On Thu, 23 Jun 2005 00:11:20 -0400, Tim Peters wrote: > Well, I try, Ivan. But lest the point be missed <wink>, 754 doesn't > _want_ +0 and -0 to act differently in "almost any" way. The only > good rationale I've seen for why it makes the distinction at all is in > Kahan's paper "Branch Cuts for Complex > Elementary Functions, or Much Ado About Nothing's Sign Bit". There > are examples in that where, when working with complex numbers, you can > easily stumble into getting real-world dead-wrong results if there's > only one flavor of 0. And, of course, atan2 exists primarily to help > convert complex numbers from rectangular to polar form.
It isn't necessary to look at complex numbers to see the difference between positive and negative zero. Just look at a graph of y=1/x. In particular, look at the behaviour of the graph around x=0. Now tell me that the sign of zero doesn't make a difference. Signed zeroes also preserve 1/(1/x) == x for all x, admittedly at the cost of y==x iff 1/y == 1/x (which fails for y=-0 and x=+0). Technically, -0 and +0 are not the same (for some definition of "technically"); but practicality beats purity and it is more useful to have -0==+0 than the alternative. > Odd bit o' trivia: following "the rules" for signed zeroes in 754 > makes exponeniation c**n ambiguous, where c is a complex number with > c.real == c.imag == 0.0 (but the zeroes may be signed), and n is a > positive integer. The signs on the zeroes coming out can depend on > the exact order in which multiplications are performed, because the > underlying multiplication isn't associative despite that it's exact. That's an implementation failure. Mathematically, the sign of 0**n should depend only on whether n is odd or even. If c**n is ambiguous, then that's a bug in the implementation, not the standard. > I stumbled into this in the 80's when KSR's Fortran compiler failed a > federal conformance test, precisely because the test did atan2 on the > components of an all-zero complex raised to an integer power, and I > had written one of the few 754-conforming libms at the time. They > wanted 0, while my atan2 dutifully returned -pi. I haven't had much > personal love for 754 esoterica since then ... Sounds to me that the Feds wanted something broken and you gave them something that was working. No wonder they failed you :-) -- Steven. -- http://mail.python.org/mailman/listinfo/python-list
