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7 <section id="vorbis-spec-floor1">
10 $Id: 07-floor1.xml,v 1.5 2003/03/11 11:02:17 xiphmont Exp $
11 <emphasis>Last update to this document: March 11, 2003</emphasis>
14 <title>Floor type 1 setup and decode</title>
17 <title>Overview</title>
20 Vorbis floor type one uses a piecewise straight-line representation to
21 encode a spectral envelope curve. The representation plots this curve
22 mechanically on a linear frequency axis and a logarithmic (dB)
23 amplitude axis. The integer plotting algorithm used is similar to
24 Bresenham's algorithm.</para>
29 <title>Floor 1 format</title>
31 <section><title>model</title>
34 Floor type one represents a spectral curve as a series of
35 line segments. Synthesis constructs a floor curve using iterative
36 prediction in a process roughly equivalent to the following simplified
40 <listitem><simpara> the first line segment (base case) is a logical line spanning
41 from x_0,y_0 to x_1,y_1 where in the base case x_0=0 and x_1=[n], the
42 full range of the spectral floor to be computed.</simpara></listitem>
44 <listitem><simpara>the induction step chooses a point x_new within an existing
45 logical line segment and produces a y_new value at that point computed
46 from the existing line's y value at x_new (as plotted by the line) and
47 a difference value decoded from the bitstream packet.</simpara></listitem>
49 <listitem><simpara>floor computation produces two new line segments, one running from
50 x_0,y_0 to x_new,y_new and from x_new,y_new to x_1,y_1. This step is
51 performed logically even if y_new represents no change to the
52 amplitude value at x_new so that later refinement is additionally
53 bounded at x_new.</simpara></listitem>
55 <listitem><simpara>the induction step repeats, using a list of x values specified in
56 the codec setup header at floor 1 initialization time. Computation
57 is completed at the end of the x value list.</simpara></listitem>
62 Consider the following example, with values chosen for ease of
63 understanding rather than representing typical configuration:</para>
66 For the below example, we assume a floor setup with an [n] of 128.
67 The list of selected X values in increasing order is
68 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave
69 as 0, 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding
70 list-order Y values as decoded from an example packet are 110, 20, -5,
71 -45, 0, -25, -10, 30 and -10. We compute the floor in the following
72 way, beginning with the first line:</para>
76 <imagedata fileref="floor1-1.png" format="PNG"/>
79 <phrase>[graph of example floor]</phrase>
84 We now draw new logical lines to reflect the correction to new_Y, and
85 iterate for X positions 32 and 96:</para>
89 <imagedata fileref="floor1-2.png" format="PNG"/>
92 <phrase>[graph of example floor]</phrase>
97 Although the new Y value at X position 96 is unchanged, it is still
98 used later as an endpoint for further refinement. From here on, the
99 pattern should be clear; we complete the floor computation as follows:</para>
103 <imagedata fileref="floor1-3.png" format="PNG"/>
106 <phrase>[graph of example floor]</phrase>
112 <imagedata fileref="floor1-4.png" format="PNG"/>
115 <phrase>[graph of example floor]</phrase>
121 A more efficient algorithm with carefully defined integer rounding
122 behavior is used for actual decode, as described later. The actual
123 algorithm splits Y value computation and line plotting into two steps
124 with modifications to the above algorithm to eliminate noise
125 accumulation through integer roundoff/truncation. </para>
129 <section><title>header decode</title>
132 A list of floor X values is stored in the packet header in interleaved
133 format (used in list order during packet decode and synthesis). This
134 list is split into partitions, and each partition is assigned to a
135 partition class. X positions 0 and [n] are implicit and do not belong
136 to an explicit partition or partition class.</para>
139 A partition class consists of a representation vector width (the
140 number of Y values which the partition class encodes at once), a
141 'subclass' value representing the number of alternate entropy books
142 the partition class may use in representing Y values, the list of
143 [subclass] books and a master book used to encode which alternate
144 books were chosen for representation in a given packet. The
145 master/subclass mechanism is meant to be used as a flexible
146 representation cascade while still using codebooks only in a scalar
151 1) [floor1_partitions] = read 5 bits as unsigned integer
152 2) [maximum_class] = -1
153 3) iterate [i] over the range 0 ... [floor1_partitions]-1 {
155 4) vector [floor1_partition_class_list] element [i] = read 4 bits as unsigned integer
