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Subject: Re: [Caml-list] Comparing floats

On 23/07/15 18:34, Boris Yakobowski wrote:
> I got confused when negating OCaml's '=' operator (a dangerous side-effect
> of writing too much C!), hence the erroneous '!=' instead of <>. Regarding,
> 'nan <> nan', I had convinced myself that all comparisons with NaN returned
> false. I wonder why <>/!= got a special treatment since e.g. 'nan < 1.' and
> '1. < nan' both return false.

Perhaps so that (using Caml syntax) "x <> y" is always equivalent to
"not (x = y)".  But I agree it can be viewed as yet another oddity
with NaNs.

Just to clarify my previous post:

  let compare_float (x: float) (y: float) = compare x y

gives a total order over floats that behaves sensibly, if somewhat
arbitrarily, over NaN arguments:  two NaNs are equal, and any NaN is
less than any non-NaN float.  In contrast,

let compare_float (x: float) (y: float) =
  if x < y then -1 else if x > y then 1 else 0

is not a proper order, because the implied equality is not transitive.
Consider:

   compare_float 0.0 nan = 0
   compare_float nan 1.0 = 0
   compare_float 0.0 1.0 = -1

So, don't use the latter definition for e.g. sorting a list of floats
that can contain NaN.  The former definition is more robust.

- Xavier Leroy