Earlier quoted context omitted.
Even a hundred million integers still adds up to only 300 MB extra for 64- vs. 16-bit. On any reasonable modern server, laptop, or desktop, that kind of memory usage probably will be the least of your worries, all the more if you really have an application that needs to hold hundreds of millions of ints in memmory at the same time. And if you are programming for a very specific embedded or otherwise constrained syste…
I'm not sure where you are getting the 300MB figure from. ((64-16)/8)x10^8/2^20 gives me 572.2MB of wasted space. What's even more interesting is looking at the percentage of wasted space. (((64-16)/8)x10^8/2^20)/(((64)/8)x10^8/2^20) means a whopping 75% of the memory use of our program is completely useless wasted space. Using more space than you need to will also impact performance. First there's the cache issues.…
If you need to crunch all those numbers at once, then yes, your cache will become your bottleneck. But if you were, say, keeping the count on a 100 million things, you most of the time will not be worried about that or your RAM usage, as most counts typically tend to follow a power-law distribution. Therefore, contention to make sure you are tracking every count will probably become a far worse problem for your app than your ability to shuffle data to/from the CPUs. Only in the corner case where you crunch a matrix or vectors or numbers of that size at once, you will start to get worried. But as said, I think the tensor-crunching use-case is the exception, not the norm.