The compiler can substitute the value how it sees fit. It's like #define, but type-safe and scoped.
Maybe it's folded into expressions, propagated through constant expressions, or used it in contexts that require compile-time constants (template parameters, array sizes, static_assert, other constexpr expressions).
I mean, not in this case of pi/2, where it's more about announcing semantics, but in general those are the purposes and uses.
It can do this with const too or even a normal variable that just happens to not vary.
It depends on what you want to do with it.
If you just want the optimizer to be able to constant-fold a value, then yes, either of those will work.
If you want to be able to use the value in the other contexts the parent mentioned that require constant expressions as a language rule, then you generally need constexpr. As an exception, non-constexpr variable values can be used if they’re const (not ‘happens to not vary’) and have integer or enum type (no floats, structs, pointers, etc.). This exception exists for legacy reasons and there’s no particular reason to rely on it unless you’re aiming for compatibility with older versions of C++ or C.
Even if you don’t need to use a variable in those contexts, constexpr evaluation is different from optimizer constant evaluation, and generally better if you can use it. In particular, the optimizer will give up if an expression is too hard to evaluate (depending on implementation-specific heuristics), whereas constexpr will either succeed or give an error (depending only on language rules). It’s also a completely separate code path in the compiler. There are some cases where optimizer constant evaluation can do things constexpr can’t, but most of those have been removed or ameliorated in recent C++ standards.
So it’s often an improvement to tag anything you want to be evaluated at compile time as constexpr, and rarely worse. However, if an expression is so trivial that it’s obvious the optimizer will be able to evaluate it, and you don’t need it in contexts that require a constant expression, then there’s no concrete benefit either way and it becomes a matter of taste. Personally, I wouldn’t tag this particular pi/2 variable constexpr or const, because it does satisfy those criteria and I personally prefer brevity. But I understand why some people prefer a rule of “always constexpr if possible”, either because they like the explicitness or because it’s a simpler rule.
I'd like something like this in C or C++ quite honestly.
Something like a struct that I can say "this struct is global to the whole program and everyone can see it, but once this function exits those values are locked in". Maybe something like that one function is allowed to unlock and update it, but nowhere else.
Think in terms of storing a bunch of precomputed coefficients that are based on the samplerate of a system, where you really only need to set it up once on startup and it is unlikely to change during the application's running lifetime.
I feel like there probably is a way to do this, and if I was good at high level languages like C I'd know what it is. If you know, tell me what I'm not understanding ;-)