I can see four problems with the posted code that would make it run slower:

1. You are using alternation when a character class would be faster.
2. You are using capturing parentheses when you don't use the results of those captures.
3. You are using the "+" Additive operator instead of the more efficient "+=" assignment operator.
4. You are looping over the same string 28 or 29 times, depending on the value of $ftype, when you probably should only have to loop over the string twice.

For example:

    while ($string=~m{(B|C|P|T|Z|a|b|d|h|k|n|p|q|u|v|x)}g){
        $count=$count+($tbsz*0.5625);
    }
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Would be more efficient as:

    while ($string=~m{[BCPTZabdhknpquvx]}g){
        $count+=($tbsz*0.5625);
    }
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That would cover points 1, 2 and 3.    For point 4 you could use hash tables for the calculations, something like:

my %start_table = (
    '\s'    => 1,
    '<ems>' => 1,
    '<195>' => 1,
    '\.'    => 0.25,
    '<ths>' => 0.25,
    '<193>' => 0.25,
    '<ens>' => 0.5,
    '<194>' => 0.5,
    );
my $start_lookup = join '|', keys %start_table;

my %ftype_table = (
    W    => 1,
    '\s' => 1,
    '%'  => 1,    ### % is added temporarily for some testing purpose
    w    => 0.84375,
    '\)' => 0.84375,    ### need to escape meta-characters!!!
    '\(' => 0.84375,
    M    => 0.8125,
    m    => 0.8125,
    N    => 0.7188,
    Q    => 0.7188,
    # etc,
    );
my $ftype_lookup = join '', keys %ftype_table;

my %non_ftype_table = (
    W    => 0.7844,
    w    => 0.6999,
    A    => 0.5656,
    X    => 0.55,
    Q    => 0.5469,
    O    => 0.5469,
    R    => 0.5375,
    K    => 0.5375,
    Y    => 0.5375,
    # etc.
    );
my $non_ftype_lookup = join '' keys %non_ftype_table;


while ( $string =~ /($start_lookup)/og ) {
    $count += $tbsz * $start_table{ $1 };
    }
$string =~ s/<[A-Z\[\\\]\^_`a-z]+>//g;

if ( $ftype == 1 ) {
    while ( $string =~ /([$ftype_lookup])/og ) {
        $count += $tbsz * $ftype_table{ $1 };
        }
else {
    while ( $string =~ /([$non_ftype_lookup])/og ) {
        $count += $tbsz * $non_ftype_table{ $1 };
        }
    }
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