How to work around 14.5.5, 14.7.3/18 and related?

[Stephen Waits]

Occasionally we want to perform a Sqrt where we don't need accuracy
and/or we have a good initial guess - a situation where an N-step Sqrt
series may be more optimal than a full on Sqrt(). For example:

template <unsigned int iterations>
T SqrtApprox(cons t T x, const T guess)
{
return SqrtApprox<iter ations-1>( x, T(0.5f) * (guess + (x/guess)) );
}

template <>
T SqrtApprox<0>(c onst T x, const T guess)
{
return guess;
}

The problems came when I attempted to get this little template
metaprogram into our main Math<T> class which looks something like
this:

template <typename T>
class Math
{
public:
static T Sqrt(T x);
static T Sin(T x);
static T ASin(T x);
... // SqrtApprox should be in here
};
So, I've coded up a few simple examples describing the process I've
gone through in trying to get this to work...
This working example shows basically what I want to do - only in a
global scope.

template <unsigned int I>
float Iterative(float x)
{
return x + Iterative<I-1>(x);
}

template <>
float Iterative<0>(fl oat x)
{
// specialize 0th iteration to stop template recursion
return 0.0f;
}

However, when I decide to put this into a class and template out
"float" (similar to the Math<T> class above) I run into problems with
the language; for example:

[Begin BROKEN example

template <class T>
class SomeClass
{
public:

template <unsigned int I>
static T Iterative(T x);
};

template <class T>
template <unsigned int I> // not allowed!
T SomeClass<T>::I terative<I>(T x)
{
}

--end BROKEN example]

Because this is a static member I cannot specialize it (because I
believe this is a function template, of which specialization is NOT
allowed by C++). Correct me if I'm wrong.

So, my next step is attempting to put this in a nested functor:

[Begin BROKEN example

template <class T>
class SomeClass
{
public:
template <unsigned int I>
class Iterative
{
public:
static T IterativeImpl(T x);
};
};
template <class T>
template <unsigned int I>
T SomeClass<T>::I terative<I>::It erativeImpl(T x)
{
}

template <class T>
template <> // not allowed!
T SomeClass<T>::I terative<0>::It erativeImpl(T x)
{
}

--end BROKEN example]

And, of course, as you experts know already, specialization of this
nested class is not allowed because the enclosing class template is
not specialized. Again, correct me if I'm wrong here.

What do you suggest I do to work around these issues?

Thanks,
Steve

[ See http://www.gotw.ca/resources/clcm.htm for info about ]
[ comp.lang.c++.m oderated. First time posters: Do this! ]

[bartek]

st***@waits.net (Stephen Waits) wrote in
news:f3******** *************** ***@posting.goo gle.com:

Occasionally we want to perform a Sqrt where we don't need accuracy
and/or we have a good initial guess - a situation where an N-step Sqrt
series may be more optimal than a full on Sqrt(). For example:
(...)
So, my next step is attempting to put this in a nested functor:

[Begin BROKEN example

template <class T>
class SomeClass
{
public:
template <unsigned int I>
class Iterative
{
public:
static T IterativeImpl(T x);
};
};
template <class T>
template <unsigned int I>
T SomeClass<T>::I terative<I>::It erativeImpl(T x)
{
}

template <class T>
template <> // not allowed!
T SomeClass<T>::I terative<0>::It erativeImpl(T x)
{
}

--end BROKEN example]

And, of course, as you experts know already, specialization of this
nested class is not allowed because the enclosing class template is
not specialized. Again, correct me if I'm wrong here.

What do you suggest I do to work around these issues?

Actually I've been using this technique quite often. The difference was
though, that I've been putting the nested class definition inside the
outer class definition body.

