Node.js vs C++ for mathematic
Since you need the Node.js part anyway, go ahead, implement everything in Node.js. If it is fast enough, this is easy enough to maintain. It's very hard to predict the power of a virtual machine / JIT compiler.
If it is not fast enough, first think about algorithmic improvements. If this doesn't help and if profiling shows that the computation is the problem, go ahead, re-implement it in C++. But be aware that writing performant C++ code is not trivial. Make sure that you have a good profiler at hand and measure often.
In general I'd say C++ code is faster if written correctly. The tricky part is to write it correctly. Please check this article Google Paper on C++, Java, Scala, Go for more information. The gist is - managed languages make it a lot easier to write & maintain the code but if you need raw performance, C++ is the best. But it comes at the price of needing a lot of expertise and that the code is harder to maintain.
denshade, your C implementation goes only to 2e5 not 2e6, like you've done for js (linking to today's revs on Github):
Piping to /dev/null, and changing js also to 2e5, I get about 6.5 seconds for C and about 8.5 seconds for js (using some version of node) on my current computer.
Since your algorithm is O(n^2), I would expect 2e6 to take some 15 minutes, not 15 hours, but I haven't tried it. Maybe it does fall apart that bad for some reason.
(Note that I couldn't comment directly, since I'm brand new on SO and have no rep.)
it's pretty much impossible to answer this kind of question. The answer as always for these things is it depends on your skills and how much time and effort you are willing to put into it.
C++ always has the potential to be faster and more efficient as you have much closer control over all the things that matter. The downside it that you have to do all the things that matter and the generic implementations in the other language are probably done by someone who knows what they are doing and could well be better than a naive or quick implementation in c++
Plus often you'll find that the bottleneck isn't what you think it will be anyway, for example if reading in your data turns out to take 20 times as long as the calculations which isn't impossible then it hardly matters how fast the calculations are. And intuition about where the bottlenecks lie is often badly wrong even for experienced developers.