Chris@1: 
Chris@1: % -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
Chris@1: %!TEX root = Vorbis_I_spec.tex
Chris@1: % $Id$
Chris@1: \section{Codec Setup and Packet Decode} \label{vorbis:spec:codec}
Chris@1: 
Chris@1: \subsection{Overview}
Chris@1: 
Chris@1: This document serves as the top-level reference document for the
Chris@1: bit-by-bit decode specification of Vorbis I.  This document assumes a
Chris@1: high-level understanding of the Vorbis decode process, which is
Chris@1: provided in \xref{vorbis:spec:intro}.  \xref{vorbis:spec:bitpacking} covers reading and writing bit fields from
Chris@1: and to bitstream packets.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsection{Header decode and decode setup}
Chris@1: 
Chris@1: A Vorbis bitstream begins with three header packets. The header
Chris@1: packets are, in order, the identification header, the comments header,
Chris@1: and the setup header. All are required for decode compliance.  An
Chris@1: end-of-packet condition during decoding the first or third header
Chris@1: packet renders the stream undecodable.  End-of-packet decoding the
Chris@1: comment header is a non-fatal error condition.
Chris@1: 
Chris@1: \subsubsection{Common header decode}
Chris@1: 
Chris@1: Each header packet begins with the same header fields.
Chris@1: 
Chris@1: 
Chris@1: \begin{Verbatim}[commandchars=\\\{\}]
Chris@1:   1) [packet\_type] : 8 bit value
Chris@1:   2) 0x76, 0x6f, 0x72, 0x62, 0x69, 0x73: the characters 'v','o','r','b','i','s' as six octets
Chris@1: \end{Verbatim}
Chris@1: 
Chris@1: Decode continues according to packet type; the identification header
Chris@1: is type 1, the comment header type 3 and the setup header type 5
Chris@1: (these types are all odd as a packet with a leading single bit of '0'
Chris@1: is an audio packet).  The packets must occur in the order of
Chris@1: identification, comment, setup.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{Identification header}
Chris@1: 
Chris@1: The identification header is a short header of only a few fields used
Chris@1: to declare the stream definitively as Vorbis, and provide a few externally
Chris@1: relevant pieces of information about the audio stream. The
Chris@1: identification header is coded as follows:
Chris@1: 
Chris@1: \begin{Verbatim}[commandchars=\\\{\}]
Chris@1:  1) [vorbis\_version] = read 32 bits as unsigned integer
Chris@1:  2) [audio\_channels] = read 8 bit integer as unsigned
Chris@1:  3) [audio\_sample\_rate] = read 32 bits as unsigned integer
Chris@1:  4) [bitrate\_maximum] = read 32 bits as signed integer
Chris@1:  5) [bitrate\_nominal] = read 32 bits as signed integer
Chris@1:  6) [bitrate\_minimum] = read 32 bits as signed integer
Chris@1:  7) [blocksize\_0] = 2 exponent (read 4 bits as unsigned integer)
Chris@1:  8) [blocksize\_1] = 2 exponent (read 4 bits as unsigned integer)
Chris@1:  9) [framing\_flag] = read one bit
Chris@1: \end{Verbatim}
Chris@1: 
Chris@1: \varname{[vorbis\_version]} is to read '0' in order to be compatible
Chris@1: with this document.  Both \varname{[audio\_channels]} and
Chris@1: \varname{[audio\_sample\_rate]} must read greater than zero.  Allowed final
Chris@1: blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in
Chris@1: Vorbis I.  \varname{[blocksize\_0]} must be less than or equal to
Chris@1: \varname{[blocksize\_1]}.  The framing bit must be nonzero.  Failure to
Chris@1: meet any of these conditions renders a stream undecodable.
Chris@1: 
Chris@1: The bitrate fields above are used only as hints. The nominal bitrate
Chris@1: field especially may be considerably off in purely VBR streams.  The
Chris@1: fields are meaningful only when greater than zero.
Chris@1: 
Chris@1: \begin{itemize}
Chris@1:   \item All three fields set to the same value implies a fixed rate, or tightly bounded, nearly fixed-rate bitstream
Chris@1:   \item Only nominal set implies a VBR or ABR stream that averages the nominal bitrate
Chris@1:   \item Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits
Chris@1:   \item None set indicates the encoder does not care to speculate.
Chris@1: \end{itemize}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{Comment header}
Chris@1: Comment header decode and data specification is covered in
Chris@1: \xref{vorbis:spec:comment}.
