std.math.TAU

[Steven Schveighoffer]

On Tue, 05 Jul 2011 04:31:09 -0400, James Fisher <jameshfisher at gmail.com>  
wrote:

> Hopefully this won't be taken as frivolous.  I (and possibly some of you)
> have been convinced by the argument at http://tauday.com/.  It's very
> convincing, and I won't rehash it here.
>
> The use of τ instead of π will only become really convenient when one  
> does
> not have to preface everything with "let τ = 2π".
>
> For example, in D, in order to think in terms of τ instead of π, one must
> define `enum real TAU = std.math.PI * 2;`, and possibly also TAU_2,  
> TAU_4,
> etc.
>
> As well as being a typing inconvenience, I also think things are not that
> easy due to loss of precision (though I'm far from an expert on  
> intricacies
> of floating point).
>
> There is an initiative to add TAU to the Python standard library:
> http://www.python.org/dev/peps/pep-0628/
>
> To this end, I suggest adding the constant TAU to std.math, and possibly
> also TAU_2 as an alias for PI, TAU_4 as an alias for PI_2, TAU_8 as PI_4.
>
> In any case, I'd like to know what's necessary in order for me to define
> these constants without loss of precision.
> d

I read an article about this recently, it's definitely interesting.  The  
one place where I haven't seen it mentioned is what happens when you want  
the area of a circle, since that necessarily involves the radius.  I'd  
guess you'd have to use τ/2 * r^2, but even then, that's one formula vs.  
the rest.  It's probably a good tradeoff.  I can definitely see the  
advantage when using radians.  Never thought I'd have to re-learn trig  
again...

One thing I like about Pi vs Tau is that it cannot be mistaken for a  
normal character.

I'm not a floating point expert, but I would expect since floating point  
is stored in binary, dividing or multiplying by 2 loses no precision at  
all.  But I could be wrong...

-Steve