Semantics of ^^

[KennyTM~]

On Dec 8, 09 19:16, 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
>
> Bye,
> bearophile

Other non-essential special cases are 2^^n == 1<<n and x^^2 == x*x, but 
these should be put in the optimizer, not the language. (And an integer 
power algorithm http://www.c2.com/cgi/wiki?IntegerPowerAlgorithm should 
be used instead of a simple foreach loop implementation-wise.)