<commit_before><?xml version='1.0'?>
<!DOCTYPE rfc SYSTEM 'rfc2629.dtd'>
<?rfc toc="yes" symrefs="yes" ?>

<rfc ipr="trust200902" category="std" docName="draft-ietf-codec-opus-02">

<front>
<title abbrev="Interactive Audio Codec">Definition of the Opus Audio Codec</title>


<author initials="JM" surname="Valin" fullname="<NAME>">
<organization>Octasic Inc.</organization>
<address>
<postal>
<street>4101, Molson Street</street>
<city>Montreal</city>
<region>Quebec</region>
<code></code>
<country>Canada</country>
</postal>
<phone>+1 514 282-8858</phone>
<email><EMAIL></email>
</address>
</author>

<author initials="K." surname="Vos" fullname="<NAME>">
<organization>Skype Technologies S.A.</organization>
<address>
<postal>
<street>Stadsgarden 6</street>
<city>Stockholm</city>
<region></region>
<code>11645</code>
<country>SE</country>
</postal>
<phone>+46 855 921 989</phone>
<email><EMAIL></email>
</address>
</author>


<date day="14" month="November" year="2010" />

<area>General</area>

<workgroup></workgroup>

<abstract>
<t>
This document describes the Opus codec, designed for interactive speech and audio 
transmission over the Internet.
</t>
</abstract>
</front>

<middle>

<section anchor="introduction" title="Introduction">
<t>
We propose the Opus codec based on a linear prediction layer (LP) and an
MDCT-based enhancement layer. The main idea behind the proposal is that
the speech low frequencies are usually more efficiently coded using
linear prediction codecs (such as CELP variants), while the higher frequencies
are more efficiently coded in the transform domain (e.g. MDCT). For low 
sampling rates, the MDCT layer is not useful and only the LP-based layer is
used. On the other hand, non-speech signals are not always adequately coded
using linear prediction, so for music only the MDCT-based layer is used.
</t>

<t>
In this proposed prototype, the LP layer is based on the 
<eref target='http://developer.skype.com/silk'>SILK</eref> codec 
<xref target="SILK"></xref> and the MDCT layer is based on the 
<eref target='http://www.celt-codec.org/'>CELT</eref>  codec
 <xref target="CELT"></xref>.
</t>

<t>This is a work in progress.</t>
</section>

<section anchor="hybrid" title="Opus Codec">

<t>
In hybrid mode, each frame is coded first by the LP layer and then by the MDCT 
layer. In the current prototype, the cutoff frequency is 8 kHz. In the MDCT
layer, all bands below 8 kHz are discarded, such that there is no coding
redundancy between the two layers. Also both layers use the same instance of 
the range coder to encode the signal, which ensures that no "padding bits" are
wasted. The hybrid approach makes it easy to support both constant bit-rate
(CBR) and varaible bit-rate (VBR) coding. Although the SILK layer used is VBR,
it is easy to make the bit allocation of the CELT layer produce a final stream
that is CBR by using all the bits left unused by the SILK layer.
</t>

<t>The implementation of SILK-based LP layer is similar to the description in
the <xref target="SILK">SILK Internet-Draft</xref> with the main exception that 
SILK was modified to 
use the same range coder as CELT. The implementation of the CELT-based MDCT
layer is available from the CELT website and is a more recent version (0.8.1) 
of the <xref target="CELT">CELT Internet-Draft</xref>. 
The main changes
include better support for 20 ms frames as well as the ability to encode 
only the higher bands using a range coder partially filled by the SILK layer.</t>

<t>
In addition to their frame size, the SILK and CELT codecs require
a look-ahead of 5.2 ms and 2.5 ms, respectively. SILK's look-ahead is due to
noise shaping estimation (5 ms) and the internal resampling (0.2 ms), while
CELT's look-ahead is due to the overlapping MDCT windows. To compensate for the
difference, the CELT encoder input is delayed by 2.7 ms. This ensures that low
frequencies and high frequencies arrive at the same time.
</t>


<section title="Source Code">
<t>
The source code is currently available in a
<eref target='git://git.xiph.org/users/jm/ietfcodec.git'>Git repository</eref> 
which references two other
repositories (for SILK and CELT). Some snapshots are provided for 
convenience at <eref target='http://people.xiph.org/~jm/ietfcodec/'/> along
with sample files.
Although the build system is very primitive, some instructions are provided 
in the toplevel README file.
This is very early development so both the quality and feature set should
greatly improve over time. In the current version, only 48 kHz audio is 
supported, but support for all configurations listed in 
<xref target="modes"></xref> is planned. 
</t>
</section>

</section>

<section anchor="modes" title="Codec Modes">
<t>
There are three possible operating modes for the proposed prototype:
<list style="numbers">
<t>A linear prediction (LP) mode for use in low bit-rate connections with up to 8 kHz audio bandwidth (16 kHz sampling rate)</t>
<t>A hybrid (LP+MDCT) mode for full-bandwidth speech at medium bitrates</t>
<t>An MDCT-only mode for very low delay speech transmission as well as music transmission.</t>
</list>
Each of these modes supports a number of difference frame sizes and sampling
rates. In order to distinguish between the various modes and configurations,
we need to define a simple header that can used in the transport layer 
(e.g RTP) to signal this information. The following describes the proposed
header.
</t>

<t>
The LP mode supports the following configurations (numbered from 00000...01011 in binary):
<list style="symbols">
<t>8 kHz:  10, 20, 40, 60 ms (00000...00011)</t>
<t>12 kHz: 10, 20, 40, 60 ms (00100...00111)</t>
<t>16 kHz: 10, 20, 40, 60 ms (01000...01011)</t>
</list>
for a total of 12 configurations.
</t>

<t>
The hybrid mode supports the following configurations (numbered from 01100...01111):
<list style="symbols">
<t>32 kHz: 10, 20 ms (01100...01101)</t>
<t>48 kHz: 10, 20 ms (01110...01111)</t>
</list>
for a total of 4 configurations.
</t>

