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authorMonty <xiphmont@xiph.org>2011-08-11 07:04:25 +0000
committerMonty <xiphmont@xiph.org>2011-08-11 07:04:25 +0000
commit228e3c57e366f43e3f9cc97a5c3b7d221717ac1d (patch)
treebed2801d024078a0aec762b1b47df97556ddb868
parentaa5080563d76215060f7a0c8aaf6cf8bbf63518b (diff)
downloadlibvorbis-git-228e3c57e366f43e3f9cc97a5c3b7d221717ac1d.tar.gz
Hack to deal with the fact that underscores in a \mathtt{} were showing
up as the letter 'X', but using \texttt{} instead caused incorrect type scaling in math typesetting svn path=/trunk/vorbis/; revision=18066
Diffstat
-rw-r--r--doc/06-floor0.tex76
-rw-r--r--doc/Vorbis_I_spec.html38
-rw-r--r--doc/Vorbis_I_spec.pdf1025
-rw-r--r--doc/Vorbis_I_spec10x.pngbin3002 -> 2871 bytes
-rw-r--r--doc/Vorbis_I_spec11x.pngbin3521 -> 3485 bytes
-rw-r--r--doc/Vorbis_I_spec12x.pngbin3388 -> 2946 bytes
-rw-r--r--doc/Vorbis_I_spec7x.pngbin2247 -> 1962 bytes
-rw-r--r--doc/Vorbis_I_spec8x.pngbin2513 -> 2365 bytes
8 files changed, 573 insertions, 566 deletions
diff --git a/doc/06-floor0.tex b/doc/06-floor0.tex
index 4d423675..021c5188 100644
--- a/doc/06-floor0.tex
+++ b/doc/06-floor0.tex
@@ -28,18 +28,18 @@ 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;
+ 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
+\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.
@@ -48,24 +48,24 @@ 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
+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
+ 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
+ 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
+ 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
\}
@@ -82,16 +82,16 @@ 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]} -
+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
+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
+\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
@@ -104,9 +104,9 @@ decode. The extra values are not used and may be ignored or discarded.
\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 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.
@@ -119,7 +119,7 @@ synthesized:
\mathrm{map}_i = \left\{
\begin{array}{ll}
\min (
- \mathtt{floor0\_bark\_map\_size} - 1,
+ \mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1,
foobar
) & \textrm{for } i \in [0,n-1] \\
-1 & \textrm{for } i = n
@@ -132,7 +132,7 @@ synthesized:
\begin{displaymath}
foobar =
\left\lfloor
- \mathrm{bark}\left(\frac{\mathtt{floor0\_rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\_bark\_map\_size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\_rate})}
+ \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}
@@ -149,37 +149,37 @@ Similarly, the below calculation synthesizes the output LSP curve \varname{[outp
\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 ) {
+ \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\_order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
- q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
+ 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 {
+ } else \varname{[floor0\_order]} is even {
\begin{enumerate}
\item calculate \varname{[p]} and \varname{[q]} according to:
\begin{eqnarray*}
- p & = & \frac{(1 - \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
- q & = & \frac{(1 + \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
+ 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:
+ \item calculate \varname{[linear\_floor\_value]} according to:
\begin{displaymath}
- \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\_amplitute\_offset}}{(2^{\mathtt{floor0\_amplitude\_bits}}-1)\sqrt{p+q}}
- - \mathtt{floor0\_amplitude\_offset} \right) \right)
+ \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 \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 ( 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}
diff --git a/doc/Vorbis_I_spec.html b/doc/Vorbis_I_spec.html
index 94f5bbb9..6e7fa02a 100644
--- a/doc/Vorbis_I_spec.html
+++ b/doc/Vorbis_I_spec.html
@@ -7,7 +7,7 @@
<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
<!-- html -->
<meta name="src" content="Vorbis_I_spec.tex">
-<meta name="date" content="2011-08-11 02:26:00">
+<meta name="date" content="2011-08-11 03:03:00">
<link rel="stylesheet" type="text/css" href="Vorbis_I_spec.css">
</head><body
>
@@ -5735,9 +5735,9 @@ class="cmtt-12">[coefficients] </span>is to to read a total of twelve scalars
id="x1-940006.2.3"></a>curve computation</h5>
<!--l. 106--><p class="noindent" >Given an <span
class="cmtt-12">[amplitude] </span>integer and <span
-class="cmtt-12">[coefficients] </span>vector from packet decode as well
-as the [floor0&#x02D9;order], [floor0&#x02D9;rate], [floor0&#x02D9;bark&#x02D9;map&#x02D9;size], [floor0&#x02D9;amplitude&#x02D9;bits] and
-[floor0&#x02D9;amplitude&#x02D9;offset] values from floor setup, and an output vector size <span
+class="cmtt-12">[coefficients] </span>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 <span
class="cmtt-12">[n] </span>specified by the
decode process, we compute a floor output vector.