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{Setup header}
Chris@1: 
Chris@1: Vorbis codec setup is configurable to an extreme degree:
Chris@1: 
Chris@1: \begin{center}
Chris@1: \includegraphics[width=\textwidth]{components}
Chris@1: \captionof{figure}{decoder pipeline configuration}
Chris@1: \end{center}
Chris@1: 
Chris@1: 
Chris@1: The setup header contains the bulk of the codec setup information
Chris@1: needed for decode.  The setup header contains, in order, the lists of
Chris@1: codebook configurations, time-domain transform configurations
Chris@1: (placeholders in Vorbis I), floor configurations, residue
Chris@1: configurations, channel mapping configurations and mode
Chris@1: configurations. It finishes with a framing bit of '1'.  Header decode
Chris@1: proceeds in the following order:
Chris@1: 
Chris@1: \paragraph{Codebooks}
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1: \item \varname{[vorbis\_codebook\_count]} = read eight bits as unsigned integer and add one
Chris@1: \item Decode \varname{[vorbis\_codebook\_count]} codebooks in order as defined
Chris@1: in \xref{vorbis:spec:codebook}.  Save each configuration, in
Chris@1: order, in an array of
Chris@1: codebook configurations \varname{[vorbis\_codebook\_configurations]}.
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \paragraph{Time domain transforms}
Chris@1: 
Chris@1: These hooks are placeholders in Vorbis I.  Nevertheless, the
Chris@1: configuration placeholder values must be read to maintain bitstream
Chris@1: sync.
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1: \item \varname{[vorbis\_time\_count]} = read 6 bits as unsigned integer and add one
Chris@1: \item read \varname{[vorbis\_time\_count]} 16 bit values; each value should be zero.  If any value is nonzero, this is an error condition and the stream is undecodable.
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \paragraph{Floors}
Chris@1: 
Chris@1: Vorbis uses two floor types; header decode is handed to the decode
Chris@1: abstraction of the appropriate type.
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item \varname{[vorbis\_floor\_count]} = read 6 bits as unsigned integer and add one
Chris@1:  \item For each \varname{[i]} of \varname{[vorbis\_floor\_count]} floor numbers:
Chris@1:   \begin{enumerate}
Chris@1:    \item read the floor type: vector \varname{[vorbis\_floor\_types]} element \varname{[i]} =
Chris@1: read 16 bits as unsigned integer
Chris@1:    \item If the floor type is zero, decode the floor
Chris@1: configuration as defined in \xref{vorbis:spec:floor0}; save
Chris@1: this
Chris@1: configuration in slot \varname{[i]} of the floor configuration array \varname{[vorbis\_floor\_configurations]}.
Chris@1:    \item If the floor type is one,
Chris@1: decode the floor configuration as defined in \xref{vorbis:spec:floor1}; save this configuration in slot \varname{[i]} of the floor configuration array \varname{[vorbis\_floor\_configurations]}.
Chris@1:    \item If the the floor type is greater than one, this stream is undecodable; ERROR CONDITION
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \paragraph{Residues}
Chris@1: 
Chris@1: Vorbis uses three residue types; header decode of each type is identical.
Chris@1: 
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1: \item \varname{[vorbis\_residue\_count]} = read 6 bits as unsigned integer and add one
Chris@1: 
Chris@1: \item For each of \varname{[vorbis\_residue\_count]} residue numbers:
Chris@1:  \begin{enumerate}
Chris@1:   \item read the residue type; vector \varname{[vorbis\_residue\_types]} element \varname{[i]} = read 16 bits as unsigned integer
Chris@1:   \item If the residue type is zero,
Chris@1: one or two, decode the residue configuration as defined in \xref{vorbis:spec:residue}; save this configuration in slot \varname{[i]} of the residue configuration array \varname{[vorbis\_residue\_configurations]}.
Chris@1:   \item If the the residue type is greater than two, this stream is undecodable; ERROR CONDITION
Chris@1:  \end{enumerate}
Chris@1: 
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \paragraph{Mappings}
Chris@1: 
Chris@1: Mappings are used to set up specific pipelines for encoding
Chris@1: multichannel audio with varying channel mapping applications. Vorbis I
Chris@1: uses a single mapping type (0), with implicit PCM channel mappings.
Chris@1: 
Chris@1: % FIXME/TODO: LaTeX cannot nest enumerate that deeply, so I have to use
Chris@1: % itemize at the innermost level. However, it would be much better to 
Chris@1: % rewrite this pseudocode using listings or algoritmicx or some other
Chris@1: % package geared towards this.
Chris@1: \begin{enumerate}
Chris@1:  \item \varname{[vorbis\_mapping\_count]} = read 6 bits as unsigned integer and add one
Chris@1:  \item For each \varname{[i]} of \varname{[vorbis\_mapping\_count]} mapping numbers:
Chris@1:   \begin{enumerate}
Chris@1:    \item read the mapping type: 16 bits as unsigned integer.  There's no reason to save the mapping type in Vorbis I.
Chris@1:    \item If the mapping type is nonzero, the stream is undecodable
Chris@1:    \item If the mapping type is zero:
Chris@1:     \begin{enumerate}
Chris@1:      \item read 1 bit as a boolean flag
Chris@1:       \begin{enumerate}
Chris@1:        \item if set, \varname{[vorbis\_mapping\_submaps]} = read 4 bits as unsigned integer and add one
Chris@1:        \item if unset, \varname{[vorbis\_mapping\_submaps]} = 1
Chris@1:       \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1:      \item read 1 bit as a boolean flag
Chris@1:        \begin{enumerate}
Chris@1:          \item if set, square polar channel mapping is in use:
Chris@1:            \begin{itemize}
Chris@1:              \item \varname{[vorbis\_mapping\_coupling\_steps]} = read 8 bits as unsigned integer and add one
Chris@1:              \item for \varname{[j]} each of \varname{[vorbis\_mapping\_coupling\_steps]} steps:
Chris@1:                \begin{itemize}
Chris@1:                  \item vector \varname{[vorbis\_mapping\_magnitude]} element \varname{[j]}= read \link{vorbis:spec:ilog}{ilog}(\varname{[audio\_channels]} - 1) bits as unsigned integer
Chris@1:                  \item vector \varname{[vorbis\_mapping\_angle]} element \varname{[j]}= read \link{vorbis:spec:ilog}{ilog}(\varname{[audio\_channels]} - 1) bits as unsigned integer
Chris@1:                  \item the numbers read in the above two steps are channel numbers representing the channel to treat as magnitude and the channel to treat as angle, respectively.  If for any coupling step the angle channel number equals the magnitude channel number, the magnitude channel number is greater than \varname{[audio\_channels]}-1, or the angle channel is greater than \varname{[audio\_channels]}-1, the stream is undecodable.
Chris@1:                \end{itemize}
Chris@1: 
Chris@1: 
Chris@1:            \end{itemize}
Chris@1: 
Chris@1: 
Chris@1:          \item if unset, \varname{[vorbis\_mapping\_coupling\_steps]} = 0
Chris@1:        \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1:      \item read 2 bits (reserved field); if the value is nonzero, the stream is undecodable
Chris@1:      \item if \varname{[vorbis\_mapping\_submaps]} is greater than one, we read channel multiplex settings. For each \varname{[j]} of \varname{[audio\_channels]} channels:
Chris@1:       \begin{enumerate}
Chris@1:        \item vector \varname{[vorbis\_mapping\_mux]} element \varname{[j]} = read 4 bits as unsigned integer
Chris@1:        \item if the value is greater than the highest numbered submap (\varname{[vorbis\_mapping\_submaps]} - 1), this in an error condition rendering the stream undecodable
Chris@1:       \end{enumerate}
Chris@1: 
Chris@1:      \item for each submap \varname{[j]} of \varname{[vorbis\_mapping\_submaps]} submaps, read the floor and residue numbers for use in decoding that submap:
Chris@1:       \begin{enumerate}
Chris@1:        \item read and discard 8 bits (the unused time configuration placeholder)
Chris@1:        \item read 8 bits as unsigned integer for the floor number; save in vector \varname{[vorbis\_mapping\_submap\_floor]} element \varname{[j]}
Chris@1:        \item verify the floor number is not greater than the highest number floor configured for the bitstream. If it is, the bitstream is undecodable
Chris@1:        \item read 8 bits as unsigned integer for the residue number; save in vector \varname{[vorbis\_mapping\_submap\_residue]} element \varname{[j]}
Chris@1:        \item verify the residue number is not greater than the highest number residue configured for the bitstream.  If it is, the bitstream is undecodable
Chris@1:       \end{enumerate}
Chris@1: 
Chris@1:      \item save this mapping configuration in slot \varname{[i]} of the mapping configuration array \varname{[vorbis\_mapping\_configurations]}.