<t>
The MDCT-only mode supports the following configurations (numbered from 10000...11101):
<list style="symbols">
<t>8 kHz:  2.5, 5, 10, 20 ms (10000...10011)</t>
<t>16 kHz: 2.5, 5, 10, 20 ms (10100...10111)</t>
<t>32 kHz: 2.5, 5, 10, 20 ms (11000...11011)</t>
<t>48 kHz: 2.5, 5, 10, 20 ms (11100...11111)</t>
</list>
for a total of 16 configurations.
</t>

<t>
There is thus a total of 32 configurations, so 5 bits are necessary to 
indicate the mode, frame size and sampling rate (MFS). This leaves 3 bits for the number of frames per packets (codes 0 to 7):
<list style="symbols">
<t>0-2:  1-3 frames in the packet, each with equal compressed size</t>
<t>3:    arbitrary number of frames in the packet, each with equal compressed size (one size needs to be encoded)</t>
<t>4-5:  2-3 frames in the packet, with different compressed sizes, which need to be encoded (except the last one)</t>
<t>6:    arbitrary number of frames in the packet, with different compressed sizes, each of which needs to be encoded</t>
<t>7:    The first frame has this MFS, but others have different MFS. Each compressed size needs to be encoded.</t>
</list>
When code 7 is used and the last frames of a packet have the same MFS, it is 
allowed to switch to another code for them.
</t>

<t>
The compressed size of the frames (if needed) is indicated -- usually -- with one byte, with the following meaning:
<list style="symbols">
<t>0:          No frame (DTX or lost packet)</t>
<t>1-251:    Size of the frame in bytes</t>
<t>252-255: A second byte is needed. The total size is (size[1]*4)+(size[0]%4)+252</t>
</list>
</t>

<t>
The maximum size representable is 255*4+3+252=1275 bytes. For 20 ms frames, that 
represents a bit-rate of 510 kb/s, which is really the highest rate anyone would want 
to use in stereo mode (beyond that point, lossless codecs would be more appropriate).
</t>

<section anchor="examples" title="Examples">
<t>
Simplest case: one packet
</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   MFS   |0|0|0|               compressed data...              |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>

<t>
Four frames of the same compressed size:
</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   MFS   |0|1|1|               compressed data...              |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>

<t>
Two frames of different compressed size:
</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   MFS   |1|0|1|   frame size  |        compressed data...     |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>

<t>
Three frames of different <spanx style="emph">durations</spanx>:

</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 1st MFS |1|1|1|   frame size  | 2nd MFS |1|1|1|   frame size  |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 3rd MFS |1|1|1|   frame size  |      compressed data...       |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>
</section>


</section>

<section title="Codec Encoder">
<t>
Opus encoder block diagram.
</t>

<section anchor="range-encoder" title="Range Coder">
<t>
Opus uses an entropy coder based upon <xref target="range-coding"></xref>, 
which is itself a rediscovery of the FIFO arithmetic code introduced by <xref target="coding-thesis"></xref>.
It is very similar to arithmetic encoding, except that encoding is done with
digits in any base instead of with bits, 
so it is faster when using larger bases (i.e.: an octet). All of the
calculations in the range coder must use bit-exact integer arithmetic.
</t>

<t>
The range coder also acts as the bit-packer for Opus. It is
used in three different ways, to encode:
<list style="symbols">
<t>entropy-coded symbols with a fixed probability model using ec_encode(), (rangeenc.c)</t>
<t>integers from 0 to 2^M-1 using ec_enc_uint() or ec_enc_bits(), (entenc.c)</t>
<t>integers from 0 to N-1 (where N is not a power of two) using ec_enc_uint(). (entenc.c)</t>
</list>
</t>

<t>
The range encoder maintains an internal state vector composed of the
four-tuple (low,rng,rem,ext), representing the low end of the current
range, the size of the current range, a single buffered output octet,
and a count of additional carry-propagating output octets. Both rng
and low are 32-bit unsigned integer values, rem is an octet value or
the special value -1, and ext is an integer with at least 16 bits.
This state vector is initialized at the start of each each frame to
the value (0,2^31,-1,0).
</t>

<t>
Each symbol is drawn from a finite alphabet and coded in a separate
context which describes the size of the alphabet and the relative
frequency of each symbol in that alphabet. Opus only uses static
contexts; they are not adapted to the statistics of the data that is
coded.
</t>

<section anchor="encoding-symbols" title="Encoding Symbols">
<t>
   The main encoding function is ec_encode() (rangeenc.c),
   which takes as an argument a three-tuple (fl,fh,ft)
   describing the range of the symbol to be encoded in the current
   context, with 0 &lt;= fl &lt; fh &lt;= ft &lt;= 65535. The values of this tuple
   are derived from the probability model for the symbol. Let f(i) be
   the frequency of the ith symbol in the current context. Then the
   three-tuple corresponding to the kth symbol is given by
   <![CDATA[
fl=sum(f(i),i<k), fh=fl+f(i), and ft=sum(f(i)).
]]>
</t>
<t>
   ec_encode() updates the state of the encoder as follows. If fl is
   greater than zero, then low = low + rng - (rng/ft)*(ft-fl) and 
   rng = (rng/ft)*(fh-fl). Otherwise, low is unchanged and
   rng = rng - (rng/ft)*(fh-fl). The divisions here are exact integer
   division. After this update, the range is normalized.
</t>
<t>
   To normalize the range, the following process is repeated until
   rng > 2^23. First, the top 9 bits of low, (low>>23), are placed into
   a carry buffer. Then, low is set to <![CDATA[(low << 8 & 0x7FFFFFFF) and rng
   is set to (rng<<8)]]>. This process is carried out by
   ec_enc_normalize() (rangeenc.c).
</t>
<t>
   The 9 bits produced in each iteration of the normalization loop
   consist of 8 data bits and a carry flag. The final value of the
   output bits is not determined until carry propagation is accounted
   for. Therefore the reference implementation buffers a single
   (non-propagating) output octet and keeps a count of additional
   propagating (0xFF) output octets. An implementation MAY choose to use
   any mathematically equivalent scheme to perform carry propagation.
</t>
<t>
   The function ec_enc_carry_out() (rangeenc.c) performs
   this buffering. It takes a 9-bit input value, c, from the normalization
   8-bit output and a carry bit. If c is 0xFF, then ext is incremented
   and no octets are output. Otherwise, if rem is not the special value
   -1, then the octet (rem+(c>>8)) is output. Then ext octets are output
   with the value 0 if the carry bit is set, or 0xFF if it is not, and
   rem is set to the lower 8 bits of c. After this, ext is set to zero.
</t>
<t>
   In the reference implementation, a special version of ec_encode()
   called ec_encode_bin() (rangeenc.c) is defined to
   take a two-tuple (fl,ftb), where <![CDATA[0 <= fl < 2^ftb and ftb < 16. It is
   mathematically equivalent to calling ec_encode() with the three-tuple
   (fl,fl+1,1<<ftb)]]>, but avoids using division.

