Some of you may know the solution to this problem already. If you do, please wait to post your answer until other people have had a chance.
Challenge: Write a function which computes the square root of a double precision value. RESTRICTION: You may execute the division operator ONE TIME at the most. I don't mean that it can only appear in one place in the code, I mean that it cannot happen more than once, period.
RESTRICTION 2: This should be obvious, but I'll spell it out. You cannot use any function declared in math.h. In fact, you may not use any functions whatsoever (except for the function you are writing).
Accuracy requirement: When the value returned by your function is squared, the resulting value must not differ from the original by more than 1 part in 100000.
You may assume that the values passed to your function will never exceed 1e9. (This used to be 1e20, but I realized that is probably too difficult)
Be as efficient as possible.