Jon Lang wrote: > Moritz Lenz wrote: >> Jon Lang wrote: >>> By the principle of least surprise, I'd recommend against this. Most >>> programmers, when they see 'sqrt(1)', will expect a return value of 1, >> >> And that's what they get unless they write it as sqrt(1 + 0i). > > I suppose that you _could_ use the programmer's choice of whether or > not to use complex numbers in the argument list as the indicator of > whether to return one answer or a junction of them. Of course, this > could lead to subtle bugs where the programmer assigns a complex value > to $x and later takes the sqrt($x), but forgets that he assigned a > complex number earlier. This may or may not be sufficient grounds for > requiring an explicit declaration that you want junctions.

## Advertising

If the programmer errs on what he thinks is in a variable, it'll always be a bug. >>> and won't want to jump through the hurdles involved in picking '1' out >>> of 'any(1, -1)'. >> >> 1 and -1 aren't just separated by a complex plane, they are really >> distinct numbers > > True enough. I fail to see how that invalidates my point, though: if > you're going to mess with multiple complex planes, why wouldn't you > also address the issue of distinct numbers as well? Principle of least surprise: Suppose sqrt(1) returns any(1, -1): if sqrt($x) < 0.5 { do something } I can see the big, fat WTF written in the face of programmer who tries to debug that code, and doesn't know about junctions. It just won't DTRT. > The latter issue > is intimately connected to the former, as I demonstrate below. > >>> And even then, I'm concerned that it might very quickly get out of >>> hand. Consider: >>> >>> pow(1, 1/pi() ) :any - 1 >>> >>> (I think I got that right...) >> >> Not quite. Afaict the only functions that might return a junction are >> Complex.angle and Complex.log. > > Why is that? As I pointed out above it's insane to return a junction of logically distinct values. It might even be insane to do it for Complex.log: my $a = (Num::e * 1i).log.angle; What do you expect $a to be? Let's see, 1i can be written as exp(1i*(1/2 + 2 *$k) * pi), for Int $k. So log(Nom::e * 1i) would 1 + any(..., -1.5 * pi, 0.5 * pi, 2.5 * pi, 4.5*pi)*1i if you imagine this, all these values have re = 1, and lie on a straight line. So their angle are discrete (but not dense) values between -pi and +pi. There' no way you can represent that in finite space without a fair bit of algebra, something we don't want to burden on our implementors. And somehow I also don't think that meets the "principle of least surprise" criterion. I think that I don't have to comment on the rest of the mail to make clear that Larry's proposal, although being quite interesting, is a very bad idea to actually implement (and very hard to implement as well) (unless somebody comes to its rescue with a really clever idea on how to resolve all these weirdnesses). Cheers, Moritz -- Moritz Lenz http://moritz.faui2k3.org/ | http://perl-6.de/