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Re: Mathematica bugs?

• To: mathgroup at smc.vnet.net
• Subject: [mg67326] Re: Mathematica bugs?
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Sun, 18 Jun 2006 05:13:23 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On 6/17/06 at 4:36 AM, yaroslavvb at gmail.com (Yaroslav Bulatov) wrote:

>When I run the following line x = Pi/4; For[i = 0, i < 56, i += 1, x
>= 2*Abs[x - 1/2]]; N[x] I get 3.

>But x should always stay between 0 and 1, why do I get 3?

>Also x = Pi/4; For[i = 0, i < 50, i += 1, x = 2*Abs[x - 1/2]];
>N[Log[x]] gives me Indeterminate

>How can I get an indeterminate here?

The answer to both questions is loss of precision.

Note,

In[14]:=
x=Pi/4;For[i=0,i<56,i+=1,x=2*Abs[x-1/2]]

In[15]:=
x//FullSimplify

Out[15]=
56593902016227523-18014398509481984 Ï?

That is x is the difference between two large numbers.

In[16]:=
N[x,20]

Out[16]=
0.79387245267980382900

In[17]:=
%%//N

Out[17]=
0.

And finally the same computation is done more efficiently as

Nest[2 Abs[x-1/2]&, Pi/4, 55]//FullSimplify
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