Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0

[John Cowan <cowan@x>]

Sascha Ziemann scripsit:
> 2012/12/14 John Cowan <cowan@x>:
> >> For example, this reversal means that (max 1.0+0.0i 1.0-0.0i) is
> >> permitted, and the result is no longer uniquely determined.
> >> What should the result be?
> >
> > I'd say it's correct to return either one, since they are =.
> 
> Wolfram thinks it is neither the first nor the second:
> 
> http://www.wolframalpha.com/input/?i=max+%281.0%2B0.0i%2C+1.0-0.0i%29

Wolfram, like Common Lisp, takes a structural view of complex numbers:
a number is complex just in case it has an imaginary part.  In Scheme,
complex numbers subsume real ones, but the answers of different Scheme
standards have varied when the imaginary part is an inexact zero.
R5RS and R7RS say such a number is real, R6RS (and Pure, which shares
Scheme's numeric tower) say it is not.

A similar question is what to do when the inexact arguments of `max`
have different precisions.  In CL, there is a rule of precision contagion
such that (max 0.0d0 0.0f0) must return 0.0d0.  In Scheme there is no
such rule (though it is required that when a number is converted from
exact to inexact because the exact system can't represent it, it gets
the highest available precision), and it seems to me that either 0.0d0 or
0.0f0 is a valid answer.  Racket is one of the few Schemes that supports
32-bit floats, and it returns 0.0d0 (printed as 0.0) in this case.

-- 
I marvel at the creature: so secret and         John Cowan
so sly as he is, to come sporting in the pool   cowan@x
before our very window.  Does he think that     http://www.ccil.org/~cowan
Men sleep without watch all night?

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