A possible solution for the opIndexXxxAssign morass

[Don]

Lars T. Kyllingstad wrote:
> Don wrote:
>> Andrei Alexandrescu wrote:
>>> Right now we're in trouble with operators: opIndex and opIndexAssign 
>>> don't seem to be up to snuff because they don't catch operations like
>>>
>>> a[b] += c;
>>>
>>> with reasonable expressiveness and efficiency.
>>>
>>> Last night this idea occurred to me: we could simply use overloading 
>>> with the existing operator names. Consider:
>>>
>>> a += b
>>>
>>> gets rewritten as
>>>
>>> a.opAddAssign(b)
>>>
>>> Then how about this - rewrite this:
>>>
>>> a[b] += c
>>>
>>> as
>>>
>>> a.opAddAssign(b, c);
>>>
>>> There's no chance of ambiguity because the parameter counts are 
>>> different. Moreover, this scales to multiple indexes:
>>>
>>> a[b1, b2, ..., bn] = c
>>>
>>> gets rewritten as
>>>
>>> a.opAddAssign(b1, b2, ..., bn, c)
>>>
>>> What do you think? I may be missing some important cases or threats.
>>>
>>>
>>> Andrei
>>
>> Well timed. I just wrote this operator overloading proposal, part 1.
>> http://www.prowiki.org/wiki4d/wiki.cgi?LanguageDevel/DIPs/DIP7
>> I concentrated on getting the use cases established.
>>
>> The indexing thing was something I didn't have a solution for.
>>
>> BTW we need to deal with slices as well as indexes. I think the way to 
>> do this is to make a slice into a type of index.
> 
> 
> I like the idea of enforcing relationships between operators. In fact, I 
> think we can take it even further, and require that operator overloading 
> in general *must* follow mathematical rules, and anything else leads to 
> undefined behaviour. For example, if n is an integer, a and b are 
> scalars, and x and y are general types, the compiler should be free to 
> rewrite
> 
>          n*x  <-->  x + x + ... + x    <-->  2*x + 2*x + ...
>         x^^n  <-->  x * x * ... * x    <-->  x^^2 * x^^2 * ...
>    x/a + y/b  <-->  (b*x + a*y)/(a*b)
> 
> and so on, based on what it finds to be the most efficient operations. 

Unfortunately, the last one doesn't work for reals. a*b could overflow 
or underflow.
x/ real.max + y / real.max   is exactly 2.0 if x and y are both real.max
But
(real.max * x + real.max *y)/(real.max * real.max) is infinity/infinity 
= NaN.

The others don't always work in general, either. I'm worried about 
decimal floats. Say n==10, then it's an exact operation; but addition 
isn't exact. It always works for n==2, since there's at most one 
roundoff in both cases.

But I do feel that with floating-point, we've lost so many identities, 
that we must preserve every one which we have left.

> (Note how I snuck my favourite suggestion for an exponentiation operator 
> in there. I *really* want that.)

I want it too. Heck, I might even make a patch for it <g>.