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RE: Very odd behaviour in Mod/
I would like to be able to do the following:
In[17]:= t = Mod[Q, 2 Pi]
Out[17]= 1000000000000000000  318309886183790670 Pi
In[18]:= N[t,3]
Out[18]= 4.83677
Where the correct value is:
4.831039164951128133.......
If you want to be sure even a few digits are right, you can currently
use N[t,17].
Then Mathematica will go to all the trouble to get 17 digits correct,
when you only care about a few of them.
Ted Ersek

From: "megalith"@jimc.demon.co.uk@PMDF@PAXMB1 To:
mathgroup@smc.vnet.net
To: ersek ted; "mathgroup"@smc.vnet.net@PMDF@PAXMB1 Subject: [mg12133] [mg12048]
Very odd behaviour in Mod/N Date: Friday, April 24, 1998 8:57AM 
<<File Attachment: 00000000.TXT>>
Hi there,
I've observed some very odd behaviour when using Mod and N. It seems
that, when handling very large numbers, Mathematica (3.0.1, Win32)
does not display machineprecision results correctly. Here's an
example which behaves as it should:

In[12]:= Q = 10^8
Out[12]= 100000000

In[13]:= t = Mod[Q, 2 Pi]
Out[13]= 100000000  31830988 Pi

In[14]:= N[t]
Out[14]= 1.9427

In[15]:= N[t, 20]
Out[15]= 1.9426951345040144600

Now for a very similar example which obviously behaves wrongly: 
In[16]:= Q = 10^18
Out[16]= 1000000000000000000

In[17]:= t = Mod[Q, 2 Pi]
Out[17]= 1000000000000000000  318309886183790670 Pi 
In[18]:= N[t]
Out[18]= 128.

In[19]:= N[t, 20]
Out[19]= 4.831039164951128133

What exactly is going on here?

Thanks, cheers,
Adrian Cable.

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What kind of math problem is this?
 