New submission from Mark Dickinson <dicki...@gmail.com>: For floats x and y, x ** y and math.pow(x, y) mostly agree. There are three points of difference:
1. if x is finite and negative and y is finite and non-integral, then x ** y returns a complex number, while math.pow(x, y) raises ValueError 2. for cases where x ** y raises ZeroDivisionError (for example, 0.0 ** -1.0), math.pow(x, y) raises ValueError instead 3. the special cases 0.0 ** -inf and (-0.0) ** -inf return inf, but the equivalent math.pow calls raise ValueError That third discrepancy is a surprising one: in particular, it's the only case where math.pow does not follow IEEE 754 rules. Note that the math.pow behaviour is not accidental. The special cases were based on C99 Annex F (and are documented to do so), but the standards themselves have evolved here. In chronological order: - IEEE 754-1985 did not cover transcendental functions, so has nothing to say on the topic of special values for pow. - C99 §F.9.4.4 implies that pow(0, -inf) should raise the "divide-by-zero" exception; the relevant clause covers pow(0, y) for any y satisfying y < 0 and y not an odd integer - IEEE 754-2008 §9.2.1 has an explicit clause specifying that pow(0, -inf) should be inf and that the operation does not raise any exception. - C11 §F.10.4.4 mentions the case pow(0, -inf) explicitly and now says "may raise the divide-by-zero floating-point exception". The "may" is significant: other clauses simply say "raises the "divide-by-zero" floating-point exception". - IEEE 754-2019 §9.2.1 is unchanged from IEEE 754-2008 for this particular special case. - Similarly, C17 is unchanged from C11 in this respect. For Python 3.11, I propose changing the behaviour of math.pow in this corner case so that it returns inf instead of raising. This would make math.pow conformant with IEEE 754, consistent with C11 and later, and consistent with the built-in pow function. ---------- messages: 395277 nosy: mark.dickinson priority: normal severity: normal status: open title: Discrepancy between math.pow(0.0, -inf) and 0.0**-inf versions: Python 3.11 _______________________________________ Python tracker <rep...@bugs.python.org> <https://bugs.python.org/issue44339> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: https://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com
