Semantics of ^^

[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?