RFR: JDK-8283124: Add constant for tau to Math and StrictMath

[Joe Darcy]

On Mon, 14 Mar 2022 20:52:39 GMT, Joe Darcy <darcy at openjdk.org> wrote:

> Add a constant for tau, 2*pi, to Math and StrictMath. Since 2*pi is a very common value in mathematical formulas, it is helpful to give it a distinct constant.
> 
> Please also review the CSR https://bugs.openjdk.java.net/browse/JDK-8283136

> _Mailing list message from [Hans Boehm](mailto:hboehm at google.com) on [core-libs-dev](mailto:core-libs-dev at mail.openjdk.java.net):_
> 
> Couldn't the apiNote just say TAU == 2 * PI instead? I think the fact that this is actually a guaranteed floating point equality aids clarity.
> 
> On Mon, Mar 14, 2022 at 2:33 PM Raffaello Giulietti < raffaello.giulietti at gmail.com> wrote:
> 
> > Hello,
> > I find it a bit disturbing that PI is specified with 21 digits whereas
> > TAU has 16.
> > I think that specifying PI as
> > public static final double PI = 3.141592653589793;
> > doesn't harm anybody and makes it visually more consistent with TAU-
> > Greetings
> > Raffaello
> > On 3/14/22 22:13, Brian Burkhalter wrote:
> > > On Mon, 14 Mar 2022 20:52:39 GMT, Joe Darcy <darcy at openjdk.org> wrote:
> > > > Add a constant for tau, 2*pi, to Math and StrictMath. Since 2*pi is a
> > > > very common value in mathematical formulas, it is helpful to give it a
> > > > distinct constant.
> > > > Please also review the CSR
> > > > https://bugs.openjdk.java.net/browse/JDK-8283136

Yes; after further thought, I agree having tau = 2.0*pi is preferable.

Just to go through the logic, 2.0 is exactly representable in binary floating-point and an in-range multiple by two is just an exponent adjustment.

Floating-point exponent transitions occur at 2.0 = 0x1 * 2^1, 4.0 = 0x1 * 2^2, and 8.0 = 0x1 * 2^3. The value of pi is between 2.0 and 4.0 and has an exponent of 1 while the value of tau ~= 6.28 is between 4.0 and 8.0 and has an exponent of 2.

So whatever the closest floating-point value to exact pi is, 2.0 * Math.pi will be the closest floating-point value to tau.

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PR: https://git.openjdk.java.net/jdk/pull/7813