Oh, it is.
Somehow roundreal did not make it into the collected definitions.
I guess I should add it there.
Thanks,
--
Raul
On Tue, Mar 1, 2022 at 7:10 PM 'Michael Day' via Programming
<programm...@jsoftware.com> wrote:
>
> We're back from the Pub Quiz - 4th place, so "just outside the money"
>
> Raul asked about roundreal - it's one of the utilities in the J wiki
> article on FFT multiplication:
> roundreal
> [: (<.) 0.5 + 9&o.
>
> Henry wondered about dividing ffts when non-zero remainders would
> exist. it seems to fail, so we
> can only use it safely when assured of divisibility:
>
> fft"1 ] 8 {."1 ] 1 5 20 10 5 1,: 1 3 3 1
> 42 _8.2426407j29.899495 _14j_4 0.24264069j_10.100505 10
> 0.24264069j10.100505 _14j4 _8.2426407j_29.899495
> 8 2.4142136j5.8284271 _2j2 _0.41421356j_0.17157288 0
> _0.41421356j0.17157288 _2j_2 2.4142136j_5.8284271
> %/fft"1 ] 8 {."1 ] 1 5 20 10 5 1,: 1 3 3 1
> 5.25 3.8786797j3.0208153 2.5j4.5 8.1213203j21.020815 _
> 8.1213203j_21.020815 2.5j_4.5 3.8786797j_3.0208153
> ifft %/fft"1 ] 8 {."1 ] 1 5 20 10 5 1,: 1 3 3 1
> _ __ _ __ _ __ _ __
>
> OK - here's ctfft without the inadvertent calls to ct :
>
> ctfft=: {{ assert.0<y
> if. y = 1 do. _1 1 return. end.
> 'q p'=. __ q: y
> if. 1=#q do.
> ,(y%*/q) {."0 q#1
> elseif.2={.q do.
> ,(y%*/q) {."0 (* 1 _1 $~ #) ctfft */}.q
> elseif. 1 e. 1 < p do.
> ,(y%*/q) {."0 ctfft */q
> else.
> lgl =. {:$ ctlist =. ctfft "0 }:*/@>,{1,each q NB. ctlist
> is 2-d table of polynomial divisors
> lgd =. # dividend =. _1,(-y){.1 NB. (x^n) -
> 1, and its size
> lg =. >.&.(2&^.) lgl >. lgd NB. required
> lengths of all polynomials for fft transforms
> fftdivis=. */ fft"1 lg{."1 ctlist NB. FFT
> article doesn't deal with lists of multiplicands
> unpad roundreal ifft"1 fftdivis %~ fft lg{.dividend NB. similar
> to FFT article's multiplication
> end.
> }} M.
>
> NB. ... and crude measure of performance
>
> NB. timer returns elpased time in minutes & seconds
> timer'cyclotomic taskorderu 5' NB. before cache/memoisation
> established!
> ┌─────────┬───────────────────┐
> │1.0940018│1 105 385 1365 1785│
> └─────────┴───────────────────┘
> timer'ctfft taskorderu 5'
> ┌─────────┬───────────────────┐
> │4.3660049│1 105 385 1365 1785│
> └─────────┴───────────────────┘
> NB. continuing with cache/memoisation as above
> timer'cyclotomic taskorderu 10'
> ┌───────────┬─────────────────────────────────────────────┐
> │4 35.623001│1 105 385 1365 1785 2805 3135 6545 6545 10465│
> └───────────┴─────────────────────────────────────────────┘
> timer'ctfft taskorderu 10' NB. some improvement cf cyclotomic
> ┌───────────┬─────────────────────────────────────────────┐
> │3 58.355003│1 105 385 1365 1785 2805 3135 6545 6545 10465│
> └───────────┴─────────────────────────────────────────────┘
>
> So not much significant difference in the running times from those in my
> earlier report.
>
> Cheers,
>
> Mike
>
> On 01/03/2022 19:17, 'Michael Day' via Programming wrote:
> > Oops - ct was my memoised version of cyclotomic, while still using pDiv.
> > I expect the results will be much the same, but I'll have a look
> > later as I've
> > got to go out now. I'll have to replace ct by ctfft - perhaps you'd
> > like to try
> > while I'm pub-quizzing!
> >
> > Cheers,
> >
> > Mike
> >
> >
> > On 01/03/2022 19:02, Raul Miller wrote:
> >> Ah, I had forgotten about that bit of code. Thanks.
> >>
> >> Next question:
> >>
> >> What is 'ct' here?
> >>
> >> Thanks again,
> >>
> >
> >
>
>
> --
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