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,
> >>>>>
> >>>>
> >>>> ------------------------------------------------------------
> ----------
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> forums.htm
> >>>
> >>>
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> >>
> >>
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