Chris@1:     \end{enumerate}
Chris@1: 
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \paragraph{Modes}
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item \varname{[vorbis\_mode\_count]} = read 6 bits as unsigned integer and add one
Chris@1:  \item For each of \varname{[vorbis\_mode\_count]} mode numbers:
Chris@1:   \begin{enumerate}
Chris@1:   \item \varname{[vorbis\_mode\_blockflag]} = read 1 bit
Chris@1:   \item \varname{[vorbis\_mode\_windowtype]} = read 16 bits as unsigned integer
Chris@1:   \item \varname{[vorbis\_mode\_transformtype]} = read 16 bits as unsigned integer
Chris@1:   \item \varname{[vorbis\_mode\_mapping]} = read 8 bits as unsigned integer
Chris@1:   \item verify ranges; zero is the only legal value in Vorbis I for
Chris@1: \varname{[vorbis\_mode\_windowtype]}
Chris@1: and \varname{[vorbis\_mode\_transformtype]}.  \varname{[vorbis\_mode\_mapping]} must not be greater than the highest number mapping in use.  Any illegal values render the stream undecodable.
Chris@1:   \item save this mode configuration in slot \varname{[i]} of the mode configuration array
Chris@1: \varname{[vorbis\_mode\_configurations]}.
Chris@1:  \end{enumerate}
Chris@1: 
Chris@1: \item read 1 bit as a framing flag.  If unset, a framing error occurred and the stream is not
Chris@1: decodable.
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: After reading mode descriptions, setup header decode is complete.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsection{Audio packet decode and synthesis}
Chris@1: 
Chris@1: Following the three header packets, all packets in a Vorbis I stream
Chris@1: are audio.  The first step of audio packet decode is to read and
Chris@1: verify the packet type. \emph{A non-audio packet when audio is expected
Chris@1: indicates stream corruption or a non-compliant stream. The decoder
Chris@1: must ignore the packet and not attempt decoding it to audio}.
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{packet type, mode and window decode}
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item read 1 bit \varname{[packet\_type]}; check that packet type is 0 (audio)
Chris@1:  \item read \link{vorbis:spec:ilog}{ilog}([vorbis\_mode\_count]-1) bits
Chris@1: \varname{[mode\_number]}
Chris@1:  \item decode blocksize \varname{[n]} is equal to \varname{[blocksize\_0]} if
Chris@1: \varname{[vorbis\_mode\_blockflag]} is 0, else \varname{[n]} is equal to \varname{[blocksize\_1]}.
Chris@1:  \item perform window selection and setup; this window is used later by the inverse MDCT:
Chris@1:   \begin{enumerate}
Chris@1:    \item if this is a long window (the \varname{[vorbis\_mode\_blockflag]} flag of this mode is
Chris@1: set):
Chris@1:     \begin{enumerate}
Chris@1:      \item read 1 bit for \varname{[previous\_window\_flag]}
Chris@1:      \item read 1 bit for \varname{[next\_window\_flag]}
Chris@1:      \item if \varname{[previous\_window\_flag]} is not set, the left half
Chris@1:          of the window will be a hybrid window for lapping with a
Chris@1:          short block.  See \xref{vorbis:spec:window} for an illustration of overlapping
Chris@1: dissimilar
Chris@1:          windows. Else, the left half window will have normal long
Chris@1:          shape.
Chris@1:      \item if \varname{[next\_window\_flag]} is not set, the right half of
Chris@1:          the window will be a hybrid window for lapping with a short
Chris@1:          block.  See \xref{vorbis:spec:window} for an
Chris@1: illustration of overlapping dissimilar
Chris@1:          windows. Else, the left right window will have normal long
Chris@1:          shape.
Chris@1:     \end{enumerate}
Chris@1: 
Chris@1:    \item  if this is a short window, the window is always the same
Chris@1:        short-window shape.
