It's mostly all in the title. How do you report the runtime of a C++ program that has intensive calculations at compile-time?
If I have a program that, when I use the bash time command on it, appears to run in .5 seconds, but the COMPILE TIME CALCULATIONS take over 10 minutes, can I honestly say my program runs in .5 seconds?
You don't. Run-time is not compile-time, and nobody except the developer cares in the least how long compilation took.
(But also what Peter said: if your system really works like this, then something is very wrong to begin with.)
The Sieve of Eratosthenes calculates all prime numbers up to any given limit. If you're calculating primes at compile time you're simply shifting what would have been a run time speed cost to a space cost. Yes your program runs faster when ran for primes "under a certain limit" but the bigger that limit the bigger your program.
It's called the space time tradeoff. It's why algorithms aren't only rated in big O for speed but also space.
In terms of speed the Sieve is O(n log log n). Space is O(n).
Your pre-calculated Sieve has speed at O(1) and space is the same. Except the pre-calculation invents a new big O category to consider: distribution size. Where the classic Sieve algorithm's distribution size is O(1) your pre-calculated Sieve distribution size is O(n).
Congrats. It's a different way to tradeoff. One that requires maintaining and distributing n binaries. Enjoy.
