sorting performance - need help with math

im doing research on sorting algorithms. i have 2 articles about radix sort. one says radix sort is O(n), in other words linear. the other says it is only linear if the wordsize of the computer(32 or 64 nowadays) is >= log n, otherwize it its O(n log n). isnt log 1,000,000 only 6?

even if they mean log base 2, 2^32 is a huge number
ps: the second article introduces an algorithm with O(n log log n)
[ April 18, 2004: Message edited by: Randall Twede ]

Originally posted by Randall Twede:
even if they mean log base 2, 2^32 is a huge number

About 4 Billion, in fact.
However, some people deal with data sets larger than that.

ok, so for normal folks it would be linear. i get the idea though.

im really getting into this research, it's cool!
i should have known it was base 2 but i think in my paper i use subscript to make it clear

[ April 18, 2004: Message edited by: Randall Twede ]

Side note, lg is a common representation for log base 2.

another note: log is used to mean base 2 in all applications except computing (for some reason) unless a base is specified.
log base e is generally written as ln.
So possibly the authors meant log base 2.

Um, in applications outside computing, log usually means base 10. In my experience at least. Perhaps it's different in Europe? I doubt it - outside of computing, base 2 just isn't as useful to most people as base 10 is. Errr, was. The main motivation for using logs was as a faster replacement for multiplication, back in the dark ages before calculators and computers. This is easiest if you use logs base 10, to match our number system.

As a former math teacher, log always meant base 10. And Jim, it still is quite relevant - It's how my slide rule works. You know what a slide rule is, right?

Sure. I found an old one once, wouldn't rest until I'd figured out how to use it. (Including the trig functions). Never actually used it in real life though.

sorry, meant base 10