Passing arguments to constexpr functions

Question

I'm new into programming and I started to learn about it using the book Programming principles and practice using C++. Today I'm here because I have some problems in understanding constexpr functions. In chapter 8 the author introduces them in some lines and a brief example using these words:

A function represents a calculation, and sometimes we want to do a calculation at compile time. The reason to want a calculation evaluated by the compiler is usually to avoid having the same calculation done millions of times at run time.

We convey our intend to have a function evaluated at compile time by declaring the function as a constexpr function. A constepxr function can be evaluated at compile time just if it is given constant expressions as arguments.

constexpr double xscale = 10; // scaling factors 
constexpr double yscale = 0.8; 
constexpr Point scale(Point p) { return { xscale*p.x, yscale*p.y }; };

Assume that point is a simple struct with members x and y representing 2D coordinates. Now, when we give scale() a Point argument, it returns a point with coordinates scaled according to the factors xscale and yscale. For example:

void user(Point p1) {

Point p2{10,10}; 

Point p3 = scale(p1); 
Point p4 = scale(p2) // p4 == {100,8}

constexpr Point p5 = scale(p1); // error : scale(p1) is not a constant expression
constexpr Point p6 = scale(p2); // p6 == {100,8};

My question is: Why we can use p2 as an argument to scale()? Is p2 considered a constant expression? And if yes, why?

Can the data members x and y be considered constant expressions?

My book doesn't give too much information so I'm having some problems with this concept.

Answer 1

Basically, constexpr functions can be executed at compile time or run time depending on the context. It is guaranteed to execute at compile time only if all its parameters are constexpr and its result is used in a context requiring constexpr (e.g. assignment to constexpr value, template parameter, or, say, c-style array size). Otherwise, it is evaluated at runtime as any other function. So the p3 and p4 lines are executed at runtime, whereas p5 gives an error because scale(p1) is not constexpr, and actually p6 should also give you an error unless you add a constexpr to the definition of p2. See an example here.

Answer 2

It looks to me, that it's gotcha in book. It looks like it should be

constexpr Point p2{10,10};

only in this case any modern compiler will not give error on call

constexpr Point p6 = scale(p2); // p6 == {100,8};

that's because you are trying to initialize constexpr variable with result of function, which will be evaluated in runtime (if p2 is not declared constexpr).