This is what the Extended Precision Functions page does with more finesse. For example, computing ^1e6 with your approach would take many terms. Instead, one can scale the argument so that you only need to do the series on a very restricted domain (for exp, bounded by 2%~^.2, approximately 0.35), on which convergence is very fast.
On Sun, Dec 22, 2013 at 8:13 AM, Raul Miller <[email protected]> wrote: > On Sun, Dec 22, 2013 at 10:50 AM, Roger Hui <[email protected]> > wrote: > > I expect exp can be improved. The details are left as an exercise for > the > > reader. :-) > > And, perhaps, the concept of what "improved" means can be an exercise > for the reader? Here, I'll optimize for useless accuracy (or at least > accuracy which I have no immediate use for) at the expense of speed > and space: > > 1163j1160":(%!i.512x)&p. 1 > > > 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069551702761838606261331384583000752044933826560297606737113200709328709127443747047230696977209310141692836819025515108657463772111252389784425056953696770785449969967946864454905987931636889230098793127736178215424999229576351482208269895193668033182528869398496465105820939239829488793320362509443117301238197068416140397019837679320683282376464804295311802328782509819455815301756717361332069811250996181881593041690351598888519345807273866738589422879228499892086805825749279610484198444363463244968487560233624827041978623209002160990235304369941849146314093431738143640546253152096183690888707016768396424378140592714563549061303107208510383750510115747704171898610687396965521267154688957 03 > 50354021234078498193343210... > > I've left three extra characters to the left of the fractional part: > one for the decimal point, one for the 2 and one for the absence of a > negative sign. > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
