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}
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/*The remaining input should have been the next free end.*/
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return end-low!=_this->dif;
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}
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return 1;
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}
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#endif
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#include <stddef.h>
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#include "entenc.h"
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#include "mfrngcod.h"
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/*A multiply-free range encoder.
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See mfrngdec.c and the references for implementation details
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\cite{Mar79,MNW98,SM98}.
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@INPROCEEDINGS{Mar79,
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author="Martin, G.N.N.",
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title="Range encoding: an algorithm for removing redundancy from a digitised
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message",
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booktitle="Video \& Data Recording Conference",
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year=1979,
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address="Southampton",
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month=Jul
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}
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@ARTICLE{MNW98,
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author="Alistair Moffat and Radford Neal and Ian H. Witten",
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title="Arithmetic Coding Revisited",
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journal="{ACM} Transactions on Information Systems",
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year=1998,
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volume=16,
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number=3,
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pages="256--294",
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month=Jul,
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URL="http://www.stanford.edu/class/ee398/handouts/papers/Moffat98ArithmCoding.pdf"
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}
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@INPROCEEDINGS{SM98,
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author="Lang Stuiver and Alistair Moffat",
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title="Piecewise Integer Mapping for Arithmetic Coding",
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booktitle="Proceedings of the {IEEE} Data Compression Conference",
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pages="1--10",
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address="Snowbird, UT",
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month="Mar./Apr.",
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year=1998
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}*/
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/*Outputs a symbol, with a carry bit.
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If there is a potential to propagate a carry over several symbols, they are
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buffered until it can be determined whether or not an actual carry will
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occur.
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If the counter for the buffered symbols overflows, then the stream becomes
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undecodable.
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This gives a theoretical limit of a few billion symbols in a single packet on
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32-bit systems.
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The alternative is to truncate the range in order to force a carry, but
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requires similar carry tracking in the decoder, needlessly slowing it down.*/
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static void ec_enc_carry_out(ec_enc *_this,int _c){
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if(_c!=EC_SYM_MAX){
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/*No further carry propagation possible, flush buffer.*/
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int carry;
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carry=_c>>EC_SYM_BITS;
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/*Don't output a byte on the first write.
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This compare should be taken care of by branch-prediction thereafter.*/
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if(_this->rem>=0)ec_byte_write1(_this->buf,_this->rem+carry);
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if(_this->ext>0){
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unsigned sym;
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sym=EC_SYM_MAX+carry&EC_SYM_MAX;
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do ec_byte_write1(_this->buf,sym);
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while(--(_this->ext)>0);
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}
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_this->rem=_c&EC_SYM_MAX;
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}
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else _this->ext++;
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}
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static void ec_enc_normalize(ec_enc *_this){
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/*If the range is too small, output some bits and rescale it.*/
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while(_this->rng<=EC_CODE_BOT){
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ec_enc_carry_out(_this,(int)(_this->low>>EC_CODE_SHIFT));
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/*Move the next-to-high-order symbol into the high-order position.*/
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_this->low=_this->low<<EC_SYM_BITS&EC_CODE_TOP-1;
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_this->rng<<=EC_SYM_BITS;
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}
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}
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void ec_enc_init(ec_enc *_this,ec_byte_buffer *_buf){
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_this->buf=_buf;
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_this->rem=-1;
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_this->ext=0;
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_this->low=0;
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|
||||||
_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);
|
|
||||||
}
|
|
||||||
|
|
||||||
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){
|
|
||||||
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 flush it into the output buffer.*/
|
|
||||||
if(_this->rem>=0){
|
|
||||||
ec_enc_carry_out(_this,0);
|
|
||||||
_this->rem=-1;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue