       Re: Low precision exponentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg129839] Re: Low precision exponentiation
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Mon, 18 Feb 2013 06:00:23 -0500 (EST)
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```On 2/17/13 at 4:08 AM, blaise at blaisefegan.me.uk (Blaise F Egan)
wrote:

>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.

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

A couple of things. First, you need to be aware by default
Mathematica displays 6 digits. But the actual result has more
digits. You can see this with

In:= a = N[2.5^125, 30]

Out= 5.52715*10^49

In:= FullForm[a]

Out//FullForm= 5.527147875260444`*^49

Second, 2.5 is a machine precision number with ~16 digits of
precision. You should not expect to be able to get 30 digits of
precision when taking a value with less precision and raising it
to a high power. If you want the value to have 30 digits of
than machine precision to begin with. That is

In:= Precision[a]

Out= MachinePrecision

The result is a machine precision value not a value with 30
digits of precision

Try

In:= b = N[(5/2)^125, 30]

Out= 5.52714787526044456024726519219*10^49

In:= Precision[b]

Out= 30.

```

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