AoC day 12 (pt 2), Perl

#!/usr/bin/perl

use strict;
use warnings;

$| = 1;

use List::AllUtils  qw(pairwise sum);

my %Dirs   = ( 'E' => [1,0], 'N' => [0,1], 'W' => [-1,0], 'S' => [0,-1] );
my @Widder = ([ [ 1, 0], [ 0, 1] ],     # 0 tau
              [ [ 0,-1], [ 1, 0] ],     #   tau / 4
              [ [-1, 0], [ 0,-1] ],     #   tau / 2
              [ [ 0, 1], [-1, 0] ]);    # 3 tau / 4

my @Pos  = (0,0);
my @Grad = (10,1);

while (<>) {
    m#(\w)(\d+)#;

    if ($1 eq 'F') {
        @Pos = pairwise { $a + $2 * $b } @Pos, @Grad;
    } elsif ($1 eq 'L' || $1 eq 'R') {
        my @rot = @{$Widder[ $2 / 90 * (($1 eq 'R') ? -1 : 1) ]};
        @Grad = map { sum pairwise { $a * $b } @Grad, @$_ } @rot;
    } else {
        @Grad = pairwise { $a + $2 * $b } @Grad, @{$Dirs{$1}};
    }
}

print "Part 2: ", (sum map { abs } @Pos), "\n";