Why do M_PI_2, M_PI_4, M_1_PI, and M_2_PI exist? [closed]

Question

I do understand why we have this in standard headers:

#define M_PI       3.14159265358979323846   // pi

However, I don't see much benefit in having these:

#define M_PI_2     1.57079632679489661923   // pi/2
#define M_PI_4     0.785398163397448309616  // pi/4
#define M_1_PI     0.318309886183790671538  // 1/pi
#define M_2_PI     0.636619772367581343076  // 2/pi

Is there any advantage in using these instead of M_PI/2, M_PI/4, 1/M_PI and 2/M_PI in actual code? (In 2020 and beyond?)

Aren't the spelled-out expressions much more readable?

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I'm asking for a couple of reasons really.

Firstly, one day I accidentally mixed up M_PI_2 and M_2_PI (and maybe even 2 * M_PI). Took a while to figure out something was wrong, and after that took another while to find out what exactly was the root cause. Still think it's not super obvious what M_PI_2 and M_2_PI mean, if you are just reading code using them and don't see the definitions. And why should I memorize something like that? So, is it safe to say that using these definitions is actually an anti-pattern that degrades code readability?

Secondly, having these definitions available may still be an issue, e.g. in Windows (Visual C++). Instead of defining all these, I'd prefer to define only M_PI, and then say M_PI/2 and not M_PI_2 in the code. Is there something I'm missing?

Answer 1

Because 2 and 4 are powers of two, M_PI_2 and M_PI_4 really are redundant and 100% equivalent to M_PI/2 and M_PI/4. However, M_1_PI is not necessarily equivalent to 1/M_PI; the latter has two roundings (approximation of pi, then inexact division) rather than just one (approximation of 1/pi).