Number of occurrence of characters?

Hi,

I have a need to fairly often select data where the number of
occurrences of a character in the field is "x". Semantically, it's
literally "SELECT something FROM table WHERE numch('/', field)=$x".

The problem is how to do it efficiently. I see there isn't a built-in
function that counts character occurrences so I'd have to write it
myself. An additional constraint is that it must be implemented with
built-in capabilities, i.e. SQL and plpsql languages. I can do it the
brute force way, looping over the string and processing one by one
character with substring(), but is there a faster way?

Whatever the function is, I intend to create an index on it.