[16] | 1 | <?xml version="1.0" standalone="no"?> |
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| 2 | <!DOCTYPE section PUBLIC "-//OASIS//DTD DocBook XML V4.2//EN" |
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| 3 | "http://www.oasis-open.org/docbook/xml/4.2/docbookx.dtd" [ |
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| 4 | |
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| 5 | ]> |
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| 6 | |
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| 7 | <section id="vorbis-spec-floor1"> |
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| 8 | <sectioninfo> |
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| 9 | <releaseinfo> |
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| 10 | $Id: 07-floor1.xml 10466 2005-11-28 00:34:44Z giles $ |
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| 11 | </releaseinfo> |
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| 12 | </sectioninfo> |
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| 13 | <title>Floor type 1 setup and decode</title> |
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| 14 | |
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| 15 | <section> |
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| 16 | <title>Overview</title> |
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| 17 | |
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| 18 | <para> |
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| 19 | Vorbis floor type one uses a piecewise straight-line representation to |
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| 20 | encode a spectral envelope curve. The representation plots this curve |
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| 21 | mechanically on a linear frequency axis and a logarithmic (dB) |
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| 22 | amplitude axis. The integer plotting algorithm used is similar to |
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| 23 | Bresenham's algorithm.</para> |
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| 24 | |
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| 25 | </section> |
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| 26 | |
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| 27 | <section> |
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| 28 | <title>Floor 1 format</title> |
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| 29 | |
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| 30 | <section><title>model</title> |
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| 31 | |
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| 32 | <para> |
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| 33 | Floor type one represents a spectral curve as a series of |
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| 34 | line segments. Synthesis constructs a floor curve using iterative |
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| 35 | prediction in a process roughly equivalent to the following simplified |
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| 36 | description:</para> |
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| 37 | |
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| 38 | <para> |
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| 39 | <itemizedlist> |
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| 40 | <listitem><simpara> the first line segment (base case) is a logical line spanning |
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| 41 | from x_0,y_0 to x_1,y_1 where in the base case x_0=0 and x_1=[n], the |
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| 42 | full range of the spectral floor to be computed.</simpara></listitem> |
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| 43 | |
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| 44 | <listitem><simpara>the induction step chooses a point x_new within an existing |
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| 45 | logical line segment and produces a y_new value at that point computed |
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| 46 | from the existing line's y value at x_new (as plotted by the line) and |
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| 47 | a difference value decoded from the bitstream packet.</simpara></listitem> |
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| 48 | |
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| 49 | <listitem><simpara>floor computation produces two new line segments, one running from |
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| 50 | x_0,y_0 to x_new,y_new and from x_new,y_new to x_1,y_1. This step is |
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| 51 | performed logically even if y_new represents no change to the |
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| 52 | amplitude value at x_new so that later refinement is additionally |
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| 53 | bounded at x_new.</simpara></listitem> |
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| 54 | |
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| 55 | <listitem><simpara>the induction step repeats, using a list of x values specified in |
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| 56 | the codec setup header at floor 1 initialization time. Computation |
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| 57 | is completed at the end of the x value list.</simpara></listitem> |
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| 58 | |
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| 59 | </itemizedlist> |
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| 60 | </para> |
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| 61 | |
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| 62 | <para> |
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| 63 | Consider the following example, with values chosen for ease of |
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| 64 | understanding rather than representing typical configuration:</para> |
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| 65 | |
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| 66 | <para> |
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| 67 | For the below example, we assume a floor setup with an [n] of 128. |
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| 68 | The list of selected X values in increasing order is |
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| 69 | 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave |
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| 70 | as 0, 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding |
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| 71 | list-order Y values as decoded from an example packet are 110, 20, -5, |
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| 72 | -45, 0, -25, -10, 30 and -10. We compute the floor in the following |
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| 73 | way, beginning with the first line:</para> |
