Sum to a Million
I spent this past weekend trying to sum the numbers from 1 to a million as fast as possible. Here’s what I learned.
This function ran very fast:
(defn bigsum1  (let [sum (atom 0)] (dotimes [i 1000000] (swap! sum + (inc 1))) @sum))
This one only barely slower:
(defn bigsum2  (apply + (range 1 (inc 1000000))))
I ran each one of the above in a “test harness” like so:
(dotimes [i 100] (time (bigsum1)))
It’s not a perfect solution, but it gives you a pretty good idea of how long a typical run lasts.
Out of curiosity, I ran the following to get a sense of how long it takes to walk a list, since, if I understand what Clojure’s doing under the hood correctly,
count both have to walk the given lazy list from head to tail without taking any shortcuts.
(last (range 1 (inc 1000000))) (count (range 1 (inc 1000000)))
count both took longer than the
I thought perhaps spawning a bunch of threads, each to update a counter might perform better, which was the motivation for my next variation:
(defn bigsum3  (let [sum (agent 0)] (dotimes [i 1000000] (send sum + (inc i))) (await sum) @sum))
I think agents nicely match the solution I was trying for. I created a thread-safe object to hold the sum and then dispatched a bunch of updates to it using the
send function which would be executed in a Clojure-managed threadpool.
+ is associative and commutative so it doesn’t matter what order those updates were actually executed in as long as they all got executed. So finally, the code makes sure that all of those updates got executed by calling
await before returning the current value of the sum.
This function took a looong time. Much longer than I expected it to, and much longer than any variant before it. Before actually using them, I had it in my mind that agents used threads and threads were another word for speedspeedspeed. I thought that, for sure, this code would run faster than bigsum1 and 2. Not out of any reasoned analysis, but simply based on the fact that they used those magical things called threads. I’m not saying that Clojure agents are slow, or that with some tweaking I couldn’t get an agent-based function to run very very fast, merely that my initial impressions of them were askew. I would love to hear from the Clojure-verse how I might tweak my agents example to make it fly.
Side-bar: What not to do:
Faced with the initial slowness of the agents solution, I was tempted to write this:
(defn bigsum4  (let [sum (atom 0)] (dotimes [i 1000000] (.send (Thread. (fn  (swap! sum + (inc i)))))) @sum))
I figured that maybe if I spawned the threads myself and used a thread-safe
atom, my code would be faster than bigsum3. Not only was this code no faster than bigsum3, it’s incorrect. All of the threads it spawn may not have finished by the time it derefs sum. This code is very likely to return some intermediate result, atomically updated, but no less wrong. The lesson I learned here was not to confuse thread-safe with “don’t have to think about threads”.