[racket] Inconsistency of `in-range` and numerical issues
I feel like swapping out flonums by default to rationals by default would
cause unexpected slowness in a large number of programs though. Would it be
possible to make it a reader extension like at-exp is currently? So I can
say "#lang exact-decimals racket", and the reader would read the decimals
as rationals?
On Thu, Feb 26, 2015 at 9:13 AM, Neil Toronto <neil.toronto at gmail.com>
wrote:
> On 02/24/2015 01:11 PM, Konrad Hinsen wrote:
>
>> On 24/02/2015 16:41, Laurent wrote:
>>
>> I've discovered a rather troubling behaviour when using `in-range` with
>>> floating point numbers, which I think is worth knowing in case you
>>> hadn't consider the issue before:
>>>
>>> On my machine, I get the following:
>>>
>>> (length (for/list ([i (in-range .1 .7 .1)]) i)) ; 6
>>> (length (for/list ([i (in-range .1 .8 .1)]) i)) ; 8 (!)
>>>
>>> But:
>>> (length (for/list ([i (in-range 1/10 7/10 1/10)]) i)) ; 6
>>> (length (for/list ([i (in-range 1/10 8/10 1/10)]) i)) ; 7
>>>
>>>
>>> Would it be a good idea to safe-guard these kinds of cases directly in
>>> `in-range`?
>>>
>>
>> The problem is an old one that already troubled programmers in the age
>> of Fortran. I suspect there is no reasonable safe-guard, with
>> "reasonable" meaning that it does what people expect in all situations.
>>
>> The only way to stay out of trouble is to avoid loops defined by an
>> accumulating floating-point value. This means either don't use floats
>> (write the loop over integers or rationals and convert to floats when
>> using the loop index), or don't use accumulation (define your range by
>> two points and the number of subdivisions, rather than the width of
>> subintervals).
>>
>
> I should have chimed in to support this two days ago, but this is exactly
> the right answer. Here's what Konrad means by his first alternative (write
> the loop over integers or rationals):
>
> (length
> (for*/list ([i (in-range 1 8 1)]
> [i (in-value (* i 0.1))])
> i))
>
> The second alternative is a little harder to get right because of
> fencepost errors [1]. Fortunately, Racket has a library function for it.
> Unfortunately, it's buried in `plot/utils`. Here it is in action:
>
> > (require (only-in plot/utils linear-seq))
>
> > (linear-seq 0.0 1.0 4)
> '(0.0 0.3333333333333333 0.6666666666666666 1.0)
>
> > (linear-seq 0.0 1.0 4 #:start? #f)
> '(0.14285714285714285 0.42857142857142855 0.7142857142857142 1.0)
>
> > (linear-seq 0.0 1.0 4 #:start? #f #:end? #f)
> '(0.125 0.375 0.625 0.875)
>
> I should really move this function into `math/base`.
>
> If you must use a flonum step size, do something like this:
>
> (define (flonum-range start end step)
> (define n (exact-ceiling (/ (- end start) step)))
> (for/list ([i (in-range 0 n)])
> (+ start (* i step))))
>
> To get points with 0.5 ulp error each, which is the best you can do, add
> (require math/flonum) to your program and change the loop body to (flfma
> step (fl i) start).
>
> Arguably, `in-range` should do something like the above when given
> floating-point step lengths. I don't know how feasible that is, though.
>
> Neil ⊥
>
> [1] http://en.wikipedia.org/wiki/Off-by-one_error#Fencepost_error
>
>
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