Kyle Furlong wrote:
> Don Clugston wrote:
>> Thomas Kuehne wrote:
>>> -----BEGIN PGP SIGNED MESSAGE-----
>>> Hash: SHA1
>>>
>>> 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.

Don Clugston wrote:
> Kyle Furlong wrote:
>> Don Clugston wrote:
>>> Thomas Kuehne wrote:
>>>> -----BEGIN PGP SIGNED MESSAGE-----
>>>> Hash: SHA1
>>>>
>>>> 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.

As long as its well documented and doesn't introduce bugs, why not?

>>>> 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.
> 
> As long as its well documented and doesn't introduce bugs, why not?

I really don't think it's a good idea (mathematicians would laugh at us). If you want to compare the magnitudes, you should say so. But, I find it interesting that the NCEG operators allow you to define meaningful ordering comparisons for quantities for which a strict weak ordering does not exist.

Kyle Furlong schrieb am 2006-03-03:
> Don Clugston wrote:
>> Kyle Furlong wrote:
>>> Don Clugston wrote:
>>>> Thomas Kuehne wrote:
>>>>> 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.
>
> As long as its well documented and doesn't introduce bugs, why not?

http://www.digitalmars.com/d/float.html
# Floating Point Comparisons
#
# In addition to the usual < <= > >= == != comparison operators, D adds
# more that are specific to floating point. These are !<>= <> <>= !<= !<
# !>= !> !<> and match the semantics for the NCEG extensions to C.

creal/cdouble/cfloat are "Floating Point Types" and "Floating Point Comparisons" are those stated by NCEG.

So what does NCEG say on compairing _Complex?
(Couldn't find any useful NCEG documents ...)

Thomas