159 5) [maximum_class] = largest integer scalar value in vector [floor1_partition_class_list]
160 6) iterate [i] over the range 0 ... [maximum_class] {
162 7) vector [floor1_class_dimensions] element [i] = read 3 bits as unsigned integer and add 1
163 8) vector [floor1_class_subclasses] element [i] = read 2 bits as unsigned integer
164 9) if ( vector [floor1_class_subclasses] element [i] is nonzero ) {
166 10) vector [floor1_class_masterbooks] element [i] = read 8 bits as unsigned integer
170 11) iterate [j] over the range 0 ... (2 exponent [floor1_class_subclasses] element [i]) - 1 {
172 12) array [floor1_subclass_books] element [i],[j] =
173 read 8 bits as unsigned integer and subtract one
177 13) [floor1_multiplier] = read 2 bits as unsigned integer and add one
178 14) [rangebits] = read 4 bits as unsigned integer
179 15) vector [floor1_X_list] element [0] = 0
180 16) vector [floor1_X_list] element [1] = 2 exponent [rangebits];
181 17) [floor1_values] = 2
182 18) iterate [i] over the range 0 ... [floor1_partitions]-1 {
184 19) [current_class_number] = vector [floor1_partition_class_list] element [i]
185 20) iterate [j] over the range 0 ... ([floor1_class_dimensions] element [current_class_number])-1 {
186 21) vector [floor1_X_list] element ([j] + [floor1_values]) =
187 read [rangebits] bits as unsigned integer
188 22) increment [floor1_values] by one
196 An end-of-packet condition while reading any aspect of a floor 1
197 configuration during setup renders a stream undecodable. In
198 addition, a <varname>[floor1_class_masterbooks]</varname> or
199 <varname>[floor1_subclass_books]</varname> scalar element greater than the
200 highest numbered codebook configured in this stream is an error
201 condition that renders the stream undecodable.</para>
203 <section id="vorbis-spec-floor1-decode">
204 <title>packet decode</title>
207 Packet decode begins by checking the <varname>[nonzero]</varname> flag:</para>
210 1) [nonzero] = read 1 bit as boolean
214 If <varname>[nonzero]</varname> is unset, that indicates this channel contained
215 no audio energy in this frame. Decode immediately returns a status
216 indicating this floor curve (and thus this channel) is unused this
217 frame. (A return status of 'unused' is different from decoding a
218 floor that has all points set to minimum representation amplitude,
219 which happens to be approximately -140dB).
223 Assuming <varname>[nonzero]</varname> is set, decode proceeds as follows:</para>
226 1) [range] = vector { 256, 128, 86, 64 } element ([floor1_multiplier]-1)
227 2) vector [floor1_Y] element [0] = read <link linkend="vorbis-spec-ilog">ilog</link>([range]-1) bits as unsigned integer
228 3) vector [floor1_Y] element [1] = read <link linkend="vorbis-spec-ilog">ilog</link>([range]-1) bits as unsigned integer
230 5) iterate [i] over the range 0 ... [floor1_partitions]-1 {
232 6) [class] = vector [floor1_partition_class] element [i]
233 7) [cdim] = vector [floor1_class_dimensions] element [class]
234 8) [cbits] = vector [floor1_class_subclasses] element [class]
235 9) [csub] = (2 exponent [cbits])-1
237 11) if ( [cbits] is greater than zero ) {
239 12) [cval] = read from packet using codebook number
240 (vector [floor1_class_masterbooks] element [class]) in scalar context
243 13) iterate [j] over the range 0 ... [cdim]-1 {
245 14) [book] = array [floor1_subclass_books] element [class],([cval] bitwise AND [csub])
246 15) [cval] = [cval] right shifted [cbits] bits
247 16) if ( [book] is not less than zero ) {
249 17) vector [floor1_Y] element ([j]+[offset]) = read from packet using codebook
250 [book] in scalar context
252 } else [book] is less than zero {
254 18) vector [floor1_Y] element ([j]+[offset]) = 0
259 19) [offset] = [offset] + [cdim]
267 An end-of-packet condition during curve decode should be considered a
268 nominal occurrence; if end-of-packet is reached during any read
269 operation above, floor decode is to return 'unused' status as if the
270 <varname>[nonzero]</varname> flag had been unset at the beginning of decode.
274 Vector <varname>[floor1_Y]</varname> contains the values from packet decode
275 needed for floor 1 synthesis.</para>
279 <section id="vorbis-spec-floor1-synth">
280 <title>curve computation</title>
283 Curve computation is split into two logical steps; the first step
284 derives final Y amplitude values from the encoded, wrapped difference
285 values taken from the bitstream. The second step plots the curve
286 lines. Also, although zero-difference values are used in the
287 iterative prediction to find final Y values, these points are
288 conditionally skipped during final line computation in step two.
289 Skipping zero-difference values allows a smoother line fit. </para>
292 Although some aspects of the below algorithm look like inconsequential
293 optimizations, implementors are warned to follow the details closely.
