So, you just want to know if a number is a perfect square? If so, then return square root? Otherwise, I'm confused.

This thread seems to cover both fast exclusion and calculation:
http://board.flatassembler.net/topic.php?p=134231#134231

Multiple limb algorithms will use a fast approximation, and newtons method. A good initial guess is just to clip the binary string to half the length.

Yes - if it is a perfect square, it should return the square root, otherwise fail.
I really though you had a purely integer clever solution...

I do, but it's not faster unless (r) and (s) are needed. One use was for a modified Fermat factoring algorithm. The internal square root is faster for the single limb case, and newton's is faster for multi-limb, afaik. Anyhow my cleaver implementation is at the end of that thread.

Alright, the new version checks if sqrt(x) and x/y are integers during evaluation. It also has an SSA-based optimizer which can speed up loops by about 30%.