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: Vorbis windows all use the slope function $y=\sin(\frac{\pi}{2} * \sin^2((x+0.5)/n * \pi))$,
Chris@1: where $n$ is window size and $x$ ranges $0 \ldots n-1$, but dissimilar
Chris@1: lapping requirements can affect overall shape.  Window generation
Chris@1: proceeds as follows:
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item  \varname{[window\_center]} = \varname{[n]} / 2
Chris@1:  \item  if (\varname{[vorbis\_mode\_blockflag]} is set and \varname{[previous\_window\_flag]} is
Chris@1: not set) then
Chris@1:   \begin{enumerate}
Chris@1:    \item \varname{[left\_window\_start]} = \varname{[n]}/4 -
Chris@1: \varname{[blocksize\_0]}/4
Chris@1:    \item \varname{[left\_window\_end]} = \varname{[n]}/4 + \varname{[blocksize\_0]}/4
Chris@1:    \item \varname{[left\_n]} = \varname{[blocksize\_0]}/2
Chris@1:   \end{enumerate}
Chris@1:  else
Chris@1:   \begin{enumerate}
Chris@1:    \item \varname{[left\_window\_start]} = 0
Chris@1:    \item \varname{[left\_window\_end]} = \varname{[window\_center]}
Chris@1:    \item \varname{[left\_n]} = \varname{[n]}/2
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1:  \item  if (\varname{[vorbis\_mode\_blockflag]} is set and \varname{[next\_window\_flag]} is not
Chris@1: set) then
Chris@1:   \begin{enumerate}
Chris@1:    \item \varname{[right\_window\_start]} = \varname{[n]*3}/4 -
Chris@1: \varname{[blocksize\_0]}/4
Chris@1:    \item \varname{[right\_window\_end]} = \varname{[n]*3}/4 +
Chris@1: \varname{[blocksize\_0]}/4
Chris@1:    \item \varname{[right\_n]} = \varname{[blocksize\_0]}/2
Chris@1:   \end{enumerate}
Chris@1:  else
Chris@1:   \begin{enumerate}
Chris@1:    \item \varname{[right\_window\_start]} = \varname{[window\_center]}
Chris@1:    \item \varname{[right\_window\_end]} = \varname{[n]}
Chris@1:    \item \varname{[right\_n]} = \varname{[n]}/2
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1:  \item  window from range 0 ... \varname{[left\_window\_start]}-1 inclusive is zero
Chris@1:  \item  for \varname{[i]} in range \varname{[left\_window\_start]} ...
Chris@1: \varname{[left\_window\_end]}-1, window(\varname{[i]}) = $\sin(\frac{\pi}{2} * \sin^2($ (\varname{[i]}-\varname{[left\_window\_start]}+0.5) / \varname{[left\_n]} $* \frac{\pi}{2})$ )
Chris@1:  \item  window from range \varname{[left\_window\_end]} ... \varname{[right\_window\_start]}-1
Chris@1: inclusive is one\item  for \varname{[i]} in range \varname{[right\_window\_start]} ... \varname{[right\_window\_end]}-1, window(\varname{[i]}) = $\sin(\frac{\pi}{2} * \sin^2($ (\varname{[i]}-\varname{[right\_window\_start]}+0.5) / \varname{[right\_n]} $ * \frac{\pi}{2} + \frac{\pi}{2})$ )
Chris@1: \item  window from range \varname{[right\_window\_start]} ... \varname{[n]}-1 is
Chris@1: zero
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: An end-of-packet condition up to this point should be considered an
Chris@1: error that discards this packet from the stream.  An end of packet
Chris@1: condition past this point is to be considered a possible nominal
Chris@1: occurrence.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{floor curve decode}
Chris@1: 
Chris@1: From this point on, we assume out decode context is using mode number
Chris@1: \varname{[mode\_number]} from configuration array
Chris@1: \varname{[vorbis\_mode\_configurations]} and the map number
Chris@1: \varname{[vorbis\_mode\_mapping]} (specified by the current mode) taken
Chris@1: from the mapping configuration array
Chris@1: \varname{[vorbis\_mapping\_configurations]}.
Chris@1: 
Chris@1: Floor curves are decoded one-by-one in channel order.
Chris@1: 
Chris@1: For each floor \varname{[i]} of \varname{[audio\_channels]}
Chris@1:  \begin{enumerate}
Chris@1:   \item \varname{[submap\_number]} = element \varname{[i]} of vector [vorbis\_mapping\_mux]
Chris@1:   \item \varname{[floor\_number]} = element \varname{[submap\_number]} of vector
Chris@1: [vorbis\_submap\_floor]
Chris@1:   \item if the floor type of this
Chris@1: floor (vector \varname{[vorbis\_floor\_types]} element
Chris@1: \varname{[floor\_number]}) is zero then decode the floor for
Chris@1: channel \varname{[i]} according to the
Chris@1: \xref{vorbis:spec:floor0-decode}
Chris@1:   \item if the type of this floor
Chris@1: is one then decode the floor for channel \varname{[i]} according
Chris@1: to the \xref{vorbis:spec:floor1-decode}
Chris@1:   \item save the needed decoded floor information for channel for later synthesis
Chris@1:   \item if the decoded floor returned 'unused', set vector \varname{[no\_residue]} element
Chris@1: \varname{[i]} to true, else set vector \varname{[no\_residue]} element \varname{[i]} to
Chris@1: false
Chris@1:  \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: An end-of-packet condition during floor decode shall result in packet
Chris@1: decode zeroing all channel output vectors and skipping to the
Chris@1: add/overlap output stage.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{nonzero vector propagate}
Chris@1: 
Chris@1: A possible result of floor decode is that a specific vector is marked
Chris@1: 'unused' which indicates that that final output vector is all-zero
Chris@1: values (and the floor is zero).  The residue for that vector is not
Chris@1: coded in the stream, save for one complication.  If some vectors are
Chris@1: used and some are not, channel coupling could result in mixing a
Chris@1: zeroed and nonzeroed vector to produce two nonzeroed vectors.
