forked from LosaDev/ls-2019-source
197 lines
6.0 KiB
HTML
197 lines
6.0 KiB
HTML
<HTML><HEAD><TITLE>xiph.org: Ogg Vorbis documentation</TITLE>
|
|
<BODY bgcolor="#ffffff" text="#202020" link="#006666" vlink="#000000">
|
|
<nobr><img src="white-ogg.png"><img src="vorbisword2.png"></nobr><p>
|
|
|
|
<h1><font color=#000070>
|
|
Ogg Vorbis I format specification: helper equations
|
|
</font></h1>
|
|
|
|
<em>Last update to this document: July 18, 2002</em><p>
|
|
|
|
<h1>Overview</h1>
|
|
|
|
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 int he main documents
|
|
where appropriate.<p>
|
|
|
|
<a name=log><h2>ilog</h2></a>
|
|
|
|
|
|
The "ilog(x)" function returns 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.
|
|
|
|
<pre>
|
|
1) [return_value] = 0;
|
|
2) if ( [x] is greater than nonzero ){
|
|
|
|
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>
|
|
|
|
Examples:
|
|
|
|
<ul><li> ilog(0) = 0;
|
|
<li> ilog(1) = 1;
|
|
<li> ilog(2) = 2;
|
|
<li> ilog(3) = 2;
|
|
<li> ilog(4) = 3;
|
|
<li> ilog(7) = 3;
|
|
<li> ilog(negative number) = 0;
|
|
</uL>
|
|
|
|
<a name=float32_unpack><h2>float32_unpack</h2></a>
|
|
|
|
"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 left 21 bits (unsigned result)
|
|
4) if ( [mantissa] is nonzero ) then negate [mantissa]
|
|
5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) )
|
|
</pre>
|
|
|
|
<a name=lookup1_values><h2>lookup1_values</h2></a>
|
|
|
|
"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>
|
|
|
|
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>'.
|
|
|
|
<a name=low_neighbor><h2>low_neighbor</h2></a>
|
|
|
|
"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>.
|
|
|
|
<a name=high_neighbor><h2>high_neighbor</h2></a>
|
|
|
|
"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>.
|
|
|
|
<a name=render_point><h2>render_point</h2></a>
|
|
|
|
"render_point(x0,x1,y0,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>
|
|
|
|
<a name=render_line><h2>render_line</h2></a>
|
|
|
|
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.
|
|
|
|
<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] - [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>
|
|
|
|
<hr>
|
|
<a href="http://www.xiph.org/">
|
|
<img src="white-xifish.png" align=left border=0>
|
|
</a>
|
|
<font size=-2 color=#505050>
|
|
|
|
Ogg is a <a href="http://www.xiph.org">Xiph.org Foundation</a> effort
|
|
to protect essential tenets of Internet multimedia from corporate
|
|
hostage-taking; Open Source is the net's greatest tool to keep
|
|
everyone honest. See <a href="http://www.xiph.org/about.html">About
|
|
the Xiph.org Foundation</a> for details.
|
|
<p>
|
|
|
|
Ogg Vorbis is the first Ogg audio CODEC. Anyone may freely use and
|
|
distribute the Ogg and Vorbis specification, whether in a private,
|
|
public or corporate capacity. However, the Xiph.org Foundation and
|
|
the Ogg project (xiph.org) reserve the right to set the Ogg Vorbis
|
|
specification and certify specification compliance.<p>
|
|
|
|
Xiph.org's Vorbis software CODEC implementation is distributed under a
|
|
BSD-like license. This does not restrict third parties from
|
|
distributing independent implementations of Vorbis software under
|
|
other licenses.<p>
|
|
|
|
Ogg, Vorbis, Xiph.org Foundation and their logos are trademarks (tm)
|
|
of the <a href="http://www.xiph.org/">Xiph.org Foundation</a>. These
|
|
pages are copyright (C) 1994-2002 Xiph.org Foundation. All rights
|
|
reserved.<p>
|
|
|
|
</body>
|
|
|