That sounds a lot like a bug to me. (GMP bug?)
On Wed, 25 Jan 2023, Raul Miller wrote:
Actually, after thinking about this, an epsilon at or near 2^_1021x
(or 4e_308) would probably be a better default. Having an epsilon
which can be safely represented as a floating point value is probably
for the best, especially initially.
Technically, 1e_318 might be used, but anything much smaller than
4e_308 can only be represented as a denormalized floating point
number, which means casting to rational and then back to float turns
it into a zero, and I haven't quite convinced myself that this is a
bug.
Thanks,
--
Raul
On Wed, Jan 25, 2023 at 8:45 AM Raul Miller <[email protected]> wrote:
I haven't looked at math/calculus recently.
However, it sounds like it could use a few epsilons...
Perhaps a default of 2^_1024x would be appropriate?
Thanks,
--
Raul
On Wed, Jan 25, 2023 at 6:17 AM Ian Clark <[email protected]> wrote:
>
> Thanks Raul.
>
> This saves me locating the source of math/tabula and friends, to update it.
> It's several years now since I touched the code, and I've forgotten how to
> do it -- and it's possibly changed.
>
> But I ought to be grateful for the current j904 breaking the code, because
> it has alerted me to latent bugs regarding the use of rational numbers by
> math/cal and math/uu. For me this is the tip of a murky iceberg.
>
> It's not so much that I want to retain a sensible looking constant for
> rational-infinity, as the fact that infinities (or exploding large finite
> number representations in general) can arise in so many ways, and there's
> no guarantee they will equate with whatever I settle on as a "reference"
> rational-infinity. In particular, math/cal's use of Newton's method with
> rational numbers is particularly fraught, with an emerging host of spooky
> reasons for non-convergence I don't have words to describe (some play on
> the terms Moiré, resonance, Nyquist … might be needed). This is the
> flagship feature of math/cal we're talking about.
>
> Hitherto math/cal has played whack-a-mole with issues as they arose. I fear
> that the move to new arithmetic routines will deliver a fresh load of moles
> to whack. And just when my attention is diverted elsewhere.
>
> Ian
>
> On Wed, 25 Jan 2023 at 04:36, Raul Miller <[email protected]> wrote:
>
> > I've noticed an odd quirk here.
> >
> > 1.2r3.4
> > 0.352941
> > _r3.4
> > |ill-formed number
> >
> > This issue is present in j903.
> >
> > I have opted to retain this quirk for j904, because it doesn't seem to
> > be important and it makes the implementation a bit simpler.
> >
> > (Also, other than this quirk, _r1 and friends will work in the next
> > update to j904.)
> >
> > Thanks,
> >
> > --
> > Raul
> >
> > On Tue, Jan 24, 2023 at 10:38 PM Raul Miller <[email protected]>
> > wrote:
> > >
> > > Right... Aside from adding libgmp support, a change from j903 is that
> > > j903 had an extended precision infinity which was used in parsing
> > > numeric constants, but j904 does not.
> > >
> > > And, when I was rewriting the bit that handles rational constants, I
> > > overlooked some of the ways of representing rational infinity.
> > >
> > > I'm testing a fix for this problem right now. It should be ready soon.
> > >
> > > Thanks,
> > >
> > > --
> > > Raul
> > >
> > > On Tue, Jan 24, 2023 at 10:18 PM Henry Rich <[email protected]>
> > wrote:
> > > >
> > > > Decision, decisions. How /should/ you specify an extended infinity?
> > I say
> > > >
> > > > _x
> > > > |ill-formed number
> > > >
> > > > There could be alternatives. _r(any finite) and (any non0)r0 are both
> > > > reasonable.
> > > >
> > > > NOTE that the GMP library that we have moved to has no way to represent
> > > > extended infinity. Raul has chosen 1r0 as our internal representation
> > > > of extended infinity, so infinity will always have rational precision,
> > > > not extended integer.
> > > >
> > > > For display, we get it right:
> > > >
> > > > 1r0
> > > > _
> > > >
> > > > It seems that _r(any) should be converted to infinity - and _x and __x
> > > > too I think. This is in Raul's area.
> > > >
> > > > If you have a dependency on the internal representation of infinity it
> > > > will be on you to update it.
> > > >
> > > > Henry Rich
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > On 1/24/2023 9:00 PM, Ian Clark wrote:
> > > > > j903 accepts -- but j904 rejects -- this way of defining rational
> > infinity:
> > > > >
> > > > > _r1
> > > > >
> > > > > |ill-formed number
> > > > >
> > > > > | _r1
> > > > >
> > > > > | ^
> > > > >
> > > > > JVERSION
> > > > >
> > > > > Engine: j904/j64arm/darwin
> > > > >
> > > > > Beta-k: commercial/2023-01-24T04:42:28
> > > > >
> > > > > Library: 9.04.10
> > > > >
> > > > > Qt IDE: 2.0.3/6.2.4(6.2.4)
> > > > >
> > > > > Platform: Darwin 64
> > > > >
> > > > > Installer: J904 install
> > > > >
> > > > > InstallPath: /applications/j904
> > > > >
> > > > > Contact: www.jsoftware.com
> > > > >
> > > > > A workaround is to use 1r0 instead:
> > > > >
> > > > >
> > > > > 1r0
> > > > >
> > > > > _
> > > > >
> > > > > datatype 1r0
> > > > >
> > > > > rational
> > > > >
> > > > >
> > > > > Not a lot of j-ers willl have a use for rational [minus] infinity,
> > but IMO
> > > > > a beginner might find it more intuitive to define it as _r1 rather
> > than 1r0
> > > > > . Maybe it's no big deal in itself, but it breaks 3 addons, viz:
> > math/cal,
> > > > > math/uu -- and in consequence math/tabula:
> > > > >
> > > > >
> > > > > load'math/uu' NB. Launch UU only
> > > > > |ill-formed number in script, executing monad 0!: 0
> > > > > |any word beginning with a digit or _ must be a valid number
> > > > > | BADRAT=: __r1
> > > > > | ^
> > > > > |[-33] /applications/j904/addons/math/uu/uu.ijs
> > > > >
> > > > > load'math/cal'
> > > > > |ill-formed number in script, executing monad 0!: 0
> > > > > |any word beginning with a digit or _ must be a valid number
> > > > > | BAD_EXE_VALUE=: __r1
> > > > > | ^
> > > > > |[-92] /applications/j904/addons/math/cal/cal.ijs
> > > > >
> > > > >
> > > > > So I'd call it a bug.
> > > > >
> > > > >
> > > > > There's been plenty of time to discover this. Sorry it's taken me so
> > long.
> > > > >
> > > > >
> > > > > Ian Clark
> > > > >
> > ----------------------------------------------------------------------
> > > > > For information about J forums see
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> > > >
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> >
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