Here's a working solution, I think.

let raw_min = min
let raw_max = max

let nan_or_equal x y =
  not (x < y) && not (x > y)

(** min and max that choose nan if its there *)
let min x y =
  if x = y then x
  else if nan_or_equal x y then nan
  else raw_min x y

let max x y =
  if x = y then x
  else if nan_or_equal x y then nan
  else raw_max x y


> min and max have pretty strange behavior when it comes to nan's.  Here's
> an example:
>
> # min 3. nan;;
> - : float = 3.
> # min  nan 3.;;
> - : float = nan
>
> When you think about it, the reason for this is clear.  comparisons
> involving nan's always return false, so if you simply implement min as
> follows:
>
>    if x < y then x else y
>
> the the result will depend on the order.
>
> Now here's the weird bit.  I decided I wanted a polymorphic comparison
> that wouldn't have this problem.  But this is a little harder than it
> seems, since it turns out that specialized float version of equality is
> different from the polymorphic version.  Here's the example:
>
> # let raw_min = min
> val raw_min : 'a -> 'a -> 'a = <fun>
> # let min x y =
>   if not (y = y) then y
>   else if not (x = x) then x
>   else raw_min x y
> ;;
>         val min : 'a -> 'a -> 'a = <fun>
> # let fmin (x:float) y =
>   if not (y = y) then y
>   else if not (x = x) then x
>   else raw_min x y
> ;;
>         val fmin : float -> float -> float = <fun>
> # fmin 3. nan;;
> - : float = nan
> # fmin nan 3.;;
> - : float = nan
> # min nan 3.;;
> - : float = nan
> # min 3. nan;;
> - : float = 3.
>
> So, does this count as a bug?  Any ideas about how to fix this behavior in
> a reasonably efficient way?
>
> Yaron
>
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