</t>
</section>

<section anchor="encoding-ints" title="Encoding Uniformly Distributed Integers">
<t>
   Functions ec_enc_uint() or ec_enc_bits() are based on ec_encode() and 
   encode one of N equiprobable symbols, each with a frequency of 1,
   where N may be as large as 2^32-1. Because ec_encode() is limited to
   a total frequency of 2^16-1, this is done by encoding a series of
   symbols in smaller contexts.
</t>
<t>
   ec_enc_bits() (entenc.c) is defined, like
   ec_encode_bin(), to take a two-tuple (fl,ftb), with <![CDATA[0 <= fl < 2^ftb
   and ftb < 32. While ftb is greater than 8, it encodes bits (ftb-8) to
   (ftb-1) of fl, e.g., (fl>>ftb-8&0xFF) using ec_encode_bin() and
   subtracts 8 from ftb. Then, it encodes the remaining bits of fl, e.g.,
   (fl&(1<<ftb)-1)]]>, again using ec_encode_bin().
</t>
<t>
   ec_enc_uint() (entenc.c) takes a two-tuple (fl,ft),
   where ft is not necessarily a power of two. Let ftb be the location
   of the highest 1 bit in the two's-complement representation of
   (ft-1), or -1 if no bits are set. If ftb>8, then the top 8 bits of fl
   are encoded using ec_encode() with the three-tuple
   (fl>>ftb-8,(fl>>ftb-8)+1,(ft-1>>ftb-8)+1), and the remaining bits
   are encoded with ec_enc_bits using the two-tuple
   <![CDATA[(fl&(1<<ftb-8)-1,ftb-8). Otherwise, fl is encoded with ec_encode()
   directly using the three-tuple (fl,fl+1,ft)]]>.
</t>
</section>

<section anchor="encoder-finalizing" title="Finalizing the Stream">
<t>
   After all symbols are encoded, the stream must be finalized by
   outputting a value inside the current range. Let end be the integer
   in the interval [low,low+rng) with the largest number of trailing
   zero bits. Then while end is not zero, the top 9 bits of end, e.g.,
   <![CDATA[(end>>23), are sent to the carry buffer, and end is replaced by
   (end<<8&0x7FFFFFFF). Finally, if the value in carry buffer, rem, is]]>
   neither zero nor the special value -1, or the carry count, ext, is
   greater than zero, then 9 zero bits are sent to the carry buffer.
   After the carry buffer is finished outputting octets, the rest of the
   output buffer is padded with zero octets. Finally, rem is set to the
   special value -1. This process is implemented by ec_enc_done()
   (rangeenc.c).
</t>
</section>

<section anchor="encoder-tell" title="Current Bit Usage">
<t>
   The bit allocation routines in Opus need to be able to determine a
   conservative upper bound on the number of bits that have been used
   to encode the current frame thus far. This drives allocation
   decisions and ensures that the range code will not overflow the
   output buffer. This is computed in the reference implementation to
   fractional bit precision by the function ec_enc_tell() 
   (rangeenc.c).
   Like all operations in the range encoder, it must
   be implemented in a bit-exact manner.
</t>
</section>

</section>

<section title="SILK Encoder">
<t>
Copy from SILK draft.
</t>
</section>

<section title="CELT Encoder">
<t>
Copy from CELT draft.
</t>
</section>
<commit_msg>CELT encoder<commit_after><?xml version='1.0'?>
<!DOCTYPE rfc SYSTEM 'rfc2629.dtd'>
<?rfc toc="yes" symrefs="yes" ?>

<rfc ipr="trust200902" category="std" docName="draft-ietf-codec-opus-02">

<front>
<title abbrev="Interactive Audio Codec">Definition of the Opus Audio Codec</title>


<author initials="JM" surname="Valin" fullname="<NAME>">
<organization>Octasic Inc.</organization>
<address>
<postal>
<street>4101, Molson Street</street>
<city>Montreal</city>
<region>Quebec</region>
<code></code>
<country>Canada</country>
</postal>
<phone>+1 514 282-8858</phone>
<email><EMAIL></email>
</address>
</author>

<author initials="K." surname="Vos" fullname="<NAME>">
<organization>Skype Technologies S.A.</organization>
<address>
<postal>
<street>Stadsgarden 6</street>
<city>Stockholm</city>
<region></region>
<code>11645</code>
<country>SE</country>
</postal>
<phone>+46 855 921 989</phone>
<email><EMAIL></email>
</address>
</author>


<date day="14" month="November" year="2010" />

<area>General</area>

<workgroup></workgroup>

<abstract>
<t>
This document describes the Opus codec, designed for interactive speech and audio 
transmission over the Internet.
</t>
</abstract>
</front>

<middle>

<section anchor="introduction" title="Introduction">
<t>
We propose the Opus codec based on a linear prediction layer (LP) and an
MDCT-based enhancement layer. The main idea behind the proposal is that
the speech low frequencies are usually more efficiently coded using
linear prediction codecs (such as CELP variants), while the higher frequencies
are more efficiently coded in the transform domain (e.g. MDCT). For low 
sampling rates, the MDCT layer is not useful and only the LP-based layer is
used. On the other hand, non-speech signals are not always adequately coded
using linear prediction, so for music only the MDCT-based layer is used.
</t>

