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