Bear in mind my later comments about performance on this laptop.
Either extended arithmetic or other tricks to deal with high exponents
are necessary in some cases. And, of course, I didn't deal with edge
effects. I've dealt with one such, introducing assert. , ie
assert. 2 <: n =. 2 + x -&# y ,
instead of the bare assignment for the number of loops. I see that
dblo & dbhi do still yield results for denominator >&# numerator
which I'll think about.
Anyway, would you, Raul, mind amending that article's comments on
the remainder with dbho, introducing a definition of E and changing "e"
to "E",
as I don't trust myself to get it right?! As it stands the remainder
should be 6#0 .
There's an article by Pascal Jasmin, which might be relevant, but I don't
understand it (yet!?) -
https://code.jsoftware.com/wiki/User:Pascal_Jasmin/A(2022)fast(2220)polynomial_division_algorithm#division_and_other_code
Cheers,
Mike
On 20/02/2022 15:34, Raul Miller wrote:
Very nice, thank you.
This took my code from me using jbreak during a division because I was
tired of starting at the hourglass to having that operation complete
nearly instantly.
Thanks again,
On Sun, Feb 20, 2022 at 6:31 AM 'Mike Day' via Programming
<programm...@jsoftware.com> wrote:
>
> This approach, from my A-level Maths perhaps, seems far too simple
compared to that of the article, but works, on this iPad running J701
(no, it can’t run Ian’s J902!), including when dbho or dblo throws a
domain error for, eg, dividing order 50 by order 30. I haven’t tried in
J903 on the laptop yet.
>
> BTW, I couldn’t understand why the article shows a remainder,
> ]q=. e dbho c 1 3 3 1
> ]r=.e-c t q 0 0 0 0 2 3
> But I realised there’s a missing definition, eg E =. 1 5 10 10 7 4,
with e replaced by E in the next 2 lines.
>
> Anyway,
>
> NB. binomial coefficients for (1+z)^y
> binc =: !~i.@>:
>
> NB. x % y
> div =: 3 : 0 NB. similar result to Ken's dbho
> :
> q =. ''
> yx=. y,:x
> n =. 2 + x -&# y
> while. n =. <: n do.
> q =. q, r =. %~/ {."1 yx
> yx =. y,: }. -~/ yx * r,1
> end.
> q
> )
>
> divlo =: div&.:|. NB. Like Ken's dblo
>
> diva =: 3 : 0 NB. a bit less elegant. Similar performance
> :
> q =. ''
> n =. 2 + x -&# y
> ly=. #y
> while. n =. <: n do.
> q =. q, r =. x %&{. y
> if. |r do.
> d =. (ly{.x) -&}. r * y
> x =. d, ly}.x
> else.
> x =. }. x
> end.
> end.
> q
> )
> 5 div&binc 3
> 1 2 1
> 5 div&binc 2
> 1 3 3 1
>
> ts
> 6!:2 , 7!:2@]
> ts'50 diva&binc 10'
> 0.000554 9216
> ts'50 div&binc 10'
> 0.000661 13824
> ts'50 dbho&binc 10'
> 0.002024 211840
> ts'50 dbho&binc 30'
> |domain error: dbho
> | (d{.x) %.(2#d=.<./$M){.M=.y+/ .*y bq x
>
> I slightly prefer div to diva.
>
> Cheers,
>
> Mike
> Sent from my iPad
>
>> On 20 Feb 2022, at 03:46, Raul Miller <rauldmil...@gmail.com> wrote:
>>
>> https://code.jsoftware.com/wiki/Essays/Polynomial+Division
>>
>> Iverson's method for polynomial division is elegant, but it's a bit
>> slow for large polynomials (order greater than 2000).
>>
>> Does anyone have a more efficient approach? Or is this one of those
>> situations where it doesn't get any better?
>>
>> Thanks,
>>
>> --
>> Raul
>> ----------------------------------------------------------------------
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