Quickly find whether a value is present in a C array?

Question

I have an embedded application with a time-critical ISR that needs to iterate through an array of size 256 (preferably 1024, but 256 is the minimum) and check if a value matches

Answer 1

If the set of constants in your table is known in advance, you can use perfect hashing to ensure that only one access is made to the table. Perfect hashing determines a hash function that maps every interesting key to a unique slot (that table isn't always dense, but you can decide how un-dense a table you can afford, with less dense tables typically leading to simpler hashing functions).

Usually, the perfect hash function for the specific set of keys is relatively easy to compute; you don't want that to be long and complicated because that competes for time perhaps better spent doing multiple probes.

Perfect hashing is a "1-probe max" scheme. One can generalize the idea, with the thought that one should trade simplicity of computing the hash code with the time it takes to make k probes. After all, the goal is "least total time to look up", not fewest probes or simplest hash function. However, I've never seen anybody build a k-probes-max hashing algorithm. I suspect one can do it, but that's likely research.

One other thought: if your processor is extremely fast, the one probe to memory from a perfect hash probably dominates the execution time. If the processor is not very fast, than k>1 probes might be practical.