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

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Wed 29 Jun 2005 - 23:47:43 EST

On 6/29/2005 9:31 AM, Robin Hankin wrote:
> 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?>

Shouldn't you ask the gsl maintainer that? :-)

> 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)

Then that user should submit the patch, not you. But whoever does it should include an argument to convince an R core member that the change is worth looking at, and do it well enough that the patch is accepted. Changes to the way R does arithmetic affect everyone, so they had better be done right, and checking them takes time.

Duncan Murdoch

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