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diff --git a/vorbis/doc/07-floor1.tex b/vorbis/doc/07-floor1.tex deleted file mode 100644 index 47ad798..0000000 --- a/vorbis/doc/07-floor1.tex +++ /dev/null @@ -1,404 +0,0 @@ -% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*- -%!TEX root = Vorbis_I_spec.tex -\section{Floor type 1 setup and decode} \label{vorbis:spec:floor1} - -\subsection{Overview} - -Vorbis floor type one uses a piecewise straight-line representation to -encode a spectral envelope curve. The representation plots this curve -mechanically on a linear frequency axis and a logarithmic (dB) -amplitude axis. The integer plotting algorithm used is similar to -Bresenham's algorithm. - - - -\subsection{Floor 1 format} - -\subsubsection{model} - -Floor type one represents a spectral curve as a series of -line segments. Synthesis constructs a floor curve using iterative -prediction in a process roughly equivalent to the following simplified -description: - -\begin{itemize} - \item the first line segment (base case) is a logical line spanning -from x_0,y_0 to x_1,y_1 where in the base case x_0=0 and x_1=[n], the -full range of the spectral floor to be computed. - -\item the induction step chooses a point x_new within an existing -logical line segment and produces a y_new value at that point computed -from the existing line's y value at x_new (as plotted by the line) and -a difference value decoded from the bitstream packet. - -\item floor computation produces two new line segments, one running from -x_0,y_0 to x_new,y_new and from x_new,y_new to x_1,y_1. This step is -performed logically even if y_new represents no change to the -amplitude value at x_new so that later refinement is additionally -bounded at x_new. - -\item the induction step repeats, using a list of x values specified in -the codec setup header at floor 1 initialization time. Computation -is completed at the end of the x value list. - -\end{itemize} - - -Consider the following example, with values chosen for ease of -understanding rather than representing typical configuration: - -For the below example, we assume a floor setup with an [n] of 128. -The list of selected X values in increasing order is -0,16,32,48,64,80,96,112 and 128. In list order, the values interleave -as 0, 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding -list-order Y values as decoded from an example packet are 110, 20, -5, --45, 0, -25, -10, 30 and -10. We compute the floor in the following -way, beginning with the first line: - -\begin{center} -\includegraphics[width=8cm]{floor1-1} -\captionof{figure}{graph of example floor} -\end{center} - -We now draw new logical lines to reflect the correction to new_Y, and -iterate for X positions 32 and 96: - -\begin{center} -\includegraphics[width=8cm]{floor1-2} -\captionof{figure}{graph of example floor} -\end{center} - -Although the new Y value at X position 96 is unchanged, it is still -used later as an endpoint for further refinement. From here on, the -pattern should be clear; we complete the floor computation as follows: - -\begin{center} -\includegraphics[width=8cm]{floor1-3} -\captionof{figure}{graph of example floor} -\end{center} - -\begin{center} -\includegraphics[width=8cm]{floor1-4} -\captionof{figure}{graph of example floor} -\end{center} - -A more efficient algorithm with carefully defined integer rounding -behavior is used for actual decode, as described later. The actual -algorithm splits Y value computation and line plotting into two steps -with modifications to the above algorithm to eliminate noise -accumulation through integer roundoff/truncation. - - - -\subsubsection{header decode} - -A list of floor X values is stored in the packet header in interleaved -format (used in list order during packet decode and synthesis). This -list is split into