Shuffled input is important
Yes, good catch! The GRT makes each comparison faster, but it seems like the number of comparisons is far lower for already sorted or nearly sorted input. It looks like the pack method is better no matter what because with this (and a list from -50 to 250): 
vr_map => sub { # https://www.perlmonks.org/?node_id=1229415
                my @list = @input;
                @list = unpack 'i*', pack 'I*', sort { $a <=> $b }
                        map { ~$_ } @list; # Doesn't even give the cor
+rect answer, there's an offset of 1
                Compare(\@list,\@output) or die "@list" if DO_CHECK;
              },

[download]
your implementation is still noticeably faster (my version falls behind pretty fast on a non-sorted list): 
             Rate      Eily    vr_map grepfirst sortfirst        vr
Eily       5208/s        --      -53%      -64%      -67%      -71%
vr_map    11021/s      112%        --      -25%      -31%      -38%
grepfirst 14623/s      181%       33%        --       -8%      -17%
sortfirst 15977/s      207%       45%        9%        --      -10%
vr        17701/s      240%       61%       21%       11%        --

[download]

In reply to Re^2: Fastest way to sort a list of integers into 0,1,2,3,-3,-2,-1 by Eily
in thread Fastest way to sort a list of integers into 0,1,2,3,-3,-2,-1 by haukex

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