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

From: Ken Knoblauch <knoblauch_at_lyon.inserm.fr>
Date: Wed 29 Jun 2005 - 22:16:49 EST


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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France
tel: +33 (0)4 72 91 34 77
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http://www.lyon.inserm.fr/371/

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Received on Wed Jun 29 22:19:43 2005

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