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 > > > > > > > > > > ---------------------------------------------------------------------- > > > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
