Intel has 32 bit integer division. It now may have 64 bit division.
On Wed, Sep 13, 2017 at 8:34 AM, Raul Miller <[email protected]> wrote:
> Hmm... actually... no...
>
> The relevant implementation here is in ve.c:
>
> static D jtremdd(J jt,D a,D b){D q,x,y;
> if(!a)R b;
> ASSERT(!INF(b),EVNAN);
> if(a==inf )R 0<=b?b:a;
> if(a==infm)R 0>=b?b:a;
> q=b/a; x=tfloor(q); y=tceil(q); R teq(x,y)?0:b-a*x;
> }
>
> No hint of fmod here (though it does get used elsewhere).
>
> FYI,
>
> --
> Raul
>
>
> On Wed, Sep 13, 2017 at 10:28 AM, Raul Miller <[email protected]>
> wrote:
> > I took a look at the core j implementation, and it looks like it's
> > using the c fmod() mechanism.
> >
> > So this is really a bug inherited from c.
> >
> > I think.
> >
> > FYI,
> >
> > --
> > Raul
> >
> >
> > On Wed, Sep 13, 2017 at 10:06 AM, Erling Hellenäs
> > <[email protected]> wrote:
> >> 196x|57290824867848391x
> >> 99
> >>
> >> I wonder how they manage to handle this in Nial:
> >>
> >> 57290824867848391 - ( 196 * floor ( 57290824867848391 / 196 ) )
> >> 99
> >>
> >> Floor creates an integer, but the precision should be lost in the
> division
> >> if they represent their floats as IEEE double. So, maybe they have
> another
> >> representation or they change it when needed. The division does create a
> >> floating point number.
> >>
> >> Cheers,
> >>
> >> Erling
> >>
> >>
> >>
> >> Den 2017-09-13 kl. 15:44, skrev Erling Hellenäs:
> >>>
> >>> Yes.
> >>>
> >>> (14^2)|!.0 [ 5729082486784839
> >>>
> >>> 147
> >>>
> >>>
> >>> /Erling
> >>>
> >>>
> >>> Den 2017-09-13 kl. 15:25, skrev Don Guinn:
> >>>>
> >>>> That is true, but the problem is not in J, but in IEEE as it cannot
> >>>> represent that number exactly in float double. Before 64 bit integers
> >>>> came
> >>>> out all integers were included exactly in float double. So converting
> >>>> integer to float never caused a loss in precision. Now it does.
> >>>>
> >>>> 2^.57290824867848391
> >>>>
> >>>> 55.6692
> >>>>
> >>>> 0j0":{.57290824867848391 0.5
> >>>>
> >>>> 57290824867848392
> >>>>
> >>>>
> >>>> When things are pushed to their limits and possibly beyond, strange
> >>>> things
> >>>> happen. Comparison tolerance address many problems that bite other
> >>>> programming languages, but it's not perfect. That decimal numbers with
> >>>> fractional values cannot be represented exactly in binary computers
> >>>> causes
> >>>> a lot of grief in all programming languages.
> >>>>
> >>>>
> >>>> I'm just relieved to understand the problem and that it is easy to get
> >>>> around up to the limits of IEEE float double.
> >>>>
> >>>> On Wed, Sep 13, 2017 at 7:06 AM, Erling Hellenäs
> >>>> <[email protected]>
> >>>> wrote:
> >>>>
> >>>>> So, the perceived problem is related to comparison tolerance. The
> >>>>> question
> >>>>> is then how it is used and if this use is rational?
> >>>>>
> >>>>> With comparison tolerance at 0, when we add another digit, we get a
> new
> >>>>> incorrect result, now related to lost precision?
> >>>>>
> >>>>> 9!:19]0
> >>>>> 196x|57290824867848391x
> >>>>> 99
> >>>>> ({.196 0.5)|57290824867848391
> >>>>> 104
> >>>>>
> >>>>> Cheers,
> >>>>>
> >>>>> Erling
> >>>>>
> >>>>>
> >>>>> Den 2017-09-13 kl. 14:38, skrev Don Guinn:
> >>>>>
> >>>>>> I think I found the culprit.