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| 74 | |
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| 75 | <mediaobject> |
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| 76 | <imageobject> |
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| 77 | <imagedata fileref="floor1-1.png" format="PNG"/> |
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| 78 | </imageobject> |
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| 79 | <textobject> |
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| 80 | <phrase>[graph of example floor]</phrase> |
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| 81 | </textobject> |
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| 82 | </mediaobject> |
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| 83 | |
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| 84 | <para> |
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| 85 | We now draw new logical lines to reflect the correction to new_Y, and |
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| 86 | iterate for X positions 32 and 96:</para> |
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| 87 | |
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| 88 | <mediaobject> |
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| 89 | <imageobject> |
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| 90 | <imagedata fileref="floor1-2.png" format="PNG"/> |
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| 91 | </imageobject> |
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| 92 | <textobject> |
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| 93 | <phrase>[graph of example floor]</phrase> |
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| 94 | </textobject> |
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| 95 | </mediaobject> |
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| 96 | |
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| 97 | <para> |
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| 98 | Although the new Y value at X position 96 is unchanged, it is still |
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| 99 | used later as an endpoint for further refinement. From here on, the |
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| 100 | pattern should be clear; we complete the floor computation as follows:</para> |
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| 101 | |
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| 102 | <mediaobject> |
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| 103 | <imageobject> |
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| 104 | <imagedata fileref="floor1-3.png" format="PNG"/> |
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| 105 | </imageobject> |
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| 106 | <textobject> |
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| 107 | <phrase>[graph of example floor]</phrase> |
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| 108 | </textobject> |
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| 109 | </mediaobject> |
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| 110 | |
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| 111 | <mediaobject> |
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| 112 | <imageobject> |
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| 113 | <imagedata fileref="floor1-4.png" format="PNG"/> |
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| 114 | </imageobject> |
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| 115 | <textobject> |
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| 116 | <phrase>[graph of example floor]</phrase> |
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| 117 | </textobject> |
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| 118 | </mediaobject> |
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| 119 | |
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| 120 | |
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| 121 | <para> |
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| 122 | A more efficient algorithm with carefully defined integer rounding |
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| 123 | behavior is used for actual decode, as described later. The actual |
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| 124 | algorithm splits Y value computation and line plotting into two steps |
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| 125 | with modifications to the above algorithm to eliminate noise |
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| 126 | accumulation through integer roundoff/truncation. </para> |
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| 127 | |
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| 128 | </section> |
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| 129 | |
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| 130 | <section><title>header decode</title> |
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| 131 | |
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| 132 | <para> |
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| 133 | A list of floor X values is stored in the packet header in interleaved |
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| 134 | format (used in list order during packet decode and synthesis). This |
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| 135 | list is split into partitions, and each partition is assigned to a |
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| 136 | partition class. X positions 0 and [n] are implicit and do not belong |
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| 137 | to an explicit partition or partition class.</para> |
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| 138 | |
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| 139 | <para> |
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| 140 | A partition class consists of a representation vector width (the |
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| 141 | number of Y values which the partition class encodes at once), a |
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| 142 | 'subclass' value representing the number of alternate entropy books |
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| 143 | the partition class may use in representing Y values, the list of |
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| 144 | [subclass] books and a master book used to encode which alternate |
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| 145 | books were chosen for representation in a given packet. The |
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| 146 | master/subclass mechanism is meant to be used as a flexible |
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| 147 | representation cascade while still using codebooks only in a scalar |
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| 148 | context.</para> |
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| 149 | |
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| 150 | <screen> |
