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Problem with base 2 logs and Floor

• To: mathgroup at smc.vnet.net
• Subject: [mg73001] Problem with base 2 logs and Floor
• From: neillclift at msn.com
• Date: Sun, 28 Jan 2007 01:11:55 -0500 (EST)

Hi,

When I use an expression like this:

r - Floor[Log[2, r]] - 1 /. r -> 4

I get precision errors in Mathematica 5.2. If I use an expression like 
this:

N[r - Floor[Log[2, r]] - 1] /. r -> 4

I get a correct result of 1 and no errors. If I use an expression like 
this I get the same result:

N[r - Ceiling[Log[2, r]] - 1] /. r -> 4

This is to be expected as Floor[Log[2, r]]  = Ceiling[Log[2, r]]  when 
r is a power of two.
Unfortunatly the expessions diverge for r=8:

N[r - Floor[Log[2, r]] - 1] /. r -> 8 gives 5
N[r - Ceiling[Log[2, r]] - 1] /. r -> 8 gives 4

How can I get exacts results for expessions like this?
Thanks.
Neill.

• Follow-Ups:
  • Re: Problem with base 2 logs and Floor
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>