00001 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
00002 <html>
00003 <head>
00004
00005 <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-15"/>
00006 <title>Ogg Vorbis Documentation</title>
00007
00008 <style type="text/css">
00009 body {
00010 margin: 0 18px 0 18px;
00011 padding-bottom: 30px;
00012 font-family: Verdana, Arial, Helvetica, sans-serif;
00013 color: #333333;
00014 font-size: .8em;
00015 }
00016
00017 a {
00018 color: #3366cc;
00019 }
00020
00021 img {
00022 border: 0;
00023 }
00024
00025 #xiphlogo {
00026 margin: 30px 0 16px 0;
00027 }
00028
00029 #content p {
00030 line-height: 1.4;
00031 }
00032
00033 h1, h1 a, h2, h2 a, h3, h3 a {
00034 font-weight: bold;
00035 color: #ff9900;
00036 margin: 1.3em 0 8px 0;
00037 }
00038
00039 h1 {
00040 font-size: 1.3em;
00041 }
00042
00043 h2 {
00044 font-size: 1.2em;
00045 }
00046
00047 h3 {
00048 font-size: 1.1em;
00049 }
00050
00051 li {
00052 line-height: 1.4;
00053 }
00054
00055 #copyright {
00056 margin-top: 30px;
00057 line-height: 1.5em;
00058 text-align: center;
00059 font-size: .8em;
00060 color: #888888;
00061 clear: both;
00062 }
00063 </style>
00064
00065 </head>
00066
00067 <body>
00068
00069 <div id="xiphlogo">
00070 <a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.org"/></a>
00071 </div>
00072
00073 <h1>Ogg Vorbis I format specification: helper equations</h1>
00074
00075 <h1>Overview</h1>
00076
00077 <p>The equations below are used in multiple places by the Vorbis codec
00078 specification. Rather than cluttering up the main specification
00079 documents, they are defined here and linked in the main documents
00080 where appropriate.</p>
00081
00082 <h2><a name="log">ilog</a></h2>
00083
00084 <p>The "ilog(x)" function returns the position number (1 through n) of the
00085 highest set bit in the two's complement integer value
00086 <tt>[x]</tt>. Values of <tt>[x]</tt> less than zero are defined to return zero.</p>
00087
00088 <pre>
00089 1) [return_value] = 0;
00090 2) if ( [x] is greater than zero ){
00091
00092 3) increment [return_value];
00093 4) logical shift [x] one bit to the right, padding the MSb with zero
00094 5) repeat at step 2)
00095
00096 }
00097
00098 6) done
00099 </pre>
00100
00101 <p>Examples:</p>
00102
00103 <ul>
00104 <li>ilog(0) = 0;</li>
00105 <li>ilog(1) = 1;</li>
00106 <li>ilog(2) = 2;</li>
00107 <li>ilog(3) = 2;</li>
00108 <li>ilog(4) = 3;</li>
00109 <li>ilog(7) = 3;</li>
00110 <li>ilog(negative number) = 0;</li>
00111 </ul>
00112
00113 <h2><a name="float32_unpack">float32_unpack</a></h2>
00114
00115 <p>"float32_unpack(x)" is intended to translate the packed binary
00116 representation of a Vorbis codebook float value into the
00117 representation used by the decoder for floating point numbers. For
00118 purposes of this example, we will unpack a Vorbis float32 into a
00119 host-native floating point number.</p>
00120
00121 <pre>
00122 1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result)
00123 2) [sign] = [x] bitwise AND 0x80000000 (unsigned result)
00124 3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result)
00125 4) if ( [sign] is nonzero ) then negate [mantissa]
00126 5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) )
00127 </pre>
00128
00129 <h2><a name="lookup1_values">lookup1_values</a></h2>
00130
00131 <p>"lookup1_values(codebook_entries,codebook_dimensions)" is used to
00132 compute the correct length of the value index for a codebook VQ lookup
00133 table of lookup type 1. The values on this list are permuted to
00134 construct the VQ vector lookup table of size
00135 <tt>[codebook_entries]</tt>.</p>
00136
00137 <p>The return value for this function is defined to be 'the greatest
00138 integer value for which <tt>[return_value] to the power of
00139 [codebook_dimensions] is less than or equal to
00140 [codebook_entries]</tt>'.</p>
00141
00142 <h2><a name="low_neighbor">low_neighbor</a></h2>
00143
00144 <p>"low_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
00145 the greatest value scalar element for which <i>n</i> is less than
00146 <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is less
00147 than vector [v] element [x]</tt>.</p>
00148
00149 <h2><a name="high_neighbor">high_neighbor</a></h2>
00150
00151 <p>"high_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
00152 the lowest value scalar element for which <i>n</i> is less than
00153 <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is greater
00154 than vector [v] element [x]</tt>.</p>
00155
00156 <h2><a name="render_point">render_point</a></h2>
00157
00158 <p>"render_point(x0,y0,x1,y1,X)" is used to find the Y value at point X
00159 along the line specified by x0, x1, y0 and y1. This function uses an
00160 integer algorithm to solve for the point directly without calculating
00161 intervening values along the line.</p>
00162
00163 <pre>
00164 1) [dy] = [y1] - [y0]
00165 2) [adx] = [x1] - [x0]
00166 3) [ady] = absolute value of [dy]
00167 4) [err] = [ady] * ([X] - [x0])
00168 5) [off] = [err] / [adx] using integer division
00169 6) if ( [dy] is less than zero ) {
00170
00171 7) [Y] = [y0] - [off]
00172
00173 } else {
00174
00175 8) [Y] = [y0] + [off]
00176
00177 }
00178
00179 9) done
00180 </pre>
00181
00182 <h2><a name="render_line">render_line</a></h2>
00183
00184 <p>Floor decode type one uses the integer line drawing algorithm of
00185 "render_line(x0, y0, x1, y1, v)" to construct an integer floor
00186 curve for contiguous piecewise line segments. Note that it has not
00187 been relevant elsewhere, but here we must define integer division as
00188 rounding division of both positive and negative numbers toward zero.</p>
00189
00190 <pre>
00191 1) [dy] = [y1] - [y0]
00192 2) [adx] = [x1] - [x0]
00193 3) [ady] = absolute value of [dy]
00194 4) [base] = [dy] / [adx] using integer division
00195 5) [x] = [x0]
00196 6) [y] = [y0]
00197 7) [err] = 0
00198
00199 8) if ( [dy] is less than 0 ) {
00200
00201 9) [sy] = [base] - 1
00202
00203 } else {
00204
00205 10) [sy] = [base] + 1
00206
00207 }
00208
00209 11) [ady] = [ady] - (absolute value of [base]) * [adx]
00210 12) vector [v] element [x] = [y]
00211
00212 13) iterate [x] over the range [x0]+1 ... [x1]-1 {
00213
00214 14) [err] = [err] + [ady];
00215 15) if ( [err] >= [adx] ) {
00216
00217 15) [err] = [err] - [adx]
00218 16) [y] = [y] + [sy]
00219
00220 } else {
00221
00222 17) [y] = [y] + [base]
00223
00224 }
00225
00226 18) vector [v] element [x] = [y]
00227
00228 }
00229 </pre>
00230
00231 <div id="copyright">
00232 The Xiph Fish Logo is a
00233 trademark (™) of Xiph.Org.<br/>
00234
00235 These pages © 1994 - 2005 Xiph.Org. All rights reserved.
00236 </div>
00237
00238 </body>
00239 </html>
