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Very odd behaviour in Mod/N

To: mathgroup@smc.vnet.net
Subject: [mg12048] Very odd behaviour in Mod/N
From: Adrian Cable <megalith@jimc.demon.co.uk>
Date: Fri, 24 Apr 1998 01:52:19 -0400
Organization: MeGALiTH Software Ltd

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 machine-precision 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.

Follow-Ups:
- Re: Very odd behaviour in Mod/N
  - From: Daniel Lichtblau <danl@wolfram.com>

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