Chris@1: 
Chris@1: for each \varname{[i]} from 0 ... \varname{[vorbis\_mapping\_coupling\_steps]}-1
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item if either \varname{[no\_residue]} entry for channel
Chris@1: (\varname{[vorbis\_mapping\_magnitude]} element \varname{[i]})
Chris@1: or channel
Chris@1: (\varname{[vorbis\_mapping\_angle]} element \varname{[i]})
Chris@1: are set to false, then both must be set to false.  Note that an 'unused'
Chris@1: floor has no decoded floor information; it is important that this is
Chris@1: remembered at floor curve synthesis time.
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{residue decode}
Chris@1: 
Chris@1: Unlike floors, which are decoded in channel order, the residue vectors
Chris@1: are decoded in submap order.
Chris@1: 
Chris@1: for each submap \varname{[i]} in order from 0 ... \varname{[vorbis\_mapping\_submaps]}-1
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item \varname{[ch]} = 0
Chris@1:  \item for each channel \varname{[j]} in order from 0 ... \varname{[audio\_channels]} - 1
Chris@1:   \begin{enumerate}
Chris@1:    \item if channel \varname{[j]} in submap \varname{[i]} (vector \varname{[vorbis\_mapping\_mux]} element \varname{[j]} is equal to \varname{[i]})
Chris@1:     \begin{enumerate}
Chris@1:      \item if vector \varname{[no\_residue]} element \varname{[j]} is true
Chris@1:       \begin{enumerate}
Chris@1:        \item vector \varname{[do\_not\_decode\_flag]} element \varname{[ch]} is set
Chris@1:       \end{enumerate}
Chris@1:      else
Chris@1:       \begin{enumerate}
Chris@1:        \item vector \varname{[do\_not\_decode\_flag]} element \varname{[ch]} is unset
Chris@1:       \end{enumerate}
Chris@1: 
Chris@1:      \item increment \varname{[ch]}
Chris@1:     \end{enumerate}
Chris@1: 
Chris@1:   \end{enumerate}
Chris@1:  \item \varname{[residue\_number]} = vector \varname{[vorbis\_mapping\_submap\_residue]} element \varname{[i]}
Chris@1:  \item \varname{[residue\_type]} = vector \varname{[vorbis\_residue\_types]} element \varname{[residue\_number]}
Chris@1:  \item decode \varname{[ch]} vectors using residue \varname{[residue\_number]}, according to type \varname{[residue\_type]}, also passing vector \varname{[do\_not\_decode\_flag]} to indicate which vectors in the bundle should not be decoded. Correct per-vector decode length is \varname{[n]}/2.
