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Re: Low precision exponentiation
Posted:
Feb 18, 2013 5:59 AM


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



