mirror of
https://github.com/cookiengineer/audacity
synced 2025-11-03 23:53:55 +01:00
240 lines
5.6 KiB
HTML
240 lines
5.6 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
|
<html>
|
|
<head>
|
|
|
|
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-15"/>
|
|
<title>Ogg Vorbis Documentation</title>
|
|
|
|
<style type="text/css">
|
|
body {
|
|
margin: 0 18px 0 18px;
|
|
padding-bottom: 30px;
|
|
font-family: Verdana, Arial, Helvetica, sans-serif;
|
|
color: #333333;
|
|
font-size: .8em;
|
|
}
|
|
|
|
a {
|
|
color: #3366cc;
|
|
}
|
|
|
|
img {
|
|
border: 0;
|
|
}
|
|
|
|
#xiphlogo {
|
|
margin: 30px 0 16px 0;
|
|
}
|
|
|
|
#content p {
|
|
line-height: 1.4;
|
|
}
|
|
|
|
h1, h1 a, h2, h2 a, h3, h3 a {
|
|
font-weight: bold;
|
|
color: #ff9900;
|
|
margin: 1.3em 0 8px 0;
|
|
}
|
|
|
|
h1 {
|
|
font-size: 1.3em;
|
|
}
|
|
|
|
h2 {
|
|
font-size: 1.2em;
|
|
}
|
|
|
|
h3 {
|
|
font-size: 1.1em;
|
|
}
|
|
|
|
li {
|
|
line-height: 1.4;
|
|
}
|
|
|
|
#copyright {
|
|
margin-top: 30px;
|
|
line-height: 1.5em;
|
|
text-align: center;
|
|
font-size: .8em;
|
|
color: #888888;
|
|
clear: both;
|
|
}
|
|
</style>
|
|
|
|
</head>
|
|
|
|
<body>
|
|
|
|
<div id="xiphlogo">
|
|
<a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.Org"/></a>
|
|
</div>
|
|
|
|
<h1>Ogg Vorbis I format specification: helper equations</h1>
|
|
|
|
<h1>Overview</h1>
|
|
|
|
<p>The equations below are used in multiple places by the Vorbis codec
|
|
specification. Rather than cluttering up the main specification
|
|
documents, they are defined here and linked in the main documents
|
|
where appropriate.</p>
|
|
|
|
<h2><a name="log">ilog</a></h2>
|
|
|
|
<p>The "ilog(x)" function returns the position number (1 through n) of the
|
|
highest set bit in the two's complement integer value
|
|
<tt>[x]</tt>. Values of <tt>[x]</tt> less than zero are defined to return zero.</p>
|
|
|
|
<pre>
|
|
1) [return_value] = 0;
|
|
2) if ( [x] is greater than zero ){
|
|
|
|
3) increment [return_value];
|
|
4) logical shift [x] one bit to the right, padding the MSb with zero
|
|
5) repeat at step 2)
|
|
|
|
}
|
|
|
|
6) done
|
|
</pre>
|
|
|
|
<p>Examples:</p>
|
|
|
|
<ul>
|
|
<li>ilog(0) = 0;</li>
|
|
<li>ilog(1) = 1;</li>
|
|
<li>ilog(2) = 2;</li>
|
|
<li>ilog(3) = 2;</li>
|
|
<li>ilog(4) = 3;</li>
|
|
<li>ilog(7) = 3;</li>
|
|
<li>ilog(negative number) = 0;</li>
|
|
</ul>
|
|
|
|
<h2><a name="float32_unpack">float32_unpack</a></h2>
|
|
|
|
<p>"float32_unpack(x)" is intended to translate the packed binary
|
|
representation of a Vorbis codebook float value into the
|
|
representation used by the decoder for floating point numbers. For
|
|
purposes of this example, we will unpack a Vorbis float32 into a
|
|
host-native floating point number.</p>
|
|
|
|
<pre>
|
|
1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result)
|
|
2) [sign] = [x] bitwise AND 0x80000000 (unsigned result)
|
|
3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result)
|
|
4) if ( [sign] is nonzero ) then negate [mantissa]
|
|
5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) )
|
|
</pre>
|
|
|
|
<h2><a name="lookup1_values">lookup1_values</a></h2>
|
|
|
|