partitions, and each partition is assigned to a -partition class. X positions 0 and [n] are implicit and do not belong -to an explicit partition or partition class. - -A partition class consists of a representation vector width (the -number of Y values which the partition class encodes at once), a -'subclass' value representing the number of alternate entropy books -the partition class may use in representing Y values, the list of -[subclass] books and a master book used to encode which alternate -books were chosen for representation in a given packet. The -master/subclass mechanism is meant to be used as a flexible -representation cascade while still using codebooks only in a scalar -context. - -\begin{Verbatim}[commandchars=\\\{\}] - - 1) [floor1\_partitions] = read 5 bits as unsigned integer - 2) [maximum\_class] = -1 - 3) iterate [i] over the range 0 ... [floor1\_partitions]-1 \{ - - 4) vector [floor1\_partition\_class\_list] element [i] = read 4 bits as unsigned integer - - \} - - 5) [maximum\_class] = largest integer scalar value in vector [floor1\_partition\_class\_list] - 6) iterate [i] over the range 0 ... [maximum\_class] \{ - - 7) vector [floor1\_class\_dimensions] element [i] = read 3 bits as unsigned integer and add 1 - 8) vector [floor1\_class\_subclasses] element [i] = read 2 bits as unsigned integer - 9) if ( vector [floor1\_class\_subclasses] element [i] is nonzero ) \{ - - 10) vector [floor1\_class\_masterbooks] element [i] = read 8 bits as unsigned integer - - \} - - 11) iterate [j] over the range 0 ... (2 exponent [floor1\_class\_subclasses] element [i]) - 1 \{ - - 12) array [floor1\_subclass\_books] element [i],[j] = - read 8 bits as unsigned integer and subtract one - \} - \} - - 13) [floor1\_multiplier] = read 2 bits as unsigned integer and add one - 14) [rangebits] = read 4 bits as unsigned integer - 15) vector [floor1\_X\_list] element [0] = 0 - 16) vector [floor1\_X\_list] element [1] = 2 exponent [rangebits]; - 17) [floor1\_values] = 2 - 18) iterate [i] over the range 0 ... [floor1\_partitions]-1 \{ - - 19) [current\_class\_number] = vector [floor1\_partition\_class\_list] element [i] - 20) iterate [j] over the range 0 ... ([floor1\_class\_dimensions] element [current\_class\_number])-1 \{ - 21) vector [floor1\_X\_list] element ([floor1\_values]) = - read [rangebits] bits as unsigned integer - 22) increment [floor1\_values] by one - \} - \} - - 23) done -\end{Verbatim} - -An end-of-packet condition while reading any aspect of a floor 1 -configuration during setup renders a stream undecodable. In addition, -a \varname{[floor1\_class\_masterbooks]} or -\varname{[floor1\_subclass\_books]} scalar element greater than the -highest numbered codebook configured in this stream is an error -condition that renders the stream undecodable. Vector -[floor1\_x\_list] is limited to a maximum length of 65 elements; a -setup indicating more than 65 total elements (including elements 0 and -1 set prior to the read loop) renders the stream undecodable. All -vector [floor1\_x\_list] element values must be unique within the -vector; a non-unique value renders the stream undecodable. - -\subsubsection{packet decode} \label{vorbis:spec:floor1-decode} - -Packet decode begins by checking the \varname{[nonzero]} flag: - -\begin{Verbatim}[commandchars=\\\{\}] - 1) [nonzero] = read 1 bit as boolean -\end{Verbatim} - -If \varname{[nonzero]} is unset, that indicates this channel contained -no audio energy in this frame. Decode immediately returns a status -indicating this floor curve (and thus this channel) is unused this -frame. (A return status of 'unused' is different from decoding a -floor that has all points set to minimum representation amplitude, -which happens to be approximately -140dB). - - -Assuming \varname{[nonzero]} is set, decode proceeds as follows: - -\begin{Verbatim}[commandchars=\\\{\}] - 1) [range] = vector \{ 256, 128, 86, 64 \} element ([floor1\_multiplier]-1) - 2) vector [floor1\_Y] element [0] = read \link{vorbis:spec:ilog}{ilog}([range]-1) bits as unsigned integer - 3) vector [floor1\_Y] element [1] = read \link{vorbis:spec:ilog}{ilog}([range]-1) bits as unsigned integer - 4) [offset] = 2; - 5) iterate [i] over the range 0 ... [floor1\_partitions]-1 \{ - - 6) [class] = vector [floor1\_partition\_class] element [i] - 7) [cdim] = vector [floor1\_class\_dimensions] element [class] - 8) [cbits] = vector [floor1\_class\_subclasses] element [class] - 9) [csub] = (2 exponent [cbits])-1 - 10) [cval] = 0 - 11) if ( [cbits] is greater than zero ) \{ - - 12) [cval] = read from packet using codebook number - (vector [floor1\_class\_masterbooks] element [class]) in scalar context - \} - - 13) iterate [j] over the range 0 ... [cdim]-1 \{ - - 14) [book] = array [floor1\_subclass\_books] element [class],([cval] bitwise AND [csub]) - 15) [cval] = [cval] right shifted [cbits] bits - 16) if ( [book] is not less than zero ) \{ - - 17) vector [floor1\_Y] element ([j]+[offset]) = read from packet using codebook - [book] in scalar context - - \} else [book] is less than zero \{ - - 18) vector [floor1\_Y] element ([j]+[offset]) = 0 - - \} - \} - - 19) [offset] = [offset] + [cdim] - - \} - - 20) done -\end{Verbatim} - -An end-of-packet condition during curve decode should be considered a -nominal occurrence; if end-of-packet is reached during any read -operation above, floor decode is to return 'unused' status as if the -\varname{[nonzero]} flag had been unset at the beginning of decode. - - -Vector \varname{[floor1\_Y]} contains the values from packet decode -needed for floor 1 synthesis. - - - -\subsubsection{curve computation} \label{vorbis:spec:floor1-synth} - -Curve computation is split into two logical steps; the first step -derives final Y amplitude values from the encoded, wrapped difference -values taken from the bitstream. The second step plots the curve -lines. Also, although zero-difference values are used in the -iterative prediction to find final Y values, these points are -conditionally skipped during final line computation in step two. -Skipping zero-difference values allows a smoother line fit. - -Although some aspects of the below algorithm look like inconsequential -optimizations, implementors are warned to follow the details closely. -Deviation from implementing a strictly equivalent algorithm can result -in serious decoding errors. - -{\em Additional note:} Although \varname{[floor1\_final\_Y]} values in -the prediction loop and at the end of step 1 are inherently limited by -the prediction algorithm to [0, \varname{[range]}), it is possible to - abuse the setup and codebook machinery to produce negative or - over-range results. We suggest that decoder implementations guard - the values in vector \varname{[floor1\_final\_Y]} by clamping each - element to [0, \varname{[range]}) after step 1. Variants of this - suggestion are acceptable as valid floor1 setups cannot produce - out of range values. - -\begin{description} -\item[step 1: amplitude value synthesis] - -Unwrap the always-positive-or-zero values read from the packet into -+/- difference values, then apply to line prediction. - -\begin{Verbatim}[commandchars=\\\{\}] - 1) [range] = vector \{ 256, 128, 86, 64 \} element ([floor1\_multiplier]-1) - 2) vector [floor1\_step2\_flag] element [0] = set - 3) vector [floor1\_step2\_flag] element [1] = set - 4) vector [floor1\_final\_Y] element [0] = vector [floor1\_Y] element [0] - 5) vector [floor1\_final\_Y] element [1] = vector [floor1\_Y] element [1] - 6) iterate [i] over the range 2 ... [floor1\_values]-1 \{ - - 7) [low\_neighbor\_offset] = \link{vorbis:spec:low:neighbor}{low\_neighbor}([floor1\_X\_list],[i]) - 