<t>
In this proposed prototype, the LP layer is based on the 
<eref target='http://developer.skype.com/silk'>SILK</eref> codec 
<xref target="SILK"></xref> and the MDCT layer is based on the 
<eref target='http://www.celt-codec.org/'>CELT</eref>  codec
 <xref target="CELT"></xref>.
</t>

<t>This is a work in progress.</t>
</section>

<section anchor="hybrid" title="Opus Codec">

<t>
In hybrid mode, each frame is coded first by the LP layer and then by the MDCT 
layer. In the current prototype, the cutoff frequency is 8 kHz. In the MDCT
layer, all bands below 8 kHz are discarded, such that there is no coding
redundancy between the two layers. Also both layers use the same instance of 
the range coder to encode the signal, which ensures that no "padding bits" are
wasted. The hybrid approach makes it easy to support both constant bit-rate
(CBR) and varaible bit-rate (VBR) coding. Although the SILK layer used is VBR,
it is easy to make the bit allocation of the CELT layer produce a final stream
that is CBR by using all the bits left unused by the SILK layer.
</t>

<t>The implementation of SILK-based LP layer is similar to the description in
the <xref target="SILK">SILK Internet-Draft</xref> with the main exception that 
SILK was modified to 
use the same range coder as CELT. The implementation of the CELT-based MDCT
layer is available from the CELT website and is a more recent version (0.8.1) 
of the <xref target="CELT">CELT Internet-Draft</xref>. 
The main changes
include better support for 20 ms frames as well as the ability to encode 
only the higher bands using a range coder partially filled by the SILK layer.</t>

<t>
In addition to their frame size, the SILK and CELT codecs require
a look-ahead of 5.2 ms and 2.5 ms, respectively. SILK's look-ahead is due to
noise shaping estimation (5 ms) and the internal resampling (0.2 ms), while
CELT's look-ahead is due to the overlapping MDCT windows. To compensate for the
difference, the CELT encoder input is delayed by 2.7 ms. This ensures that low
frequencies and high frequencies arrive at the same time.
</t>


<section title="Source Code">
<t>
The source code is currently available in a
<eref target='git://git.xiph.org/users/jm/ietfcodec.git'>Git repository</eref> 
which references two other
repositories (for SILK and CELT). Some snapshots are provided for 
convenience at <eref target='http://people.xiph.org/~jm/ietfcodec/'/> along
with sample files.
Although the build system is very primitive, some instructions are provided 
in the toplevel README file.
This is very early development so both the quality and feature set should
greatly improve over time. In the current version, only 48 kHz audio is 
supported, but support for all configurations listed in 
<xref target="modes"></xref> is planned. 
</t>
</section>

</section>

<section anchor="modes" title="Codec Modes">
<t>
There are three possible operating modes for the proposed prototype:
<list style="numbers">
<t>A linear prediction (LP) mode for use in low bit-rate connections with up to 8 kHz audio bandwidth (16 kHz sampling rate)</t>
<t>A hybrid (LP+MDCT) mode for full-bandwidth speech at medium bitrates</t>
<t>An MDCT-only mode for very low delay speech transmission as well as music transmission.</t>
</list>
Each of these modes supports a number of difference frame sizes and sampling
rates. In order to distinguish between the various modes and configurations,
we need to define a simple header that can used in the transport layer 
(e.g RTP) to signal this information. The following describes the proposed
header.
</t>

<t>
The LP mode supports the following configurations (numbered from 00000...01011 in binary):
<list style="symbols">
<t>8 kHz:  10, 20, 40, 60 ms (00000...00011)</t>
<t>12 kHz: 10, 20, 40, 60 ms (00100...00111)</t>
<t>16 kHz: 10, 20, 40, 60 ms (01000...01011)</t>
</list>
for a total of 12 configurations.
</t>

<t>
The hybrid mode supports the following configurations (numbered from 01100...01111):
<list style="symbols">
<t>32 kHz: 10, 20 ms (01100...01101)</t>
<t>48 kHz: 10, 20 ms (01110...01111)</t>
</list>
for a total of 4 configurations.
</t>

<t>
The MDCT-only mode supports the following configurations (numbered from 10000...11101):
<list style="symbols">
<t>8 kHz:  2.5, 5, 10, 20 ms (10000...10011)</t>
<t>16 kHz: 2.5, 5, 10, 20 ms (10100...10111)</t>
<t>32 kHz: 2.5, 5, 10, 20 ms (11000...11011)</t>
<t>48 kHz: 2.5, 5, 10, 20 ms (11100...11111)</t>
</list>
for a total of 16 configurations.
</t>

<t>
There is thus a total of 32 configurations, so 5 bits are necessary to 
indicate the mode, frame size and sampling rate (MFS). This leaves 3 bits for the number of frames per packets (codes 0 to 7):
<list style="symbols">
<t>0-2:  1-3 frames in the packet, each with equal compressed size</t>
<t>3:    arbitrary number of frames in the packet, each with equal compressed size (one size needs to be encoded)</t>
<t>4-5:  2-3 frames in the packet, with different compressed sizes, which need to be encoded (except the last one)</t>
<t>6:    arbitrary number of frames in the packet, with different compressed sizes, each of which needs to be encoded</t>
<t>7:    The first frame has this MFS, but others have different MFS. Each compressed size needs to be encoded.</t>
</list>
When code 7 is used and the last frames of a packet have the same MFS, it is 
allowed to switch to another code for them.
</t>

<t>
The compressed size of the frames (if needed) is indicated -- usually -- with one byte, with the following meaning:
<list style="symbols">
<t>0:          No frame (DTX or lost packet)</t>
<t>1-251:    Size of the frame in bytes</t>
<t>252-255: A second byte is needed. The total size is (size[1]*4)+(size[0]%4)+252</t>
</list>
</t>

<t>
The maximum size representable is 255*4+3+252=1275 bytes. For 20 ms frames, that 
represents a bit-rate of 510 kb/s, which is really the highest rate anyone would want 
to use in stereo mode (beyond that point, lossless codecs would be more appropriate).
</t>