<p>"lookup1_values(codebook_entries,codebook_dimensions)" is used to
|
|
compute the correct length of the value index for a codebook VQ lookup
|
|
table of lookup type 1. The values on this list are permuted to
|
|
construct the VQ vector lookup table of size
|
|
<tt>[codebook_entries]</tt>.</p>
|
|
|
|
<p>The return value for this function is defined to be 'the greatest
|
|
integer value for which <tt>[return_value] to the power of
|
|
[codebook_dimensions] is less than or equal to
|
|
[codebook_entries]</tt>'.</p>
|
|
|
|
<h2><a name="low_neighbor">low_neighbor</a></h2>
|
|
|
|
<p>"low_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
|
|
the greatest value scalar element for which <i>n</i> is less than
|
|
<tt>[x]</tt> and <tt>vector [v] element <i>n</i> is less
|
|
than vector [v] element [x]</tt>.</p>
|
|
|
|
<h2><a name="high_neighbor">high_neighbor</a></h2>
|
|
|
|
<p>"high_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
|
|
the lowest value scalar element for which <i>n</i> is less than
|
|
<tt>[x]</tt> and <tt>vector [v] element <i>n</i> is greater
|
|
than vector [v] element [x]</tt>.</p>
|
|
|
|
<h2><a name="render_point">render_point</a></h2>
|
|
|
|
<p>"render_point(x0,y0,x1,y1,X)" is used to find the Y value at point X
|
|
along the line specified by x0, x1, y0 and y1. This function uses an
|
|
integer algorithm to solve for the point directly without calculating
|
|
intervening values along the line.</p>
|
|
|
|
<pre>
|
|
1) [dy] = [y1] - [y0]
|
|
2) [adx] = [x1] - [x0]
|
|
3) [ady] = absolute value of [dy]
|
|
4) [err] = [ady] * ([X] - [x0])
|
|
5) [off] = [err] / [adx] using integer division
|
|
6) if ( [dy] is less than zero ) {
|
|
|
|
7) [Y] = [y0] - [off]
|
|
|
|
} else {
|
|
|
|
8) [Y] = [y0] + [off]
|
|
|
|
}
|
|
|
|
9) done
|
|
</pre>
|
|
|
|
<h2><a name="render_line">render_line</a></h2>
|
|
|
|
<p>Floor decode type one uses the integer line drawing algorithm of
|
|
"render_line(x0, y0, x1, y1, v)" to construct an integer floor
|
|
curve for contiguous piecewise line segments. Note that it has not
|
|
been relevant elsewhere, but here we must define integer division as
|
|
rounding division of both positive and negative numbers toward zero.</p>
|
|
|
|
<pre>
|
|
1) [dy] = [y1] - [y0]
|
|
2) [adx] = [x1] - [x0]
|
|
3) [ady] = absolute value of [dy]
|
|
4) [base] = [dy] / [adx] using integer division
|
|
5) [x] = [x0]
|
|
6) [y] = [y0]
|
|
7) [err] = 0
|
|
|
|
8) if ( [dy] is less than 0 ) {
|
|
|
|
9) [sy] = [base] - 1
|
|
|
|
} else {
|
|
|
|
10) [sy] = [base] + 1
|
|
|
|
}
|
|
|
|
11) [ady] = [ady] - (absolute value of [base]) * [adx]
|
|
12) vector [v] element [x] = [y]
|
|
|
|
13) iterate [x] over the range [x0]+1 ... [x1]-1 {
|
|
|
|
14) [err] = [err] + [ady];
|
|
15) if ( [err] >= [adx] ) {
|
|
|
|
15) [err] = [err] - [adx]
|
|
16) [y] = [y] + [sy]
|
|
|
|
} else {
|
|
|
|
17) [y] = [y] + [base]
|
|
|
|
}
|
|
|
|
18) vector [v] element [x] = [y]
|
|
|
|
}
|
|
</pre>
|
|
|
|
<div id="copyright">
|
|
The Xiph Fish Logo is a
|
|
trademark (™) of Xiph.Org.<br/>
|
|
|
|
These pages © 1994 - 2005 Xiph.Org. All rights reserved.
|
|
</div>
|
|
|
|
</body>
|
|
</html>
|