Re: [Bug-apl] Access to rational number numerator and denominator

[Frederick Pitts]

Louis,

        Thanks for the quick response.

        After working with the technique a bit, I observe that as long
as the rational number denominator is well within the range of integers
representable by floating numbers, 1 ∧ n returns the correct result.
But if the absolute value of the denominator exceeds 2 ⋆ 35, the
technique returns incorrect results.  For instance,

      fiMax ← × / 53 ⍴ 2 ⍝ largest integer 53-bit f.p. mantissa holds
      fiMax
╔════════════════╗
║9007199254740992║
╚════════════════╝
      1 ∧ fiMax ⍝ Correct result for fiMax
╔════════════════╗
║9007199254740992║
╚════════════════╝
      1 ∧ ÷ fiMax ⍝ Incorrect result. 1 is numerator of reciprocal.
╔═╗
║0║
╚═╝

        I was hoping to be able to access correct rational number parts
even when they approach the ⎕SYL[20;2] limit of 9200000000000000000.
It seems a shame to loose so much of the integer range because floating
point operations are sneaking into the numerator and denominator access
methods.

Regards,

Fred

On Tue, 2017-08-29 at 00:08 +0200, Louis de Forcrand wrote:
> Hi,
> 
> No APL kb with me right now, sorry :(
> 
> 1 LCM n
> 
> gives the numerator of a fraction (floating or exact). If you need
> the denominator, do the same with the inverse of n. If you need both,
> for example:
> 
> 1 LCM n POW 1 _1
> 
> Cheers,
> Louis
> 
> > On 28 Aug 2017, at 23:24, Frederick Pitts <address@hidden>
> > wrote:
> > 
> > Hello,
> > 
> >    Is there an existing mechanism for accessing rational number
> > numerator and denominator parts analogous to that for accessing
> > complex
> > number real and imaginary parts?  If yes, please let me know
> > how.  If
> > no, can a mechanism be implemented?
> > 
> > Respectfully,
> > 
> > Fred
> > 
> 
>