As has been mentioned in previous posts, a ^^ b should be right associative and have a precedence between multiplication and unary operators. That much is clear.

Operations involving integers are far less obvious (and are actually where a major benefit of an operator can come in).

Using the normal promotion rules, 10^^2 is an integer. The range checking already present in D2 could be extended so that the compiler knows it'll even fit in a byte. This gets rid of one of the classic annoyances of C pow: int x = pow(2, 10); doesn't compile without a cast.

But the difficult question is, what's the type of 10^^-2 ? Should it be an error? (since the result, 0.01, is not representable as an integer). Should it return zero? (just as 1/2 doesn't return 0.5). For an example of these semantics, see http://www.tcl.tk/cgi-bin/tct/tip/123.html).
Or should it return a double?
Or should 10^^2 also be a double, but implicitly castable to byte because of the range checking rules?

I currently favour making it an error, so that the normal promotion rules apply. It seems reasonable to me to require a cast to floating point in there somewhere. This is analagous to the similar case f ^^ 0.1; where f is known to be negative. This gives a complex result, creating a run-time error (returns a NaN). But, there's no standard error and no NaNs for integer underflow.

One could also make int ^^ uint defined (returning an int), but not int ^^ int. Again thanks to range checking, int ^^ uint ^^ uint would work, because although uint ^^ uint is an int, it's known to be positive, so would implicitly convert to int. But would making int ^^ int illegal, make it too much of an annoying special case?

I strongly suspect that x^^y, where x and y are integers, and the value of y is not known at compile time, is an extremely rare operation.

Also, should int^^uint generate some kind of overflow error? Although other arithmeic integer operators don't, it's fantastically easy to hit an overflow with x^^y. Unless x is 1, y must be tiny (< 64 to avoid overflowing a ulong).

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