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

From: Robin Hankin <r.hankin_at_noc.soton.ac.uk>
Date: Wed 29 Jun 2005 - 23:31:02 EST

Hi Duncan

On Jun 29, 2005, at 02:04 pm, Duncan Murdoch wrote:

> On 6/29/2005 7:32 AM, Robin Hankin wrote:
>
>> 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)}
>>

[snip]

>
> If you look in src/main/arithmetic.c, you'll see that R does a
> general real-valued power (using C's pow() function) whenever
> either one of the args is real (except for a few special cases,
> e.g. non-numbers, or powers of 2 or 0.5). There is an internal R
> function equivalent to your f3, but it is not used in the situation
> of real^integer (and in any case, x^8 is real^real).
>
> I suppose if you wanted to submit a patch someone would take a
> look, but the question is whether there is really any calculation
> whose execution time would be materially affected by this. Most
> computations are not dominated by integer power calculations, so is
> this really worth the trouble?
>
> Duncan Murdoch
>

well, the Gnu Scientific Library has the pow_int() functions, which are a generalization
of f3(), so someone thinks so. I did a speed test of them but they were much slower than
R (for any of f1(), f2(), f3()):

library(gsl)
system.time(ignore <- pow_int(a,8))

[1] 1.07 1.11 3.08 0.00 0.00

<why the slow execution time?>

But I'm far more interested in the philosophy behind your comments. I would say that it definitely *is* worth the trouble because someone, somewhere, will want fast integer powers, and possibly use R for nothing else.

Ken's point about matrix exponentiation is relevant here too.

This is a stated design consideration in Mathematica, I think.

(Of course, I'm not suggesting that other programming tasks be suspended! All I'm pointing
out is that there may exist a user to whom fast integer powers are
very very important)

very best wishes

rksh

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

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Received on Wed Jun 29 23:37:07 2005

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