(+%)/cv_e y and ecf y where ecf=: 3 : '1+2*(+%)/0 1,6+4*i.y' give roughly the same number of correct digits. The fewer number of terms in the continued fraction for ecf makes a substantial difference in execution time. e.g.
timer '(+%)/cv_e 200x' 1.45177 timer 'ecf 200x' 0.258876 ----- Original Message ----- From: Cliff Reiter <[email protected]> Date: Saturday, February 27, 2010 9:27 Subject: Re: [Jprogramming] extrended precision e To: Programming forum <[email protected]> > Also using continued fractions: > > cv_e=:3 : '2,,1,.~1,.+:>:i.y' > > cv_e 5x NB. coef's > for e are nice > 2 1 2 1 1 4 1 1 6 1 1 8 1 1 10 1 > > (+%)/cv_e 5x > 566827r208524 > 18j16":(+%)/cv_e 5x > 2.7182818284705837 > 18j16":^1 > 2.7182818284590451 > > den2_dp=:<:@#@":@*:@{:@:(2&x:) > fmte=:j.@:den2_dp ": ] > > fmte (+%)/cv_e 5x NB. show > correct digits (last rounded) > 2.7182818285 > > 6!:2 'e=:fmte (+%)/cv_e 170x' > 0.966068 > #e NB. 820 > digits in under a second > 822 > e > 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746639193200305992181741359662904357290033429526059563073813232862794349076323382988075319525101901157383418793070215408914993488416750924476146066808226... > > > Roger Hui wrote: > > 0j140 ": 1+2*(+%)/0 1,6+4*i.20x > > > 2.71828182845904523536028747135266249775724709369995957496696762780815565912122705251606184329220759673523337928244478046337596165670491497455> > 0j140 ": 1+2*(+%)/0 1,6+4*i.40x > > > 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746639193200305992181741359662904357290> > > > > > > > ----- Original Message ----- > > From: "R.E. Boss" <[email protected]> > > Date: Saturday, February 27, 2010 8:35 > > Subject: [Jprogramming] extrended precision e > > To: 'Programming forum' <[email protected]> > > > >> 100<....@%~+/(10^101x)*%!i.75x > >> > 2718281828459045235360287471352662497757247093699959574966967627724076630353>> > 547594571382178525166427 > >> > >> gives the first 100 digits of ^1 > >> > >> For N digits, find k such that (10^N)<!k and determine > >> 100<....@%~+/(10^x:1+N)*%!i.x:k > >> > >> The first 1e5 digits can be found at > >> http://www.mu.org/~doug/exp/100000.html ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
