Thank you. That adapts:

sub f {
    my( $n, $g, $m ) = @_;
    $n % $g + $g * int(($m - $n) / $g);
};;
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to every situation I can think I might need:

[0] Perl> print join ' ', map f( $_, 8, 15 ), 0 .. 15;;
8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7

[0] Perl> print join ' ', map f( $_, 4, 15 ), 0 .. 15;;
12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3

[0] Perl> print join ' ', map f( $_, 2, 15 ), 0 .. 15;;
14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1

[0] Perl> print join ' ', map f( $_, 1, 15 ), 0 .. 15;;
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

[0] Perl> print join ' ', map f( $_, 12, 23 ), 0 .. 23;;
12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11

[0] Perl> print join ' ', map f( $_, 8, 23 ), 0 .. 23;;
16 17 18 19 20 21 22 23 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7

[0] Perl> print join ' ', map f( $_, 6, 23 ), 0 .. 23;;
18 19 20 21 22 23 12 13 14 15 16 17 6 7 8 9 10 11 0 1 2 3 4 5

[0] Perl> print join ' ', map f( $_, 4, 23 ), 0 .. 23;;
20 21 22 23 16 17 18 19 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3

[0] Perl> print join ' ', map f( $_, 2, 23 ), 0 .. 23;;
22 23 20 21 18 19 16 17 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1

[0] Perl> print join ' ', map f( $_, 1, 23 ), 0 .. 23;;
23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
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Even the basket cases:

[0] Perl> print join ' ', map f( $_, 9, 26 ), 0 .. 26;;
18 19 20 21 22 23 24 25 26 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8

[0] Perl> print join ' ', map f( $_, 6, 26 ), 0 .. 26;;
24 25 26 21 22 23 18 19 20 15 16 17 12 13 14 9 10 11 6 7 8 3 4 5 0 1 2

[0] Perl> print join ' ', map f( $_, 3, 26 ), 0 .. 26;;
24 25 26 21 22 23 18 19 20 15 16 17 12 13 14 9 10 11 6 7 8 3 4 5 0 1 2
[download]