From 373dc625f82b47096893add42c4472e4a57ab7eb Mon Sep 17 00:00:00 2001
From: Aki <please@ignore.pl>
Date: Wed, 9 Feb 2022 22:23:03 +0100
Subject: Moved third-party libraries to a separate subdirectory

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 vorbis/doc/06-floor0.tex | 201 -----------------------------------------------
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-% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
-%!TEX root = Vorbis_I_spec.tex
-\section{Floor type 0 setup and decode} \label{vorbis:spec:floor0}
-
-\subsection{Overview}
-
-Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately
-known as Line Spectral Frequency or LSF) representation to encode a
-smooth spectral envelope curve as the frequency response of the LSP
-filter.  This representation is equivalent to a traditional all-pole
-infinite impulse response filter as would be used in linear predictive
-coding; LSP representation may be converted to LPC representation and
-vice-versa.
-
-
-
-\subsection{Floor 0 format}
-
-Floor zero configuration consists of six integer fields and a list of
-VQ codebooks for use in coding/decoding the LSP filter coefficient
-values used by each frame.
-
-\subsubsection{header decode}
-
-Configuration information for instances of floor zero decodes from the
-codec setup header (third packet).  configuration decode proceeds as
-follows:
-
-\begin{Verbatim}[commandchars=\\\{\}]
-  1) [floor0\_order] = read an unsigned integer of 8 bits
-  2) [floor0\_rate] = read an unsigned integer of 16 bits
-  3) [floor0\_bark\_map\_size] = read an unsigned integer of 16 bits
-  4) [floor0\_amplitude\_bits] = read an unsigned integer of six bits
-  5) [floor0\_amplitude\_offset] = read an unsigned integer of eight bits
-  6) [floor0\_number\_of\_books] = read an unsigned integer of four bits and add 1
-  7) array [floor0\_book\_list] = read a list of [floor0\_number\_of\_books] unsigned integers of eight bits each;
-\end{Verbatim}
-
-An end-of-packet condition during any of these bitstream reads renders
-this stream undecodable.  In addition, any element of the array
-\varname{[floor0\_book\_list]} that is greater than the maximum codebook
-number for this bitstream is an error condition that also renders the
-stream undecodable.
-
-
-
-\subsubsection{packet decode} \label{vorbis:spec:floor0-decode}
-
-Extracting a floor0 curve from an audio packet consists of first
-decoding the curve amplitude and \varname{[floor0\_order]} LSP
-coefficient values from the bitstream, and then computing the floor
-curve, which is defined as the frequency response of the decoded LSP
-filter.
-
-Packet decode proceeds as follows:
-\begin{Verbatim}[commandchars=\\\{\}]
-  1) [amplitude] = read an unsigned integer of [floor0\_amplitude\_bits] bits
-  2) if ( [amplitude] is greater than zero ) \{
-       3) [coefficients] is an empty, zero length vector
-       4) [booknumber] = read an unsigned integer of \link{vorbis:spec:ilog}{ilog}( [floor0\_number\_of\_books] ) bits
-       5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable
-       6) [last] = zero;
-       7) vector [temp\_vector] = read vector from bitstream using codebook number [floor0\_book\_list] element [booknumber] in VQ context.
-       8) add the scalar value [last] to each scalar in vector [temp\_vector]
-       9) [last] = the value of the last scalar in vector [temp\_vector]
-      10) concatenate [temp\_vector] onto the end of the [coefficients] vector
-      11) if (length of vector [coefficients] is less than [floor0\_order], continue at step 6
-
-     \}
-
- 12) done.
-
-\end{Verbatim}
-
-Take note of the following properties of decode:
-\begin{itemize}
- \item An \varname{[amplitude]} value of zero must result in a return code that indicates this channel is unused in this frame (the output of the channel will be all-zeroes in synthesis).  Several later stages of decode don't occur for an unused channel.
- \item An end-of-packet condition during decode should be considered a
-nominal occruence; if end-of-packet is reached during any read
-operation above, floor decode is to return 'unused' status as if the
-\varname{[amplitude]} value had read zero at the beginning of decode.
-
- \item The book number used for decode
-can, in fact, be stored in the bitstream in \link{vorbis:spec:ilog}{ilog}( \varname{[floor0\_number\_of\_books]} -
-1 ) bits.  Nevertheless, the above specification is correct and values
-greater than the maximum possible book value are reserved.
