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Re: Low precision exponentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg129838] Re: Low precision exponentiation
• From: awnl <awnl at gmx-topmail.de>
• Date: Mon, 18 Feb 2013 06:00:03 -0500 (EST)
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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