[Python-Dev] Controversial patch (cmath)

[Tim Peters]

I just voted to accept a patch that's broken.  If you want to argue it, be
my guest, but I'm out of it now <wink>.

Here's the patch:

https://sourceforge.net/patch/?func=detailpatch&patch_id=100651&group_id=547
0

Here's my comment (also available on that page):

Accepted (but reluctantly; see below), and assigned back to Guido for
checkin.

cmathmodule is not production quality, and this patch isn't either, but its
asinh and acosh are better than what's there now.

The author avoided some of the numerical foolishness in the original, but
didn't avoid all of it.  For example, it's harder to get asinh to do
something ridiculous now than it was before, but still possible:

>>> cmath.acosh(1e200)
(461.210165779+0j)
>>> cmath.asinh(1e200)
(1.#INF+0j)
>>>

asinh should have returned something approximately equal to what acosh
returned.

That may not be the patch's problem, though!  I suspect that's due to one of
the module's other functions that's too naive about the limits of floating
point.  In any case, it is much easier to provoke the *current* cmath
functions into cases like this one.

Another possible problem has to do with principal values.  My reference
books are in storage, so about the best I can do right now is compare what
this code does to Macsyma (which I have on my laptop).  The acosh in this
patch often returns the negative of what Macysma computes.  For example,

>>> cmath.acosh(-1-1j)
(1.06127506191-2.23703575929j)
>>>

Macsyma returns the negation of that.  On the other hand, the *original*
acosh doesn't agree with Macsyma on some signs where this acosh does.  So
call this one a wash.

I may have mentioned this before <wink>:  robust math libraries are
extremely difficult to get right.  It would take several months to write a
production-quality cmath module from scratch, which is several months more
than were devoted to Python's current cmath <wink>.  I vote we check this in
anyway (since it *is*, overall, an improvement), and look into borrowing
some other language's complex math library later (note in particular that
C9X adds complex numbers and these functions on them, so if we sit on our
asses long enough, we can inherit libc's!).