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

Tim Peters tim.peters at gmail.com
Fri Oct 12 21:42:34 CEST 2012 
[Mark Dickinson]
> ...
> And as for sqrt(-0.0) returning -0.0...  Grr.  I've never understood
> the motivation for that one, especially as it disagrees with the usual
> recommendations for complex square root (where the real part of the
> result *always* has its sign bit cleared).

The only rationale I've seen for this is in Kahan's obscure paper
"Branch Cuts for Complex Elementary Functions or Much Ado About
Nothing's Sign Bit".  Hard to find.  Here's a mostly readable scan:

http://port70.net/~nsz/articles/float/kahan_branch_cuts_complex_elementary_functions_1987.pdf

In part it's to preserve various identities, such as that
sqrt(conjugate(z)) is the same as conjugate(sqrt(z)).  When z is +0,
that becomes

    sqrt(conjugate(+0)) same_as conjugate(sqrt(+0))

which is

    sqrt(-0) same_as conjugate(+0)

which is

    sqrt(-0) same as -0

Conviced?  LOL.  There are others in the paper ;-)
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