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