Re: [pure-lang-users] ln

[Albert G. <Dr....@t-...>]

Eddie Rucker wrote:
> Yes, ln x -> -inf as x -> 0.

Errm, of course I meant that ln x -> -inf as x -> +0.

Oh well. I see no merit in fighting the standard there, it seems to be 
well-thought out after all, and backed up by substantial mathematical 
theory to make sure that it all makes sense, in a twisted way.

> But x aint zero here, it is something close to zero. If you look at Ln x in the complex plain, the y-
> axis is an asymptote and hence Ln 0 has no value at all i.e. undefined.

That's why IEEE 754 distinguishes between positive and negative zero. So 
the C log() function can return -inf for +0.0 and nan for -0.0 (at least 
that's what Goldberg's IEEE 754 paper suggests). Moreover, the C99 
clog() function is supposed to return clog(z) = log(cabs(z)) + i * 
carg(z), and that's exactly how math.pure implements the complex ln 
function as well. So Pure's ln function should work properly to the 
extent that the C log() function does.

Unfortunately, on my Linux system both c_log (1/inf) and c_log (1/-inf) 
return -inf in Pure, even though Pure correctly displays 1/inf as 0.0 
and 1/-inf as -0.0. So it seems that the glibc log() function at least 
does *not* distinguish between positive and negative zero. Maybe that's 
a non-conformance in glibc, I'll have to check POSIX to see whether it 
has something to say about log(-0.0).

Cheers,
Albert

-- 
Dr. Albert Gr"af
Dept. of Music-Informatics, University of Mainz, Germany
Email:  Dr....@t-..., ag...@mu...
WWW:    http://www.musikinformatik.uni-mainz.de/ag