My struggle to find a diffent way was because I can't understand: M 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 ~:/M 0 1 1 0 0 0 1
Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Linda Alvord Sent: Friday, May 31, 2013 5:49 PM To: [email protected] Subject: Re: [Jprogramming] Dot conjunction in the leap year verb Raul's simplifies even better. ly2 ] #~ [: ~:/ 0 = 4 100 400 |/ ] Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Linda Alvord Sent: Friday, May 31, 2013 3:53 PM To: [email protected] Subject: Re: [Jprogramming] Dot conjunction in the leap year verb ly=: 13 :'(((+/"2) 0=4 100 400 |/ y)e. 1 3)#y' Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Linda Alvord Sent: Friday, May 31, 2013 3:43 PM To: [email protected] Subject: Re: [Jprogramming] Dot conjunction in the leap year verb More testing seems to hold up. YEAR=:1900 2000 2012 2013 2014 2015 2016 ly=:] #~ 1 3 e.~ [: (+/"2) 0 = 4 100 400 |/ ] ly YEAR 2000 2012 2016 ly ] #~ 1 3 e.~ [: (+/"2) 0 = 4 100 400 |/ ] Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Roger Hui Sent: Friday, May 31, 2013 10:15 AM To: Programming forum Subject: Re: [Jprogramming] Dot conjunction in the leap year verb Trying it on 1900+i.500 would be a better test. On Fri, May 31, 2013 at 3:22 AM, Linda Alvord <[email protected]>wrote: > OOPS, Not done yet. Linda > > -----Original Message----- > From: [email protected] [mailto: > [email protected]] On Behalf Of Linda Alvord > Sent: Friday, May 31, 2013 4:46 AM > To: [email protected] > Subject: Re: [Jprogramming] Dot conjunction in the leap year verb > > YEAR=:1900 2000 2001 2002 2003 2004 > ly=: 13 :'((400|/ y) e. 0 4)#y' > ly YEAR > 2000 2004 > ly > ] #~ 0 4 e.~ 400 |/ ] > > Is this OK for leap year? > > Linda > > -----Original Message----- > From: [email protected] [mailto: > [email protected]] On Behalf Of Roger Hui > Sent: Thursday, May 30, 2013 11:55 PM > To: Programming forum > Subject: Re: [Jprogramming] Dot conjunction in the leap year verb > > That phrase is "mine" and embodies some history. When I started in > APL decades ago I found it amusing to find novel inner products, and > the one used to find leap years is ≠.= in APL, not-equal dot equal. > The phrase found its way into the J phrase book by translation from > APL. There was no @ or @: in APL. > > Since u . v is defined in terms of @, there is not (and can not) be > much of an advantage of . over @ . I suppose @ is more open ended and using . > provides more of a hint to the system what you intend to compute. > > > > > On Thu, May 30, 2013 at 8:39 PM, elton wang <[email protected]> wrote: > > > Thanks. > > Is the any advantage of ~:/ .= over ~:/ @:= here in m11? > > > > > > > > ________________________________ > > From: Raul Miller <[email protected]> > > To: Programming forum <[email protected]> > > Sent: Thursday, May 30, 2013 8:35 AM > > Subject: Re: [Jprogramming] Dot conjunction in the leap year verb > > > > > > I imagine you are talking about the definition of m11 at > > http://www.jsoftware.com/help/phrases/date_time.htm > > > > In other words: 0: ~:/ .= 4 100 400"_ |/ ] > > > > For example: > > (0: ~:/ .= 4 100 400"_ |/ ]) 1900 2000 2001 2002 2003 2004 > > 0 1 0 0 0 1 > > > > 1900 is not a leap hear, but 2000 is. > > > > First off, I should perhaps note that this is old - nowadays we > > would leave off the "_ from 4 100 400 because it is implied. But > > that's ok, either way works: > > (0: ~:/ .= 4 100 400 |/ ]) 1900 2000 2001 2002 2003 2004 > > 0 1 0 0 0 1 > > > > Anyways, as I am sure you have already determined, the first step is > > to find remainders: > > > > (4 100 400"_ |/ ]) 1900 2000 2001 2002 2003 2004 > > 0 0 1 2 3 0 > > 0 0 1 2 3 4 > > 300 0 1 2 3 4 > > > > Also, from a reference manual point of view, here's the definition > > of > > "dot": http://www.jsoftware.com/help/dictionary/d300.htm > > > > In other words ~:/ .= is like matrix inner product, with addition > > being replaced by "not equals" (or "exclusive or") and with > > multiplication being replaced by = > > > > Or, put diferently, ~:/ .= is ~:/@(v"1 _) > > > > In this case: > > (0 (="1 _) 4 100 400"_ |/ ]) 1900 2000 2001 2002 2003 2004 > > 1 1 0 0 0 1 > > 1 1 0 0 0 0 > > 0 1 0 0 0 0 > > > > (0 ~:/@(="1 _) 4 100 400"_ |/ ]) 1900 2000 2001 2002 2003 2004 > > 0 1 0 0 0 1 > > > > In other words, if the year is divisible evenly by an odd number of > > integers from the list 4 100 400 it's a leap year, but if it's > > divisible evenly by an even number of those integers it's not a leap > > year. > > > > This corresponds to a nested if structure like this (pseudocode): > > > > if (year evenly divisible by 4) then > > if (year evenly divisible by 100) then > > if (year evenly divisible by 400) then > > leap year > > else > > not a leap year > > else > > leap year > > else > > not a leap year > > > > (And, of course, modern cpu instruction piplelines struggle with > > conditional statements, so there are some real advantages to > > avoiding "if statements". See, for example: > > > > http://software.intel.com/en-us/articles/branch-and-loop-reorganizat > > io n-to-prevent-mispredicts but, also, mathematical equivalences are > > a powerful tool of thought.) > > > > Thanks, > > > > -- > > Raul > > > > On Thu, May 30, 2013 at 12:23 AM, <[email protected]> wrote: > > > Can anyone show me how's the leap year verb work? I am confused on > > > the > > use of dot. <br/><br/>m11=: 0: ~:/ .= 4 100 400"_ |/ ] NB. Is y a leap > > year?<br/>Why does it use ~:/ .= here? Is it the same as ~:/@:= ? > > <br/><br/><br/><br/> > > > ------------------------------------------------------------------ > > > -- > > > -- 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 > > ---------------------------------------------------------------------- > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
