[R] x*x*x*... vs x^n

[Ken Knoblauch]

Something like this is exploited very nicely in the mtx.exp 
for matrix powers in the Malmig package, actually.


****************************
Hi

I have been wondering if there one can speed up calculating small powers
of numbers such as x^8 using multiplication.

In addition, one can be a bit clever and calculate x^8 using only 3  
multiplies.

look at this:


 > f1 <- function(x){x*x*x*x*x*x*x*x}
 > f2 <- function(x){x^8}
 > f3 <- function(x){x2 <- x*x;x4 <- x2*x2;return(x4*x4)}

[so f1() and f2() and f3() are algebraically identical]


 > a <- rnorm(1000000)
 > system.time(ignore <- f1(a))
[1] 0.50 0.17 2.88 0.00 0.00

 > system.time(ignore <- f2(a))
[1] 0.31 0.03 1.40 0.00 0.00

 > system.time(ignore <- f3(a))
[1] 0.10 0.07 0.18 0.00 0.00


[these figures show little variance from trial to trial]


I was expecting f2() and f3() to be about the same.
I was not expecting a factor of 3 there!

anyone got any comments?




--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

____________________
Ken Knoblauch
Inserm U371, Cerveau et Vision
Department of Cognitive Neurosciences
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