Does C++11, 14, 17 or 20 introduce a standard constant for pi?

Question

There is a rather silly problem with the number pi in C and C++. As far as I know M_PI defined in math.h is not required by any standard.

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Answer 1

M_PI is defined by "a standard", if not a language standard: POSIX with the X/Open System Interfaces extension (which is very commonly supported and required for official UNIX branding).

It's (still) not certain what will be in C++20, but since you asked: it probably will have such constants. The paper was merged in the last round of C++20 features (for the Committee Draft in August 2019).

Specifically, there will both be std::numbers::pi (of type double) and a variable template that you can use if you want a different floating point type, e.g. std::numbers::pi_v<float>. The full list of constants can be see in [numbers.syn].

Answer 2

It is not obviously a good idea because there is no obvious type with which define pi that is universally applicable across domains.

Pi is, of course, an irrational number so it cannot be correctly represented by any C++ type. You might argue that the natural approach, therefore, is to define it in the largest floating point type available. However, the size of the largest standard floating point type long double is not defined by the C++ standard so the value of the constant would vary between systems. Worse, for any program in which the working type was not this largest type, the definition of pi would be inappropriate since it would impose a performance cost on every use of pi.

It is also trivial for any programmer to find the value of pi and define their own constant suitable for use, so it does not provide any great advantage to include it in the maths headers.

Answer 3

Edited - To remove the term necessary, because it proved controversial. It is too much of an absolute term.

C++ is a large and complex language, for that reason the Standards Committee only include things which are strongly required. As much as possible is left to non-language standard libraries... like Boost.
boost::math::constants

Answer 4

As others said there is no std::pi but if you want precise PI value you can use:

constexpr double pi = std::acos(-1);

This assumes that your C++ implementation produces a correctly-rounded value of PI from acos(-1.0), which is common but not guaranteed.

It's not constexpr, but in practice optimizing compilers like gcc and clang evaluate it at compile time. Declaring it const is important for the optimizer to do a good job, though.

Answer 5

Up to and including C++17 pi is not a constant introduced into the language, and it's a pain in the neck.

I'm fortunate in that I use boost and they define pi with a sufficiently large number of decimal places for even a 128 bit long double.

If you don't use Boost then hardcode it yourself. Defining it with a trigonometric function is tempting but if you do that you can't then make it a constexpr. The accuracy of the trigonometric functions is also not guaranteed by any standard I know of (cf. std::sqrt), so really you are on dangerous ground indeed relying on such a function.

There is a way of getting a constexpr value for pi using metaprogramming: see http://timmurphy.org/2013/06/27/template-metaprogramming-in-c/

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From C++20 some good news. There is a defininition for pi. C++20 adds some mathematical constants in <numbers>. For example std::numbers::pi is a double type.

Reference: https://en.cppreference.com/w/cpp/numeric/constants

Answer 6

Up to C++20, no, none of the standards introduces the constant that would represent the number pi (π). You can approximate the number in your code:

constexpr double pi = 3.14159265358979323846;

Other languages such as C# have the constant declared in their libraries.

Update: Starting with the C++20, there indeed is a pi constant declared inside the <numbers> header. It is accessed via: std::numbers::pi.