ref: c35883d74bafa558e145643a35c18d9aad6deb3a
parent: e4475871fbfd903d4b28e34ba3847b0d95cb6be8
author: Jean-Marc Valin <[email protected]>
date: Mon Feb 11 05:16:31 EST 2008
Remove multiplier-free version since we don't need it
--- a/libcelt/mfrngdec.c
+++ /dev/null
@@ -1,271 +1,0 @@
-#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="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 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().*/
-}
-
-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
--- a/libcelt/mfrngenc.c
+++ /dev/null
@@ -1,175 +1,0 @@
-#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://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 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);
-}
-
-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;
- }
-}