www.digitalmars.com         C & C++   DMDScript  

digitalmars.D - Fixing the imaginary/complex mess

reply Don <nospam nospam.com> writes:
D currently allows some conversions between complex/imaginary types and 
real types, which are highly dubious.

Given creal z, ireal y, these casts are legal:
real x = cast(real)z;
x = cast(real)y; // always sets x==0, regardless of the value of y.
But I believe that should not be legal.

For the first case, it should be written as:   real x = z.re;
(which is shorter and clearer), and the second case is probably a bug, 
and should be x = y.im; (unless the intention really was to set x=0!).

By the same logic, we could have sqrt(-1)==0, since the real part is 0.

The most important effect of disallowing these casts would be to fix a 
host of bugs and wierd behaviour. All the A op= B operations involve a 
cast to A. If those nonsensical casts become illegal, the nonsensical 
op= operations become illegal automatically.

Eg, ireal y;
y *= y; // mathematically nonsense, y*y is real, so can't be stored in a 
pure imaginary type!

There are a few segfault/ICE bugs (eg 718, 2839) which involve 
int/=complex, an operation which never makes any sense anyway.

I think we're just making problems for ourselves by allowing these 
useless operations. I think they should be killed.
Does anyone object? (If not, I'll create a patch to do it; it's not very 
difficult).
Apr 30 2009
next sibling parent dsimcha <dsimcha yahoo.com> writes:
== Quote from Don (nospam nospam.com)'s article
 D currently allows some conversions between complex/imaginary types and
 real types, which are highly dubious.
 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.
 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a bug,
 and should be x = y.im; (unless the intention really was to set x=0!).
 By the same logic, we could have sqrt(-1)==0, since the real part is 0.
 The most important effect of disallowing these casts would be to fix a
 host of bugs and wierd behaviour. All the A op= B operations involve a
 cast to A. If those nonsensical casts become illegal, the nonsensical
 op= operations become illegal automatically.
 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored in a
 pure imaginary type!
 There are a few segfault/ICE bugs (eg 718, 2839) which involve
 int/=complex, an operation which never makes any sense anyway.
 I think we're just making problems for ourselves by allowing these
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not very
 difficult).

I'm totally ok with you creating such a patch and applying it, as I don't use complex numbers anyhow, but if we're going to look at fixing complex numbers, shouldn't we discuss whether they even still belong in the core language? IMHO they don't because D's user defined types have advanced pretty significantly since the decision was made to put them in, and they're a *very* niche feature. The only people who need complex and imaginary numbers are scientific computing people, and not all or even most scientific computing people need them. Show of hands, how many people here actually use D's complex numbers on a regular enough basis that you would miss them if they were removed from the core language completely?
Apr 30 2009
prev sibling next sibling parent reply Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Don wrote:
 D currently allows some conversions between complex/imaginary types and 
 real types, which are highly dubious.
 
 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.
 
 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a bug, 
 and should be x = y.im; (unless the intention really was to set x=0!).
 
 By the same logic, we could have sqrt(-1)==0, since the real part is 0.
 
 The most important effect of disallowing these casts would be to fix a 
 host of bugs and wierd behaviour. All the A op= B operations involve a 
 cast to A. If those nonsensical casts become illegal, the nonsensical 
 op= operations become illegal automatically.
 
 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored in a 
 pure imaginary type!
 
 There are a few segfault/ICE bugs (eg 718, 2839) which involve 
 int/=complex, an operation which never makes any sense anyway.
 
 I think we're just making problems for ourselves by allowing these 
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not very 
 difficult).

Since you're looking into this already, I suggest we move for the kill and eliminate built-in complex. Andrei
Apr 30 2009
next sibling parent reply Robert Fraser <fraserofthenight gmail.com> writes:
Andrei Alexandrescu wrote:
 Don wrote:
 D currently allows some conversions between complex/imaginary types 
 and real types, which are highly dubious.

