[racket] Untyped arithmetics performance

I’m not sure, but if I understand correctly (and someone please correct me if I don’t),
summing up lots of things with the same denominator (in this case 10000) means that the denominator of the result of the sum never grows, but if the denominator is changing from 10000 to 9999 to 9998 etc. the denominator of the result would grow to (lcm 10000 9999 9998 …) so about 10000 factorial except without the common factors, so it would be less, but still a lot more than just 10000.  And the numerator would have to grow just like the denominator. So then the second one would be doing a lot more work on much bigger numbers, But I’m not sure.  

On Jan 24, 2015, at 11:39 AM, Daniel Kvasnička <daniel.kvasnicka at me.com> wrote:

> Hi, I'm observing the following difference in performance:
> 
>> (time (exact->inexact (for/sum ([x (in-range 10000)]) (/ x 10000))))
> cpu time: 6 real time: 6 gc time: 0
> 4999.5
>> (time (exact->inexact (for/sum ([x (in-range 10000)]) (/ x (- 10000 x)))))
> cpu time: 3624 real time: 3622 gc time: 39
> 87876.06036044382
> 
> The difference seems huge to me and I'm wondering whether it's "normal" and what are the right tools to overcome it.
> If I understand it correctly, it's about contract checking and the fact that there is one more math opeartion involved does not in itself lead to such difference. The division operator needs to be sure that the outcome of the minus op. is of the right type, is that correct?
> 
> If so -- and the increase in time cannot be considered a "bug" -- what is the right way to get around that. I've employed 2 ways: Typed Racket and switching the portion of code to racket/flonum. Both of these approaches resulted in big perf. improvement and basically make the computation instant again. Are these the right, "rackety", solutions? I've also tried to use unchecked ops but Racket 6.1.1 is constantly segfaulting on me when running this (from my digging I think unsafe-fl/ is what segfaults it):
> 
> (time (exact->inexact (for/sum ([x (in-range 10000)]) (unsafe-fl/ (->fl x) (unsafe-fx- 10000 x)))))
> 
> Daniel
> ____________________
>  Racket Users list:
>  http://lists.racket-lang.org/users