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

[Ravi Varadhan]

I ran 100 repetitions of the 3 multiplications that Robin had compared.
Here are the summaries of system times (I only took the first component of
system.time) that I obtained.  It is clear that f1() is nearly twice as slow
as f2() which is slightly slower (not 3 times slower as claimed by Robin)
than f3(). So, I don't think that there is much to choose between the
"cleverer" way and the most obvious way to compute integer powers.

> summary(f1time)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.060   0.170   0.210   0.199   0.230   0.300 
> summary(f2time)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.060   0.100   0.110   0.128   0.170   0.190 
> summary(f3time)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0300  0.0950  0.0779  0.1100  0.1300 

Ravi.

--------------------------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,  The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email:  rvaradhan at jhmi.edu
--------------------------------------------------------------------------
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
> bounces at stat.math.ethz.ch] On Behalf Of Tuszynski, Jaroslaw W.
> Sent: Wednesday, June 29, 2005 8:25 AM
> To: 'Robin Hankin'; r-help
> Subject: Re: [R] x*x*x*... vs x^n
> 
> I tried your code and got different results:
> 	 system.time(ignore <- f1(a))
> 	[1] 0.83 0.09 1.08   NA   NA
> 	> system.time(ignore <- f2(a))
> 	[1] 0.38 0.01 0.41   NA   NA
> 	> system.time(ignore <- f3(a))
> 	[1] 0.32 0.04 0.43   NA   NA
> 
> So I tried it again but with a loop and got:
> 
> 	>  for(i in 1:10) cat(system.time(ignore <- f2(a)), "\n")
> 	0.36 0.04 0.44 NA NA
> 	0.32 0.01 0.34 NA NA
> 	0.28 0.03 0.32 NA NA
> 	0.29 0.03 0.35 NA NA
> 	0.3 0.02 0.32 NA NA
> 	0.28 0.03 0.32 NA NA
> 	0.3 0.02 0.32 NA NA
> 	0.29 0.02 0.34 NA NA
> 	0.23 0.03 0.32 NA NA
> 	0.42 0 0.45 NA NA
> 
> 	> for(i in 1:10) cat(system.time(ignore <- f3(a)), "\n")
> 	0.19 0.04 0.25 NA NA
> 	0.17 0.04 0.25 NA NA
> 	0.21 0.02 0.25 NA NA
> 	0.21 0.02 0.23 NA NA
> 	0.18 0.04 0.23 NA NA
> 	0.18 0.05 0.23 NA NA
> 	0.18 0.04 0.25 NA NA
> 	0.17 0.06 0.23 NA NA
> 	0.2 0.02 0.23 NA NA
> 	0.14 0.06 0.25 NA NA
> 
> It seems to me that f3 is 50% slower than f2 not 300%.
> 
> My System is:
> - R version: R 2.1.1
> - Operating System: Win XP
> - Compiler: mingw32-gcc-3.4.2
> 
> Jarek
> ====================================================\=======
> 
>  Jarek Tuszynski, PhD.                           o / \
>  Science Applications International Corporation  <\__,|
>  (703) 676-4192                                   ">   \
>  Jaroslaw.W.Tuszynski at saic.com                     `    \
> 
> 
> 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Robin Hankin
> Sent: Wednesday, June 29, 2005 7:32 AM
> To: r-help
> Subject: [R] x*x*x*... vs x^n
> 
> 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
> 
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