8) [high\_neighbor\_offset] = \link{vorbis:spec:high:neighbor}{high\_neighbor}([floor1\_X\_list],[i]) - - 9) [predicted] = \link{vorbis:spec:render:point}{render\_point}( vector [floor1\_X\_list] element [low\_neighbor\_offset], - vector [floor1\_final\_Y] element [low\_neighbor\_offset], - vector [floor1\_X\_list] element [high\_neighbor\_offset], - vector [floor1\_final\_Y] element [high\_neighbor\_offset], - vector [floor1\_X\_list] element [i] ) - - 10) [val] = vector [floor1\_Y] element [i] - 11) [highroom] = [range] - [predicted] - 12) [lowroom] = [predicted] - 13) if ( [highroom] is less than [lowroom] ) \{ - - 14) [room] = [highroom] * 2 - - \} else [highroom] is not less than [lowroom] \{ - - 15) [room] = [lowroom] * 2 - - \} - - 16) if ( [val] is nonzero ) \{ - - 17) vector [floor1\_step2\_flag] element [low\_neighbor\_offset] = set - 18) vector [floor1\_step2\_flag] element [high\_neighbor\_offset] = set - 19) vector [floor1\_step2\_flag] element [i] = set - 20) if ( [val] is greater than or equal to [room] ) \{ - - 21) if ( [highroom] is greater than [lowroom] ) \{ - - 22) vector [floor1\_final\_Y] element [i] = [val] - [lowroom] + [predicted] - - \} else [highroom] is not greater than [lowroom] \{ - - 23) vector [floor1\_final\_Y] element [i] = [predicted] - [val] + [highroom] - 1 - - \} - - \} else [val] is less than [room] \{ - - 24) if ([val] is odd) \{ - - 25) vector [floor1\_final\_Y] element [i] = - [predicted] - (([val] + 1) divided by 2 using integer division) - - \} else [val] is even \{ - - 26) vector [floor1\_final\_Y] element [i] = - [predicted] + ([val] / 2 using integer division) - - \} - - \} - - \} else [val] is zero \{ - - 27) vector [floor1\_step2\_flag] element [i] = unset - 28) vector [floor1\_final\_Y] element [i] = [predicted] - - \} - - \} - - 29) done - -\end{Verbatim} - - - -\item[step 2: curve synthesis] - -Curve synthesis generates a return vector \varname{[floor]} of length -\varname{[n]} (where \varname{[n]} is provided by the decode process -calling to floor decode). Floor 1 curve synthesis makes use of the -\varname{[floor1\_X\_list]}, \varname{[floor1\_final\_Y]} and -\varname{[floor1\_step2\_flag]} vectors, as well as [floor1\_multiplier] -and [floor1\_values] values. - -Decode begins by sorting the scalars from vectors -\varname{[floor1\_X\_list]}, \varname{[floor1\_final\_Y]} and -\varname{[floor1\_step2\_flag]} together into new vectors -\varname{[floor1\_X\_list]'}, \varname{[floor1\_final\_Y]'} and -\varname{[floor1\_step2\_flag]'} according to ascending sort order of the -values in \varname{[floor1\_X\_list]}. That is, sort the values of -\varname{[floor1\_X\_list]} and then apply the same permutation to -elements of the other two vectors so that the X, Y and step2\_flag -values still match. - -Then compute the final curve in one pass: - -\begin{Verbatim}[commandchars=\\\{\}] - 1) [hx] = 0 - 2) [lx] = 0 - 3) [ly] = vector [floor1\_final\_Y]' element [0] * [floor1\_multiplier] - 4) iterate [i] over the range 1 ... [floor1\_values]-1 \{ - - 5) if ( [floor1\_step2\_flag]' element [i] is set ) \{ - - 6) [hy] = [floor1\_final\_Y]' element [i] * [floor1\_multiplier] - 7) [hx] = [floor1\_X\_list]' element [i] - 8) \link{vorbis:spec:render:line}{render\_line}( [lx], [ly], [hx], [hy], [floor] ) - 9) [lx] = [hx] - 10) [ly] = [hy] - \} - \} - - 11) if ( [hx] is less than [n] ) \{ - - 12) \link{vorbis:spec:render:line}{render\_line}( [hx], [hy], [n], [hy], [floor] ) - - \} - - 13) if ( [hx] is greater than [n] ) \{ - - 14) truncate vector [floor] to [n] elements - - \} - - 15) for each scalar in vector [floor], perform a lookup substitution using - the scalar value from [floor] as an offset into the vector \link{vorbis:spec:floor1:inverse:dB:table}{[floor1\_inverse\_dB\_static\_table]} - - 16) done - -\end{Verbatim} - -\end{description} |