Chris@1:  \item \varname{[ch]} = 0
Chris@1:  \item for each channel \varname{[j]} in order from 0 ... \varname{[audio\_channels]}
Chris@1:   \begin{enumerate}
Chris@1:    \item if channel \varname{[j]} is in submap \varname{[i]} (vector \varname{[vorbis\_mapping\_mux]} element \varname{[j]} is equal to \varname{[i]})
Chris@1:     \begin{enumerate}
Chris@1:      \item residue vector for channel \varname{[j]} is set to decoded residue vector \varname{[ch]}
Chris@1:      \item increment \varname{[ch]}
Chris@1:     \end{enumerate}
Chris@1: 
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{inverse coupling}
Chris@1: 
Chris@1: for each \varname{[i]} from \varname{[vorbis\_mapping\_coupling\_steps]}-1 descending to 0
Chris@1: 
Chris@1: \begin{enumerate}
Chris@1:  \item \varname{[magnitude\_vector]} = the residue vector for channel
Chris@1: (vector \varname{[vorbis\_mapping\_magnitude]} element \varname{[i]})
Chris@1:  \item \varname{[angle\_vector]} = the residue vector for channel (vector
Chris@1: \varname{[vorbis\_mapping\_angle]} element \varname{[i]})
Chris@1:  \item for each scalar value \varname{[M]} in vector \varname{[magnitude\_vector]} and the corresponding scalar value \varname{[A]} in vector \varname{[angle\_vector]}:
Chris@1:   \begin{enumerate}
Chris@1:    \item if (\varname{[M]} is greater than zero)
Chris@1:     \begin{enumerate}
Chris@1:      \item if (\varname{[A]} is greater than zero)
Chris@1:       \begin{enumerate}
Chris@1:        \item \varname{[new\_M]} = \varname{[M]}
Chris@1:        \item \varname{[new\_A]} = \varname{[M]}-\varname{[A]}
Chris@1:       \end{enumerate}
Chris@1:      else
Chris@1:       \begin{enumerate}
Chris@1:        \item \varname{[new\_A]} = \varname{[M]}
Chris@1:        \item \varname{[new\_M]} = \varname{[M]}+\varname{[A]}
Chris@1:       \end{enumerate}
Chris@1: 
Chris@1:     \end{enumerate}
Chris@1:    else
Chris@1:     \begin{enumerate}
Chris@1:      \item if (\varname{[A]} is greater than zero)
Chris@1:       \begin{enumerate}
Chris@1:        \item \varname{[new\_M]} = \varname{[M]}
Chris@1:        \item \varname{[new\_A]} = \varname{[M]}+\varname{[A]}
Chris@1:       \end{enumerate}
Chris@1:      else
Chris@1:       \begin{enumerate}
Chris@1:        \item \varname{[new\_A]} = \varname{[M]}
Chris@1:        \item \varname{[new\_M]} = \varname{[M]}-\varname{[A]}
Chris@1:       \end{enumerate}
Chris@1: 
Chris@1:     \end{enumerate}
Chris@1: 
Chris@1:    \item set scalar value \varname{[M]} in vector \varname{[magnitude\_vector]} to \varname{[new\_M]}
Chris@1:    \item set scalar value \varname{[A]} in vector \varname{[angle\_vector]} to \varname{[new\_A]}
Chris@1:   \end{enumerate}
Chris@1: 
Chris@1: \end{enumerate}
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{dot product}
Chris@1: 
Chris@1: For each channel, synthesize the floor curve from the decoded floor
Chris@1: information, according to packet type. Note that the vector synthesis
Chris@1: length for floor computation is \varname{[n]}/2.
Chris@1: 
Chris@1: For each channel, multiply each element of the floor curve by each
Chris@1: element of that channel's residue vector.  The result is the dot
Chris@1: product of the floor and residue vectors for each channel; the produced
Chris@1: vectors are the length \varname{[n]}/2 audio spectrum for each
Chris@1: channel.
Chris@1: 
Chris@1: % TODO/FIXME: The following two paragraphs have identical twins
Chris@1: %   in section 1 (under "compute floor/residue dot product")
Chris@1: One point is worth mentioning about this dot product; a common mistake
Chris@1: in a fixed point implementation might be to assume that a 32 bit
Chris@1: fixed-point representation for floor and residue and direct
Chris@1: multiplication of the vectors is sufficient for acceptable spectral
Chris@1: depth in all cases because it happens to mostly work with the current
Chris@1: Xiph.Org reference encoder.
Chris@1: 
Chris@1: However, floor vector values can span \~140dB (\~24 bits unsigned), and
Chris@1: the audio spectrum vector should represent a minimum of 120dB (\~21
Chris@1: bits with sign), even when output is to a 16 bit PCM device.  For the
Chris@1: residue vector to represent full scale if the floor is nailed to
Chris@1: $-140$dB, it must be able to span 0 to $+140$dB.  For the residue vector
Chris@1: to reach full scale if the floor is nailed at 0dB, it must be able to
Chris@1: represent $-140$dB to $+0$dB.  Thus, in order to handle full range
Chris@1: dynamics, a residue vector may span $-140$dB to $+140$dB entirely within
Chris@1: spec.  A 280dB range is approximately 48 bits with sign; thus the
Chris@1: residue vector must be able to represent a 48 bit range and the dot
Chris@1: product must be able to handle an effective 48 bit times 24 bit
Chris@1: multiplication.  This range may be achieved using large (64 bit or
Chris@1: larger) integers, or implementing a movable binary point
Chris@1: representation.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{inverse MDCT}
Chris@1: 
Chris@1: Convert the audio spectrum vector of each channel back into time
Chris@1: domain PCM audio via an inverse Modified Discrete Cosine Transform
Chris@1: (MDCT).  A detailed description of the MDCT is available in \cite{Sporer/Brandenburg/Edler}.  The window
Chris@1: function used for the MDCT is the function described earlier.
