I was told by a long-time user whose opinions I respect that it would be more useful to be able compute to some specified precision than to have symbolic manipulations. So, some day, Joey will be able to say in J:
y=: 40 x: 2.5 y 2.5d40 ^ y 12.18249396070347343807017595116796618318 1 o. y 0.5984721441039564940518547021861622717035 ^. y 0.9162907318741550651835272117680110714501 And there will be no degradation in the speed of computations on ordinary 64 bit IEEE floating point numbers. ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Wednesday, December 6, 2006 12:16 pm Subject: Re: [Jgeneral] Bug? Sin of pi. > Joey K Tuttle wrote: > > At 07:18 -0500 2006/12/06, John Randall wrote: > >>Joey Tuttle writes: > >>>In any case, I'm happy to sit back and wait for arbitrary > >>>precision/accuracy facilities to be introduced in J. > >> > >>Symbolic languages such as Maple and Mathematica have arbitrary > >>precision, but you hit a switch to do native floating-point > >>calculation when you want speed. > >> > > > > Of course, as the case with 123x currently, I presume that a > > switch to (surely slower) arbitrary precision would continue > > to be required. That is what I'm happy to wait for... > > Fair enough, but you still pay the price for the slower > simplification/evaluation model anyway. That is why Maple and > Mathematicaare not used for serious numerical calculation, except > as front ends to > standard libraries like LAPACK. > > Even with arbitrary precision, pi is not representable exactly, > since you > are still limited to rational numbers. If argument reduction is > used in > calculating sin, it is quite likely that sin(pi) is not 0: you need > symbolic representation (or luck) for that. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
