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
>
--
Clifford A. Reiter
Mathematics Department, Lafayette College
Easton, PA 18042 USA, 610-330-5277
http://www.lafayette.edu/~reiterc
----------------------------------------------------------------------
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