-
- \item The number of scalars read into the vector \varname{[coefficients]}
-may be greater than \varname{[floor0\_order]}, the number actually
-required for curve computation.  For example, if the VQ codebook used
-for the floor currently being decoded has a
-\varname{[codebook\_dimensions]} value of three and
-\varname{[floor0\_order]} is ten, the only way to fill all the needed
-scalars in \varname{[coefficients]} is to to read a total of twelve
-scalars as four vectors of three scalars each.  This is not an error
-condition, and care must be taken not to allow a buffer overflow in
-decode. The extra values are not used and may be ignored or discarded.
-\end{itemize}
-
-
-
-
-\subsubsection{curve computation} \label{vorbis:spec:floor0-synth}
-
-Given an \varname{[amplitude]} integer and \varname{[coefficients]}
-vector from packet decode as well as the [floor0\_order],
-[floor0\_rate], [floor0\_bark\_map\_size], [floor0\_amplitude\_bits] and
-[floor0\_amplitude\_offset] values from floor setup, and an output
-vector size \varname{[n]} specified by the decode process, we compute a
-floor output vector.
-
-If the value \varname{[amplitude]} is zero, the return value is a
-length \varname{[n]} vector with all-zero scalars.  Otherwise, begin by
-assuming the following definitions for the given vector to be
-synthesized:
-
-   \begin{displaymath}
-     \mathrm{map}_i = \left\{
-       \begin{array}{ll}
-          \min (
-            \mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1,
-            foobar
-          ) & \textrm{for } i \in [0,n-1] \\
-          -1 & \textrm{for } i = n
-        \end{array}
-      \right.
-    \end{displaymath}
-
-    where
-
-    \begin{displaymath}
-    foobar =
-      \left\lfloor
-        \mathrm{bark}\left(\frac{\mathtt{floor0\texttt{\_}rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\texttt{\_}rate})}
-      \right\rfloor
-    \end{displaymath}
-
-    and
-
-    \begin{displaymath}
-      \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2) + .0001x
-    \end{displaymath}
-
-The above is used to synthesize the LSP curve on a Bark-scale frequency
-axis, then map the result to a linear-scale frequency axis.
-Similarly, the below calculation synthesizes the output LSP curve \varname{[output]} on a log
-(dB) amplitude scale, mapping it to linear amplitude in the last step:
-
-\begin{enumerate}
- \item  \varname{[i]} = 0
- \item  \varname{[$\omega$]} = $\pi$ * map element \varname{[i]} / \varname{[floor0\_bark\_map\_size]}
- \item if ( \varname{[floor0\_order]} is odd ) {
-  \begin{enumerate}
-   \item calculate \varname{[p]} and \varname{[q]} according to:
-           \begin{eqnarray*}
-             p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
-             q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
-           \end{eqnarray*}
-
-  \end{enumerate}
-  } else \varname{[floor0\_order]} is even {
-  \begin{enumerate}[resume]
-   \item calculate \varname{[p]} and \varname{[q]} according to:
-           \begin{eqnarray*}
-             p & = & \frac{(1 - \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
-             q & = & \frac{(1 + \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
-           \end{eqnarray*}
-
-  \end{enumerate}
-  }
-
- \item calculate \varname{[linear\_floor\_value]} according to:
-         \begin{displaymath}
-           \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\texttt{\_}amplitute\texttt{\_}offset}}{(2^{\mathtt{floor0\texttt{\_}amplitude\texttt{\_}bits}}-1)\sqrt{p+q}}
-                  - \mathtt{floor0\texttt{\_}amplitude\texttt{\_}offset} \right) \right)
-         \end{displaymath}
-
- \item \varname{[iteration\_condition]} = map element \varname{[i]}
- \item \varname{[output]} element \varname{[i]} = \varname{[linear\_floor\_value]}
- \item increment \varname{[i]}
- \item if ( map element \varname{[i]} is equal to \varname{[iteration\_condition]} ) continue at step 5
- \item if ( \varname{[i]} is less than \varname{[n]} ) continue at step 2
- \item done
-\end{enumerate}
-
-\paragraph{Errata 20150227: Bark scale computation}
-
-Due to a typo when typesetting this version of the specification from the original HTML document, the Bark scale computation previously erroneously read:
-
-    \begin{displaymath}
-      \hbox{\sout{$
-      \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x)
-      $}}
-    \end{displaymath}
-
-Note that the last parenthesis is misplaced.  This document now uses the correct equation as it appeared in the original HTML spec document:
-
-    \begin{displaymath}
-      \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2) + .0001x
-    \end{displaymath}
-
-- 
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