It is easy to find an integer with binary search even if it can be arbitrarily large: first guess the order of magnitude, then keep dividing the interval. This answer describes how to find an arbitrary rational number.
Having set the scene, my question is similar: how can we guess a IEEE 754 floating point number? Assume it is not NaN, but everything else is fair game. For each guess, your program will be told whether the number in question is higher, equal or lower. Minimize the number of guesses required in the worst case.
(This is not a homework assignment. Though, I might make it one, if this turns out to have an interesting answer that's not just "beat the floating point numerical difficulties to death with lots and lots of special case handling.")
Edit: if I were better at searching I could have found the answer---but that only works if you already know that reinterpretation as int works (with certain caveats). So leaving this up. Thanks to Harold for a great answer!