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
>> > > http://www.jsoftware.com/forums.htm
>> > > > >
>> > > > >
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