# [R] Spreadsheet math problem (exponentiation)

John McKown john.archie.mckown at gmail.com
Fri Sep 18 16:31:02 CEST 2015

```On Fri, Sep 18, 2015 at 8:39 AM, John Kane <jrkrideau at inbox.com> wrote:

> It appears that at least three major spreadsheets, Excel, Apache
> OpenOffice Cal and gnumeric have a problem with the correct order of
> operations when dealing with exponents. The gnumeric result is very strange.
>
> This problem has probably been reported before but just in case it has
> not, it would appear to be one more serious problem with spreadsheets. It
> might be useful in warning people away from using a spreadsheet for serious
> analysis.
>
> Excel
>
> -2^2 = 4
>
> 2^2^3 = 64
>
> Apache OpenOffice
>
> -2^2 = 4
>
> 2^2^3 = 64
>

My opinion: One correct, one error!​ R agrees with me on this:
> 2^2
 4
> 2^2^3
 256
> 2^(2^3)
 256
> -2^2
 -4
> (-2)^2
 4
>

>
> gnumeric # note one correct, one error!
>

​My opinion: two correct!​

>
> -2^2 = 4
>
> 2^2^3 = 256
>
> John Kane
>
>
​Seems to be a bit off-topic. Unless your point to is to use R for
important work instead of some spreadsheet. A point with which I completely
agree!​

​MS-Excel, and Apache OpenOffice, appear to implement the above as
(2^2)^3==64. ​Whereas gnumeric implements appears to implement this as:
2^(2^3)==256. Which is "correct"? Depends on whom you ask.

ref: https://en.wikipedia.org/wiki/Order_of_operations
<quote>

If exponentiation is indicated by stacked symbols, the usual rule is to
work from the top down, thus:
[image: a^{b^c} = a^{(b^c)}],

which typically is not equal to [image: (a^b)^c]. However, some computer
systems may resolve the ambiguous expression differently. For example,
Microsoft
Office Excel <https://en.wikipedia.org/wiki/Microsoft_Office_Excel>
evaluates *a*^*b*^*c* as (*a*^*b*)^*c*, which is opposite of normally
accepted convention of top-down order of execution for exponentiation. If
a=4, p=3, and q=2, [image: a^{p^q}] is evaluated to 4096 in Microsoft Excel
2013, the same as [image: (a^p)^q]. The expression [image: a^{(p^q)}], on
the other hand, results in 262144 using the same program.
</quote>

​Gnumeric abides by the above definition. FWIW. BTW - MS-Excel also has
1900 as a friggin' leap year (due to Lotus 1-2-3 apparently), so I don't
consider MS-Excel (or anything else from MS for that matter) to be a
definitive source of correctness.​ Personal opinion. FSF associate member.
Penguinista.

--

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Maranatha! <><
John McKown

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