J lacks a long precision decimal type, probably because Ken realized that base 10 is a silliness tied to our biology. Instead, j supports extended rationals, which let us access many more numbers than I triple E 754 floating point. There are many problems which require computations to so many decimal digits. This is somewhat reasonable as measurement uncertainties are often expressed in base 10. J indirectly supports long decimal in that the complex format of a rational number can be any (reasonable) length. We compute series to different term tally to find the number of literal digits remaining the same. Note that j does not support a rational result from rational to the power of funky rational.
2 2r3 ^&.> 2r3 2 +------+---+ |1.5874|4r9| +------+---+ x:inv".'x',~500#'1' NB. x:inv 1111111...111x _ 3j1 ": 22 + 1r10 *** Thoughts on long decimal arithmetic. 1) The Digits adverb, u Digits y computes u to y significant decimal digits, returning that number. Meanwhile the verb u y calls u with increasing integral y, from 1, typically the number of terms. u >:y should be more accurate than u y . u can be memoized and recursive since it's forced to recompute successively deeper. Taylor series is easily recurrent. The "50" in Digits is arbitrary and might be replaced with some function of logarithm. Digits=: adverb define NB. u Digits yu u yu is less accurate than u yu+1 NB. returns u to at least y significant digits format=. ' _.' -.~ ((j.~ 50&+) y)&": i =. 1 current=. format u i whilst. last -.@-: current do. last =. current i =. i + 2 NB. increment by 2 for no good reason. current=. format result =. u i end. result ) And 2) Following some arithmetic on rationals can result in long numerators and denominators. The cf dyad computes a perhaps wieldly fraction within x tolerance of y. cf=: 0.1&$: :(4 :0) NB. tolerance cf value -> continued fraction approximation of value to tolerance Y =. y X =. 0 >. x terms =. 0 $ 0x whilst. X < | approximation - y do. 'term Y' =. <.`([:%1&|)`:0 Y terms =. terms , term approximation =. +`%/ }: 1j1 #!.1 terms end. ) assert (-: 0&cf) 649r200 assert 13r4 (-: cf) 649r200 references: http://rosettacode.org/wiki/Ramanujan%27s_constant#J jpath'~addons/math/misc/contfrac.ins' labs of which I am unaware. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
