use Data::Dumper;

my $site1 = 'AATKKM' x 20;
my $site2 = 'GGGGGA' x 20;

# brute force
my (%hash, $loops);
for my $base1( split //, $site1 ) {
    for my $base2( split //, $site2 ) {
        $hash{"${base1}_$base2"}++;
        $loops++;
    }
}

# precount incidence of tokens
my (%s1, %s2, %hash_e, $loops_e);
do{ $s1{$_}++; $loops_e++ } for split //, $site1;
do{ $s2{$_}++; $loops_e++ } for split //, $site2;

# still loop within loop but the are now far fewer loops to do
# as we only do one per token pair and calculate the total pairs
# from our precount data
for my $base1( keys %s1 ) {
    for my $base2( keys %s2 ) {
        $hash_e{"${base1}_$base2"} = $s1{$base1}*$s2{$base2};
        $loops_e++;
    }
}
print "Brute force loops $loops\nEfficeient Loops  $loops_e\n\n";
print Data::Dumper->Dump([\%hash, \%s1, \%s2, \%hash_e], [qw( hash s1 s2 hash_e)] );

__DATA__
Brute force loops 14400
Efficeient Loops  248

$hash = {
          'T_G' => '2000',
          'A_A' => '800',
          'T_A' => '400',
          'M_G' => '2000',
          'M_A' => '400',
          'K_G' => '4000',
          'K_A' => '800',
          'A_G' => '4000'
        };
$s1 = {
        'A' => '40',
        'K' => '40',
        'T' => '20',
        'M' => '20'
      };
$s2 = {
        'G' => '100',
        'A' => '20'
      };
$hash_e = {
            'T_G' => '2000',
            'A_A' => '800',
            'T_A' => '400',
            'M_G' => '2000',
            'M_A' => '400',
            'K_G' => '4000',
            'K_A' => '800',
            'A_G' => '4000'
          };