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Bring in flac, ogg, vorbis
author Chris Cannam
date Tue, 19 Mar 2013 17:37:49 +0000
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Chris@1 1 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
Chris@1 2 <html>
Chris@1 3 <head>
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Chris@1 5 <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-15"/>
Chris@1 6 <title>Ogg Vorbis Documentation</title>
Chris@1 7
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Chris@1 29 #content p {
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Chris@1 33 h1, h1 a, h2, h2 a, h3, h3 a {
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Chris@1 54
Chris@1 55 #copyright {
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Chris@1 63 </style>
Chris@1 64
Chris@1 65 </head>
Chris@1 66
Chris@1 67 <body>
Chris@1 68
Chris@1 69 <div id="xiphlogo">
Chris@1 70 <a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.Org"/></a>
Chris@1 71 </div>
Chris@1 72
Chris@1 73 <h1>Ogg Vorbis I format specification: helper equations</h1>
Chris@1 74
Chris@1 75 <h1>Overview</h1>
Chris@1 76
Chris@1 77 <p>The equations below are used in multiple places by the Vorbis codec
Chris@1 78 specification. Rather than cluttering up the main specification
Chris@1 79 documents, they are defined here and linked in the main documents
Chris@1 80 where appropriate.</p>
Chris@1 81
Chris@1 82 <h2><a name="log">ilog</a></h2>
Chris@1 83
Chris@1 84 <p>The "ilog(x)" function returns the position number (1 through n) of the
Chris@1 85 highest set bit in the two's complement integer value
Chris@1 86 <tt>[x]</tt>. Values of <tt>[x]</tt> less than zero are defined to return zero.</p>
Chris@1 87
Chris@1 88 <pre>
Chris@1 89 1) [return_value] = 0;
Chris@1 90 2) if ( [x] is greater than zero ){
Chris@1 91
Chris@1 92 3) increment [return_value];
Chris@1 93 4) logical shift [x] one bit to the right, padding the MSb with zero
Chris@1 94 5) repeat at step 2)
Chris@1 95
Chris@1 96 }
Chris@1 97
Chris@1 98 6) done
Chris@1 99 </pre>
Chris@1 100
Chris@1 101 <p>Examples:</p>
Chris@1 102
Chris@1 103 <ul>
Chris@1 104 <li>ilog(0) = 0;</li>
Chris@1 105 <li>ilog(1) = 1;</li>
Chris@1 106 <li>ilog(2) = 2;</li>
Chris@1 107 <li>ilog(3) = 2;</li>
Chris@1 108 <li>ilog(4) = 3;</li>
Chris@1 109 <li>ilog(7) = 3;</li>
Chris@1 110 <li>ilog(negative number) = 0;</li>
Chris@1 111 </ul>
Chris@1 112
Chris@1 113 <h2><a name="float32_unpack">float32_unpack</a></h2>
Chris@1 114
Chris@1 115 <p>"float32_unpack(x)" is intended to translate the packed binary
Chris@1 116 representation of a Vorbis codebook float value into the
Chris@1 117 representation used by the decoder for floating point numbers. For
Chris@1 118 purposes of this example, we will unpack a Vorbis float32 into a
Chris@1 119 host-native floating point number.</p>
Chris@1 120
Chris@1 121 <pre>
Chris@1 122 1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result)
Chris@1 123 2) [sign] = [x] bitwise AND 0x80000000 (unsigned result)
Chris@1 124 3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result)
Chris@1 125 4) if ( [sign] is nonzero ) then negate [mantissa]
Chris@1 126 5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) )
Chris@1 127 </pre>
Chris@1 128
Chris@1 129 <h2><a name="lookup1_values">lookup1_values</a></h2>
Chris@1 130
Chris@1 131 <p>"lookup1_values(codebook_entries,codebook_dimensions)" is used to
Chris@1 132 compute the correct length of the value index for a codebook VQ lookup
Chris@1 133 table of lookup type 1. The values on this list are permuted to
Chris@1 134 construct the VQ vector lookup table of size
Chris@1 135 <tt>[codebook_entries]</tt>.</p>
Chris@1 136
