If you want to avoid "-0", my order of prefence would be: 1) store it as decimal; 2) store it as [$sign, $deg, $min, $sec] where all four are integers, with sign taking on -1 for negative angles; 3) store it as [$deg, $min, $sec, $sign] (but I don't like that order as much).

For accepting integer input, I'd just only allow sign on the degrees... so if you wanted to allow "-0 1 0", that would be interpreted as -1min. Since "input" implies "text" in my mind, you can just check for (and strip) the sign using text processing, and then re-apply the sign once you are done:

$input = "-0 1 0"; 
my $sign = ($input =~ /^\s*-/) ? -1 : 1; 
my ($d,$m,$s) = map abs, split / /, $input; 
my $decdegrees = $sign * ($d + $m/60 + $s/3600);
print $decdegrees
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$input = "-0 1 0"; 
my ($sign, $d, $m, $s) = ($input =~ /(-{0,1})(\d+)\s+(\d+)\s+(\d+)/); 
my $decdegrees = (($sign)?-1:1) * ($d + $m/60 + $s/3600); 
print $decdegrees
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update: fix missing code tags