# Replace:
    my @sorted=
        map { RESTORE($_) }
        sort { COMPARE($a,$b) }
        map { XFORM($_) }
        @list;

# with:
    my @sortOn= map { XFORM($_) } @list;
    my @index= sort {
        COMPARE($sortOn[$a],sortOn[$b]) || $a <=> $b
    } 0..$#sortOn;
    my @sorted= @list[@index];

# or with (to avoid temporaries remaining in scope):
    my @sorted= do {
        my @sortOn= map { XFORM($_) } @list;
        @list[
            sort {
                COMPARE($sortOn[$a],sortOn[$b]) || $a <=> $b
            } 0..$#sortOn;
        ];
    };