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| 151 | |
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| 152 | 1) [floor1_partitions] = read 5 bits as unsigned integer |
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| 153 | 2) [maximum_class] = -1 |
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| 154 | 3) iterate [i] over the range 0 ... [floor1_partitions]-1 { |
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| 155 | |
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| 156 | 4) vector [floor1_partition_class_list] element [i] = read 4 bits as unsigned integer |
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| 157 | |
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| 158 | } |
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| 159 | |
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| 160 | 5) [maximum_class] = largest integer scalar value in vector [floor1_partition_class_list] |
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| 161 | 6) iterate [i] over the range 0 ... [maximum_class] { |
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| 162 | |
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| 163 | 7) vector [floor1_class_dimensions] element [i] = read 3 bits as unsigned integer and add 1 |
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| 164 | 8) vector [floor1_class_subclasses] element [i] = read 2 bits as unsigned integer |
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| 165 | 9) if ( vector [floor1_class_subclasses] element [i] is nonzero ) { |
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| 166 | |
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| 167 | 10) vector [floor1_class_masterbooks] element [i] = read 8 bits as unsigned integer |
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| 168 | |
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| 169 | } |
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| 170 | |
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| 171 | 11) iterate [j] over the range 0 ... (2 exponent [floor1_class_subclasses] element [i]) - 1 { |
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| 172 | |
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| 173 | 12) array [floor1_subclass_books] element [i],[j] = |
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| 174 | read 8 bits as unsigned integer and subtract one |
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| 175 | } |
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| 176 | } |
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| 177 | |
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| 178 | 13) [floor1_multiplier] = read 2 bits as unsigned integer and add one |
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| 179 | 14) [rangebits] = read 4 bits as unsigned integer |
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| 180 | 15) vector [floor1_X_list] element [0] = 0 |
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| 181 | 16) vector [floor1_X_list] element [1] = 2 exponent [rangebits]; |
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| 182 | 17) [floor1_values] = 2 |
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| 183 | 18) iterate [i] over the range 0 ... [floor1_partitions]-1 { |
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| 184 | |
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| 185 | 19) [current_class_number] = vector [floor1_partition_class_list] element [i] |
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| 186 | 20) iterate [j] over the range 0 ... ([floor1_class_dimensions] element [current_class_number])-1 { |
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| 187 | 21) vector [floor1_X_list] element ([floor1_values]) = |
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| 188 | read [rangebits] bits as unsigned integer |
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| 189 | 22) increment [floor1_values] by one |
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| 190 | } |
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| 191 | } |
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| 192 | |
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| 193 | 23) done |
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| 194 | </screen> |
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| 195 | |
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| 196 | <para> |
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| 197 | An end-of-packet condition while reading any aspect of a floor 1 |
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| 198 | configuration during setup renders a stream undecodable. In |
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| 199 | addition, a <varname>[floor1_class_masterbooks]</varname> or |
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| 200 | <varname>[floor1_subclass_books]</varname> scalar element greater than the |
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| 201 | highest numbered codebook configured in this stream is an error |
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| 202 | condition that renders the stream undecodable.</para> |
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| 203 | |
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| 204 | <section id="vorbis-spec-floor1-decode"> |
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| 205 | <title>packet decode</title> |
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| 206 | |
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| 207 | <para> |
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| 208 | Packet decode begins by checking the <varname>[nonzero]</varname> flag:</para> |
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| 209 | |
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| 210 | <screen> |
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| 211 | 1) [nonzero] = read 1 bit as boolean |
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| 212 | </screen> |
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| 213 | |
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| 214 | <para> |
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| 215 | If <varname>[nonzero]</varname> is unset, that indicates this channel contained |
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| 216 | no audio energy in this frame. Decode immediately returns a status |
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| 217 | indicating this floor curve (and thus this channel) is unused this |
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| 218 | frame. (A return status of 'unused' is different from decoding a |
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| 219 | floor that has all points set to minimum representation amplitude, |
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| 220 | which happens to be approximately -140dB). |
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| 221 | </para> |
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| 222 | |
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| 223 | <para> |
