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@@ -307,6 +307,7 @@
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 .bp
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 .SUBSUBSECTION "the Residual"
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+.nr ZR \n%
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 .PP
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 Though the FLAC format allows for different forms of
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 residual coding, two forms of partitioned Rice are the only ones
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@@ -708,7 +709,7 @@
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 .PP
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 In this example, @\[*D] sup 1@'s value of 26 is the smallest.
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 Therefore, when compressing this set of samples in a FIXED subframe,
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-it is best to use a predictor order of 1.
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+it's best to use a predictor order of 1.
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 .PP
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 The predictor order indicates how many warm-up samples to take from
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 the PCM stream.
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@@ -731,4 +732,65 @@
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 4:@"Residual" sub i = "Sample" sub i~~-~~((4 * "Sample" sub {i~-~1})~~-~~(6 * "Sample" sub {i~-~2})~~+~~(4 * "Sample" sub {i~-~3})~~-~~"Sample" sub {i~-~4})@
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 _
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 .TE
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+.\"In this example, the residual values are: -1 1 1 1 0 3 0 -4 -1 0 1 1 1 4 -3 1 4 -1 -1
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+.bp
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+.SUBSUBSECTION "the Residual"
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+.PP
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+Given a stream of residual values, one must place them in one or more
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+partitions, each with its own Rice parameter, and prepended with a
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+small header.\(dg
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+.FS
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+\(dg See page \n(ZR for full details of how the residual is organized.
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+.FE
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+The residual's coding method is typically 0, unless one is encoding
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+audio with more than 16 bits-per-sample and one of the partitions
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+requests a Rice parameter higher than @2 sup 4@.
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+The residual's partition order is chosen exhaustively, which means
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+trying all of them within a certain range (e.g. 0 to 5) such that
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+the residuals can be divided evenly between them and then the partiton
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+order which uses the smallest estimated amount of space is chosen.
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+.PP
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+Choosing the best Rice parameter is a matter of selecting the smallest
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+value of `x' such that:
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+.EQ
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+"sample count" * {2 sup x}~~>~~{sum from {i = 0} to {"residual count"~-~1}
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+|{"residual" sub i}|}
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+.EN
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+.LP
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+Again, this is easier to understand with a block of example residuals,
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+19 in total:
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+.TS
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+tab(:);
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+| c | c | c |
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+| c | r | r |.
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+_
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+index:@residual sub i@:@|~{residual sub i}~|@
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+=
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+0:-1:1
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+1:1:1
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+2:1:1
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+3:1:1
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+4:0:0
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+5:3:3
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+6:0:0
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+7:-4:4
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+8:-1:1
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+9:0:0
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+10:1:1
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+11:1:1
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+12:1:1
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+13:4:4
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+14:-3:3
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+15:1:1
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+16:4:4
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+17:-1:1
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+18:-1:1
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+_
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+@|~{roman "sum"}~|@::29
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+_
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+.TE
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+@19 * {2 sup 0}@ is not larger than 29.
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+.br
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+@19 * {2 sup 1}@ is larger than 29, so the best Rice parameter
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+for this block of residuals is 1.