I am using a TStream to read binary data (thanks to this post: http://stackoverflow.com/questions/2878180/how-to-use-a-tfilestream-to-read-2d-matrices-into-dynamic-array).

My next problem is that the data is Big Endian. From my reading, the Swap() method is seemingly deprecated. How would I swap the types below?

 16-bit two's complement binary integer
 32-bit two's complement binary integer
 64-bit two's complement binary integer
 IEEE single precision floating-point - Are IEEE affected by Big Endian?

And, finally, since the data is unsigned, the creators of this dataset have stored the unsigned values as signed integers (excluding the IEEE). They instruct that one need only add an offset (2^15, 2^31, and 2^63) to recover the unsigned data. But, they note that flipping the most significant bit is the fastest way to do that. How does one efficiently flip the most significant bit of a 16, 32, or 64-bit integer?

So, if the data on disk (16-bit) is "85 FB" - the desired result after reading the data and swapping and bit flipping would be 1531.

Is there a way to accomplish the swapping and bit flipping with generics so it fits into the generic answer at the link above?

Yes, kids, THIS is how scientific astronomical data is stored by NASA, ESO, and all professional astronomers. This FITS standard is considered by some to be one of the most successful standards ever created in its proliferation and flexibility!