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MathGroup Archive 2007

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Re: Problem with base 2 logs and Floor

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73022] Re: Problem with base 2 logs and Floor
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Mon, 29 Jan 2007 04:43:39 -0500 (EST)
  • References: <ephdk1$s2c$1@smc.vnet.net>

Something like?

Block[{Message}, r - Floor[Log[2, r]] - 1 /. r -> 4]
FullSimplify[%]

3 - Floor[Log[4]/Log[2]]
1

Block[{Message}, r - Ceiling[Log[2, r]] - 1 /. r -> 4]
FullSimplify[%]

3 - Ceiling[Log[4]/Log[2]]
1

Block[{Message}, r - Floor[Log[2, r]] - 1 /. r -> 8]
FullSimplify[%]

7 - Floor[Log[8]/Log[2]]
4

Block[{Message}, r - Ceiling[Log[2, r]] - 1 /. r -> 8]
FullSimplify[%]

7 - Ceiling[Log[8]/Log[2]]
4

Dimitris

On Jan 28, 7:50 am, neillcl... at msn.com wrote:
> 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.


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