<section anchor="examples" title="Examples">
<t>
Simplest case: one packet
</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   MFS   |0|0|0|               compressed data...              |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>

<t>
Four frames of the same compressed size:
</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   MFS   |0|1|1|               compressed data...              |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>

<t>
Two frames of different compressed size:
</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   MFS   |1|0|1|   frame size  |        compressed data...     |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>

<t>
Three frames of different <spanx style="emph">durations</spanx>:

</t>

<t>
<figure>
<artwork><![CDATA[
 0                   1                   2                   3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 1st MFS |1|1|1|   frame size  | 2nd MFS |1|1|1|   frame size  |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 3rd MFS |1|1|1|   frame size  |      compressed data...       |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
]]></artwork>
</figure>
</t>
</section>


</section>

<section title="Codec Encoder">
<t>
Opus encoder block diagram.
</t>

<section anchor="range-encoder" title="Range Coder">
<t>
Opus uses an entropy coder based upon <xref target="range-coding"></xref>, 
which is itself a rediscovery of the FIFO arithmetic code introduced by <xref target="coding-thesis"></xref>.
It is very similar to arithmetic encoding, except that encoding is done with
digits in any base instead of with bits, 
so it is faster when using larger bases (i.e.: an octet). All of the
calculations in the range coder must use bit-exact integer arithmetic.
</t>

<t>
The range coder also acts as the bit-packer for Opus. It is
used in three different ways, to encode:
<list style="symbols">
<t>entropy-coded symbols with a fixed probability model using ec_encode(), (rangeenc.c)</t>
<t>integers from 0 to 2^M-1 using ec_enc_uint() or ec_enc_bits(), (entenc.c)</t>
<t>integers from 0 to N-1 (where N is not a power of two) using ec_enc_uint(). (entenc.c)</t>
</list>
</t>

<t>
The range encoder maintains an internal state vector composed of the
four-tuple (low,rng,rem,ext), representing the low end of the current
range, the size of the current range, a single buffered output octet,
and a count of additional carry-propagating output octets. Both rng
and low are 32-bit unsigned integer values, rem is an octet value or
the special value -1, and ext is an integer with at least 16 bits.
This state vector is initialized at the start of each each frame to
the value (0,2^31,-1,0).
</t>

<t>
Each symbol is drawn from a finite alphabet and coded in a separate
context which describes the size of the alphabet and the relative
frequency of each symbol in that alphabet. Opus only uses static
contexts; they are not adapted to the statistics of the data that is
coded.
</t>

<section anchor="encoding-symbols" title="Encoding Symbols">
<t>
   The main encoding function is ec_encode() (rangeenc.c),
   which takes as an argument a three-tuple (fl,fh,ft)
   describing the range of the symbol to be encoded in the current
   context, with 0 &lt;= fl &lt; fh &lt;= ft &lt;= 65535. The values of this tuple
   are derived from the probability model for the symbol. Let f(i) be
   the frequency of the ith symbol in the current context. Then the
   three-tuple corresponding to the kth symbol is given by
   <![CDATA[
fl=sum(f(i),i<k), fh=fl+f(i), and ft=sum(f(i)).
]]>
</t>
<t>
   ec_encode() updates the state of the encoder as follows. If fl is
   greater than zero, then low = low + rng - (rng/ft)*(ft-fl) and 
   rng = (rng/ft)*(fh-fl). Otherwise, low is unchanged and
   rng = rng - (rng/ft)*(fh-fl). The divisions here are exact integer
   division. After this update, the range is normalized.
</t>
<t>
   To normalize the range, the following process is repeated until
   rng > 2^23. First, the top 9 bits of low, (low>>23), are placed into
   a carry buffer. Then, low is set to <![CDATA[(low << 8 & 0x7FFFFFFF) and rng
   is set to (rng<<8)]]>. This process is carried out by
   ec_enc_normalize() (rangeenc.c).
</t>
<t>
   The 9 bits produced in each iteration of the normalization loop
   consist of 8 data bits and a carry flag. The final value of the
   output bits is not determined until carry propagation is accounted
   for. Therefore the reference implementation buffers a single
   (non-propagating) output octet and keeps a count of additional
   propagating (0xFF) output octets. An implementation MAY choose to use
   any mathematically equivalent scheme to perform carry propagation.
</t>
<t>
   The function ec_enc_carry_out() (rangeenc.c) performs
   this buffering. It takes a 9-bit input value, c, from the normalization
   8-bit output and a carry bit. If c is 0xFF, then ext is incremented
   and no octets are output. Otherwise, if rem is not the special value
   -1, then the octet (rem+(c>>8)) is output. Then ext octets are output
   with the value 0 if the carry bit is set, or 0xFF if it is not, and
   rem is set to the lower 8 bits of c. After this, ext is set to zero.
</t>
<t>
   In the reference implementation, a special version of ec_encode()
   called ec_encode_bin() (rangeenc.c) is defined to
   take a two-tuple (fl,ftb), where <![CDATA[0 <= fl < 2^ftb and ftb < 16. It is
   mathematically equivalent to calling ec_encode() with the three-tuple
   (fl,fl+1,1<<ftb)]]>, but avoids using division.