 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.

 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a bug, 
 and should be x = y.im; (unless the intention really was to set x=0!).

 By the same logic, we could have sqrt(-1)==0, since the real part is 0.

 The most important effect of disallowing these casts would be to fix a 
 host of bugs and wierd behaviour. All the A op= B operations involve a 
 cast to A. If those nonsensical casts become illegal, the nonsensical 
 op= operations become illegal automatically.

 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored in 
 a pure imaginary type!

 There are a few segfault/ICE bugs (eg 718, 2839) which involve 
 int/=complex, an operation which never makes any sense anyway.

 I think we're just making problems for ourselves by allowing these 
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not 
 very difficult).

Since you're looking into this already, I suggest we move for the kill and eliminate built-in complex. Andrei

Ehhh.... why not leave complex and just kill imaginary? That'd solve most of the problems.
Apr 30 2009
next sibling parent reply bearophile <bearophileHUGS lycos.com> writes:
Robert Fraser:
 Ehhh.... why not leave complex and just kill imaginary? That'd solve 
 most of the problems.

You can't remove only half of a feature of the language, so I don't like this idea. I accept to remove them fully if their semantics can be fully replaced by the std lib. Otherwise just let Don fix the broken things. Bye, bearophile
Apr 30 2009
parent reply Robert Fraser <fraserofthenight gmail.com> writes:
bearophile wrote:
 Robert Fraser:
 Ehhh.... why not leave complex and just kill imaginary? That'd solve 
 most of the problems.

You can't remove only half of a feature of the language, so I don't like this idea. I accept to remove them fully if their semantics can be fully replaced by the std lib. Otherwise just let Don fix the broken things. Bye, bearophile

It's not necessarily "removing half a feature". Imaginary numbers aren't closed under many operations. The idea is that imaginary literals are turned into complex. So "ireal x = 10i;" becomes "creal x = 0 + 10i;". Since complex numbers are closed under all the builtin operators, it eliminates many of the problems (casts from complex to real). Putting it in a library eliminates the ability to use complex/imaginary literals (unless it's a runtime type).
Apr 30 2009
parent Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Robert Fraser wrote:
 Putting it in a library eliminates the ability to use complex/imaginary 
 literals (unless it's a runtime type).

Yah, but then I'm thinking: how many numeric literals are in a program at all? I think the vision of the mad scientist that uses one imaginary literal every five lines of code is quite unreal :o). Andrei
Apr 30 2009
prev sibling parent "Joel C. Salomon" <joelcsalomon gmail.com> writes:
Robert Fraser wrote:
 Ehhh.... why not leave complex and just kill imaginary? That'd solve
 most of the problems.

The reasons for a separate imaginary type are listed in the D docs at <http://digitalmars.com/d/2.0/cppcomplex.html>, referencing William Kahan’s “Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing’s Sign Bit”. It just doesn’t have to be a built-in type anymore. —Joel Salomon
Apr 30 2009
prev sibling next sibling parent reply Don <nospam nospam.com> writes:
Andrei Alexandrescu wrote:
 Don wrote:
 D currently allows some conversions between complex/imaginary types 
 and real types, which are highly dubious.

 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.

 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a bug, 
 and should be x = y.im; (unless the intention really was to set x=0!).

 By the same logic, we could have sqrt(-1)==0, since the real part is 0.

 The most important effect of disallowing these casts would be to fix a 
 host of bugs and wierd behaviour. All the A op= B operations involve a 
 cast to A. If those nonsensical casts become illegal, the nonsensical 
 op= operations become illegal automatically.

 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored in 
 a pure imaginary type!

 There are a few segfault/ICE bugs (eg 718, 2839) which involve 
 int/=complex, an operation which never makes any sense anyway.

 I think we're just making problems for ourselves by allowing these 
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not 
 very difficult).

Since you're looking into this already, I suggest we move for the kill and eliminate built-in complex.

