On Fri, Apr 29, 2011 at 11:35, Alexander Belopolsky <alexander.belopol...@gmail.com> wrote: > On Fri, Apr 29, 2011 at 11:31 AM, Robert Kern <robert.k...@gmail.com> wrote: > .. >> And in fact, 0.0/0.0 is covered by the more general rule that x/0.0 raises >> ZeroDivisionError, not a rule that converts IEEE-754 INVALID exceptions into >> Python exceptions. > > It is unfortunate that official text of IEEE-754 is not freely > available and as a result a lot of discussion in this thread is based > on imperfect information. > > I find Kahan's "Lecture Notes on the Status of IEEE Standard 754 for > Binary Floating-Point Arithmetic" [1] a reasonable reference in the > absence of the official text. According to Kahan's notes, INVALID > operation is defined as follows: > > """ > Exception: INVALID operation. > > Signaled by the raising of the INVALID flag whenever an operation's > operands lie outside its domain, this exception's default, delivered > only because any other real or infinite value would most likely cause > worse confusion, is NaN , which means “ Not a Number.” IEEE 754 > specifies that seven invalid arithmetic operations shall deliver a NaN > unless they are trapped: > > real √(Negative) , 0*∞ , 0.0/0.0 , ∞/∞, > REMAINDER(Anything, 0.0) , REMAINDER( ∞, Anything) , > ∞ - ∞ when signs agree (but ∞ + ∞ = ∞ when signs agree). > > Conversion from floating-point to other formats can be INVALID too, if > their limits are violated, even if no NaN can be delivered. > """ > > In contrast, Kahan describes DIVIDE by ZERO exception as "a misnomer > perpetrated for historical reasons. A better name for this exception > is 'Infinite result computed Exactly from Finite operands.'"
Nonetheless, the reason that *Python* raises a ZeroDivisionError is because it checks that the divisor is 0.0, not because 0.0/0.0 would issue an INVALID signal. I didn't mean that 0.0/0.0 is a "Division by Zero" error as defined in IEEE-754. This is another area where Python ignores the INVALID signal and does its own thing. >> Other operations that produce a NaN and issue an IEEE-754 >> INVALID signal do not raise a Python exception. > > Some do: > >>>> math.sqrt(-1) > Traceback (most recent call last): > File "<stdin>", line 1, in <module> > ValueError: math domain error Right. Elsewhere I gave a more exhaustive list including this one. The other is int(nan), though that becomes a Python exception for a more fundamental reason (there is no integer value that can represent it) than that the IEEE-754 standard specifies that the operation should signal INVALID. Arithmetic operations on signalling NaNs don't raise an exception either. These are the minority *exceptions* to the majority of cases where operations on Python floats that would issue an INVALID signal do not raise Python exceptions. If you want to lump all of the inf-related cases together, that's fine, but arithmetic operations on signalling NaNs and comparisons with NaNs form two more groups of INVALID operations that do not raise Python exceptions. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco _______________________________________________ Python-Dev mailing list Python-Dev@python.org http://mail.python.org/mailman/listinfo/python-dev Unsubscribe: http://mail.python.org/mailman/options/python-dev/archive%40mail-archive.com