The following works for me:

template <typename T>
struct Outer {
template <unsigned i>
struct Inner {
static T pow(T x)
{ return Inner<i-1>::pow(x)*x; }
};
template <>
struct Inner<1> {
static T pow(T x)
{ return x; }
};
template <>
struct Inner<0> {
static T pow(T x)
{ return 1; }
};
};

#include <iostream>

int main()
{
std::cout << Outer<float>::I nner<4>::pow(2) << std::endl;
return 0;
}

PS: Don't cross-post to a moderated group at the same time you're posting
here. You'll get more replies quicker. :)

[bartek]

st***@waits.net (Stephen Waits) wrote in
news:f3******** *************** ***@posting.goo gle.com:

Occasionally we want to perform a Sqrt where we don't need accuracy
and/or we have a good initial guess - a situation where an N-step Sqrt
series may be more optimal than a full on Sqrt(). For example:
(...)
So, my next step is attempting to put this in a nested functor:

[Begin BROKEN example

template <class T>
class SomeClass
{
public:
template <unsigned int I>
class Iterative
{
public:
static T IterativeImpl(T x);
};
};
template <class T>
template <unsigned int I>
T SomeClass<T>::I terative<I>::It erativeImpl(T x)
{
}

template <class T>
template <> // not allowed!
T SomeClass<T>::I terative<0>::It erativeImpl(T x)
{
}

--end BROKEN example]

And, of course, as you experts know already, specialization of this
nested class is not allowed because the enclosing class template is
not specialized. Again, correct me if I'm wrong here.

What do you suggest I do to work around these issues?

Actually I've been using this technique quite often. The difference was
though, that I've been putting the nested class definition inside the
outer class definition body.

The following works for me:

template <typename T>
struct Outer {
template <unsigned i>
struct Inner {
static T pow(T x)
{ return Inner<i-1>::pow(x)*x; }
};
template <>
struct Inner<1> {
static T pow(T x)
{ return x; }
};
template <>
struct Inner<0> {
static T pow(T x)
{ return 1; }
};
};

#include <iostream>

int main()
{
std::cout << Outer<float>::I nner<4>::pow(2) << std::endl;
return 0;
}

PS: Don't cross-post to a moderated group at the same time you're posting
here. You'll get more replies quicker. :)

[tom_usenet]

On Wed, 7 Apr 2004 15:05:46 +0000 (UTC), bartek
<ba*****@qwerty uiop.o2.pl> wrote:

Actually I've been using this technique quite often. The difference was
though, that I've been putting the nested class definition inside the
outer class definition body.
But adding specializations there is illegal - specializations may only
appear at namespace scope.
The following works for me:

template <typename T>
struct Outer {
template <unsigned i>
struct Inner {
static T pow(T x)
{ return Inner<i-1>::pow(x)*x; }
};
template <>
struct Inner<1> {
static T pow(T x)
{ return x; }
};
template <>
struct Inner<0> {
static T pow(T x)
{ return 1; }
};
};

#include <iostream>

int main()
{
std::cout << Outer<float>::I nner<4>::pow(2) << std::endl;
return 0;

(Comeau C++ strict mode)

"main.cpp", line 9: error: explicit specialization is not allowed in
the current scope
template <>
^

Comeau compiles it in "Microsoft mode", and VC7.1 compiles it, so I
guess it is a Microsoft extension.

Tom
--
C++ FAQ: http://www.parashift.com/c++-faq-lite/
C FAQ: http://www.eskimo.com/~scs/C-faq/top.html

[tom_usenet]

On Wed, 7 Apr 2004 15:05:46 +0000 (UTC), bartek
<ba*****@qwerty uiop.o2.pl> wrote:

Actually I've been using this technique quite often. The difference was
though, that I've been putting the nested class definition inside the
outer class definition body.
But adding specializations there is illegal - specializations may only
appear at namespace scope.
The following works for me:

template <typename T>
struct Outer {
template <unsigned i>
struct Inner {
static T pow(T x)
{ return Inner<i-1>::pow(x)*x; }
};
template <>
struct Inner<1> {
static T pow(T x)
{ return x; }
};
template <>
struct Inner<0> {
static T pow(T x)
{ return 1; }
};
};

#include <iostream>

int main()
{
std::cout << Outer<float>::I nner<4>::pow(2) << std::endl;
return 0;

(Comeau C++ strict mode)

"main.cpp", line 9: error: explicit specialization is not allowed in
the current scope
template <>
^

Comeau compiles it in "Microsoft mode", and VC7.1 compiles it, so I
guess it is a Microsoft extension.

