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Re[2]: Low precision exponentiation
Posted:
Feb 18, 2013 6:00 AM
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Thanks to all the nice people who took the time to explain it to a
newbie.
Best wishes
Blaise
------ Original Message ------
From: "Murray Eisenberg" <murray@math.umass.edu>
To: "mathgroup" <mathgroup@smc.vnet.net>
Sent: 17/02/2013 16:24:08
Subject: Re: Low precision exponentiation
>You are not doing anything "silly"; you're just being caught by two common traps for Mathematica beginners.
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>First, by default Mathematica treats 2.5 as a machine-precision number; no matter what you do with it as is, you won't get any more than machine-precision as result. You need to specify you mean exactly that number, to the desired precision, e.g.:
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> 2.5`30
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>Second, no matter what the precision of a number, by default Mathematica only _displays_ 6 significant digits. To get more digits, use NumberForm (or depending on the format you want, perhaps ScientificForm, EngineeringForm, or AccountingForm), with second argument the number of digits to display.
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>Thus:
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> NumberForm[N[2.5`30^125, 30], 30]
>5.527147875260444560247265192*10^(49)
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>Actually, in such an example you probably want to be more careful, since the calculation may lose precision. In fact:
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> Precision[N[2.5`30^125, 30]]
>27.9031
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>You've lost 2 to 3 digits of precision. So just increase the precision in the calculation:
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> Precision[N[2.5`40^125, 40]]
>37.9031
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>Which means that when you display 30 digits of N[2.5`40^125, 40] with NumberForm, all 30 digits will be correct.
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>On Feb 17, 2013, at 4:08 AM, Blaise F Egan <blaise@blaisefegan.me.uk> wrote:
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>
>>
>>I am trying to evaluate 2.5^125 to high precision.
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>>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.
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>>I am inexperienced at Mathematica. Am I doing something silly?
>>
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>---
>Murray Eisenberg murray@math.umass.edu
>Mathematics & Statistics Dept.
>Lederle Graduate Research Tower phone 413 549-1020 (H)
>University of Massachusetts 413 545-2838 (W)
>710 North Pleasant Street fax 413 545-1801
>Amherst, MA 01003-9305
>
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