294 Deviation from implementing a strictly equivalent algorithm can result
295 in serious decoding errors.</para>
298 <title>step 1: amplitude value synthesis</title>
301 Unwrap the always-positive-or-zero values read from the packet into
302 +/- difference values, then apply to line prediction.</para>
305 1) [range] = vector { 256, 128, 86, 64 } element ([floor1_multiplier]-1)
306 2) vector [floor1_step2_flag] element [0] = set
307 3) vector [floor1_step2_flag] element [1] = set
308 4) vector [floor1_final_Y] element [0] = vector [floor1_Y] element [0]
309 5) vector [floor1_final_Y] element [1] = vector [floor1_Y] element [1]
310 6) iterate [i] over the range 2 ... [floor1_values]-1 {
312 7) [low_neighbor_offset] = <link linkend="vorbis-spec-low_neighbor">low_neighbor</link>([floor1_X_list],[i])
313 8) [high_neighbor_offset] = <link linkend="vorbis-spec-high_neighbor">high_neighbor</link>([floor1_X_list],[i])
315 9) [predicted] = <link linkend="vorbis-spec-render_point">render_point</link>( vector [floor1_X_list] element [low_neighbor_offset],
316 vector [floor1_final_Y] element [low_neighbor_offset],
317 vector [floor1_X_list] element [high_neighbor_offset],
318 vector [floor1_final_Y] element [high_neighbor_offset],
319 vector [floor1_X_list] element [i] )
321 10) [val] = vector [floor1_Y] element [i]
322 11) [highroom] = [range] - [predicted]
323 12) [lowroom] = [predicted]
324 13) if ( [highroom] is less than [lowroom] ) {
326 14) [room] = [highroom] * 2
328 } else [highroom] is not less than [lowroom] {
330 15) [root] = [lowroom] * 2
334 16) if ( [val] is nonzero ) {
336 17) vector [floor1_step2_flag] element [low_neighbor_offset] = set
337 18) vector [floor1_step2_flag] element [high_neighbor_offset] = set
338 19) vector [floor1_step2_flag] element [i] = set
339 20) if ( [val] is greater than or equal to [room] ) {
341 21) if ( [hiroom] is greater than [lowroom] ) {
343 22) vector [floor1_final_Y] element [i] = [val] - [lowroom] + [predicted]
345 } else [hiroom] is not greater than [lowroom] {
347 23) vector [floor1_final_Y] element [i] = [predicted] - [val] + [hiroom] - 1
351 } else [val] is less than [room] {
353 24) if ([val] is odd) {
355 25) vector [floor1_final_Y] element [i] =
356 [predicted] - (([val] + 1) divided by 2 using integer division)
358 } else [val] is even {
360 26) vector [floor1_final_Y] element [i] =
361 [predicted] + ([val] / 2 using integer division)
367 } else [val] is zero {
369 27) vector [floor1_step2_flag] element [i] = unset
370 28) vector [floor1_final_Y] element [i] = [predicted]
383 <title>step 2: curve synthesis</title>
386 Curve synthesis generates a return vector <varname>[floor]</varname> of length
387 <varname>[n]</varname> (where <varname>[n]</varname> is provided by the decode process
388 calling to floor decode). Floor 1 curve synthesis makes use of the
389 <varname>[floor1_X_list]</varname>, <varname>[floor1_final_Y]</varname> and
390 <varname>[floor1_step2_flag]</varname> vectors, as well as [floor1_multiplier]
391 and [floor1_values] values.</para>
394 Decode begins by sorting the scalars from vectors
395 <varname>[floor1_X_list]</varname>, <varname>[floor1_final_Y]</varname> and
396 <varname>[floor1_step2_flag]</varname> together into new vectors
397 <varname>[floor1_X_list]'</varname>, <varname>[floor1_final_Y]'</varname> and
398 <varname>[floor1_step2_flag]'</varname> according to ascending sort order of the
399 values in <varname>[floor1_X_list]</varname>. That is, sort the values of
400 <varname>[floor1_X_list]</varname> and then apply the same permutation to
401 elements of the other two vectors so that the X, Y and step2_flag
402 values still match.</para>
405 Then compute the final curve in one pass:</para>
410 3) [ly] = vector [floor1_final_Y]' element [0] * [floor1_multiplier]
411 4) iterate [i] over the range 1 ... [floor1_values]-1 {
413 5) if ( [floor1_step2_flag]' is set ) {
415 6) [hy] = [floor1_final_Y]' element [i] * [floor1_multiplier]
416 7) [hx] = [floor1_X_list]' element [i]
417 8) <link linkend="vorbis-spec-render_line">render_line</link>( [lx], [ly], [hx], [hy], [floor] )
423 11) if ( [hx] is less than [n] ) {
425 12) <link linkend="vorbis-spec-render_line">render_line</link>( [hx], [hy], [n], [hy], [floor] )
429 13) if ( [hx] is greater than [n] ) {
431 14) truncate vector [floor] to [n] elements
435 15) for each scalar in vector [floor], perform a lookup substitution using
436 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>