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| 4 |
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| 5 | <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-15"/>
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| 6 | <title>Ogg Vorbis Documentation</title>
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| 28 |
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| 29 | #content p {
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| 30 | line-height: 1.4;
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| 31 | }
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| 32 |
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| 33 | h1, h1 a, h2, h2 a, h3, h3 a {
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| 41 | }
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| 45 | }
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| 65 | </head>
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| 66 |
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| 67 | <body>
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| 68 |
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| 69 | <div id="xiphlogo">
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| 70 | <a href="https://xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.Org"/></a>
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| 71 | </div>
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| 72 |
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| 73 | <h1>Ogg Vorbis I format specification: helper equations</h1>
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| 74 |
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| 75 | <h1>Overview</h1>
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| 76 |
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| 77 | <p>The equations below are used in multiple places by the Vorbis codec
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| 78 | specification. Rather than cluttering up the main specification
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| 79 | documents, they are defined here and linked in the main documents
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| 80 | where appropriate.</p>
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| 81 |
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| 82 | <h2><a name="log">ilog</a></h2>
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| 83 |
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| 84 | <p>The "ilog(x)" function returns the position number (1 through n) of the
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| 85 | highest set bit in the two's complement integer value
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| 86 | <tt>[x]</tt>. Values of <tt>[x]</tt> less than zero are defined to return zero.</p>
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| 87 |
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| 88 | <pre>
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| 89 | 1) [return_value] = 0;
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| 90 | 2) if ( [x] is greater than zero ){
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| 91 |
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| 92 | 3) increment [return_value];
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| 93 | 4) logical shift [x] one bit to the right, padding the MSb with zero
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| 94 | 5) repeat at step 2)
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| 95 |
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| 96 | }
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| 97 |
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| 98 | 6) done
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| 99 | </pre>
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| 100 |
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| 101 | <p>Examples:</p>
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| 102 |
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| 103 | <ul>
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| 104 | <li>ilog(0) = 0;</li>
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| 105 | <li>ilog(1) = 1;</li>
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| 106 | <li>ilog(2) = 2;</li>
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| 107 | <li>ilog(3) = 2;</li>
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| 108 | <li>ilog(4) = 3;</li>
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| 109 | <li>ilog(7) = 3;</li>
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| 110 | <li>ilog(negative number) = 0;</li>
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| 111 | </ul>
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| 112 |
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| 113 | <h2><a name="float32_unpack">float32_unpack</a></h2>
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| 114 |
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| 115 | <p>"float32_unpack(x)" is intended to translate the packed binary
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| 116 | representation of a Vorbis codebook float value into the
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| 117 | representation used by the decoder for floating point numbers. For
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| 118 | purposes of this example, we will unpack a Vorbis float32 into a
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| 119 | host-native floating point number.</p>
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| 120 |
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| 121 | <pre>
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| 122 | 1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result)
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| 123 | 2) [sign] = [x] bitwise AND 0x80000000 (unsigned result)
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| 124 | 3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result)
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| 125 | 4) if ( [sign] is nonzero ) then negate [mantissa]
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| 126 | 5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) )
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| 127 | </pre>
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| 128 |
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| 129 | <h2><a name="lookup1_values">lookup1_values</a></h2>
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| 130 |
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| 131 | <p>"lookup1_values(codebook_entries,codebook_dimensions)" is used to
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| 132 | compute the correct length of the value index for a codebook VQ lookup
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| 133 | table of lookup type 1. The values on this list are permuted to
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| 134 | construct the VQ vector lookup table of size
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| 135 | <tt>[codebook_entries]</tt>.</p>
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| 136 |
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| 137 | <p>The return value for this function is defined to be 'the greatest
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| 138 | integer value for which <tt>[return_value] to the power of
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| 139 | [codebook_dimensions] is less than or equal to
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| 140 | [codebook_entries]</tt>'.</p>
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| 141 |
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| 142 | <h2><a name="low_neighbor">low_neighbor</a></h2>
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| 143 |
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| 144 | <p>"low_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
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| 145 | the greatest value scalar element for which <i>n</i> is less than
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| 146 | <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is less
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| 147 | than vector [v] element [x]</tt>.</p>
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| 148 |
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| 149 | <h2><a name="high_neighbor">high_neighbor</a></h2>
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| 150 |
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| 151 | <p>"high_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
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| 152 | the lowest value scalar element for which <i>n</i> is less than
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| 153 | <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is greater
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| 154 | than vector [v] element [x]</tt>.</p>
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| 155 |
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| 156 | <h2><a name="render_point">render_point</a></h2>
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| 157 |
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| 158 | <p>"render_point(x0,y0,x1,y1,X)" is used to find the Y value at point X
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| 159 | along the line specified by x0, x1, y0 and y1. This function uses an
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| 160 | integer algorithm to solve for the point directly without calculating
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| 161 | intervening values along the line.</p>
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| 162 |
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| 163 | <pre>
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| 164 | 1) [dy] = [y1] - [y0]
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| 165 | 2) [adx] = [x1] - [x0]
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| 166 | 3) [ady] = absolute value of [dy]
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| 167 | 4) [err] = [ady] * ([X] - [x0])
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| 168 | 5) [off] = [err] / [adx] using integer division
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| 169 | 6) if ( [dy] is less than zero ) {
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| 170 |
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| 171 | 7) [Y] = [y0] - [off]
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| 172 |
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| 173 | } else {
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| 174 |
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| 175 | 8) [Y] = [y0] + [off]
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| 176 |
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| 177 | }
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| 178 |
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| 179 | 9) done
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| 180 | </pre>
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| 181 |
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| 182 | <h2><a name="render_line">render_line</a></h2>
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| 183 |
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| 184 | <p>Floor decode type one uses the integer line drawing algorithm of
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| 185 | "render_line(x0, y0, x1, y1, v)" to construct an integer floor
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| 186 | curve for contiguous piecewise line segments. Note that it has not
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| 187 | been relevant elsewhere, but here we must define integer division as
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| 188 | rounding division of both positive and negative numbers toward zero.</p>
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| 189 |
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| 190 | <pre>
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| 191 | 1) [dy] = [y1] - [y0]
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| 192 | 2) [adx] = [x1] - [x0]
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| 193 | 3) [ady] = absolute value of [dy]
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| 194 | 4) [base] = [dy] / [adx] using integer division
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| 195 | 5) [x] = [x0]
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| 196 | 6) [y] = [y0]
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| 197 | 7) [err] = 0
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| 198 |
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| 199 | 8) if ( [dy] is less than 0 ) {
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| 200 |
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| 201 | 9) [sy] = [base] - 1
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| 202 |
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| 203 | } else {
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| 204 |
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| 205 | 10) [sy] = [base] + 1
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| 206 |
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| 207 | }
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| 208 |
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| 209 | 11) [ady] = [ady] - (absolute value of [base]) * [adx]
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| 210 | 12) vector [v] element [x] = [y]
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| 211 |
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| 212 | 13) iterate [x] over the range [x0]+1 ... [x1]-1 {
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| 213 |
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| 214 | 14) [err] = [err] + [ady];
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| 215 | 15) if ( [err] >= [adx] ) {
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| 216 |
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| 217 | 15) [err] = [err] - [adx]
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| 218 | 16) [y] = [y] + [sy]
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| 219 |
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| 220 | } else {
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| 221 |
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| 222 | 17) [y] = [y] + [base]
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| 223 |
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| 224 | }
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| 225 |
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| 226 | 18) vector [v] element [x] = [y]
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| 227 |
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| 228 | }
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| 229 | </pre>
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| 230 |
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| 231 | <div id="copyright">
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| 232 | The Xiph Fish Logo is a
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| 233 | trademark (™) of Xiph.Org.<br/>
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| 234 |
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| 235 | These pages © 1994 - 2005 Xiph.Org. All rights reserved.
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| 236 | </div>
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| 237 |
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| 238 | </body>
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| 239 | </html>
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