Comment author: warwick

I just looked at the value of pi more closely (using toplevel OCaml 3.12.0 on Mac) and I didn't realise that the floating point loses some precision, so if you put either of
let pi = 4. *. atan 1.
let pi = 3.1415926535897932384626433832795

You end up with
val pi : float = 3.14159265358979312

(ie ending with ...312 rather than ...323 or ...324 rounded)

Comment author: @xavierleroy

Hello,

You're right that, in retrospect, it would have been preferable to have a separate module for float operations in the standard library. Experience shows, however, that adding a new module in the stdlib with a nice, popular name like Math always introduces incompatibilies in existing Caml code, something that we cannot afford at this point.

Note, however, that OCaml Batteries (http://thelema.github.com/batteries-included/hdoc/) has a "BatFloat" module very much like what you propose, and it defines "BatFloat.pi" among other useful things. If you have ideas and code for additional floating-point stuff, I'm sure the Batteries people would be receptive.

Concerning the loss of precision: the float you get out of "4 *. atan 1.0" is, indeed, the 64-bit IEEE float closest to the true value of pi. That's the best one can do within the limitations of this float format.