How to use altfp_sqrt with the Nios II?

I think you should not use the PIO functions for this purpose. The approach should be as follows:

1. Make your custom component (with register addressing) and add it in the SOPC system. Follow the steps as explained in NIOS manuals for this.

2. Instead of using PIO functions, use simple assignment functions. You know the base address for this component. Instantiate a pointer in your NIOS program with this address. Use the pointer assignments for both writing a value at this address and reading it later when your component is done with the processing (You can inform NIOS of conclusion of the processing of data through interrupts etc.).