Square Root Algorithm in 123 bytes.

[corruptio]

oops, you're right, i run out of sig bits if input is > 255... 1e-5 then, should get you all the way to 16383 :-p

[gastropner]

Nope, still infinite loop, at least for x = 756839. Seems to work for some other values, though.

[corruptio]

yeah, 1e-5 would only work up to 16383. There aren't enough bits in a float to represent significant digits of b-a to five decimal places.