Including arithmetic operations when defining a constant

Question

So I often see something like this:

#define gf_PI  f32(3.14159265358979323846264338327950288419716939937510)
#define gf_PIhalf  f32(3.14159265358979323846264338327950288419716939937510 * 0.5)

This means that half PI value is calculated every time I use gf_PIhalf in my code, right?
Wouldn't it be better to literally write the value of half PI instead?

Wouldn't it be even better to do the following:

#define gf_PI f32(3.14159265358979323846264338327950288419716939937510)
const float gf_PIHalf = gf_PI * 0.5f;    // PIHalf is calculated once

Finally wouldn't it be best to do it like this (and why it doesn't seem to be a common practice):

const float gf_PI = 3.14159265358979323846264338327950288419716939937510;
const float gf_PIHalf = gf_PI * 0.5f;

Answer 1

This means that half PI value is calculated every time I use gf_PIhalf in my code, right?

Nope, not likely.

You can reasonably count on your compiler to do that multiplication at compile time, not runtime.

Answer 2

Your conclusions are somewhat right, except that the #define version will almost definitely resolve in compile time and the bit about types const globals being uncommon practice. They are common practice in modern good code. #defines are all but dead for this use. The best practice is to define your file scope globals in an unnamed namespace:

namespace
{
    const float g_SomeGlobal = 123.456f;
}

This prevents anyone outside of your translation unit from being able to 'see' g_SomeGlobal.