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{overlap\_add}
Chris@1: 
Chris@1: Windowed MDCT output is overlapped and added with the right hand data
Chris@1: of the previous window such that the 3/4 point of the previous window
Chris@1: is aligned with the 1/4 point of the current window (as illustrated in
Chris@1: \xref{vorbis:spec:window}).  The overlapped portion
Chris@1: produced from overlapping the previous and current frame data is
Chris@1: finished data to be returned by the decoder.  This data spans from the
Chris@1: center of the previous window to the center of the current window.  In
Chris@1: the case of same-sized windows, the amount of data to return is
Chris@1: one-half block consisting of and only of the overlapped portions. When
Chris@1: overlapping a short and long window, much of the returned range does not
Chris@1: actually overlap.  This does not damage transform orthogonality.  Pay
Chris@1: attention however to returning the correct data range; the amount of
Chris@1: data to be returned is:
Chris@1: 
Chris@1: \begin{programlisting}
Chris@1: window\_blocksize(previous\_window)/4+window\_blocksize(current\_window)/4
Chris@1: \end{programlisting}
Chris@1: 
Chris@1: from the center (element windowsize/2) of the previous window to the
Chris@1: center (element windowsize/2-1, inclusive) of the current window.
Chris@1: 
Chris@1: Data is not returned from the first frame; it must be used to 'prime'
Chris@1: the decode engine.  The encoder accounts for this priming when
Chris@1: calculating PCM offsets; after the first frame, the proper PCM output
Chris@1: offset is '0' (as no data has been returned yet).
Chris@1: 
Chris@1: 
Chris@1: 
Chris@1: \subsubsection{output channel order}
Chris@1: 
Chris@1: Vorbis I specifies only a channel mapping type 0.  In mapping type 0,
Chris@1: channel mapping is implicitly defined as follows for standard audio
Chris@1: applications. As of revision 16781 (20100113), the specification adds
Chris@1: defined channel locations for 6.1 and 7.1 surround.  Ordering/location
Chris@1: for greater-than-eight channels remains 'left to the implementation'.
Chris@1: 
Chris@1: These channel orderings refer to order within the encoded stream.  It
Chris@1: is naturally possible for a decoder to produce output with channels in
Chris@1: any order. Any such decoder should explicitly document channel
Chris@1: reordering behavior.
Chris@1: 
Chris@1: \begin{description} %[style=nextline]
Chris@1:  \item[one channel]
Chris@1: 	the stream is monophonic
Chris@1: 
Chris@1: \item[two channels]
Chris@1: 	the stream is stereo.  channel order: left, right
Chris@1: 
Chris@1: \item[three channels]
Chris@1: 	the stream is a 1d-surround encoding.  channel order: left,
Chris@1: center, right
Chris@1: 
Chris@1: \item[four channels]
Chris@1: 	the stream is quadraphonic surround.  channel order: front left,
Chris@1: front right, rear left, rear right
Chris@1: 
Chris@1: \item[five channels]
Chris@1: 	the stream is five-channel surround.  channel order: front left,
Chris@1: center, front right, rear left, rear right
Chris@1: 
Chris@1: \item[six channels]
Chris@1: 	the stream is 5.1 surround.  channel order: front left, center, 
Chris@1: front right, rear left, rear right, LFE
Chris@1: 
Chris@1: \item[seven channels]
Chris@1:         the stream is 6.1 surround.  channel order: front left, center, 
Chris@1: front right, side left, side right, rear center, LFE
Chris@1: 
Chris@1: \item[eight channels]
Chris@1:         the stream is 7.1 surround.  channel order: front left, center, 
Chris@1: front right, side left, side right, rear left, rear right, 
Chris@1: LFE
Chris@1: 
Chris@1: \item[greater than eight channels]
Chris@1: 	channel use and order is defined by the application
Chris@1: 
Chris@1: \end{description}
Chris@1: 
Chris@1: Applications using Vorbis for dedicated purposes may define channel
Chris@1: mapping as seen fit.  Future channel mappings (such as three and four
Chris@1: channel \href{http://www.ambisonic.net/}{Ambisonics}) will
Chris@1: make use of channel mappings other than mapping 0.
Chris@1: 
Chris@1: