Newsgroups: comp.compression
Path: utzoo!utgpu!cunews!dfs
From: dfs@doe.carleton.ca (David F. Skoll)
Subject: Re: IP gnitaluclaC rof margorP (Was Re: Program for Calculating PI)
Message-ID: <dfs.671466494@crusher>
Sender: news@ccs.carleton.ca (news)
Organization: Carleton University, Ottawa, Canada
References: <28916@dime.cs.umass.edu> <24380001@hpdmd48.boi.hp.com> 	<JPC.91Apr9141953@alfa.fct.unl.pt> <OTTO.91Apr9211427@tukki.jyu.fi> <1991Apr11.022122.26142@garfield.cs.mun.ca>
Date: 12 Apr 91 14:28:14 GMT

In <1991Apr11.022122.26142@garfield.cs.mun.ca> matthew1@garfield.cs.mun.ca
(Matthew J. Newhook) writes:

>I'd be inclined to say that you can compress pi by a considerable amount.

>Ok... Assume 8 bits per byte.  Storing, say, 1000 digits of pi would therefore
>take up 8008 bits (1000 * 8 + 1 * 8, for the . in 3.14...).
>Since we only get characters from 0-9 ignoring the . then we can encode
>any digit in 4 bits.  Like so...

So, you're expressing Pi in BCD?  Why not go whole hog and express it in
straight binary, thus using somewhat under 4 bits per digit.

But Pi is obviously immensely compressible - write a program to compute it
to any desired accuracy.  The length of such a program will be much less
than the length of the closest approximation to Pi that it can compute on
a decent computer.

The whole issue of maximum compression possible is a very sticky one.
Assuming that (for some reason!) you transmit Pi very (very!) often.
Just make your compressors and decompressors very smart about
generating Pi, use a Huffman code, and you can compress Pi down to 1
bit. (And that's about as good as it gets! :-))

--
David F. Skoll
