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.'"
> 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
I think the only exception are the operations involving infinity. The
likely rationale is that since infinity is not produced by python
arithmetics, those who use inf are likely to expect inf*0 etc. to
produce nan.
The following seems to be an oversight:
>>> 1e300 * 1e300
inf
compared to
>>> 1e300 ** 2
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
OverflowError: (34, 'Result too large')
[1] http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps
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