</t>
</section>

<section anchor="encoding-ints" title="Encoding Uniformly Distributed Integers">
<t>
   Functions ec_enc_uint() or ec_enc_bits() are based on ec_encode() and 
   encode one of N equiprobable symbols, each with a frequency of 1,
   where N may be as large as 2^32-1. Because ec_encode() is limited to
   a total frequency of 2^16-1, this is done by encoding a series of
   symbols in smaller contexts.
</t>
<t>
   ec_enc_bits() (entenc.c) is defined, like
   ec_encode_bin(), to take a two-tuple (fl,ftb), with <![CDATA[0 <= fl < 2^ftb
   and ftb < 32. While ftb is greater than 8, it encodes bits (ftb-8) to
   (ftb-1) of fl, e.g., (fl>>ftb-8&0xFF) using ec_encode_bin() and
   subtracts 8 from ftb. Then, it encodes the remaining bits of fl, e.g.,
   (fl&(1<<ftb)-1)]]>, again using ec_encode_bin().
</t>
<t>
   ec_enc_uint() (entenc.c) takes a two-tuple (fl,ft),
   where ft is not necessarily a power of two. Let ftb be the location
   of the highest 1 bit in the two's-complement representation of
   (ft-1), or -1 if no bits are set. If ftb>8, then the top 8 bits of fl
   are encoded using ec_encode() with the three-tuple
   (fl>>ftb-8,(fl>>ftb-8)+1,(ft-1>>ftb-8)+1), and the remaining bits
   are encoded with ec_enc_bits using the two-tuple
   <![CDATA[(fl&(1<<ftb-8)-1,ftb-8). Otherwise, fl is encoded with ec_encode()
   directly using the three-tuple (fl,fl+1,ft)]]>.
</t>
</section>

<section anchor="encoder-finalizing" title="Finalizing the Stream">
<t>
   After all symbols are encoded, the stream must be finalized by
   outputting a value inside the current range. Let end be the integer
   in the interval [low,low+rng) with the largest number of trailing
   zero bits. Then while end is not zero, the top 9 bits of end, e.g.,
   <![CDATA[(end>>23), are sent to the carry buffer, and end is replaced by
   (end<<8&0x7FFFFFFF). Finally, if the value in carry buffer, rem, is]]>
   neither zero nor the special value -1, or the carry count, ext, is
   greater than zero, then 9 zero bits are sent to the carry buffer.
   After the carry buffer is finished outputting octets, the rest of the
   output buffer is padded with zero octets. Finally, rem is set to the
   special value -1. This process is implemented by ec_enc_done()
   (rangeenc.c).
</t>
</section>

<section anchor="encoder-tell" title="Current Bit Usage">
<t>
   The bit allocation routines in Opus need to be able to determine a
   conservative upper bound on the number of bits that have been used
   to encode the current frame thus far. This drives allocation
   decisions and ensures that the range code will not overflow the
   output buffer. This is computed in the reference implementation to
   fractional bit precision by the function ec_enc_tell() 
   (rangeenc.c).
   Like all operations in the range encoder, it must
   be implemented in a bit-exact manner.
</t>
</section>

</section>

<section title="SILK Encoder">
<t>
Copy from SILK draft.
</t>
</section>

<section title="CELT Encoder">
<t>
Copy from CELT draft.
</t>

<section anchor="forward-mdct" title="Forward MDCT">

<t>The MDCT implementation has no special characteristics. The
input is a windowed signal (after pre-emphasis) of 2*N samples and the output is N
frequency-domain samples. A <spanx style="emph">low-overlap</spanx> window is used to reduce the algorithmic delay. 
It is derived from a basic (full overlap) window that is the same as the one used in the Vorbis codec: W(n)=[sin(pi/2*sin(pi/2*(n+.5)/L))]^2. The low-overlap window is created by zero-padding the basic window and inserting ones in the middle, such that the resulting window still satisfies power complementarity. The MDCT is computed in mdct_forward() (mdct.c), which includes the windowing operation and a scaling of 2/N.
</t>
</section>

<section anchor="normalization" title="Bands and Normalization">
<t>
The MDCT output is divided into bands that are designed to match the ear's critical bands,
with the exception that each band has to be at least 3 bins wide. For each band, the encoder
computes the energy that will later be encoded. Each band is then normalized by the 
square root of the <spanx style="strong">non-quantized</spanx> energy, such that each band now forms a unit vector X.
The energy and the normalization are computed by compute_band_energies()
and normalise_bands() (bands.c), respectively.
</t>
</section>

<section anchor="energy-quantization" title="Energy Envelope Quantization">

<t>
It is important to quantize the energy with sufficient resolution because
any energy quantization error cannot be compensated for at a later
stage. Regardless of the resolution used for encoding the shape of a band,
it is perceptually important to preserve the energy in each band. CELT uses a
coarse-fine strategy for encoding the energy in the base-2 log domain, 
as implemented in quant_bands.c</t>

<section anchor="coarse-energy" title="Coarse energy quantization">
<t>
The coarse quantization of the energy uses a fixed resolution of
6 dB and is the only place where entropy coding is used.
To minimize the bitrate, prediction is applied both in time (using the previous frame)
and in frequency (using the previous bands). The 2-D z-transform of
the prediction filter is: A(z_l, z_b)=(1-a*z_l^-1)*(1-z_b^-1)/(1-b*z_b^-1)
where b is the band index and l is the frame index. The prediction coefficients are
a=0.8 and b=0.7 when not using intra energy and a=b=0 when using intra energy. 
The time-domain prediction is based on the final fine quantization of the previous
frame, while the frequency domain (within the current frame) prediction is based
on coarse quantization only (because the fine quantization has not been computed
yet). We approximate the ideal 
probability distribution of the prediction error using a Laplace distribution. The
coarse energy quantization is performed by quant_coarse_energy() and 
quant_coarse_energy() (quant_bands.c).
</t>

<t>
The Laplace distribution for each band is defined by a 16-bit (Q15) decay parameter.
Thus, the value 0 has a frequency count of p[0]=2*(16384*(16384-decay)/(16384+decay)). The 
values +/- i each have a frequency count p[i] = (p[i-1]*decay)>>14. The value of p[i] is always
rounded down (to avoid exceeding 32768 as the sum of all frequency counts), so it is possible
for the sum to be less than 32768. In that case additional values with a frequency count of 1 are encoded. The signed values corresponding to symbols 0, 1, 2, 3, 4, ... 
are [0, +1, -1, +2, -2, ...]. The encoding of the Laplace-distributed values is 
implemented in ec_laplace_encode() (laplace.c).
</t>
<!-- FIXME: bit budget consideration -->
</section> <!-- coarse energy -->

