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

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 Bill Rowe Posts: 1,647 Registered: 3/14/08
Re: Low precision exponentiation
Posted: Feb 18, 2013 5:59 AM

On 2/17/13 at 4:08 AM, blaise@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[1]:= a = N[2.5^125, 30]

Out[1]= 5.52715*10^49

In[2]:= FullForm[a]

Out[2]//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[3]:= Precision[a]

Out[3]= MachinePrecision

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

Try

In[4]:= b = N[(5/2)^125, 30]

Out[4]= 5.52714787526044456024726519219*10^49

In[5]:= Precision[b]

Out[5]= 30.

Date Subject Author
2/17/13 Blaise F Egan
2/18/13 Albert Retey
2/18/13 Bill Rowe
2/18/13 Tom D
2/18/13 svkeeley@aol.com