I have been programming in Java since 2004, mostly enterprise and web applications. But I have never used short or byte, other than a toy program just to know
I used 'byte' a lot, in C/C++ code implementing functionality like image compression (i.e. running a compression algorithm over each byte of a black-and-white bitmap), and processing binary network messages (by interpreting the bytes in the message).
However I have virtually never used 'float' or 'double'.