<section anchor="fine-energy" title="Fine energy quantization">
<t>
After the coarse energy quantization and encoding, the bit allocation is computed 
(<xref target="allocation"></xref>) and the number of bits to use for refining the
energy quantization is determined for each band. Let B_i be the number of fine energy bits 
for band i; the refinement is an integer f in the range [0,2^B_i-1]. The mapping between f
and the correction applied to the coarse energy is equal to (f+1/2)/2^B_i - 1/2. Fine
energy quantization is implemented in quant_fine_energy() 
(quant_bands.c).
</t>

<t>
If any bits are unused at the end of the encoding process, these bits are used to
increase the resolution of the fine energy encoding in some bands. Priority is given
to the bands for which the allocation (<xref target="allocation"></xref>) was rounded
down. At the same level of priority, lower bands are encoded first. Refinement bits
are added until there are no unused bits. This is implemented in quant_energy_finalise() 
(quant_bands.c).
</t>

</section> <!-- fine energy -->


</section> <!-- Energy quant -->

<section anchor="allocation" title="Bit Allocation">
<t>Bit allocation is performed based only on information available to both
the encoder and decoder. The same calculations are performed in a bit-exact
manner in both the encoder and decoder to ensure that the result is always
exactly the same. Any mismatch would cause an error in the decoded output.
The allocation is computed by compute_allocation() (rate.c),
which is used in both the encoder and the decoder.</t>

<t>For a given band, the bit allocation is nearly constant across
frames that use the same number of bits for Q1, yielding a 
pre-defined signal-to-mask ratio (SMR) for each band. Because the
bands each have a width of one Bark, this is equivalent to modeling the
masking occurring within each critical band, while ignoring inter-band
masking and tone-vs-noise characteristics. While this is not an
optimal bit allocation, it provides good results without requiring the
transmission of any allocation information.
</t>


<t>
For every encoded or decoded frame, a target allocation must be computed
using the projected allocation. In the reference implementation this is
performed by compute_allocation() (rate.c).
The target computation begins by calculating the available space as the
number of whole bits which can be fit in the frame after Q1 is stored according
to the range coder (ec_[enc/dec]_tell()) and then multiplying by 8.
Then the two projected prototype allocations whose sums multiplied by 8 are nearest
to that value are determined. These two projected prototype allocations are then interpolated
by finding the highest integer interpolation coefficient in the range 0-8
such that the sum of the higher prototype times the coefficient, plus the
sum of the lower prototype multiplied by
the difference of 16 and the coefficient, is less than or equal to the
available sixteenth-bits. 
The reference implementation performs this step using a binary search in
interp_bits2pulses() (rate.c). The target  
allocation is the interpolation coefficient times the higher prototype, plus
the lower prototype multiplied by the difference of 16 and the coefficient,
for each of the CELT bands.   
</t>

<t>
Because the computed target will sometimes be somewhat smaller than the
available space, the excess space is divided by the number of bands, and this amount
is added equally to each band. Any remaining space is added to the target one
sixteenth-bit at a time, starting from the first band. The new target now
matches the available space, in sixteenth-bits, exactly. 
</t>

<t>
The allocation target is separated into a portion used for fine energy
and a portion used for the Spherical Vector Quantizer (PVQ). The fine energy
quantizer operates in whole-bit steps. For each band the number of bits per 
channel used for fine energy is calculated by 50 minus the log2_frac(), with
1/16 bit precision, of the number of MDCT bins in the band. That result is multiplied
by the number of bins in the band and again by twice the number of                 
channels, and then the value is set to zero if it is less than zero. Added
to that result is 16 times the number of MDCT bins times the number of
channels,  and it is finally divided by 32 times the number of MDCT bins times the
number of channels. If the result times the number of channels is greater than than the
target divided by 16, the result is set to the target divided by the number of
channels divided by 16. Then if the value is greater than 7 it is reset to 7 because a
larger amount of fine energy resolution was determined not to be make an improvement in
perceived quality.  The resulting number of fine energy bits per channel is
then multiplied by the number of channels and then by 16, and subtracted
from the target allocation. This final target allocation is what is used for the
PVQ.
</t>

</section>

<section anchor="pitch-prediction" title="Pitch Prediction">
<t>
This section needs to be updated.
</t>

</section>

<section anchor="pvq" title="Spherical Vector Quantization">
<t>CELT uses a Pyramid Vector Quantization (PVQ) <xref target="PVQ"></xref>
codebook for quantizing the details of the spectrum in each band that have not
been predicted by the pitch predictor. The PVQ codebook consists of all sums
of K signed pulses in a vector of N samples, where two pulses at the same position
are required to have the same sign. Thus the codebook includes 
all integer codevectors y of N dimensions that satisfy sum(abs(y(j))) = K.
</t>

<t>
In bands where neither pitch nor folding is used, the PVQ is used to encode
the unit vector that results from the normalization in 
<xref target="normalization"></xref> directly. Given a PVQ codevector y, 
the unit vector X is obtained as X = y/||y||, where ||.|| denotes the 
L2 norm.
</t>

<section anchor="bits-pulses" title="Bits to Pulses">
<t>
Although the allocation is performed in 1/16 bit units, the quantization requires
an integer number of pulses K. To do this, the encoder searches for the value
of K that produces the number of bits that is the nearest to the allocated value
(rounding down if exactly half-way between two values), subject to not exceeding
the total number of bits available. The computation is performed in 1/16 of
bits using log2_frac() and ec_enc_tell(). The number of codebooks entries can
be computed as explained in <xref target="cwrs-encoding"></xref>. The difference
between the number of bits allocated and the number of bits used is accumulated to a
<spanx style="emph">balance</spanx> (initialised to zero) that helps adjusting the
allocation for the next bands. One third of the balance is subtracted from the
bit allocation of the next band to help achieving the target allocation. The only
exceptions are the band before the last and the last band, for which half the balance
and the whole balance are subtracted, respectively.
</t>
</section>

<section anchor="pvq-search" title="PVQ Search">

<t>
The search for the best codevector y is performed by alg_quant()
(vq.c). There are several possible approaches to the 
search with a tradeoff between quality and complexity. The method used in the reference
implementation computes an initial codeword y1 by projecting the residual signal 
R = X - p' onto the codebook pyramid of K-1 pulses:
</t>
<t>
y0 = round_towards_zero( (K-1) * R / sum(abs(R)))
</t>