> >>>>>>
> >>>>>> ({.196 0.5)|5729082486784839
> >>>>>> 0
> >>>>>> 9!:18''
> >>>>>> 5.68434e_14
> >>>>>> 2^.9!:18''
> >>>>>> _44
> >>>>>> 9!:19]0
> >>>>>>
> >>>>>> ({.196 0.5)|5729082486784839
> >>>>>> 147
> >>>>>> 9!:19]5.68434e_15
> >>>>>>
> >>>>>> ({.196 0.5)|5729082486784839
> >>>>>> 147
> >>>>>> ({.196 0.5)|57290824867848391
> >>>>>> 0
> >>>>>> 9!:19]5.68434e_16
> >>>>>>
> >>>>>> ({.196 0.5)|57290824867848391
> >>>>>> 104
> >>>>>>
> >>>>>> On Tue, Sep 12, 2017 at 4:57 PM, Raul Miller <[email protected]
> >
> >>>>>> wrote:
> >>>>>>
> >>>>>> R2=: |
> >>>>>>>
> >>>>>>> R1=: (] - [ * [: <.!.0 ] % [)"0
> >>>>>>> R0=: (|&x:)"0
> >>>>>>>
> >>>>>>> (14^2) R1 5729082486784839
> >>>>>>> 147
> >>>>>>> (14^2) R2 5729082486784839
> >>>>>>> 0
> >>>>>>>
> >>>>>>> X=: (0.1-0.1)+i.1000
> >>>>>>> Y=: 5729082486784839+i:1000
> >>>>>>>
> >>>>>>> datatype X
> >>>>>>> floating
> >>>>>>>
> >>>>>>> +/,X (R0/ ~: R2/) Y
> >>>>>>> 1845046
> >>>>>>> +/,X (R0/ ~: R1/) Y
> >>>>>>> 0
> >>>>>>>
> >>>>>>> Good question.
> >>>>>>>
> >>>>>>> Thanks,
> >>>>>>>
> >>>>>>> --
> >>>>>>> Raul
> >>>>>>>
> >>>>>>>
> >>>>>>> On Tue, Sep 12, 2017 at 4:26 AM, Erling Hellenäs
> >>>>>>> <[email protected]> wrote:
> >>>>>>>
> >>>>>>>> Residue1=: ] - [ * [: <.!.0 ] % [
> >>>>>>>>
> >>>>>>>> Residue2=: |
> >>>>>>>>
> >>>>>>>> (14^2) Residue1 5729082486784839
> >>>>>>>>
> >>>>>>>> 147
> >>>>>>>>
> >>>>>>>> (14^2) Residue2 5729082486784839
> >>>>>>>>
> >>>>>>>> 0
> >>>>>>>>
> >>>>>>>> Why is Residue2 losing precision when Residue1 is not?
> >>>>>>>>
> >>>>>>>> /Erling
> >>>>>>>>
> >>>>>>>>
> >>>>>>>>
> >>>>>>>> Den 2017-09-12 kl. 02:04, skrev Don Kelly:
> >>>>>>>>
> >>>>>>>>> I believe that Raul has hit it on the head. 14^2 will be
> floating
> >>>>>>>>> as
> >>>>>>>>>
> >>>>>>>> will
> >>>>>>>> generally be the case with % so it is possible that errors add or
> >>>>>>>> subtract
> >>>>>>>> to give an erroneous result. Note that
> >>>>>>>>>
> >>>>>>>>> (14^2) (] - [ * [: <. ] % [)5729082486784839x
> >>>>>>>>>
> >>>>>>>>> 147
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> (14^2x) (] - [ * [: <. ] % [)5729082486784839
> >>>>>>>>>
> >>>>>>>>> 147
> >>>>>>>>>
> >>>>>>>>> and
> >>>>>>>>>
> >>>>>>>>> (14^2x)|5729082486784839
> >>>>>>>>>
> >>>>>>>>> 147
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> does it more simply
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> Don
> >>>>>>>>>
> >>>>>>>>> On 2017-09-11 6:50 AM, Erling Hellenäs wrote:
> >>>>>>>>>
> >>>>>>>>>> (14^2x) (] - [ * [: <. ] % [)5729082486784839x
> >>>>>>>>>>
> >>>>>>>>>> 147
> >>>>>>>>>>
> >>>>>>>>>> (14^2) (] - [ * [: <. ] % [)5729082486784839
> >>>>>>>>>>
> >>>>>>>>>> _49
> >>>>>>>>>>
> >>>>>>>>>> (14^2) (] - [ * _1 + [: <. ] % [)5729082486784839
> >>>>>>>>>>
> >>>>>>>>>> 147
> >>>>>>>>>>
> >>>>>>>>>> /Erling
> >>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>> Den 2017-09-11 kl. 15:40, skrev Erling Hellenäs:
> >>>>>>>>>>
> >>>>>>>>>>> From what I see, floor gives an incorrect result which I
> correct
> >>>>>>>>>>> with
> >>>>>>>>>>> the " _1 + " There is not other problem. No loss of precision.
> >>>>>>>>>>> /Erling
> >>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>> Den 2017-09-11 kl. 15:27, skrev Raul Miller:
> >>>>>>>>>>>
> >>>>>>>>>>>> I do not know what you are thinking, and you have not
> illustrated
> >>>>>>>>>>>>
> >>>>>>>>>>> your
> >>>>>>>>
> >>>>>>>> thoughts sufficiently for me to grasp them.
