OK, so how do I reconcile 9!:11 (15)
fibfirst i.5 44721359549.9957 72360679774.999 11708203932.4997 18944271909.9999 30652475842.5001 with the above formula produces the first few digits of the kth fibonacci number. Bill's comment about the "phi formula" working for k up to 76 applies to computing the Fibonacci numbers to full precision, all the digits. f(77) is larger than the largest integer that can be represented exactly with 64 bit IEEE floating point numbers. Since fibfirst uses 64 bit IEEE floating point numbers, it does no good to use 80 digits of phi, because only the first 18 or so digits are relevant. ----- Original Message ----- From: "p j" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Tuesday, February 21, 2006 5:59 AM Subject: [Jprogramming] re: Numeric precision bug? Bill, thanks I guess... using phi seems to get the "right" answers for first few digits of k up to 100000 not 76, but I can see how that would explain it breaking for high k. Using phi of 80 digits or so (first row from page below), made my formula accurate enough to get right numbers for k>300000 http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap46.html Roger, It was easy to miss but the results produce useful notation after you set the global print precision to 9!:11 (15) >> I can not relate your statement the above formula produces the first few digits of the kth fibonacci number. with the following result: fibfirst i.4 5 4.47214e10 7.23607e10 1.17082e10 1.89443e10 3.06525e10 ---- fibfirst=: 3 : 0 p=. 1.61803398874991595753 NB. -: >: ( %: 5) a =. ((y.) * (10^. p)) - 10^.2.2360679774997898 a =. 10 + a - (<. a) 10^a ) the above formula produces the first few digits of the kth fibonacci number. the following list are offsets from 300000 that produce fibonacci numbers with digits 1-9 pandigital. (302079, 303585 etc...) 2079 3585 4120 4651 5079 9027 12850 16912 22309 22658 22723 24531 32770 33578 33851 34494 35588 36987 38128 41512 43091 43387 51186 57068 57512 59737 59766 70611 71824 83432 95911 97945 according to this site, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibFormula.html#LOG Most of these numbers are actually not pandigital. My formula is higher by 1-4 on the first 9 digits. Is this because I have chosen different precision for phi? If so, this would be weird because my phi number (p) is smaller than the rounding choices at that web site (so I would expect my numbers would be smaller). Is there some internal rounding in J that could create the discrepency? __________________________________________________________ Find your next car at http://autos.yahoo.ca ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
