numbers near machine precision

• To: mathgroup at smc.vnet.net
• Subject: [mg47049] numbers near machine precision
• From: Steve Story <sbstory at ncsu.edu>
• Date: Mon, 22 Mar 2004 00:15:01 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```I'm in a numerical methods class, and having difficulty adapting the
subroutines to Mathematica. For one thing, it seems that the == operator
will pronounce two numbers equal when they're much further apart than
machine epsilon.

And I don't understand why this is, but it's easy to work around for the
routines I'm using. A bigger problem, however, is that when I try to
look at a machine-precise number in different number systems, sometimes
Mathematica says they're identical, sometimes not. And I can't find a
Here's an example which I can't explain. In the first case, they're not
identical, in the second, they are:

In[132]:=
RealDigits[{a,b},2]

Out[132]=
{{{1,0,0,1,0,0,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,0,

1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0},2},{{1,0,0,1,0,0,0,1,1,0,1,1,1,1,1,0,1,

0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,
1},2}}

In[135]:=
RealDigits[{a,b},16]

Out[135]=
{{{2,4,6,15,10,5,2,9,15,13,11,3,3},1},{{2,4,6,15,10,5,2,9,15,13,11,3,3},1}}

I don't understand why those things are happening in Mathematica. If anyone
could point me to a deep discussion of these topics in Mathematica, I'd
appreciate it.

thanks,
Steve Story

```

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