> >>>>>>>>>>>>
> >>>>>>>>>>>> So, I thought I'd work through this:
> >>>>>>>>>>>>
> >>>>>>>>>>>> (14^2) (] - [ * _1 + [: <. ] % [)5729082486784839
> >>>>>>>>>>>> 147
> >>>>>>>>>>>> (14^2x) (] - [ * _1 + [: <. ] % [)5729082486784839x
> >>>>>>>>>>>> 343
> >>>>>>>>>>>>
> >>>>>>>>>>>> Clearly, the exact answer is different from the quick answer.
> >>>>>>>>>>>>
> >>>>>>>>>>>> If we compare
> >>>>>>>>>>>> load'debug/dissect'
> >>>>>>>>>>>> dissect '(14^2) (] - [ * _1 + [: <. ] %
> [)5729082486784839'
> >>>>>>>>>>>> dissect '(14^2x) (] - [ * _1 + [: <. ] %
> >>>>>>>>>>>> [)5729082486784839x'
> >>>>>>>>>>>>
> >>>>>>>>>>>> We can see the initial off-by-one errors, but the big
> difference
> >>>>>>>>>>>>
> >>>>>>>>>>> shows
> >>>>>>>>
> >>>>>>>> up at the end (where we subtract from 5729082486784839)
> >>>>>>>>>>>>
> >>>>>>>>>>>> The value we are subtracting is:
> >>>>>>>>>>>>
> >>>>>>>>>>>> (14^2x) ([ * _1 + [: <. ] % [)5729082486784839x
> >>>>>>>>>>>> 5729082486784496
> >>>>>>>>>>>> (14^2) ([ * _1 + [: <. ] % [)5729082486784839
> >>>>>>>>>>>> 5.72908e15
> >>>>>>>>>>>>
> >>>>>>>>>>>> Looking at the bits needed to represent that as an integer:
> >>>>>>>>>>>>
> >>>>>>>>>>>> 2^.(14^2) ([ * _1 + [: <. ] % [)5729082486784839
> >>>>>>>>>>>> 52.3472
> >>>>>>>>>>>>
> >>>>>>>>>>>> we can see that that's right on the edge of being the number
> of
> >>>>>>>>>>>> representable digits in a 64 bit float.
> >>>>>>>>>>>>
> >>>>>>>>>>>> But, also, it's the result of multiplying
> >>>>>>>>>>>>
> >>>>>>>>>>>> 14^2
> >>>>>>>>>>>> 196
> >>>>>>>>>>>>
> >>>>>>>>>>>> by an off-by-one amount. And...
> >>>>>>>>>>>>
> >>>>>>>>>>>> 343-196
> >>>>>>>>>>>> 147
> >>>>>>>>>>>>
> >>>>>>>>>>>> ...
> >>>>>>>>>>>>
> >>>>>>>>>>>> Anyways, I'm not sure what you were thinking, but I guess we
> can
> >>>>>>>>>>>> take
> >>>>>>>>>>>> this as a good example of the idea that errors can actually
> >>>>>>>>>>>> accumulate.
> >>>>>>>>>>>>
> >>>>>>>>>>>> Thanks,
> >>>>>>>>>>>>
> >>>>>>>>>>>> ------------------------------------------------------------
> >>>>>>>>>>
> >>>>>>>>>> ----------
> >>>>>>>>
> >>>>>>>> For information about J forums see http://www.jsoftware.com/
> >>>>>>>>>>
> >>>>>>>>>> forums.htm
> >>>>>>>>>> ------------------------------------------------------------
> >>>>>>>>>> ----------
> >>>>>>>>>> For information about J forums see
> http://www.jsoftware.com/forum
> >>>>>>>>>> s.htm
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> ------------------------------------------------------------
> ----------
> >>>>>>>>> For information about J forums see
> >>>>>>>>> http://www.jsoftware.com/forums.htm
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>> ------------------------------------------------------------
> ----------
> >>>>>>>> For information about J forums see
> >>>>>>>> http://www.jsoftware.com/forums.htm
> >>>>>>>>
> >>>>>>> ------------------------------------------------------------
> ----------
> >>>>>>> For information about J forums see http://www.jsoftware.com/
> forums.htm
> >>>>>>>
> >>>>>>> ------------------------------------------------------------
> ----------
> >>>>>>
> >>>>>> For information about J forums see http://www.jsoftware.com/
> forums.htm
> >>>>>>
> >>>>> ------------------------------------------------------------
> ----------
> >>>>> For information about J forums see http://www.jsoftware.com/
> forums.htm
> >>>>>
> >>>> ------------------------------------------------------------
> ----------
> >>>> For information about J forums see http://www.jsoftware.com/
> forums.htm
> >>>
> >>>
> >>> ----------------------------------------------------------------------
> >>> For information about J forums see http://www.jsoftware.com/forums.htm
> >>
> >>
> >> ----------------------------------------------------------------------
> >> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