Tom
--
C++ FAQ: http://www.parashift.com/c++-faq-lite/
C FAQ: http://www.eskimo.com/~scs/C-faq/top.html

[tom_usenet]

On 7 Apr 2004 10:26:04 -0400, st***@waits.net (Stephen Waits) wrote:

Occasionally we want to perform a Sqrt where we don't need accuracy
and/or we have a good initial guess - a situation where an N-step Sqrt
series may be more optimal than a full on Sqrt(). For example:

template <unsigned int iterations>
T SqrtApprox(cons t T x, const T guess)
{
return SqrtApprox<iter ations-1>( x, T(0.5f) * (guess + (x/guess)) );
}

template <>
T SqrtApprox<0>(c onst T x, const T guess)
{
return guess;
}

The problems came when I attempted to get this little template
metaprogram into our main Math<T> class which looks something like
this:

template <typename T>
class Math
{
public:
static T Sqrt(T x);
static T Sin(T x);
static T ASin(T x);
... // SqrtApprox should be in here
};
So, I've coded up a few simple examples describing the process I've
gone through in trying to get this to work... Because this is a static member I cannot specialize it (because I
believe this is a function template, of which specialization is NOT
allowed by C++). Correct me if I'm wrong.
IIRC you can specialize a member function template, as long as the
enclosing class is completely specialized.
And, of course, as you experts know already, specialization of this
nested class is not allowed because the enclosing class template is
not specialized. Again, correct me if I'm wrong here.
No, you're not wrong.
What do you suggest I do to work around these issues?

Overloading? Or you could rely on the optimizer to do a good job
passing the iteration as a normal parameter. Anyway, here's an
overloading based approach, which works around the problem without
needing to change the call syntax:

template <unsigned int N>
struct UnsignedInt
{
static unsigned int const value = N;
};

template <typename T>
class Math
{
public:
template <unsigned int iterations>
static T SqrtApprox(cons t T x, const T guess,
UnsignedInt<ite rations>* = 0)
{
return SqrtApprox(
x,
T(0.5f) * (guess + (x/guess)),
(UnsignedInt<it erations - 1>*)0
);
}

private:
static T SqrtApprox(cons t T x, const T guess, UnsignedInt<0>* )
{
return guess;
}
};

#include <iostream>

int main()
{
std::cout << Math<double>::S qrtApprox<10>(9 .5, 3.1) << '\n';
}

There may be other workarounds too.

Tom
--
C++ FAQ: http://www.parashift.com/c++-faq-lite/
C FAQ: http://www.eskimo.com/~scs/C-faq/top.html

[tom_usenet]

On 7 Apr 2004 10:26:04 -0400, st***@waits.net (Stephen Waits) wrote:

Occasionally we want to perform a Sqrt where we don't need accuracy
and/or we have a good initial guess - a situation where an N-step Sqrt
series may be more optimal than a full on Sqrt(). For example:

template <unsigned int iterations>
T SqrtApprox(cons t T x, const T guess)
{
return SqrtApprox<iter ations-1>( x, T(0.5f) * (guess + (x/guess)) );
}

template <>
T SqrtApprox<0>(c onst T x, const T guess)
{
return guess;
}

The problems came when I attempted to get this little template
metaprogram into our main Math<T> class which looks something like
this:

template <typename T>
class Math
{
public:
static T Sqrt(T x);
static T Sin(T x);
static T ASin(T x);
... // SqrtApprox should be in here
};
So, I've coded up a few simple examples describing the process I've
gone through in trying to get this to work... Because this is a static member I cannot specialize it (because I
believe this is a function template, of which specialization is NOT
allowed by C++). Correct me if I'm wrong.
IIRC you can specialize a member function template, as long as the
enclosing class is completely specialized.
And, of course, as you experts know already, specialization of this
nested class is not allowed because the enclosing class template is
not specialized. Again, correct me if I'm wrong here.
No, you're not wrong.
What do you suggest I do to work around these issues?

Overloading? Or you could rely on the optimizer to do a good job
passing the iteration as a normal parameter. Anyway, here's an
overloading based approach, which works around the problem without
needing to change the call syntax:

template <unsigned int N>
struct UnsignedInt
{
static unsigned int const value = N;
};

template <typename T>
class Math
{
public:
template <unsigned int iterations>
static T SqrtApprox(cons t T x, const T guess,
UnsignedInt<ite rations>* = 0)
{
return SqrtApprox(
x,
T(0.5f) * (guess + (x/guess)),
(UnsignedInt<it erations - 1>*)0
);
}

private:
static T SqrtApprox(cons t T x, const T guess, UnsignedInt<0>* )
{
return guess;
}
};

#include <iostream>

int main()
{
std::cout << Math<double>::S qrtApprox<10>(9 .5, 3.1) << '\n';
}

There may be other workarounds too.

