[Python-ideas] checking for identity before comparing built-in objects

[Steven D'Aprano]

On 09/10/12 11:32, Oscar Benjamin wrote:

> The main purpose of quiet NaNs is to propagate through computation
> ruining everything they touch. In a programming language like C that
> lacks exceptions this is important as it allows you to avoid checking
> all the time for invalid values, whilst still being able to know if
> the end result of your computation was ever affected by an invalid
> numerical operation.

Correct, but I'd like to point out that NaNs are a bit more
sophisticated than just "numeric contagion".

1) NaNs carry payload, so you can actually identify what sort of
calculation failed. E.g. NaN-27 might mean "logarithm of a negative
number", while NaN-95 might be "inverse trig function domain error".
Any calculation involving a single NaN is supposed to propagate the
same payload, so at the end of the calculation you can see that you
tried to take the log of a negative number and debug accordingly.


2) On rare occasions, NaNs can validly disappear from a calculation,
leaving you with a non-NaN answer. The rule is, if you can replace
the NaN with *any* other value, and still get the same result, then
the NaN is irrelevant and can be consumed. William Kahan gives an
example:

     For example, 0*NaN must be NaN because 0*∞ is an INVALID
     operation (NaN). On the other hand, for hypot(x, y) :=
     √(x*x + y*y) we find that hypot(∞, y) = +∞ for all real y,
     finite or not, and deduce that hypot(∞, NaN) = +∞ too;
     naive implementations of hypot may do differently.

Page 7 of http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF



-- 
Steven