Markus,

Actually, yes, I looked at using extended precision, and here's what
happened:

v=:2%(3r19-%x:1 2 3 245 246 247 248)

​v
_19r8 _76r13 _57r5 4655r358 9348r719 13 9424r725​

   fp=. * * 1||

fp v

_3r8 _11r13 _2r5 1r358 1r719 0 724r725

ip=: * * <.@|

ip v

_2 _5 _11 13 13 13 12


So our original definitions would work with extended precision, but the
fractional parts would be rational rather than decimal. Extended precision
still keeps the negative signs on the fractions.


I'm not so sure about Martin's approach with extended precision:

    mfp1 =: 1&|     NB. Martin's first suggestion for fractional part

    mfp1 v

5r8 2r13 3r5 1r358 1r719 0 724r725

    mfp2 =: 1&#:    NB. Martin's second suggestion for fractional part

    mfp2 v

5r8 2r13 3r5 1r358 1r719 0 724r725

     fp v      NB. First fractional part proposal

_3r8 _11r13 _2r5 1r358 1r719 0 724r725


However, mfp1 & mvfp2 have lost the sign, so combining them by adding
doesn't work for the negative numbers:

     v

_19r8 _76r13 _57r5 4655r358 9348r719 13 9424r725

     ip v

_2 _5 _11 13 13 13 12

      mfp1 v

5r8 2r13 3r5 1r358 1r719 0 724r725

       (ip v) + (mfp1 v)

_11r8 _63r13 _52r5 4655r358 9348r719 13 9424r725


   (ip v) + (mfp2 v)

_11r8 _63r13 _52r5 4655r358 9348r719 13 9424r725


   v

_19r8 _76r13 _57r5 4655r358 9348r719 13 9424r725



Skip Cave
Cave Consulting LLC

On Wed, Aug 9, 2017 at 10:45 AM, Schmidt-Gröttrup, Markus <
m.schmidt-groett...@hs-osnabrueck.de> wrote:

> Skip, have you considered to use extended precision?
> In your example only small fraction are used, and the methods discussed
> would apply as well without precision problems.
>
> v=:2%(3r19-%x:1 2 3 245 246 247 248)
>
> I haven’t read the whole thread, so sorry if this contribution doesn’t fit.
>
> Markus
>
>
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