That's nice Skip. So we agree that the closed form solution is not completely useless.
I disagree with Boyko's claim: "it holds for *all* lengths where extended numbers are needed, i.e. practically always." Practical computations can be done without using extended numbers, like this. ((0 3+*&5)^:50)1 0 NB. big numbers 8.88178e34 6.66134e34 10^.((0 3+*&5)^:50)1 0 NB. taking the log makes them smaller 34.9485 34.8236 ((0 3+*&5)^:500)1 0 NB. bigger numbers give floating point overflow _ _ 10^.((0 3+*&5)^:500)1 0 NB. damage is done before the log is taken _ _ ([:(,.3r4*<:)5&^)50 NB. closed form computation 8.88178e34 6.66134e34 10^.([:(,.3r4*<:)5&^)50 NB. closed form computation of the log 34.9485 34.8236 f=:(10^.5)&*,.(10^.3r4)+((10&^.)&-.&(5&^)&-)+(10^.5)&* NB. log of product is sum of logs f 50 NB. smarter computation of 10^.([:(,.3r4*<:)5&^)50 34.9485 34.8236 f 500 NB. smarter computation of 10^.([:(,.3r4*<:)5&^)500 349.485 349.36 10 ^ 1 | f 500 NB. factors 3.05494 2.2912 <. f 500 NB. exponents 349 349 So the value of ((0 3+*&5)^:500)1 0 is 3.05494e349 2.2912e349 This is computed without using extended precision. - Bo >________________________________ > Fra: Skip Cave <s...@caveconsulting.com> >Til: programm...@jsoftware.com >Sendt: 21:34 søndag den 23. december 2012 >Emne: Re: [Jprogramming] arithmetic sequence > >In my first post I stated: >"I make the assumption here that he wants the verb to calculate all the >values up to a specific integer in the formula". >All of my subsequent comments make the assumption that we are comparing >functions that calculate multiple values in a single call, creating a n by >2 array. I make no claims about verbs that produce a single value result. >On Dec 23, 2012 1:22 PM, "Bo Jacoby" <bojac...@yahoo.dk> wrote: > >> Skips special data does not justify his general conclusion: "The brute >> force solution is the fastest by several orders of magnitude. The closed >> form solution is slow AND uses lots of space". Other data give other >> conclusions. >> >> >> closed >> [: (,. (3r4 * <:)) 5&^ >> >> (10) 6!:2'closed 5' >> 1.82306e_5 >> (10) 6!:2'((0 3+*&5)^:5)1 0x' >> 8.04365e_5 >> >> (10) 6!:2'closed 50' >> 3.68924e_5 >> (10) 6!:2'((0 3+*&5)^:50)1 0x' >> 0.000332709 >> >> (10) 6!:2'closed 500' >> 2.99943e_5 >> (10) 6!:2'((0 3+*&5)^:500)1 0x' >> 0.00487965 >> >> >> It cannot be concluded that 'closed' is generally slower than the brute >> force computation. In the above cases 'closed' is faster. >> >> >> - Bo >> >> >> >________________________________ >> > Fra: Boyko Bantchev <boyk...@gmail.com> >> >Til: programm...@jsoftware.com >> >Sendt: 18:21 søndag den 23. december 2012 >> >Emne: Re: [Jprogramming] arithmetic sequence >> > >> >On 23 December 2012 18:06, Bo Jacoby <bojac...@yahoo.dk> wrote: >> >> Skip's conclusion did not follow from his data in the first place. >> > >> >His conclusion is based on his data for producing a 5000-items long >> >sequence. Not only is it valid but in fact it holds for *all* lengths >> >where extended numbers are needed, i.e. practically always. >> >---------------------------------------------------------------------- >> >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
