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
>
>
>
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