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TassyJim

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Joined: 07/08/2011
Location: Australia
Posts: 6269

Posted: 08:49pm 24 Apr 2015

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I just came across an interesting discussion on the PureBasic forum.
Do you treat 4^3^2 as
(4^3)^2 (left to right) or
4^(3^2) (right to left).

PRINT "4^3^2 = ";4^3^2
PRINT "(4^3)^2 = ";(4^3)^2
PRINT "4^(3^2) = ";4^(3^2)

Microsoft seems to work left to right and as MM Basic is based on GW Basic, it also uses left to right. This is stated in the manual so there should be no confusion.

It appears that many programming languages work right to left for 'power'

Quote
Mathematica 4^3^2 -> 262144
Maple 4^3^2 -> Error, power is non-associative
Maxima 4^3^2 -> 262144
Axiom 4^3^2 -> 262144
Reduce 4^3^2 -> 4096
Wolfram Language 4^3^2 -> 262144
Microsoft Visual Basic 6 4^3^2 -> 4096
MS Excel 4^3^2 -> 4096
perl 5 4^3^2 -> 262144 ie 4**(3**2)

Wikipedia says the exponential operator is right associative
http://en.wikipedia.org/wiki/Operator_associativity

Quote
In order to reflect normal usage, addition, subtraction, multiplication, and division operators are usually left-associative while an exponentiation operator (if present) is right-associative. Any assignment operators are also typically right-associative. To prevent cases where operands would be associated with two operators, or no operator at all, operators with the same precedence must have the same associativity.

Something to watch out for when translating programs and a good reason for lots of brackets.

Jim

VK7JH
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JohnS
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Joined: 18/11/2011
Location: United Kingdom
Posts: 4038

Posted: 10:10pm 24 Apr 2015

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Interesting.... though I don't think I've ever written a double exponentiation in any language!

John

Dylan
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Joined: 17/06/2013
Location: Netherlands
Posts: 81

Posted: 09:09am 25 Apr 2015

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There are two reasons to.

1) Computer Science 2^(2^5) = 2^32 = maximum memory for a 32-bit OS, for example.

2) Physical sciences (2^t)^(1/3) = volume of something doubling every t time units.

Just don't look up http://en.wikipedia.org/wiki/Tetration and all will be well.

BobD

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Joined: 07/12/2011
Location: Australia
Posts: 935

Posted: 09:54am 25 Apr 2015

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You mentioned it, I couldn't resist, I read the lot, and I am now more deranged than ever.

JohnS
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Joined: 18/11/2011
Location: United Kingdom
Posts: 4038

Posted: 03:19am 26 Apr 2015

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Dylan said There are two reasons to.

1) Computer Science 2^(2^5) = 2^32 = maximum memory for a 32-bit OS, for example.

2) Physical sciences (2^t)^(1/3) = volume of something doubling every t time units.

Just don't look up http://en.wikipedia.org/wiki/Tetration and all will be well.

For sure I've quite often used 2^32 one way or another, just never written it using a (to me pointless) double exponentiation.

John

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