Re: Problem with base 2 logs and Floor
- To: mathgroup at smc.vnet.net
- Subject: [mg73014] Re: Problem with base 2 logs and Floor
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Mon, 29 Jan 2007 04:11:33 -0500 (EST)
- Organization: The University of Western Australia
- References: <ephdk1$s2c$1@smc.vnet.net>
In article <ephdk1$s2c$1 at smc.vnet.net>, neillclift 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.
Actually, you get precision _warnings_, not errors.
> 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?
Use FullSimplify:
r - Floor[Log[2, r]] - 1 /. r -> 8 // FullSimplify
4
Alternatively, if r == 2^n, then simplify in general:
FullSimplify[r - Ceiling[Log[2, r]] - 1 /.
r -> 2^n, Element[n, Integers]]
-1 + 2^n - n
Cheers,
Paul
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