I stand a little concerned specifically about "tau" here. Could not "pi_2"
work just as well? Pi has the same meaning in a broad scope of both
mathematics and physics fields, but "tau" on the other hand may mean a
number of things.

// Robin

On Sat, Aug 24, 2024, 01:46 Jonathan Wakely via Std-Proposals <
std-proposals_at_[hidden]> wrote:

>
>
> On Sat, 24 Aug 2024, 00:26 Aaron Franke via Std-Proposals, <
> std-proposals_at_[hidden]> wrote:
>
>> Hello ISO standards mailing list members,
>>
>> As of C++20, ISO C++ has a collection of useful mathematical constants in
>> the numerics library: https://en.cppreference.com/w/cpp/numeric/constants
>>
>> However, there is an important constant missing: The circle constant
>> "Tau", symbol "𝜏", with a value of 2*𝜋 or about
>> 6.283185307179586476925286766559...
>>
>> I have written a proposal document below, I would greatly appreciate for
>> feedback on this and will do whatever I can to help move it forward. The
>> instructions for submitting a proposal also suggest to include an abstract
>> cover page, which I think is not necessary given the small scope of this
>> proposal. If more information is needed, see the link in the "Acknowledgements"
>> section.
>>
>>
>> Document number: ???
>> Date: 2024-08-23
>> Audience: Library Evolution Working Group
>> Reply-to: Aaron Franke <arnfranke_at_[hidden]>
>>
>> I. Table of Contents
>>
>> Introduction, Motivation and Scope, Impact On the Standard, Design
>> Decisions, Technical Specifications
>>
>> II. Introduction
>>
>> Tau 𝜏 is a mathematical constant representing the ratio of a
>> circle's circumference to its radius. This is also known as the circle
>> constant, and is equal to about 6.283185307179586476925286766559... or
>> exactly 2*𝜋 or 2*pi, representing one full turn in radians. The value
>> Pi 𝜋 represents half of the circle constant, it is famous in
>> mathematics and is already present in the ISO C++ standard.
>>
>> III. Motivation and Scope
>>
>> The Tau 𝜏 constant allows referring to the full circle constant
>> with one constexpr value that can be used in place of (2*pi), making many
>> expressions easier to read, since (2*pi) is so common to see in code.
>> While Pi is already present in ISO C++, Pi is usually accompanied by a
>> multiplication by 2, so 2*pi. Math libraries often define a constant for
>> this value due to how common this is. It makes sense to add the Tau
>> constant into ISO C++ to make it available for all C++ users, rather than
>> requiring libraries to define their own constant for this. This constant is
>> intended to be useful for all users, and is widespread in many programming
>> languages and libraries, including Java, Python, C#, Nim, Rust,
>> GDScript, Processing, Crystal, Raku, Zig, and even another ISO language,
>> Eiffel. Tau is also defined in many libraries and engines such as Unity,
>> Godot, MathJS, and more.
>>
>> IV. Impact On the Standard
>>
>> This constant does not depend on anything, and nothing depends on it.
>> It purely extends the available standard with one additional constant. It
>> can be implemented in current C++ compilers and libraries, but the goal
>> here is to put it in the standard along with the other mathematical
>> constants since Tau is such a common and useful mathematical constant.
>>
>> V. Design Decisions
>>
>> The only two possible alternative designs are to use a different name
>> or to not implement the constant. Some languages use "2PI" or "TWO_PI", but
>> the former starts with a number so it is tricky to use as an identifier,
>> and it can be confused with another constant in some languages, "2_PI" or "M_2_PI"
>> in GCC,
>>
>
> That constant is part of glibc, not GCC.
>
> This looks good otherwise. I don't think we need a feature test macro,
> users who need compatibility with older implementations can just use 2*pi.
>
>
> which is 2 divided by pi. The name Tau is unambiguous and is used in many
>> programming languages, including Java, Python, C#, Nim, Rust, and more
>> listed above. Therefore the design decision to use the name Tau is
>> consistent with other languages and libraries.
>>
>> VI. Technical Specifications
>>
>> The technical specification is to add constants to the standard
>> library header `<numbers>`
>> https://en.cppreference.com/w/cpp/header/numbers inside of `namespace
>> std::numbers {` for `tau_v` via `template<class T> inline constexpr T
>> tau_v = /* unspecified */;` and `template<floating_point T> inline
>> constexpr T tau_v<T> = /* see description */;`, and `tau` via `inline
>> constexpr double tau = tau_v<double>();`. The value in these constants must
>> be defined by the ISO C++ standard as being the mathematical constant 𝜏
>> (Tau), also known as the circle constant, and may be noted as being exactly
>> equal to 2*𝜋 (or 2*pi), and exactly equal to a circle's circumference
>> divided by its radius.
>>
>> VII. Acknowledgements
>>
>> Michael Hartl for "The Tau Manifesto": https://tauday.com/
>>
>> VIII. References
>>
>> C# System.Math.Tau:
>> https://learn.microsoft.com/en-us/dotnet/api/system.math.tau
>> Crystal TAU:
>> https://crystal-lang.org/api/1.13.2/Math.html#constant-summary
>> GDScript TAU:
>> https://docs.godotengine.org/en/stable/classes/class__at_[hidden]#class-gdscript-constant-tau
>> Java Math.TAU:
>> https://docs.oracle.com/en/java/javase/21/docs/api/java.base/java/lang/Math.html#TAU
>> Nim TAU: https://nim-lang.org/docs/math.html#TAU
>> Processing TAU: https://processing.org/reference/TAU.html
>> Python math.tau: https://docs.python.org/3/library/math.html#math.tau
>> Raku TAU: https://docs.raku.org/language/terms#term_tau
>> Rust TAU:
>> https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html
>> Zig std.math.tau:
>> https://github.com/ziglang/zig/blob/master/lib/std/math.zig#L18
>>
>>
>> Thank you for your consideration,
>>
>> Aaron Franke
>>
>>
>>
>> --
>> Std-Proposals mailing list
>> Std-Proposals_at_[hidden]
>> https://lists.isocpp.org/mailman/listinfo.cgi/std-proposals
>>
> --
> Std-Proposals mailing list
> Std-Proposals_at_[hidden]
> https://lists.isocpp.org/mailman/listinfo.cgi/std-proposals
>