For the below example, we assume a floor setup with an [n] of 128. The list of selected X values in increasing order is 0,16,32,48,64,80,96,112 and 128. In list order, the values interleave as 0, 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding list-order Y values as decoded from an example packet are 110, 20, -5, -45, 0, -25, -10, 30 and -10. We compute the floor in the following way, beginning with the first line:
We now draw new logical lines to reflect the correction to new_Y, and iterate for X positions 32 and 96:
Although the new Y value at X position 96 is unchanged, it is still used later as an endpoint for further refinement. From here on, the pattern should be clear; we complete the floor computation as follows:
A more efficient algorithm with carefully defined integer rounding behavior is used for actual decode, as described later. The actual algorithm splits Y value computation and line plotting into two steps with modifications to the above algorithm to eliminate noise accumulation through integer roundoff/truncation.
A partition class consists of a representation vector width (the number of Y values which the partition class encodes at once), a 'subclass' value representing the number of alternate entropy books the partition class may use in representing Y values, the list of [subclass] books and a master book used to encode which alternate books were chosen for representation in a given packet. The master/subclass mechanism is meant to be used as a flexible representation cascade while still using codebooks only in a scalar context.
1) [floor1_partitions] = read 5 bits as unsigned integer
2) [maximum_class] = 0
3) iterate [i] over the range 0 ... [floor1_partitions]-1 {
4) vector [floor1_partition_class_list] element [i] = read 4 bits as unsigned integer
}
5) [maximum_class] = largest integer scalar value in vector [floor1_partition_class_list]
6) iterate [i] over the range 0 ... [maximum_class] {
7) vector [floor1_class_dimensions] element [i] = read 3 bits as unsigned integer and add 1
8) vector [floor1_class_subclasses] element [i] = read 2 bits as unsigned integer
9) if ( vector [floor1_class_subclasses] element [i] is nonzero ) {
10) vector [floor1_class_masterbooks] element [i] = read 8 bits as unsigned integer
}
11) iterate [j] over the range 0 ... (2 exponent [floor1_class_subclasses] element [i]) - 1 {
12) array [floor1_subclass_books] element [i],[j] =
read 8 bits as unsigned integer and subtract one
}
}
13) [floor1_multiplier] = read 2 bits as unsigned integer and add one
14) [rangebits] = read 4 bits as unsigned integer
15) vector [floor1_X_list] element [0] = 0
16) vector [floor1_X_list] element [1] = 2 exponent [rangebits];
17) [floor1_values] = 1
18) iterate [i] over the range 0 ... [floor1_partitions]-1 {
19) iterate [j] over the range 0 ... ([floor1_class_dimensions] element [i])-1 {
20) vector [floor1_X_list] element ([j] + [floor1_values]) =
read [rangebits] bits as unsigned integer
}
21) [floor1_values] = [floor1_values] + [floor1_class_dimensions] element [i]
}
19) done
An end-of-packet condition while reading any aspect of a floor 1
configuration during setup renders a stream undecodable. In
addition, a [floor1_class_masterbooks] or
[floor1_subclass_books] scalar element greater than the
highest numbered codebook configured in this stream is an error
condition that renders the stream undecodable.
packet decode
Packet decode begins by checking the [nonzero] flag:
1) [nonzero] = read 1 bit as booleanIf [nonzero] is unset, that indicates this channel contained no audio energy in this frame. Decode immediately returns a status indicating this floor curve (and thus this channel) is unused this frame. (A return status of 'unused' is different from decoding a floor that has all points set to minimum representation amplitude, which happens to be approximately -140dB). Assuming [nonzero] is set, decode proceeds as follows:
1) [range] = vector { 256, 128, 86, 64 } element ([floor1_multiplier]-1)
2) vector [floor1_Y] element [0] = read ilog([range]-1) bits as unsigned integer
3) vector [floor1_Y] element [1] = read ilog([range]-1) bits as unsigned integer
4) [offset] = 2;
5) iterate [i] over the range 0 ... [floor1_partitions]-1 {
6) [class] = vector [floor1_partition_class] element [i]
7) [cdim] = vector [floor1_class_dimensions] element [class]
8) [cbits] = vector [floor1_class_subclasses] element [class]
9) [csub] = (2 exponent [cbits])-1
10) [cval] = 0
11) if ( [cbits] is greater than zero ) {
12) [cval] = read from packet using codebook number
(vector [floor1_class_masterbooks] element [class]) in scalar context
}
13) iterate [j] over the range 0 ... [cdim]-1 {
14) [book] = array [floor1_subclass_books] element [class],([cval] bitwise AND [csub])
15) if ( [book] is not less than zero ) {
16) vector [floor1_Y] element ([j]+[offset]) = read from packet using codebook
[book] in scalar context
} else [book] is less than zero {
17) vector [floor1_Y] element ([j]+[offset]) = 0
}
}
18) [offset] = [offset] + [cdim]
}
19) done
An end-of-packet condition during curve decode should be considered a
nominal occurrence; if end-of-packet is reached during any read
operation above, floor decode is to return 'unused' status as if the
[nonzero] flag had been unset at the beginning of decode.
