Le mardi 11 juillet 2006 à 14:21 +0300, Peter Dimov a écrit :
Daryle Walker wrote:
[1] If you make a fake order for "std::complex<>", would you compare real components then imaginary components, or would you use magnitude then angle?
Real, then imaginary. Compare with:
Interesting. I would have chosen magnitude and then angle. Why components.
There are two reasons for that. First, composite types use lexicographical ordering by default, and std::complex is (de facto) a (real, imag) pair. Second, the magnitude/angle ordering has the property that if you have three numbers a, b, c, where a and b are very close to one another but not to c, it is possible to have a < c and c < b.
Your reasoning is a bit flawed, since this property is also true for the lexicographic order. I assume that by "close" you mean with respect to the natural distance on the complex numbers. Then a = (1,0) and b = (2,0) are close (distance 1), yet c = (1.5,1e100) (distance ~1e100 from both a and b) is lexicographically between the two of them.
"If you make a FAKE order for std::string, would you compare left to right or right to left?"
I don't think that is a legitimate comparison. In my world view, strings have a natural order but complex numbers don't.
Possibly. So you define "fake" as "unnatural", and define "natural" as "feels natural to me". This approach can work but it's a bit subjective, isn't it?
Consider the progression:
This is not a progression. You can use vector<double> instead of struct{}, since struct{} is nothing more than a cartesian product while vector is a word monoid. But you can't use struct{} instead of complex<double>. This change would lose the whole point of complex<double>. It is supposed to (approximately) represent an algebraically closed field with characteristic 0.
complex<double> struct { double x, double y; } pair<double, double> tuple<double, double> vector<double> vector<char> string
Any set of computer data can be ordered. I don't think it means that they should all have an operator<. Best regards, Guillaume