Lots of bool operations shouldn't compile

[Don Clugston]

Kyle Furlong wrote:
> Don Clugston wrote:
>> Thomas Kuehne wrote:
>>> -----BEGIN PGP SIGNED MESSAGE-----
>>> Hash: SHA1
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>>> Don Clugston schrieb am 2006-02-28:
>>>
>>> [snip]
>>>
>>>> OK, there's another bug in there, comparing an int with an imaginary 
>>>> real should also not be legal.
>>>>
>>>>      if (1 > -2i) { assert(0); }
>>>>      if (1 > ireal.nan) { assert(0); }
>>>>
>>>> Reals and ireals cannot be compared. Ever.
>>>
>>> Sure you can. Floats and imaginary floats can both be implicitly 
>>> promoted
>>> to complex floats.
>>
>> That only gives you == and !=.
>>
>> <snip>
>>> Thus
>>>
>>>>      if (1 > -2i) { assert(0); }
>>>>      if (1 > ireal.nan) { assert(0); }
>>>
>>> are interpreted as
>>>
>>>>      if (1 + 0i > 0 - 2i) { ... }
>>>>      if (1 + 0i > 0 + ireal.nan) { ... }
>>
>> Yes, but that still doesn't work, there's no > for complex numbers.
>> Is  2 - 3i > 3 - 2i ?
> 
> One could speak of their magnitudes, I suppose.
> 
> creal i = 2 - 3i;
> creal j = 3 - 2i;
> 
> real i_m = sqrt(i * complexConjugate(i));
> real j_m = sqrt(j * complexConjugate(j));
> 
> but then I guess you are just comparing reals.

And then you have the problem (as in this case) that
(i >= j) is true, and (i <= j) is true, but (i==j) is false.

Actually, though, you _could_ bring the NCEG operators into play, and
define
a >  b  as   abs(a) > abs(b)
a >= b  as   abs(a) > abs(b) || a==b
a !< b  as   abs(a) !< abs(b)
a !<=b  as   abs(a) !< abs(b) && a!=b
a <> b  as   abs(a) != abs(b)
a !<>b  as   abs(a) == abs(b)
a == b  as   a == b
a <>=b  as   abs(a) <> abs(b) || a==b
a!<>=b  as   abs(a) == abs(b) && a!=b

which would even work correctly with NANs.
But there's no mathematical precedent for this, AFAIK.