[Haskell-cafe] pi

[Jules Bean]

jerzy.karczmarczuk at info.unicaen.fr wrote:
>> This discussion is not about adding it, but about whether or not it 
>> should have a default.
>> Are you suggesting pi should be removed from the Floating class?
>> Then, what type would you give pi?
> 
> First, I don't care whether it is there or not. When I use it, I define
> a particular instance (double, a constant formal series, a constant element
> of some differential algebra I enjoy personally, etc. No default would
> help me anyway).
> And then, I give it the type it deserves.

Evidently you use pi in more 'serious' programs than I do. I use pi 
simply for geometric reasons, when I wish to specify circular or 
elliptic paths or similar constructions. For this I am pleased that the 
language libraries give me pi, because they save me the work of defining it.

>> Given that pi is often used with sin, as in "sin (t * pi)" it would 
>> seem very odd if pi forced that to be monomorphic:
> 
> Oh yes, everybody in the world uses in ONE program several overloaded
> versions of pi, of the sine function, etc. Well, perhaps not everybody,
> for example I don't. And I use numerics quite often.

I like to write a complex function which might use multiple trig 
functions and pi, to describe the kind of thing about. I might want to 
use that function at Double, or GLdouble, or GLfloat, for various 
reasons. I don't particularly want to have to think about that kind of 
thing more than I have to.

> How often *you* needed simultaneously overloaded pi and trigs in such a way
> that a default could help you? Answer sincerely (if you wish to answer at
> all...)

The default wouldn't help me at all. The default would help a (putative) 
designer of a new Floating instance, and I have never been one of those.

If it is true of many Floating instances that (atan 1 * 4) is an 
accurate way to calculate pi (and it appears to be 'accurate enough' for 
Float and Double, on my computer) then adding it as a default doesn't 
appear to do any harm.

I can't say I think it's very important either.

Jules