Correction.
> From: Oleg Kobchenko <[email protected]> > > If x is n, round is can be written as: > roundA=: (%&)(<.&.) roundA=: (%&)(<.@(0.5&+)&.) > > 0.05 roundA 1.41 1.449 1.47 1.48 > 1.4 1.45 1.45 1.5 > > > Following "[Jprogramming] Getting the decimal values", > http://www.jsoftware.com/pipermail/programming/2009-May/014633.html > > http://www.jsoftware.com/pipermail/programming/2009-May/014641.html > > roundR=: [ (] - |) -:@[ + ] > > 0.05 roundR 1.41 1.449 1.47 1.48 > 1.4 1.45 1.45 1.5 > > Besides, Residue (dyadic |) is closely related to base. > > 0.01 (#: , |) 123.4567 > 0.0067 0.0067 > > > It would be good to illustrate how Devon's formulas are > innovative compared to the 'numeric' script; including > the use of x=0.05. > > > > > From: Devon McCormick > > > > Here's a rounding function I wrote a while ago that includes banker's > > rounding as an option. I don't know if this is available elsewhere in > > standard libraries and I often find that something I've written has already > > been done, usually better, before. > > > > However, I like my notational innovation where I specify the rounding by an > > amount, e.g. "0.05 roundNums" rounds to the nearest 0.05 (or "nickel", in > > US). > > > > Regards, > > > > Devon > > > > roundNums=: 3 : 0"1 0 > > NB.* roundNums: round numbers y to precision x, e.g. > > NB. 0.1 roundNums 1.23 3.14159 2.718 -> 1.2 3.1 2.7. > > NB. Optional 2nd left argument is single letter specifying > > NB. type of rounding: Up, Down, or Banker's. Default > > NB. banker's rounding (round halves up or down depending on > > NB. parity of next (scaled) digit) tends to randomize bias. > > 1 roundNums y > > : > > RT=. 'B' NB. Default to Banker's rounding > > TO=. x NB. Precision to which to round. > > if. (2=#x)*.1=L. x do. 'TO RT'=. x end. > > scaled=. y%TO NB. For Banker's: round down if last digit even, > > select. RT > > case. 'B' do. RN=. 0.5*(0~:2|<.scaled)+.0.5~:1|scaled NB. up if odd. > > case. 'D' do. RN=. (0.5=1|scaled){0 _0.5 NB. Round halves down. > > case. 'U' do. RN=. 0.5 NB. Round halves up. > > end. > > TO*<.scaled+RN > > NB.EG 2 2 4 4 -: 1 roundNums 1.5 2.5 3.5 4.5 NB. Banker's: odd up, > > even down > > NB.EG 2 3 4 5 -: (1;'U') roundNums 1.5 2.5 3.5 4.5 NB. round up > > NB.EG 1 2 3 4 -: (1;'D') roundNums 1.5 2.5 3.5 4.5 NB. round down > > ) > > > > > > On Sun, May 10, 2009 at 2:38 AM, Sherlock, Ric wrote: > > > > > > From: Martin Kreuzer > > > > While fumbling around with base notation, I found > > > > 5b34 > > > > 19 > > > > 5b35 > > > > 20 > > > > 5b36 > > > > 21 > > > > while I was waiting to see an error message for the second and third > > > > case (using digits not in the set for this base, beyond 0 1 2 3 4). > > > > This is puzzling me. > > > > > > Seems consistent to me. > > > 5b36 > > > There are 6 "ones" (5^0) and 3 "fives" (5^1), that makes 21. > > > > > > Obviously you can get 21 using 5b41 too. > > > > > > > 2 > > > > To use verbs like "roundint" or "roundbanker" is there a module I > > > > need to load, if so which one..? > > > > > > Yes you need to load the numeric script: > > > load 'numeric' > > > > > > If you are looking for something that you think might be available in a > > > script somewhere in the J base library, then the Find in Files utility can > > > be useful: > > > > > > Edit | Find in Files > > > > > > Choose the "Folders" tab. > > > Find what: roundbaker > > > In folders: ~system > > > > > > Click "Find" button. > > > > > > In the results: > > > Place your cursor in the line that you are interested in. > > > Click "Open" button. > > > > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > > > > > > -- > > Devon McCormick, CFA > > ^me^ at acm. > > org is my > > preferred e-mail > > ---------------------------------------------------------------------- > > 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
