Understanding N and Precision
- To: mathgroup at smc.vnet.net
- Subject: [mg71147] Understanding N and Precision
- From: Alain Cochard <alain at geophysik.uni-muenchen.de>
- Date: Thu, 9 Nov 2006 03:38:25 -0500 (EST)
- Reply-to: alain at geophysik.uni-muenchen.de
Hi. I would like to understand the following behavior:
Mathematica 5.2 for Linux
Copyright 1988-2005 Wolfram Research, Inc.
-- Motif graphics initialized --
In[1]:= MatrixForm[{{exact1=Cos[3Pi/2+Pi/7], Precision[exact1]}, \
{exact2=Cos[40139127975 Pi/14], Precision[exact2]}}]
Out[1]//MatrixForm= 23 Pi
Cos[-----]
14 Infinity
40139127975 Pi
Cos[--------------]
14 Infinity
just checking:
In[2]:= FullSimplify[exact1-exact2]
Out[2]= 0
In[3]:= MatrixForm[{{float1=N[exact1], Precision[float1]},\
{float2=N[exact2], Precision[float2]}}]
Out[3]//MatrixForm= 0.433884 MachinePrecision
0.433883 MachinePrecision
So the N of supposedly(?) 2 identical numbers is different (although
the precision is indeed the same). That's what I would like to
understand most.
Also, if I specify the precision for N, it now gives the same. E.g.:
In[4]:= MatrixForm[{{float1=N[exact1,3], Precision[float1]},\
{float2=N[exact2,3], Precision[float2]}}]
Out[4]//MatrixForm= 0.434 3.
0.434 3.
including the case where the precision asked is MachinePrecision:
In[5]:= MatrixForm[{{float1=N[exact1,$MachinePrecision], Precision[float1]},\
{float2=N[exact2,$MachinePrecision], Precision[float2]}}]
Out[5]//MatrixForm= 0.4338837391175581 15.9546
0.4338837391175581 15.9546
Why in this case does it gives a precision of "15.9546" and not
"MachinePrecision", as above, especially since
In[6]:= N[$MachinePrecision,Infinity]
Out[6]:= 15.9546
Isn't N[x] equivalent to N[x,$MachinePrecision]?
Thanks in advance for any tip.
Alain
- Follow-Ups:
- Re: Understanding N and Precision
- From: Carl Woll <carlw@wolfram.com>
- Re: Understanding N and Precision
- From: "Chris Chiasson" <chris@chiasson.name>
- Re: Understanding N and Precision
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Re: Understanding N and Precision