How is GPS RAIM availability calculated?
The website that Ralgha points out is indeed the one to look at for the US. They also provide a SOAP interface should you want to create your own app for the IPAD.

For RAIM to be available, you need to check firstly that at least 5 satellites (Space Vehicles in GPS language) are visible from you position, or 4 if your RAIM algorithm uses Baro-aiding. They have to be well above the horizon. How much depends on your satellite receiver, the FAA uses 5 degrees on their website. There are some receivers that use a masking angle of only 3 degrees.

Orbital equations can be taken from the GPS interface control document, section 30.3.3.1.3. They take almanac data as input. Apart from the Space Vehicle orbits, you also need to take into account their health from the NANU's. 

With the satellites available, you need to calculate the RAIM containment bound. This is the maximum size that a position error can grow due to a faulty satellite signal without the RAIM algorithm noticing it within 10 seconds (with a 99.9% probability). If that containment bound is more than 1 nautical mile, RAIM is said to be unavailable for terminal procedures. For NPA a 0.3 nautical mile radius is used. 

The containment bound depends very much on the geometry of the satellites, more that on the number of satellites available. 

The problem with the RAIM algorithms is that they aren't standardized. There are several ways to perform RAIM and because GPS manufacturers use proprietary solutions there is little information available to the public. So calculating the containment bound is where you will get stuck. 

So there is no easy way to implement RAIM prediction on an IPad, apart from using the FAA website. 

Europe has also a RAIM prediction website; AUGUR.