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| 224 | Assuming <varname>[nonzero]</varname> is set, decode proceeds as follows:</para> |
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| 225 | |
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| 226 | <screen> |
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| 227 | 1) [range] = vector { 256, 128, 86, 64 } element ([floor1_multiplier]-1) |
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| 228 | 2) vector [floor1_Y] element [0] = read <link linkend="vorbis-spec-ilog">ilog</link>([range]-1) bits as unsigned integer |
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| 229 | 3) vector [floor1_Y] element [1] = read <link linkend="vorbis-spec-ilog">ilog</link>([range]-1) bits as unsigned integer |
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| 230 | 4) [offset] = 2; |
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| 231 | 5) iterate [i] over the range 0 ... [floor1_partitions]-1 { |
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| 232 | |
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| 233 | 6) [class] = vector [floor1_partition_class] element [i] |
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| 234 | 7) [cdim] = vector [floor1_class_dimensions] element [class] |
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| 235 | 8) [cbits] = vector [floor1_class_subclasses] element [class] |
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| 236 | 9) [csub] = (2 exponent [cbits])-1 |
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| 237 | 10) [cval] = 0 |
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| 238 | 11) if ( [cbits] is greater than zero ) { |
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| 239 | |
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| 240 | 12) [cval] = read from packet using codebook number |
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| 241 | (vector [floor1_class_masterbooks] element [class]) in scalar context |
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| 242 | } |
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| 243 | |
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| 244 | 13) iterate [j] over the range 0 ... [cdim]-1 { |
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| 245 | |
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| 246 | 14) [book] = array [floor1_subclass_books] element [class],([cval] bitwise AND [csub]) |
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| 247 | 15) [cval] = [cval] right shifted [cbits] bits |
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| 248 | 16) if ( [book] is not less than zero ) { |
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| 249 | |
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| 250 | 17) vector [floor1_Y] element ([j]+[offset]) = read from packet using codebook |
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| 251 | [book] in scalar context |
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| 252 | |
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| 253 | } else [book] is less than zero { |
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| 254 | |
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| 255 | 18) vector [floor1_Y] element ([j]+[offset]) = 0 |
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| 256 | |
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| 257 | } |
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| 258 | } |
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| 259 | |
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| 260 | 19) [offset] = [offset] + [cdim] |
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| 261 | |
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| 262 | } |
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| 263 | |
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| 264 | 20) done |
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| 265 | </screen> |
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| 266 | |
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| 267 | <para> |
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| 268 | An end-of-packet condition during curve decode should be considered a |
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| 269 | nominal occurrence; if end-of-packet is reached during any read |
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| 270 | operation above, floor decode is to return 'unused' status as if the |
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| 271 | <varname>[nonzero]</varname> flag had been unset at the beginning of decode. |
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| 272 | </para> |
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| 273 | |
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| 274 | <para> |
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| 275 | Vector <varname>[floor1_Y]</varname> contains the values from packet decode |
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| 276 | needed for floor 1 synthesis.</para> |
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| 277 | |
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| 278 | </section> |
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| 279 | |
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| 280 | <section id="vorbis-spec-floor1-synth"> |
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| 281 | <title>curve computation</title> |
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| 282 | |
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| 283 | <para> |
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| 284 | Curve computation is split into two logical steps; the first step |
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| 285 | derives final Y amplitude values from the encoded, wrapped difference |
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| 286 | values taken from the bitstream. The second step plots the curve |
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| 287 | lines. Also, although zero-difference values are used in the |
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| 288 | iterative prediction to find final Y values, these points are |
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| 289 | conditionally skipped during final line computation in step two. |
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| 290 | Skipping zero-difference values allows a smoother line fit. </para> |
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| 291 | |
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| 292 | <para> |
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| 293 | Although some aspects of the below algorithm look like inconsequential |
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| 294 | optimizations, implementors are warned to follow the details closely. |
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| 295 | Deviation from implementing a strictly equivalent algorithm can result |
