From: ptkwt@... (Phil Tomson)
Date: 2004-09-04T05:05:17+09:00
Subject: Re: Math.log2 ?

In article <4138BC17.1030307@ieee.org>,
Steven Jenkins  <steven.jenkins@ieee.org> wrote:
>Brian Schroeder wrote:
>> That is interesting enough. Anybody here would like to explain to me, why
>> log_2 is harder than log_10 or ln. I just assumed that anything binary
>> would be nice for computers.
>
>It's neither harder nor easier, it's just not that useful. Base 2 
>logarithms aren't really needed in most math and engineering. Even in 
>computer science and information theory, where the base 2 log is an 
>important analytical concept, it's rarely employed in precision 
>calculations. Those are not the kind of problems you attack with 
>numerical methods.
>
>It takes a lot of care and skill to develop a math library; much more 
>than naively coding power series expansions of transcendental functions. 
>People tend to put that work where it's really needed.
>
>The good news is that for most purposes in computer science,
>
>log2(x) = ln(x) / ln(2)
>
>is plenty precise. :-) Note that ln(2) is a constant.


I do occassionally need Log base 2 operations.  Mostly I need to figure 
out how many bits are needed to represent some range (for example, given a 
range of 0 to 7, I need a 3 bit counter) in a hardware representation.  I 
also ran into a need for log2 when I was doing some Karnaugh map 
manipulations for a class project I did last quarter.

You're right though, I don't need any sort of precision for these 
applications,  integers only:

log2(2) => 1
log2(3) => 2 (it's actually something like 1.5849, apply ceiling op)
log2(4) => 2
log2(5) => 3
log2(6) => 3
log2(7) => 3
log2(8) => 3
log2(9) => 4
.....

As I recall, since I only needed up log2(32) (5 bits), and since it needed 
to be as fast as possible, I just defined my own method that uses a case 
statement to 'lookup' the desired value.


Phil