I'd like to actually eliminate these operations from D1. Otherwise, I can't see the related D1 bugs ever getting fixed. Any code which relies on these operations is broken; I think there's an excellent chance that there isn't any code using it. Also, these operations would not be provided by a library class, so I think it's a useful intermediate step. We can't remove the complex types until we have a library solution.
Apr 30 2009
parent Don <nospam nospam.com> writes:
Brad Roberts wrote:
 Don wrote:
 I'd like to actually eliminate these operations from D1. Otherwise, I
 can't see the related D1 bugs ever getting fixed. Any code which relies
 on these operations is broken; I think there's an excellent chance that
 there isn't any code using it.
 Also, these operations would not be provided by a library class, so I
 think it's a useful intermediate step.
 We can't remove the complex types until we have a library solution.

I think it's perfectly acceptable to not fix these in D1 and only address them in D2. There's lots of things in D1 that are only fixed in D2.

I think so many people are actually using D1, that ICE bugs really should get fixed.
 
 Later,
 Brad

Apr 30 2009
prev sibling parent Brad Roberts <braddr puremagic.com> writes:
Don wrote:
 I'd like to actually eliminate these operations from D1. Otherwise, I
 can't see the related D1 bugs ever getting fixed. Any code which relies
 on these operations is broken; I think there's an excellent chance that
 there isn't any code using it.
 Also, these operations would not be provided by a library class, so I
 think it's a useful intermediate step.
 We can't remove the complex types until we have a library solution.

I think it's perfectly acceptable to not fix these in D1 and only address them in D2. There's lots of things in D1 that are only fixed in D2. Later, Brad
Apr 30 2009
prev sibling next sibling parent bearophile <bearophileHUGS lycos.com> writes:
Don:
 I think we're just making problems for ourselves by allowing these useless
operations. I think they should be killed. Does anyone object? (If not, I'll
create a patch to do it; it's not very difficult).<

I agree to disallow/fix those things. And thanks for your work! ------------- dsimcha:
Show of hands, how many people here actually use D's complex numbers on a
regular enough basis that you would miss them if they were removed from the
core language completely?<

D is in a flux state still, so I think very few engineer/scientists are using it (I am not using complex numbers). So probably the answers your will receive will not be enough to judge future true usages of the D language. A possible solution is to remove complex types now from D2 (moving them in Phobos and Tango), and later if enough people ask for them, to put them back into the built-ins. Are there problems in adding them back later if they are asked for and regarded as useful? ------------- Andrei Alexandrescu:
Since you're looking into this already, I suggest we move for the kill and
eliminate built-in complex.<

Is the current semantics fully doable with std lib complex numbers? Bye, bearophile
Apr 30 2009
prev sibling parent reply Georg Wrede <georg.wrede iki.fi> writes:
Don wrote:
 D currently allows some conversions between complex/imaginary types and 
 real types, which are highly dubious.
 
 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.
 
 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a bug, 
 and should be x = y.im; (unless the intention really was to set x=0!).
 
 By the same logic, we could have sqrt(-1)==0, since the real part is 0.
 
 The most important effect of disallowing these casts would be to fix a 
 host of bugs and wierd behaviour. All the A op= B operations involve a 
 cast to A. If those nonsensical casts become illegal, the nonsensical 
 op= operations become illegal automatically.
 
 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored in a 
 pure imaginary type!
 
 There are a few segfault/ICE bugs (eg 718, 2839) which involve 
 int/=complex, an operation which never makes any sense anyway.
 
 I think we're just making problems for ourselves by allowing these 
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not very 
 difficult).

It might be a good idea to write in the docs why these operations are missing. Even better would of course be if the user got a message stating that this operation isn't implemented because it doesn't make mathematical sense. If the latter isn't done, then many people will just think there's something wrong with the compiler/language. Bad press we don't need.
Apr 30 2009
next sibling parent reply Don <nospam nospam.com> writes:
Georg Wrede wrote:
 Don wrote:
 D currently allows some conversions between complex/imaginary types 
 and real types, which are highly dubious.

