How do you store floating-point numbers / real numbers in OpenLDAP? I have never seen such a data type. I know you could store a string representation of a floating-point number, but that sounds like an awful practice.
You can shove arbitrary data into an OpenLDAP server, though it's likely to get base64 encoded and decoded along the way, much like sending an email attachment.
It's the matching and ordering rules that could get complicated.
The most likely candidate would be an
EQUALITY octetStringMatch ORDERING octetStringOrderingMatch SYNTAX 188.8.131.52.4.1.14184.108.40.206.40
You should be able to use it to store arbitrary data. (You may not want to include ordering as it's unlikely to achieve the desired effect.)
You may consider limiting the number of bits by tacking a byte limit on the end of the syntax OID. E.g.