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Mark Harris
Opus
Commits
56cb5cf3
Commit
56cb5cf3
authored
Oct 17, 2008
by
JeanMarc Valin
Browse files
Multiplyfree version of the range coder. Haven't yet decided which version to
use.
parent
dffd9449
Changes
2
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libcelt/mfrngdec.c
0 → 100644
View file @
56cb5cf3
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "arch.h"
#include "entdec.h"
#include "mfrngcod.h"
/*A multiplyfree 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 nearinfinite 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 rediscovers many of the principles
behind range encoding, and presents a good theoretical analysis of them.
The coder is made multiplyfree 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 nonempty 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 nonempty sequence of
zeros followed by any nonnegative 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 nonzero 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 nonempty sequence of zeros followed by a nonnegative
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 nonempty sequence of zeros followed by a
nonnegative 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 nonzero
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="256294",
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="110",
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
highorder 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 nonintegral 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>ptrec_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(endlow>=_this>rng){
unsigned msk;
msk=EC_CODE_TOP1;
do{
msk>>=1;
end=low+msk&~mskmsk+1;
}
while(endlow>=_this>rng);
}
/*The remaining input should have been the next free end.*/
return endlow!=_this>dif;
}
return 1;
}
#endif
libcelt/mfrngenc.c
0 → 100644
View file @
56cb5cf3
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "arch.h"
#include "entenc.h"
#include "mfrngcod.h"
/*A multiplyfree 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="256294",
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="110",
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
32bit 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 branchprediction 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 nexttohighorder symbol into the highorder 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 highorder 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 endpoint 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 nonintegral 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
;
}
}
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