 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.

 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a bug, 
 and should be x = y.im; (unless the intention really was to set x=0!).

 By the same logic, we could have sqrt(-1)==0, since the real part is 0.

 The most important effect of disallowing these casts would be to fix a 
 host of bugs and wierd behaviour. All the A op= B operations involve a 
 cast to A. If those nonsensical casts become illegal, the nonsensical 
 op= operations become illegal automatically.

 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored in 
 a pure imaginary type!

 There are a few segfault/ICE bugs (eg 718, 2839) which involve 
 int/=complex, an operation which never makes any sense anyway.

 I think we're just making problems for ourselves by allowing these 
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not 
 very difficult).

It might be a good idea to write in the docs why these operations are missing. Even better would of course be if the user got a message stating that this operation isn't implemented because it doesn't make mathematical sense.

I'll make sure the error messages are sensible.
 
 If the latter isn't done, then many people will just think there's 
 something wrong with the compiler/language. Bad press we don't need.

I don't think anyone expects to be able to divide an integer by an imaginary, and then assign it to an integer. I was astonished that the compiler accepted it.
Apr 30 2009
next sibling parent Georg Wrede <georg.wrede iki.fi> writes:
Don wrote:
 Georg Wrede wrote:
 Don wrote:
 D currently allows some conversions between complex/imaginary types 
 and real types, which are highly dubious.

 Given creal z, ireal y, these casts are legal:
 real x = cast(real)z;
 x = cast(real)y; // always sets x==0, regardless of the value of y.
 But I believe that should not be legal.

 For the first case, it should be written as:   real x = z.re;
 (which is shorter and clearer), and the second case is probably a 
 bug, and should be x = y.im; (unless the intention really was to set 
 x=0!).

 By the same logic, we could have sqrt(-1)==0, since the real part is 0.

 The most important effect of disallowing these casts would be to fix 
 a host of bugs and wierd behaviour. All the A op= B operations 
 involve a cast to A. If those nonsensical casts become illegal, the 
 nonsensical op= operations become illegal automatically.

 Eg, ireal y;
 y *= y; // mathematically nonsense, y*y is real, so can't be stored 
 in a pure imaginary type!

 There are a few segfault/ICE bugs (eg 718, 2839) which involve 
 int/=complex, an operation which never makes any sense anyway.

 I think we're just making problems for ourselves by allowing these 
 useless operations. I think they should be killed.
 Does anyone object? (If not, I'll create a patch to do it; it's not 
 very difficult).

It might be a good idea to write in the docs why these operations are missing. Even better would of course be if the user got a message stating that this operation isn't implemented because it doesn't make mathematical sense.

I'll make sure the error messages are sensible.
 If the latter isn't done, then many people will just think there's 
 something wrong with the compiler/language. Bad press we don't need.

I don't think anyone expects to be able to divide an integer by an imaginary, and then assign it to an integer. I was astonished that the compiler accepted it.

Just goes to show you the average math knowledge. I never would have thought of omitting it either. :-)
Apr 30 2009
prev sibling parent reply Walter Bright <newshound1 digitalmars.com> writes:
Don wrote:
 I don't think anyone expects to be able to divide an integer by an 
 imaginary, and then assign it to an integer. I was astonished that the 
 compiler accepted it.

There actually is a reason - completeness. Mathematically, there is a definite answer to it, so why not fill in all the entries for all the combinations?
May 03 2009
parent reply Don <nospam nospam.com> writes:
Walter Bright wrote:
 Don wrote:
 I don't think anyone expects to be able to divide an integer by an 
 imaginary, and then assign it to an integer. I was astonished that the 
 compiler accepted it.

There actually is a reason - completeness. Mathematically, there is a definite answer to it, so why not fill in all the entries for all the combinations?

