Don,

You're right. Your approach achieves the same result when re-combining the
fractional and integer part:

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

   ]'i f'=:|:0 1#:v

_3 _6 _12 13 13 13 12

0.625 0.153846 0.6 0.0027933 0.00139082 0 0.998621

i

_3 _6 _12 13 13 13 12

f

0.625 0.153846 0.6 0.0027933 0.00139082 0 0.998621

v = i+f

1 1 1 1 1 1 1


However,


   datatype f

floating

   datatype i

floating


Where as the original fp/ip verbs give:


    datatype fpv

floating

   datatype ipv

integer


So either approach will work, but ip returns integers, while your approach
returns floats in both i & f cases. The fact that I originally called the
verb the "integer part" probably led to the initial integer solution from
the group.


I'm not sure what advantages either approach would have, other than a space
savings for pure integers.


Skip

Skip Cave
Cave Consulting LLC

On Tue, Aug 8, 2017 at 8:04 PM, Don Guinn <dongu...@gmail.com> wrote:

> ​There are many ways to handle the fractional part of a number, depending
> on the problem at hand. The real difficulty seems to be handling negative
> numbers. I like this, which rounds down negative numbers. But others might
> want a different way.
>
>    ]'i f'=:|:0 1#:1.2 3.7 _2.1
>   1   3  _3
> 0.2 0.7 0.9
>    i
> 1 3 _3
>
>    f
> 0.2 0.7 0.9
>    i+f
> 1.2 3.7 _2.1​
>
> On Tue, Aug 8, 2017 at 3:56 PM, Skip Cave <s...@caveconsulting.com> wrote:
>
> > The purpose of the "negative fractional part" is to satisfy the identity
> > condition when the two parts are added back together:
> >
> >    ]v=:2%(3r19-%1 2 3 245 246 247 248)  NB. Create some long fractional
> > parts.
> >
> > _2.375 _5.84615 _11.4 13.0028 13.0014 13 12.9986
> >
> >
> > fp=. * * 1||     NB. The fractional part verb
> >
> > ip=: * * <.@|   NB. The integer part verb
> >
> >
> > ]fpv =: fp v     NB. Save the fractional part
> >
> > _0.375 _0.846154 _0.4 0.0027933 0.00139082 0 0.998621
> >
> >
> > ]ipv =: ip v     NB. Save the integer part
> >
> > _2 _5 _11 13 13 13 12
> >
> >
> >
> > ]sm =: ipv + fpv   NB. Add the two parts back together
> >
> > _2.375 _5.84615 _11.4 13.0028 13.0014 13 12.9986
> >
> >
> >  NB. The result of adding the two parts should be identical to the
> original
> > vector.
> >
> >
> > sm = v
> >
> > 1 1 1 1 1 1 1
> >
> > Skip Cave
> > Cave Consulting LLC
> >
> > On Tue, Aug 8, 2017 at 2:14 PM, 'Bo Jacoby' via Programming <
> > programm...@jsoftware.com> wrote:
> >
> > > The integer part  a  and the fractional part  b  of a number  x  is
> such
> > > that x=a+b and  a  is an integer and   0<:b  and  b<1 . I do know of no
> > use
> > > of a "negative fractional part".
> > >
> > >     Den 20:39 tirsdag den 8. august 2017 skrev Raul Miller <
> > > rauldmil...@gmail.com>:
> > >
> > >
> > >  I think we've mostly been using the wiki for live documents. (I'm not
> > > sure what all would be involved in changing the phrase book.)
> > >
> > > Thanks,
> > >
> > > --
> > > Raul
> > >
> > >
> > > On Tue, Aug 8, 2017 at 2:35 PM, Skip Cave <s...@caveconsulting.com>
> > wrote:
> > > > It looks like we have a reliable solution to find a fractional part
> of
> > a
> > > > floating point number, while maintaining the sign:
> > > >
> > > >    v
> > > >
> > > > _2.375 _5.84615 _11.4 13.0028 13.0014 13 12.9986
> > > >
> > > >    fp=. * * 1||    NB. Thanks to Martin
> > > >
> > > >    fp v
> > > >
> > > > _0.375 _0.846154 _0.4 0.0027933 0.00139082 0 0.998621
> > > >
> > > >
> > > > Credit should also go to the people who suggested the building
> blocks,
> > > e.g.
> > > >
> > > > (1|y) Raul  --  (1||y) Pascal  --  (*y) Raul
> > > >
> > > > It is also nice to have the companion verb - integer part:
> > > >
> > > >    ip=: * * <.@|      NB. Thanks to Louis
> > > >
> > > >    ip v
> > > >
> > > > _2 _5 _11 13 13 13 12
> > > >
> > > >
> > > > I have needed these functions more than once in my enginering work. I
> > > > believe that these two verbs need to be inserted somewhere in the
> > > "Numbers"
> > > > section of the J Phrases doc. Maybe under "8A-Numbers & Counting", or
> > > > 8C-Representations", or "8D-Arithmetic".
> > > >
> > > >
> > > > How do we get them in the document? What section do they fit the best
> > in?
> > > > Can I edit the Phrases doc?
> > > >
> > > > Skip Cave
> > > > Cave Consulting LLC
> > > >
> > > >
> > > >
> > > >>
> > > >>
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