In http://www.jsoftware.com/jwiki/Essays/Repeated_Squaring Hui described this solution already.
powG=: 4 : 0"0 if. 0=y do. 1 return. end. if. 2|y do. x * *: x powG -:<:y else. *: x powG -:y end. ) powG1=: 4 : '(*:@]`(x**:@])@.[)/,1x,~2|<[EMAIL PROTECTED]:^:a:,y'"0 powH=: 4 : '*/ *~^:(I.|.#:y) x' 5 ts '3x powG 100000' 0.38914173 332672 5 ts '3x powG1 100000' 0.38533968 343680 5 ts '3x powH 100000' 0.43796215 594048 3x (powG-:powH)100000 1 R.E. Boss > -----Oorspronkelijk bericht----- > Van: [EMAIL PROTECTED] [mailto:programming- > [EMAIL PROTECTED] Namens Arie Groeneveld > Verzonden: zondag 20 juli 2008 18:35 > Aan: Programming forum > Onderwerp: [Jprogramming] Speeding up dyad ^ for x: results > > I don't know if this already passed the forum: how to speed up > exponentiation x^y with y>:0 for integer arguments giving a x: result; > e.g. if you have to change to x: in case: > > y > ([:<.308*%@(10&^.))"0, x > > > ([:<.308*%@(10&^.))"0, 2 > 1023 > > 2^1023 > 8.988465674e307 > > 2^1024 > _ > > 2x^1024 > 17976931348................ > > > From existing algorithms: > > pow=: 4 : 0"0 > if. 0=y do. 1 return. end. > if. 2|y do. x * *: x pow -:<:y else. *: x pow -:y end. > ) > > or: > powi=: 4 : '(*:@]`(x**:@])@.[)/,1x,~2|<[EMAIL PROTECTED]:^:a:,y'"0 > > or: > powt=: ((*:@[$:-:@])`([**:@[$:-:@<:@])@.(2|]))`1:@.(0=])"0 > > and: > pow2=: (*/@:^2x^I.@|[EMAIL PROTECTED]:@])"0 > > >From ~help/dictionary/cwhile.htm : > > exp =: 4 : 0"0 > z=.1 > a=.x > n=.y > while. n do. > if. 2|n do. z=.z*a end. > a=.*:a > n=.<.-:n > end. > z > ) > > ts '3x ^ 100000' > 3.138055 362560 > > ts '3x pow 100000' > 1.298968 166464 > > ts '3 powi 100000' > 1.299312 171776 > > ts '3x powt 100000' > 3.138818 209152 > > ts '3 pow2 100000' > 3.716827 576896 > > ts '3x exp 100000' > 3.154187 231680 > > > pow and powi are reasonable candidates. Is there more to gain? > > > =@@i > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