In the case complex = int/complex, there's no problem. It's the case int = int/complex that doesn't make sense. And that's fundamentally because cast(real)(2 + 3i) doesn't have a definite answer. There's no mathematical operation to convert a complex number to a real. Normally, to get a real result, you need to do something like multiplying by the complex conjugate. You CAN take the real part of a complex number, and you can also take the modulus (which makes a lot of sense if you're using polar represantation). Of course, cast() is not a mathematical operation, it's a D operation, so we can define it however we like. But defining it cast(real)z = z.re; is an arbitrary decision, which introduces lots of complexity to the language, and the many compiler bugs are a consequence. It's confusing for newbies (there's been questions on D.learn asking, "I can get the real part of a complex number with cast(real), but how do I get the imaginary part? cast(ireal) gives me an ireal, not a real!"). Since D supports the very nice .re syntax, there's really no reason to define cast(real) at all. z.re is better in 100% of use cases. There are *NO* use cases for cast(real); any use of cast(real) is a bug. We should kill it.
May 04 2009
next sibling parent reply Frits van Bommel <fvbommel REMwOVExCAPSs.nl> writes:
Don wrote:
 In the case complex = int/complex, there's no problem. It's the case int 
 = int/complex that doesn't make sense.
 And that's fundamentally because cast(real)(2 + 3i) doesn't have a 
 definite answer.

Devil's advocate: one could argue it's the same as cast(int) of a float -- it returns the closest representable value, for some definition of "closest".
May 04 2009
next sibling parent Don <nospam nospam.com> writes:
Frits van Bommel wrote:
 Don wrote:
 In the case complex = int/complex, there's no problem. It's the case 
 int = int/complex that doesn't make sense.
 And that's fundamentally because cast(real)(2 + 3i) doesn't have a 
 definite answer.

Devil's advocate: one could argue it's the same as cast(int) of a float -- it returns the closest representable value, for some definition of "closest".

Sure, you're at liberty to argue anything. But mathematicians don't do that. Nor should we. It's misleading, and just not helpful. BTW, another equally reasonable and equally unhelpful way you could define cast(real)(x + iy) is as sqrt(x*x - y*y). The most justifiable way to do it would be to say cast(real)(x+iy) is: if (y==0) return x; else throw(CastError); But again, it's just not helpful. Make it a compile-time error.
May 04 2009
prev sibling next sibling parent Derek Parnell <derek psych.ward> writes:
On Mon, 04 May 2009 10:56:41 +0200, Frits van Bommel wrote:

 Don wrote:
 In the case complex = int/complex, there's no problem. It's the case int 
 = int/complex that doesn't make sense.
 And that's fundamentally because cast(real)(2 + 3i) doesn't have a 
 definite answer.

Devil's advocate: one could argue it's the same as cast(int) of a float -- it returns the closest representable value, for some definition of "closest".

Hmmm. not quite because we can not do ... int i = floatnum.integer; but we can do real r = complexnum.re; -- Derek Parnell Melbourne, Australia skype: derek.j.parnell
May 04 2009
prev sibling parent Jason House <jason.james.house gmail.com> writes:
Frits van Bommel Wrote:

 Don wrote:
 In the case complex = int/complex, there's no problem. It's the case int 
 = int/complex that doesn't make sense.
 And that's fundamentally because cast(real)(2 + 3i) doesn't have a 
 definite answer.

Devil's advocate: one could argue it's the same as cast(int) of a float -- it returns the closest representable value, for some definition of "closest".