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| 296 | in serious decoding errors.</para> |
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| 297 | |
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| 298 | <section> |
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| 299 | <title>step 1: amplitude value synthesis</title> |
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| 300 | |
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| 301 | <para> |
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| 302 | Unwrap the always-positive-or-zero values read from the packet into |
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| 303 | +/- difference values, then apply to line prediction.</para> |
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| 304 | |
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| 305 | <screen> |
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| 306 | 1) [range] = vector { 256, 128, 86, 64 } element ([floor1_multiplier]-1) |
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| 307 | 2) vector [floor1_step2_flag] element [0] = set |
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| 308 | 3) vector [floor1_step2_flag] element [1] = set |
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| 309 | 4) vector [floor1_final_Y] element [0] = vector [floor1_Y] element [0] |
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| 310 | 5) vector [floor1_final_Y] element [1] = vector [floor1_Y] element [1] |
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| 311 | 6) iterate [i] over the range 2 ... [floor1_values]-1 { |
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| 312 | |
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| 313 | 7) [low_neighbor_offset] = <link linkend="vorbis-spec-low_neighbor">low_neighbor</link>([floor1_X_list],[i]) |
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| 314 | 8) [high_neighbor_offset] = <link linkend="vorbis-spec-high_neighbor">high_neighbor</link>([floor1_X_list],[i]) |
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| 315 | |
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| 316 | 9) [predicted] = <link linkend="vorbis-spec-render_point">render_point</link>( vector [floor1_X_list] element [low_neighbor_offset], |
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| 317 | vector [floor1_final_Y] element [low_neighbor_offset], |
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| 318 | vector [floor1_X_list] element [high_neighbor_offset], |
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| 319 | vector [floor1_final_Y] element [high_neighbor_offset], |
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| 320 | vector [floor1_X_list] element [i] ) |
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| 321 | |
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| 322 | 10) [val] = vector [floor1_Y] element [i] |
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| 323 | 11) [highroom] = [range] - [predicted] |
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| 324 | 12) [lowroom] = [predicted] |
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| 325 | 13) if ( [highroom] is less than [lowroom] ) { |
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| 326 | |
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| 327 | 14) [room] = [highroom] * 2 |
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| 328 | |
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| 329 | } else [highroom] is not less than [lowroom] { |
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| 330 | |
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| 331 | 15) [room] = [lowroom] * 2 |
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| 332 | |
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| 333 | } |
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| 334 | |
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| 335 | 16) if ( [val] is nonzero ) { |
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| 336 | |
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| 337 | 17) vector [floor1_step2_flag] element [low_neighbor_offset] = set |
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| 338 | 18) vector [floor1_step2_flag] element [high_neighbor_offset] = set |
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| 339 | 19) vector [floor1_step2_flag] element [i] = set |
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| 340 | 20) if ( [val] is greater than or equal to [room] ) { |
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| 341 | |
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| 342 | 21) if ( [highroom] is greater than [lowroom] ) { |
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| 343 | |
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| 344 | 22) vector [floor1_final_Y] element [i] = [val] - [lowroom] + [predicted] |
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| 345 | |
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| 346 | } else [highroom] is not greater than [lowroom] { |
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| 347 | |
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| 348 | 23) vector [floor1_final_Y] element [i] = [predicted] - [val] + [highroom] - 1 |
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| 349 | |
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| 350 | } |
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| 351 | |
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| 352 | } else [val] is less than [room] { |
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| 353 | |
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| 354 | 24) if ([val] is odd) { |
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| 355 | |
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| 356 | 25) vector [floor1_final_Y] element [i] = |
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| 357 | [predicted] - (([val] + 1) divided by 2 using integer division) |
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| 358 | |
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| 359 | } else [val] is even { |
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| 360 | |
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| 361 | 26) vector [floor1_final_Y] element [i] = |
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| 362 | [predicted] + ([val] / 2 using integer division) |
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| 363 | |
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| 364 | } |
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| 365 | |
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| 366 | } |
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| 367 | |
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| 368 | } else [val] is zero { |
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| 369 | |
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| 370 | 27) vector [floor1_step2_flag] element [i] = unset |
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| 371 | 28) vector [floor1_final_Y] element [i] = [predicted] |