<t>
Depending on N, K and the input data, the initial codeword y0 may contain from 
0 to K-1 non-zero values. All the remaining pulses, with the exception of the last one, 
are found iteratively with a greedy search that minimizes the normalized correlation
between y and R:
</t>

<t>
J = -R^T*y / ||y||
</t>

<t>
The search described above is considered to be a good trade-off between quality
and computational cost. However, there are other possible ways to search the PVQ
codebook and the implementors MAY use any other search methods.
</t>
</section>


<section anchor="cwrs-encoding" title="Index Encoding">
<t>
The best PVQ codeword is encoded as a uniformly-distributed integer value
by encode_pulses() (cwrs.c).
The codeword is converted to a unique index in the same way as specified in 
<xref target="PVQ"></xref>. The indexing is based on the calculation of V(N,K) (denoted N(L,K) in <xref target="PVQ"></xref>), which is the number of possible combinations of K pulses 
in N samples. The number of combinations can be computed recursively as 
V(N,K) = V(N+1,K) + V(N,K+1) + V(N+1,K+1), with V(N,0) = 1 and V(0,K) = 0, K != 0. 
There are many different ways to compute V(N,K), including pre-computed tables and direct
use of the recursive formulation. The reference implementation applies the recursive
formulation one line (or column) at a time to save on memory use,
along with an alternate,
univariate recurrence to initialise an arbitrary line, and direct
polynomial solutions for small N. All of these methods are
equivalent, and have different trade-offs in speed, memory usage, and
code size. Implementations MAY use any methods they like, as long as
they are equivalent to the mathematical definition.
</t>

<t>
The indexing computations are performed using 32-bit unsigned integers. For large codebooks,
32-bit integers are not sufficient. Instead of using 64-bit integers (or more), the encoding
is made slightly sub-optimal by splitting each band into two equal (or near-equal) vectors of
size (N+1)/2 and N/2, respectively. The number of pulses in the first half, K1, is first encoded as an
integer in the range [0,K]. Then, two codebooks are encoded with V((N+1)/2, K1) and V(N/2, K-K1). 
The split operation is performed recursively, in case one (or both) of the split vectors 
still requires more than 32 bits. For compatibility reasons, the handling of codebooks of more 
than 32 bits MUST be implemented with the splitting method, even if 64-bit arithmetic is available.
</t>
</section>

</section>


<section anchor="stereo" title="Stereo support">
<t>
When encoding a stereo stream, some parameters are shared across the left and right channels, while others are transmitted separately for each channel, or jointly encoded. Only one copy of the flags for the features, transients and pitch (pitch period and gains) are transmitted. The coarse and fine energy parameters are transmitted separately for each channel. Both the coarse energy and fine energy (including the remaining fine bits at the end of the stream) have the left and right bands interleaved in the stream, with the left band encoded first.
</t>

<t>
The main difference between mono and stereo coding is the PVQ coding of the normalized vectors. In stereo mode, a normalized mid-side (M-S) encoding is used. Let L and R be the normalized vector of a certain band for the left and right channels, respectively. The mid and side vectors are computed as M=L+R and S=L-R and no longer have unit norm.
</t>

<t>
From M and S, an angular parameter theta=2/pi*atan2(||S||, ||M||) is computed. The theta parameter is converted to a Q14 fixed-point parameter itheta, which is quantized on a scale from 0 to 1 with an interval of 2^-qb, where qb = (b-2*(N-1)*(40-log2_frac(N,4)))/(32*(N-1)), b is the number of bits allocated to the band, and log2_frac() is defined in cwrs.c. From here on, the value of itheta MUST be treated in a bit-exact manner since 
both the encoder and decoder rely on it to infer the bit allocation.
</t>
<t>
Let m=M/||M|| and s=S/||S||; m and s are separately encoded with the PVQ encoder described in <xref target="pvq"></xref>. The number of bits allocated to m and s depends on the value of itheta. The number of bits allocated to coding m is obtained by:
</t>

<t>
<list>
<t>imid = bitexact_cos(itheta);</t>
<t>iside = bitexact_cos(16384-itheta);</t>
<t>delta = (N-1)*(log2_frac(iside,6)-log2_frac(imid,6))>>2;</t>
<t>qalloc = log2_frac((1&lt;&lt;qb)+1,4);</t>
<t>mbits = (b-qalloc/2-delta)/2;</t>
</list>
</t>

<t>where bitexact_cos() is a fixed-point cosine approximation that MUST be bit-exact with the reference implementation
in mathops.h. The spectral folding operation is performed independently for the mid and side vectors.</t>
</section>


<section anchor="synthesis" title="Synthesis">
<t>
After all the quantization is completed, the quantized energy is used along with the 
quantized normalized band data to resynthesize the MDCT spectrum. The inverse MDCT (<xref target="inverse-mdct"></xref>) and the weighted overlap-add are applied and the signal is stored in the <spanx style="emph">synthesis buffer</spanx> so it can be used for pitch prediction. 
The encoder MAY omit this step of the processing if it knows that it will not be using
the pitch predictor for the next few frames. If the de-emphasis filter (<xref target="inverse-mdct"></xref>) is applied to this resynthesized
signal, then the output will be the same (within numerical precision) as the decoder's output. 
</t>
</section>

<section anchor="vbr" title="Variable Bitrate (VBR)">
<t>
Each CELT frame can be encoded in a different number of octets, making it possible to vary the bitrate at will. This property can be used to implement source-controlled variable bitrate (VBR). Support for VBR is OPTIONAL for the encoder, but a decoder MUST be prepared to decode a stream that changes its bit-rate dynamically. The method used to vary the bit-rate in VBR mode is left to the implementor, as long as each frame can be decoded by the reference decoder.
</t>
</section>

</section>

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{'dir': 'git-commits-cleaned', 'id': '97169', 'n_tokens_mistral': 17067, 'n_tokens_neox': 15342, 'n_words': 7586}