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And based on the way he worded it, he would agree with you now. His point was that you need to apply both theory AND practice and not just blindly cite theory.

There is an aspect to theory that's comforting, though. I'm sure I would sleep better at night knowing that my application was using an O(1) hash table as its map rather than an O(n) alist, even if the constant factors are higher. More hardware helps out constant factors; it doesn't do anything with quadratic algorithms.

"Completely false" might be an overstatement. Do you have any test results you could point to? Or at least an exact specification of what the test would consist of? Particularly, are you measuring the first run from a luke warm start, guaranteed to be in memory but not in cache? Or might you be reading a page or two from disk, or making multiple passes while it still might be in some level of cache? Because I think the details are going to make a difference as to whether the break even point is n=4 or n=400, or maybe even n=4000.

Like the decade-old Erik, my intuition is still that a brute force would be hard to beat for less than 100 integer keys to pointers if one is doing multiple passes through the list. But I'd love to bring my intuition up to date. Do you have one of these new-fangled 'competently implemented hash maps' that you could yield up so I can do some cycle counting? And is it fair if we throw in a few insertions and deletions just to make it realistic?

For record, I completely agree on irrelevance of the cycles to compute the hash once one might be hitting main memory. But I also think it's worth noting that the size of your L3 cache may be comparable to the all the RAM that Erik had in his machine. I also think you might be underestimating the power of a modern prefetch unit, whether hinted or automatic. But I'll bow to data. As you said very well: "do the experiments, state the results, and walk away."

You are ignoring the fact that you have to calculate the hash-key. With association tables, pointer comparison is enough if you are searching for interned symbols.

No, he isn't; you entirely missed the point. Cache misses are expensive. Given that he specified integer keys, it's not a bad guess that a hash function will run fewer than 300 cycles on the specified Nehalem. If your association list has to run across three cachelines but your hash implementation runs across only two, the hash wins under these circumstances. Add a couple more cachelines and hashes start winning for more than just integer keys, too.

Times have changed. Incidentally, the same may be true of some of the tree alternatives to hashes, too; used to be log n lookups would beat the O(1) lookups of hashes in many real-world scenarios because of the big constant on the O(1), but running across log n cachelines vs. O(1) cachelines (without a big constant) is a different story. The gulf between computation and memory continues to widen.

Cache misses are expensive yes.

And when you have an interned string to be searched on - you always have to calculate it's hash-sum as key before looking for it in a hash-table, and you don't have to do that for a linear search (it's an interned symbol that's why). This means you might have to read one, two or more cache lines (if the cache line is 64, then it's strlen(yourstring)/8)

You can't use the pointer itself as a key - either the distribution is not good, or the language would not allow you (you can't do it in Common Lisp which Erik Naggum was talking about).

That calculation of the key might read one two or more cache lines - depending on how big the string is.

Off course it would be better for the hash-table the smaller key is, and worse if not.

And then, there are still CPUs without cache still in popular use - for example PS3's CELL SPE (spu).

And one more thing - in the linear search you always read the same cache lines, while in the hash-table you have to read everytime different memory (the strings to be searched upon).

But in both cases, there are instructions to prefetch, but again - you would be wasting less cache with the assoc table if you are looking a lot (e.g. you'll warm always from the begining and keep that in the L1), while for hash-table you would warm all the keys. It's really hard to compare, but I hope you get the picture.

isn't this making a lot of assumptions with regard to memory locality and the organization of the hash table?

for instance: what if the initial capacity isn't set properly for the hash table? what if the hash function isn't perfect and you end up with 16 buckets and 4 elements in one bucket and none in the other 15? (at which point you end up with what is essentially a list with lots of overhead). what if you start off by allocating a hash table that is too small and midway through populating it have to expand it?

the more comments I read, the more Erik becomes right.

"isn't this making a lot of assumptions with regard to memory locality and the organization of the hash table?"

Well, yeah. Always.

But if you want to talk about how Erik is right, you probably want to go looking for an algorithm specifically designed for storing alists in a cache aware manner. Not sure what such a beast would look like, but something could probably be constructed and probably has been.

Saying "what if your hash table becomes linearized" is not a fair argument when comparing linear search to hash lookup.

I don't see why this should look funny 11 years in hindsight. the important part is knowing rather than assuming. and you seem to assume quite a lot.