No, you should have read it as "I don't care". And you are incorrect that the non-zero result of sin 1p1 means that there is reduced accuracy in a newer release of J.
I had already pointed out that 1p1 - 3.141592653589793 0 Since only a true 0 can display as 0, that means 1p1 is represented exactly as 3.141592653589793. The latter is not transcendental, not irrational even. The sine of a non-zero rational number can never be zero. So what is sin 1p1, to 40-digits, say? Discussions subsequent to our interchange indicated how one can compute sin to any finite number of digits. In any case, the power series for sin and cos are topics treated in a first-year calculus course. x=: 3.141592653589793 is slightly less than true pi, that is, x=pi-c where c is a number with small magnitude. By the sum formula (sin a+b)=((sin a)*cos b)+(sin b)*cos a and so (sin pi-c)=((sin pi)*cos -c)+(sin -c)*cos pi. The first term simplifies to 0 since sin pi is 0. The second term simplifies to sin c since sin -c is - sin c and cos pi is _1 . Thus: x=: 3141592653589793x % 10^15x pi=: ((10^40x) %~ <[EMAIL PROTECTED] 10^40x) c=: pi - x 0j_8 ": c 2.38462643e_16 With c being so small the power series converges rapidly: 0j_8 ": (c^5) % !5x 6.42570115e_81 That is, three terms suffice. Thus: 0j40 ": -/ (c^i) % ! i=: 1 + 2 * i.3x 0.0000000000000002384626433832795028841971 In contrast, in J6.01: 0j40 ": sin 1p1 0.0000000000000001224606353822377300000000 Now as to the "I don't care": If you did not already know, the J interpreter is implemented in C and there is a sin() function in the C library routine. As far as I know sin(x) gives good results for most x. The question is, do I want to do anything about the cases which are slightly off, such as sin 1p1 giving a zero result in the version of C used in J4.05d in May 2001, or that in J6.01 sin 1p1 is 1.22e_16 instead of the more correct value of 2.38e_16? I do not. I did not say all these things because I had assumed a certain amount of knowledge and intelligence on the part of my interlocutor (more than that of the average interlocutor). My expectations were apparently too high. ----- Original Message ----- From: Joey K Tuttle <[EMAIL PROTECTED]> Date: Tuesday, December 5, 2006 8:39 am Subject: Re: [Jgeneral] Bug? Sin of pi. > When I got Roger's reply - I read it as "I don't know..." > Quite an unusual response about changes in J results! > > Actually, I ruled out the Phase of the moon, since both > experiments were performed quite close in time - and vagaries > in the CPU for the reason that both results were from same > machine, only seconds apart (and were reproducible). That ony > left "Changes in the C library". > > I am a bit surprised that results from C library routines would > lead to reduced accuracy in a newer release of J... I thought > perhaps a "special check" had been removed, but surely Roger > would have said that. Just to be clear - my expectations are > not that "numerical results should conform ..." --- merely > surprise that the result of 1 o. 1p1 changed between releases > of J. > > Other than Roger's rather flip/dismissive remarks, no one else > seems to wonder about that... That also surprises me. > > - joey > > > At 10:48 -0400 2006/12/05, ramacd wrote: > >Folks; > > > >Although I concur with the assessment of the level of > helpfulness, the issue > >seems to be how one responds to an impossibly high expectation, > namely that > >machine-based numerical results should conform to mathematical > identities>( 0 = sin k * pi, in this case). > > > >Perhaps the response was too obvious, like "the fact that the > perpetual>motion machine stopped is not a bug," would be. > > > >----- Original Message ----- > >From: "Richard Donovan" <[EMAIL PROTECTED]> > >To: <[email protected]> > >Sent: Tuesday, December 05, 2006 6:59 AM > >Subject: Re: [Jgeneral] Bug? Sin of pi. > > > > > >> I nominate this reply, and a previous one-liner by the same author > >> ( " This is not a bug " ) as two of the most uninformative and > unhelpful>> messages I have ever seen posted to this normally > informative and > >> very helpful forum! > >> > >> > >> > >> >From: Roger Hui <[EMAIL PROTECTED]> > >> >Reply-To: General forum <[email protected]> > >> >To: General forum <[email protected]> > >> >Subject: Re: [Jgeneral] Bug? Sin of pi. > >> >Date: Fri, 01 Dec 2006 11:06:26 -0800 > >> > > >> >Changes in the C library? Vagaries in the CPU? > >> >Phase of the moon? > >> > > >> > > >> > > >> >----- Original Message ----- > >> >From: Joey K Tuttle <[EMAIL PROTECTED]> > >> >Date: Friday, December 1, 2006 10:55 am > >> >Subject: Re: [Jgeneral] Bug? Sin of pi. > >> > > >> > > At 10:32 -0800 2006/12/01, Roger Hui wrote: > >> > > >Because > >> > > > > >> > > > 1p1 - 3.141592653589793 > >> > > >0 > >> > > > > >> > > But, as was pointed out - > >> > > > >> > > 9!:14 '' > >> > > 4.05/2001-05-16/11:30 > >> > > 1 o. 1p1 > >> > > 0 > >> > > 1p1 - 3.141592653589793 > >> > > 0 > >> > > > >> > > I think the question is, what has caused the shift? > >> > > > >> > > 9!:14 '' > >> > > j504/2005-03-16/15:30 > >> > > 1 o. 1p1 > >> > > 1.22461e_16 > >> > > 1p1 - 3.141592653589793 > >> > > 0 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
