Before you start optimizing your code I recommend writing a test suite that verifies the current behaviour. That way when you introduce errors during optimization they will be easier to spot. You have done the manual verification, put that in a test script.

For example you could do this (and leave alpha_index as it is):

#!c:\perl\bin\perl
use strict;
use warnings;
use Math::BigInt;
use Data::Dumper;
use Test::More qw(no_plan);
    
    
my %index_val = ( A => 2,
                  C => 3,
                  D => 4,
                  N => 2,
                  M => 2,
                  T => 1,
                  G => 4);

my $sequence       = "ACTGACN";
my $distance_index = 3;
my $window         = 2;

my $arr_ref = alpha_index({ sequence => $sequence,
                           distance => $distance_index,
                           aa_index => \%index_val,
                           window_size => $window });
ok($arr_ref);
diag("Testing alpha_index with window: $window, distance: $distance_in
+dex, sequence: $sequence");
is(ref($arr_ref),'ARRAY','alpha index returned an array');
is(@$arr_ref,7,'7 entries are in the array');
is($arr_ref->[0]{A},2.51025682971601);
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Take a look at Test::More for other ideas on what you can test.