Semantics of ^^

[BCS]

Hello Don,

> bearophile wrote:
> 
>> Don:
>> 
>>> Based on everyone's comments, this is what I have come up with:
>>> 
>> Looks good.
>> 
>>> * If y == 0,  x ^^ y is 1.
>>> * If both x and y are integers, and y > 0,  x^^y is equivalent to
>>> { auto u = x; foreach(i; 1..y) { u *= x; } return u; }
>> You can rewrite both of those as:
>> { typeof(x) u = 1; foreach (i; 0 .. y) { u *= x; } return u; }
>>> (1) Although the following special cases could be defined...
>>> * If x == 1,  x ^^ y is 1
>>> * If x == -1 and y is even, x^^y == 1
>>> * If x == -1 and y is odd, x^^y == -1
>>> ... they are not sufficiently useful to justify the major increase
>>> in
>>> complexity which they introduce.
>> This is not essential:
>> 
>> (-1)**n is a common enough shortcut to produce an alternating +1 -1,
>> you can see it used often enough in Python code (and in mathematics).
>> This search gives 433 results:
>> 
>> http://www.google.com/codesearch?q=\%28-1\%29\s*\*\*\s*[0-9a-zA-Z%28]
>> +lang%3Apython
>> 
>> When used for this purpose (-1) is always compile time constant, so
>> the compiler can grow a simple rule the rewrites:
>> 
>> (-1) ^^ n
>> 
>> as
>> 
>> (n & 1) ? -1 : 1
>> 
> That's an interesting one.
> With this proposal, that optimisation could still be made when it is
> known that n>=0. We *could* make a special rule for compile-time
> constant -1 ^^ n, to allow the optimisation even when n<0. But then
> you
> have to explain why:  x = -1; y = x^^-2; is illegal, but y = -1^^-2 is
> legal. Can that be justified?

Maybe. I think it's worth looking into.