<!--l. 113--><p class="noindent" >If the value <span
@@ -5748,7 +5748,7 @@ synthesized:
<center class="par-math-display" >
<img
src="Vorbis_I_spec7x.png" alt=" {
- min (floor0xbarkxmapxsize &minus; 1,foobar ) for i &isin; [0,n &minus; 1 ]
+ min (floor0_bark_map_size &minus; 1,foobar ) for i &isin; [0,n &minus; 1 ]
mapi = &minus; 1 for i = n
" class="par-math-display" ></center>
<!--l. 128--><p class="nopar" >
@@ -5756,8 +5756,8 @@ mapi = &minus; 1 for i = n
<center class="par-math-display" >
<img
src="Vorbis_I_spec8x.png" alt=" &lfloor; &rfloor;
- (floor0xrate &sdot; i) floor0xbarkxmapxsize
-foobar = bark -------2n------- &sdot;-bark(.5 &sdot; floor0xrate-)
+ (floor0_rate &sdot; i) floor0_bark_map_size
+foobar = bark -------2n------- &sdot;-bark(.5 &sdot; floor0_rate-)
" class="par-math-display" ></center>
@@ -5800,12 +5800,12 @@ class="cmtt-12">[p] </span>and <span
class="cmtt-12">[q] </span>according to: <div class="eqnarray">
<center class="math-display" >
<img
-src="Vorbis_I_spec10x.png" alt=" floor0xorder&minus;3
+src="Vorbis_I_spec10x.png" alt=" floor0_order&minus;3
2 &prod;2 2
p = (1 &minus; cos &omega;) 4(cos([coefficients ]2j+1) &minus; cos&omega; )
- j=0
- floor0x&prod;or2der&minus;1
-q = 1- 4(cos([coefficients ]2j) &minus; cos&omega; )2
+ floor0_order&minus;1 j=0
+ 1 ----&prod;2----
+q = -- 4(cos([coefficients ]2j) &minus; cos&omega; )2
4 j=0
@@ -5822,13 +5822,13 @@ class="cmtt-12">[p] </span>and <span
class="cmtt-12">[q] </span>according to: <div class="eqnarray">
<center class="math-display" >
<img
-src="Vorbis_I_spec11x.png" alt=" floor0xorder&minus;2
- (1 &minus; cos&omega; ) &prod;2 2
-p = -----2----- 4(cos([coefficients ]2j+1) &minus; cos&omega;)
+src="Vorbis_I_spec11x.png" alt=" floor0_order&minus;2
+ (1-&minus;-cos&omega;-) &prod;2 2
+p = 2 4(cos([coefficients ]2j+1) &minus; cos&omega;)
j=0
- floor0xo2rder&minus;-2
-q = (1-+-cos&omega;-) &prod; 4(cos([coefficients ] ) &minus; cos &omega;)2
- 2 j=0 2j
+ floor0_&prod;o2rder&minus;-2
+q = (1-+-cos&omega;-) 4(cos([coefficients ]2j) &minus; cos &omega;)2
+ 2 j=0
" class="math-display" ></center>
</div>
</li></ol>
@@ -5839,8 +5839,8 @@ class="cmtt-12">[linear_floor_value] </span>according to:
<center class="math-display" >
<img
src="Vorbis_I_spec12x.png" alt=" ( ( ))
- amplitude---&sdot; floor0xamplitutexoffset---
-exp .11512925 (2floor0xamplitudexbits &minus; 1)&radic; p + q &minus; floor0xamplitudexoffset
+exp .11512925 amplitude---&sdot; floor0_amplitute_&radic;offset---&minus; floor0_amplitude_offset
+ (2floor0_amplitude_bits &minus; 1) p + q
" class="math-display" ></center>
<!--l. 177--><p class="nopar" >
</li>
diff --git a/doc/Vorbis_I_spec.pdf b/doc/Vorbis_I_spec.pdf
index 4cb38ede..0bf12946 100644
--- a/doc/Vorbis_I_spec.pdf
+++ b/doc/Vorbis_I_spec.pdf
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View Lorry Controller Status