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| 372 | |
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| 373 | } |
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| 374 | |
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| 375 | } |
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| 376 | |
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| 377 | 29) done |
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| 378 | |
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| 379 | </screen> |
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| 380 | |
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| 381 | </section> |
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| 382 | |
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| 383 | <section> |
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| 384 | <title>step 2: curve synthesis</title> |
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| 385 | |
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| 386 | <para> |
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| 387 | Curve synthesis generates a return vector <varname>[floor]</varname> of length |
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| 388 | <varname>[n]</varname> (where <varname>[n]</varname> is provided by the decode process |
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| 389 | calling to floor decode). Floor 1 curve synthesis makes use of the |
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| 390 | <varname>[floor1_X_list]</varname>, <varname>[floor1_final_Y]</varname> and |
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| 391 | <varname>[floor1_step2_flag]</varname> vectors, as well as [floor1_multiplier] |
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| 392 | and [floor1_values] values.</para> |
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| 393 | |
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| 394 | <para> |
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| 395 | Decode begins by sorting the scalars from vectors |
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| 396 | <varname>[floor1_X_list]</varname>, <varname>[floor1_final_Y]</varname> and |
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| 397 | <varname>[floor1_step2_flag]</varname> together into new vectors |
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| 398 | <varname>[floor1_X_list]'</varname>, <varname>[floor1_final_Y]'</varname> and |
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| 399 | <varname>[floor1_step2_flag]'</varname> according to ascending sort order of the |
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| 400 | values in <varname>[floor1_X_list]</varname>. That is, sort the values of |
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| 401 | <varname>[floor1_X_list]</varname> and then apply the same permutation to |
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| 402 | elements of the other two vectors so that the X, Y and step2_flag |
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| 403 | values still match.</para> |
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| 404 | |
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| 405 | <para> |
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| 406 | Then compute the final curve in one pass:</para> |
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| 407 | |
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| 408 | <screen> |
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| 409 | 1) [hx] = 0 |
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| 410 | 2) [lx] = 0 |
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| 411 | 3) [ly] = vector [floor1_final_Y]' element [0] * [floor1_multiplier] |
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| 412 | 4) iterate [i] over the range 1 ... [floor1_values]-1 { |
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| 413 | |
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| 414 | 5) if ( [floor1_step2_flag]' element [i] is set ) { |
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| 415 | |
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| 416 | 6) [hy] = [floor1_final_Y]' element [i] * [floor1_multiplier] |
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| 417 | 7) [hx] = [floor1_X_list]' element [i] |
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| 418 | 8) <link linkend="vorbis-spec-render_line">render_line</link>( [lx], [ly], [hx], [hy], [floor] ) |
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| 419 | 9) [lx] = [hx] |
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| 420 | 10) [ly] = [hy] |
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| 421 | } |
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| 422 | } |
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| 423 | |
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| 424 | 11) if ( [hx] is less than [n] ) { |
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| 425 | |
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| 426 | 12) <link linkend="vorbis-spec-render_line">render_line</link>( [hx], [hy], [n], [hy], [floor] ) |
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| 427 | |
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| 428 | } |
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| 429 | |
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| 430 | 13) if ( [hx] is greater than [n] ) { |
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| 431 | |
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| 432 | 14) truncate vector [floor] to [n] elements |
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| 433 | |
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| 434 | } |
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| 435 | |
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| 436 | 15) for each scalar in vector [floor], perform a lookup substitution using |
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| 437 | the scalar value from [floor] as an offset into the vector <link linkend="vorbis-spec-floor1_inverse_dB_table">[floor1_inverse_dB_static_table]</link> |
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| 438 | |
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| 439 | 16) done |
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| 440 | |
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| 441 | </screen> |
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| 442 | |
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| 443 | </section> |
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| 444 | |
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| 445 | </section> |
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| 446 | |
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| 447 | </section> |
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| 448 | </section> |
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| 449 | </section> |
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| 450 | |
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