Re: [Jprogramming] Fractional parts

```   v=. 0 1e_40 _1e_40

v=(<.v)+(1|v)
1 1 0```
```
each version of integer part needs a matching fractional part.

On Aug 9, 2017 10:06 PM, "'Bo Jacoby' via Programming" <
programm...@jsoftware.com> wrote:

v=(<.v)+(1|v) NB. number = integer part + fractional part? Yes!
1 1 1 1 1 1 1

Den 7:00 onsdag den 9. august 2017 skrev Don Guinn <dongu...@gmail.com>:

True for 32 bit integers, but for 64 bit j integers and floats are the same
size.

On Aug 8, 2017 10:48 PM, "Skip Cave" <s...@caveconsulting.com> wrote:

> 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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