Vector [floor1_Y] contains the values from packet decode
needed for floor 1 synthesis.
curve computation
Curve computation is split into two logical steps; the first step
derives final Y amplitude values from the encoded, wrapped difference
values taken from the bitstream. The second step plots the curve
lines. Also, although zero-difference values are used in the
iterative prediction to find final Y values, these points are
conditionally skipped during final line computation in step two.
Skipping zero-difference values allows a smoother line fit.
Although some aspects of the below algorithm look like inconsequential optimizations, implementors are warned to follow the details closely. Deviation from implementing a strictly equivalent algorithm can result in serious decoding errors.
1) [range] = vector { 256, 128, 86, 64 } element ([floor1_multiplier]-1)
2) iterate [i] over the range 2 ... [floor1_values]-1 {
3) [low_neighbor_offset] = low_neighbor([floor1_X_list],[i])
4) [high_neighbor_offset] = high_neighbor([floor1_X_list],[i])
5) [predicted] = render_point( vector [floor1_X_list] element [low_neighbor_offset],
vector [floor1_X_list] element [high_neighbor_offset],
vector [floor1_Y] element [low_neighbor_offset],
vector [floor1_Y] element [high_neighbor_offset],
vector [floor1_X_list] element [i] )
6) [val] = vector [floor1_Y] element [i]
7) [highroom] = [range] - [predicted]
8) [lowroom] = [predicted]
9) if ( [highroom] is less than [lowroom] ) {
10) [room] = [highroom] * 2
} else [highroom] is not less than [lowroom] {
11) [root] = [lowroom] * 2
}
12) if ( [val] is nonzero ) {
13) vector [floor1_step2_flag] element [low_neighbor_offset] = set
14) vector [floor1_step2_flag] element [high_neighbor_offset] = set
15) vector [floor1_step2_flag] element [i] = set
16) if ( [val] is greater than or equal to [room] ) {
17) if ( [hiroom] is greater than [lowroom] ) {
18) vector [floor1_final_Y] element [i] = [val] - [lowroom] + [predicted]
} else [hiroom] is not greater than [lowroom] {
19) vector [floor1_final_Y] element [i] = [predicted] - ([val] - [lowroom]) - 1
}
} else [val] is less than [room] {
20) if ([val] is odd) {
21) vector [floor1_final_Y] element [i] =
[predicted] - (([val] - 1) divided by 2 using integer division)
} else [val] is even {
22) vector [floor1_final_Y] element [i] =
[predicted] + ([val] / 2 using integer division)
}
}
} else [val] is zero {
23) vector [floor1_step2_flag] element [i] = unset
24) vector [floor1_final_Y] element [i] = [predicted]
}
}
25) vector [floor1_step2_flag] element [0] = set
26) vector [floor1_step2_flag] element [1] = set
27) vector [floor1_final_Y] element [0] = vector [floor1_Y] element [0]
28) vector [floor1_final_Y] element [1] = vector [floor1_Y] element [1]
29) done
Decode begins by sorting the scalars from vectors [floor1_X_list], [floor1_final_Y] and [floor1_step2_flag] together into new vectors [floor1_X_list]', [floor1_final_Y]' and [floor1_step2_flag]' according to ascending sort order of the values in [floor1_X_list]. That is, sort the values of [floor1_X_list] and then apply the same permutation to elements of the other two vectors so that the X, Y and step2_flag values still match.
Then compute the final curve in one pass:
1) [hx] = 0
2) [lx] = 0
3) [ly] = vector [floor1_final_Y]' element [0] * [floor1_multiplier]
4) iterate [i] over the range 1 ... [floor1_values]-1 {
5) if ( [floor1_step2_flag]' is set ) {
6) [hy] = [floor1_final_Y]' element [i] * [floor1_multiplier]
7) [hx] = [floor1_X_list]' element [i]
8) render_line( [lx], [hx], [ly], [hy], [floor] )
9) [lx] = [hx]
10) [ly] = [hy]
}
11) if ( [hx] is less than [n] ) {
12) render_line( [hx], [hy], [n], [hy], [floor] )
}
13) if ( [hx] is greater than [n] ) {
14) truncate vector [floor] to [n] elements
}
}
15) for each scalar in vector [floor], perform a lookup substitution using
the scalar value from [floor] as an offset into the vector [floor1_inverse_dB_static_table]
16) done
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