[Tim Peters] ... >> Across platforms with a 754-conforming libm, the most portable way [to >> distinguish +0.0 from -0.0 in standard C] is via using atan2(!): >> >> >>> pz = 0.0 >> >>> mz = -pz >> >>> from math import atan2 >> >>> atan2(pz, pz) >> 0.0 >> >>> atan2(mz, mz) >> -3.1415926535897931
[Ivan Van Laningham] > Never fails. Tim, you gave me the best laugh of the day. 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. 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. 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 ... -- http://mail.python.org/mailman/listinfo/python-list