Chris@1 137 <p>The return value for this function is defined to be 'the greatest
Chris@1 138 integer value for which <tt>[return_value] to the power of
Chris@1 139 [codebook_dimensions] is less than or equal to
Chris@1 140 [codebook_entries]</tt>'.</p>
Chris@1 141
Chris@1 142 <h2><a name="low_neighbor">low_neighbor</a></h2>
Chris@1 143
Chris@1 144 <p>"low_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
Chris@1 145 the greatest value scalar element for which <i>n</i> is less than
Chris@1 146 <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is less
Chris@1 147 than vector [v] element [x]</tt>.</p>
Chris@1 148
Chris@1 149 <h2><a name="high_neighbor">high_neighbor</a></h2>
Chris@1 150
Chris@1 151 <p>"high_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
Chris@1 152 the lowest value scalar element for which <i>n</i> is less than
Chris@1 153 <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is greater
Chris@1 154 than vector [v] element [x]</tt>.</p>
Chris@1 155
Chris@1 156 <h2><a name="render_point">render_point</a></h2>
Chris@1 157
Chris@1 158 <p>"render_point(x0,y0,x1,y1,X)" is used to find the Y value at point X
Chris@1 159 along the line specified by x0, x1, y0 and y1. This function uses an
Chris@1 160 integer algorithm to solve for the point directly without calculating
Chris@1 161 intervening values along the line.</p>
Chris@1 162
Chris@1 163 <pre>
Chris@1 164 1) [dy] = [y1] - [y0]
Chris@1 165 2) [adx] = [x1] - [x0]
Chris@1 166 3) [ady] = absolute value of [dy]
Chris@1 167 4) [err] = [ady] * ([X] - [x0])
Chris@1 168 5) [off] = [err] / [adx] using integer division
Chris@1 169 6) if ( [dy] is less than zero ) {
Chris@1 170
Chris@1 171 7) [Y] = [y0] - [off]
Chris@1 172
Chris@1 173 } else {
Chris@1 174
Chris@1 175 8) [Y] = [y0] + [off]
Chris@1 176
Chris@1 177 }
Chris@1 178
Chris@1 179 9) done
Chris@1 180 </pre>
Chris@1 181
Chris@1 182 <h2><a name="render_line">render_line</a></h2>
Chris@1 183
Chris@1 184 <p>Floor decode type one uses the integer line drawing algorithm of
Chris@1 185 "render_line(x0, y0, x1, y1, v)" to construct an integer floor
Chris@1 186 curve for contiguous piecewise line segments. Note that it has not
Chris@1 187 been relevant elsewhere, but here we must define integer division as
Chris@1 188 rounding division of both positive and negative numbers toward zero.</p>
Chris@1 189
Chris@1 190 <pre>
Chris@1 191 1) [dy] = [y1] - [y0]
Chris@1 192 2) [adx] = [x1] - [x0]
Chris@1 193 3) [ady] = absolute value of [dy]
Chris@1 194 4) [base] = [dy] / [adx] using integer division
Chris@1 195 5) [x] = [x0]
Chris@1 196 6) [y] = [y0]
Chris@1 197 7) [err] = 0
Chris@1 198
Chris@1 199 8) if ( [dy] is less than 0 ) {
Chris@1 200
Chris@1 201 9) [sy] = [base] - 1
Chris@1 202
Chris@1 203 } else {
Chris@1 204
Chris@1 205 10) [sy] = [base] + 1
Chris@1 206
Chris@1 207 }
Chris@1 208
Chris@1 209 11) [ady] = [ady] - (absolute value of [base]) * [adx]
Chris@1 210 12) vector [v] element [x] = [y]
Chris@1 211
Chris@1 212 13) iterate [x] over the range [x0]+1 ... [x1]-1 {
Chris@1 213
Chris@1 214 14) [err] = [err] + [ady];
Chris@1 215 15) if ( [err] >= [adx] ) {
Chris@1 216
Chris@1 217 15) [err] = [err] - [adx]
Chris@1 218 16) [y] = [y] + [sy]
Chris@1 219
Chris@1 220 } else {
Chris@1 221
Chris@1 222 17) [y] = [y] + [base]
Chris@1 223
Chris@1 224 }
Chris@1 225
Chris@1 226 18) vector [v] element [x] = [y]
Chris@1 227
Chris@1 228 }
Chris@1 229 </pre>
Chris@1 230
Chris@1 231 <div id="copyright">
Chris@1 232 The Xiph Fish Logo is a
Chris@1 233 trademark (&trade;) of Xiph.Org.<br/>
Chris@1 234
Chris@1 235 These pages &copy; 1994 - 2005 Xiph.Org. All rights reserved.
Chris@1 236 </div>
Chris@1 237
Chris@1 238 </body>
Chris@1 239 </html>