Re: Infinity (to the nearest integer)

On Oct 8, 2010, at 9:58, Thomas Leonard wrote:

> This is a bit surprising...
>
> ? Infinity.round()
> # value: 9223372036854775807
>
> ? NaN.floor()
> # value: 0


Following the implementation, I find that both are defined directly in  
terms of java.lang.StrictMath, which has this to say:

> To help ensure portability of Java programs, the definitions of many  
> of the numeric functions in this package require that they produce  
> the same results as certain published algorithms. These algorithms  
> are available from the well-known network library netlib as the  
> package "Freely Distributable Math Library" (fdlibm).

In the field of floating-point arithmetic, I am inclined to be very  
cautious about assuming that existing systems are doing something  
wrong. However, our situation is different from these sources, in that  
we are giving *bigint* rather than float or bounded integer results.

That makes these rules arbitrary:

> 	• If the argument is negative infinity or any value less than or  
> equal to the value of Long.MIN_VALUE, the result is equal to the  
> value of Long.MIN_VALUE.
> 	• If the argument is positive infinity or any value greater than or  
> equal to the value of Long.MAX_VALUE, the result is equal to the  
> value of Long.MAX_VALUE.


In all of {-Infinity,Infinity,NaN}.{floor,round}(), I see these as  
reasonable options:

   1. Return the argument, as all-floating operations usually do.

   2. Throw an exception.

1 is an option where it is not in Java, because we do not define  
necessarily-disjoint numeric types; but neither do we well support  
"integer or NaN" and similar as a reasonable type.

Note that under sealed-exception rules throwing should never be used  
for “handled” exceptional situations; therefore option 2 implies that  
programs expecting a NaN/Infinity must test for it.


I am at the moment inclined to specify option 1. I welcome input from  
people with more numeric experience than I.

-- 
Kevin Reid                                  <http://switchb.org/kpreid/>