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12 hybrids as mixed by channel coupling.  The exact semantic content of
35 encoded and simply trusting that it is, is as follows:
49 can be thought of as forming a vector in their own right, as in the
50 illustration below. Just as the residue vectors are coded in grouped
60 codebook design dictates that each vector is encoded as the additive
81 as a black box--or cyan box or brown box--in the above figure).
89 As an example, assume a partition vector of size eight, to be encoded
96 codebook dimensions = 8 encoded as: [ 0 1 2 3 4 5 6 7 ]
98 codebook dimensions = 4 encoded as: [ 0 2 4 6 ], [ 1 3 5 7 ]
100 codebook dimensions = 2 encoded as: [ 0 4 ], [ 1 5 ], [ 2 6 ], [ 3 7 ]
102 codebook dimensions = 1 encoded as: [ 0 ], [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ]
114 vector scalars in order. As with residue 0, however, partition length
118 As an example, assume a partition vector of size eight, to be encoded
125 codebook dimensions = 8 encoded as: [ 0 1 2 3 4 5 6 7 ]
127 codebook dimensions = 4 encoded as: [ 0 1 2 3 ], [ 4 5 6 7 ]
129 codebook dimensions = 2 encoded as: [ 0 1 ], [ 2 3 ], [ 4 5 ], [ 6 7 ]
131 codebook dimensions = 1 encoded as: [ 0 ], [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ]
139 Residue type two can be thought of as a variant of residue type 1.
140 Rather than encoding multiple passed-in vectors as in residue type 1,
143 \emph{ch}*\emph{n}. Encoding then proceeds as in type 1. Decoding is
144 as in type 1 with decode interleave reversed. If operating on a single
159 1) [residue_begin] = read 24 bits as unsigned integer
160 2) [residue_end] = read 24 bits as unsigned integer
161 3) [residue_partition_size] = read 24 bits as unsigned integer and add one
162 4) [residue_classifications] = read 6 bits as unsigned integer and add one
163 5) [residue_classbook] = read 8 bits as unsigned integer
173 values as well as \varname{[residue_partition_size]}apply to
175 \varname{[residue_partition_size]} is as explained above,
197 3) [low_bits] = read 3 bits as unsigned integer
198 4) [bitflag] = read one bit as boolean
199 5) if ( [bitflag] is set ) then [high_bits] = read five bits as unsigned integer
208 stages (8 in Vorbis I, as constrained by the elements of the cascade
218 4) array [residue_books] element [i][j] = read 8 bits as unsigned integer
265 as follows. We assume that the number of vectors being encoded,
286 Packet decode proceeds as follows, matching the description offered earlier in the document.
352 Format zero decodes partitions exactly as described earlier in the
386 Format 1 decodes partitions exactly as described earlier in the
418 Format 2 is reducible to format 1. It may be implemented as an additional step prior to and an additional post-decode step after a normal format 1 decode.
431 \item Post decode: Deinterleave the single vector \varname{[v]} returned by format 1 decode as described above into \emph{ch} independent vectors, one for each outputchannel, according to: