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

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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