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Topic: Low precision exponentiation
Replies: 5   Last Post: Feb 18, 2013 6:00 AM

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Albert Retey

Posts: 688
Registered: 7/15/08
Re: Low precision exponentiation
Posted: Feb 18, 2013 5:59 AM
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Hi,

> I am trying to evaluate 2.5^125 to high precision.
>
> R gives 5.527147875260445183346e+49 as the answer but Mathematica
> with N[2.5^125,30] gives 5.52715*10^49 and says that is to machine
> precision.


There are two problems here:

1) with the standard settings, Mathematica will print only 6 digits of
machine precision numbers. You can change that in the preferences tab or
with e.g.:

NumberForm[2.5^125, {16, 16}]

2) the input you are giving is interpreted to be machine precision in
the first place. You can get an exact result like this:

(5/2)^125

and a numeric result to the desired precision like this:

N[(5/2)^125,50]

alternatively you can define the precision with this syntax:

2.5`50^125

> I am inexperienced at Mathematica. Am I doing something silly?

yes and no, Mathematica handles arbitrary precision numbers in a
somewhat unusual way. You might want to read the tutorials that are
linked to the documentation of N to learn about some details. On the
other hand, I think usually you can get away with the rule that one
should try to stay with exact results as long as possible when
requesting more than machine precision...

hth,

albert






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