I consider this to be a much different case. Assuming the float to an int results on approximately the same number... And everyone knows what to expect. It's also possible to convert back to float and still have approximately the same number. For complex to int, the same things are not true. Conversion to float and then back to real can give a much different number... And not just for overflow, but normal uses of complex numbers. It's also unclear to mathematically inclined folk like me and Don what the conversion is supposed to do. A magnitude makes as much, if not more, sense. Adding to all this, there are easier, shorter, and clearer ways to do all of these conversions, and you _have_ to agree with Don ;)
May 04 2009
prev sibling next sibling parent bearophile <bearophileHUGS lycos.com> writes:
Don Wrote:
 Since D supports the very nice .re syntax, there's really no reason to 
 define cast(real) at all. z.re is better in 100% of use cases. There are 
 *NO* use cases for cast(real); any use of cast(real) is a bug. We should 
 kill it.

I am with you. Making the language tidy is the way to go :-) Thank you for your work, and keep improving things when you can. Bye, bearophile
May 04 2009
prev sibling parent reply Georg Wrede <georg.wrede iki.fi> writes:
Don wrote:
 Walter Bright wrote:
 Don wrote:
 I don't think anyone expects to be able to divide an integer by an 
 imaginary, and then assign it to an integer. I was astonished that 
 the compiler accepted it.

There actually is a reason - completeness. Mathematically, there is a definite answer to it, so why not fill in all the entries for all the combinations?

In the case complex = int/complex, there's no problem. It's the case int = int/complex that doesn't make sense. And that's fundamentally because cast(real)(2 + 3i) doesn't have a definite answer. There's no mathematical operation to convert a complex number to a real. Normally, to get a real result, you need to do something like multiplying by the complex conjugate. You CAN take the real part of a complex number, and you can also take the modulus (which makes a lot of sense if you're using polar represantation). Of course, cast() is not a mathematical operation, it's a D operation, so we can define it however we like. But defining it cast(real)z = z.re; is an arbitrary decision, which introduces lots of complexity to the language, and the many compiler bugs are a consequence. It's confusing for newbies (there's been questions on D.learn asking, "I can get the real part of a complex number with cast(real), but how do I get the imaginary part? cast(ireal) gives me an ireal, not a real!"). Since D supports the very nice .re syntax, there's really no reason to define cast(real) at all. z.re is better in 100% of use cases. There are *NO* use cases for cast(real); any use of cast(real) is a bug. We should kill it.

Walter, could the error message then include "Please use z.re or z.im to get the parts, instead of a cast." or something. Otherwise we have to explain to all users separately what's going on, /and/ that the omission of implementing the cast in D isn't an omission.
May 04 2009
parent Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Georg Wrede wrote:
 Walter, could the error message then include "Please use z.re or z.im to 
 get the parts, instead of a cast." or something. Otherwise we have to 
 explain to all users separately what's going on, /and/ that the omission 
 of implementing the cast in D isn't an omission.

If we cut the limb, why first apply an ointment to it? Andrei
May 04 2009
prev sibling next sibling parent Bill Baxter <wbaxter gmail.com> writes:
On Sun, May 3, 2009 at 2:35 AM, Walter Bright
<newshound1 digitalmars.com> wrote:
 Don wrote:
 I don't think anyone expects to be able to divide an integer by an
 imaginary, and then assign it to an integer. I was astonished that the
 compiler accepted it.

There actually is a reason - completeness. Mathematically, there is a definite answer to it, so why not fill in all the entries for all the combinations?

But the result of int divided by imaginary is pure imaginary. So I think Don's point was that you shouldn't be able to assign that back to an int. --bb
May 03 2009
prev sibling parent "Steven Schveighoffer" <schveiguy yahoo.com> writes:
On Mon, 04 May 2009 09:44:18 -0400, Andrei Alexandrescu  
<SeeWebsiteForEmail erdani.org> wrote:

 Georg Wrede wrote:
 Walter, could the error message then include "Please use z.re or z.im  
 to get the parts, instead of a cast." or something. Otherwise we have  
 to explain to all users separately what's going on, /and/ that the  
 omission of implementing the cast in D isn't an omission.

If we cut the limb, why first apply an ointment to it?

I think the point is relevant to D1, where you can't really remove the limb, but you can apply make-up to make it look less deformed ;) -Steve
May 04 2009