Tom
--
C++ FAQ: http://www.parashift.com/c++-faq-lite/
C FAQ: http://www.eskimo.com/~scs/C-faq/top.html

[bartek]

tom_usenet <to********@hot mail.com> wrote in
news:4t******** *************** *********@4ax.c om:

But adding specializations there is illegal - specializations may only
appear at namespace scope.

The following works for me:

template <typename T>
struct Outer {
template <unsigned i>
struct Inner {
static T pow(T x)
{ return Inner<i-1>::pow(x)*x; }
};
template <>
struct Inner<1> {
static T pow(T x)
{ return x; }
};
template <>
struct Inner<0> {
static T pow(T x)
{ return 1; }
};
};

#include <iostream>

int main()
{
std::cout << Outer<float>::I nner<4>::pow(2) << std::endl;
return 0;

(Comeau C++ strict mode)

"main.cpp", line 9: error: explicit specialization is not allowed in
the current scope
template <>
^

Comeau compiles it in "Microsoft mode", and VC7.1 compiles it, so I
guess it is a Microsoft extension.

OOPS...

Funny though - I'm using VC6. I don't quite get the point of such
extensions, considering how limited is VC6's support for templates,
except for opening ways for portability issues. sheesh.

Thanks for clearing this up.

Cheers!

[bartek]

tom_usenet <to********@hot mail.com> wrote in
news:4t******** *************** *********@4ax.c om:

But adding specializations there is illegal - specializations may only
appear at namespace scope.

The following works for me:

template <typename T>
struct Outer {
template <unsigned i>
struct Inner {
static T pow(T x)
{ return Inner<i-1>::pow(x)*x; }
};
template <>
struct Inner<1> {
static T pow(T x)
{ return x; }
};
template <>
struct Inner<0> {
static T pow(T x)
{ return 1; }
};
};

#include <iostream>

int main()
{
std::cout << Outer<float>::I nner<4>::pow(2) << std::endl;
return 0;

(Comeau C++ strict mode)

"main.cpp", line 9: error: explicit specialization is not allowed in
the current scope
template <>
^

Comeau compiles it in "Microsoft mode", and VC7.1 compiles it, so I
guess it is a Microsoft extension.

OOPS...

Funny though - I'm using VC6. I don't quite get the point of such
extensions, considering how limited is VC6's support for templates,
except for opening ways for portability issues. sheesh.

Thanks for clearing this up.

Cheers!

[bartek]

tom_usenet <to********@hot mail.com> wrote in
news:0j******** *************** *********@4ax.c om:

On 7 Apr 2004 10:26:04 -0400, st***@waits.net (Stephen Waits) wrote:

Occasionall y we want to perform a Sqrt where we don't need accuracy
and/or we have a good initial guess - a situation where an N-step Sqrt
series may be more optimal than a full on Sqrt(). For example:

template <unsigned int iterations>
T SqrtApprox(cons t T x, const T guess)
{
return SqrtApprox<iter ations-1>( x, T(0.5f) * (guess + (x/guess)) );
}

template <>
T SqrtApprox<0>(c onst T x, const T guess)
{
return guess;
}

The problems came when I attempted to get this little template
metaprogram into our main Math<T> class which looks something like
this:

template <typename T>
class Math
{
public:
static T Sqrt(T x);
static T Sin(T x);
static T ASin(T x);
... // SqrtApprox should be in here
};
So, I've coded up a few simple examples describing the process I've
gone through in trying to get this to work...

Because this is a static member I cannot specialize it (because I
believe this is a function template, of which specialization is NOT
allowed by C++). Correct me if I'm wrong.

IIRC you can specialize a member function template, as long as the
enclosing class is completely specialized.

And, of course, as you experts know already, specialization of this
nested class is not allowed because the enclosing class template is
not specialized. Again, correct me if I'm wrong here.

No, you're not wrong.

What do you suggest I do to work around these issues?

Overloading? Or you could rely on the optimizer to do a good job
passing the iteration as a normal parameter. Anyway, here's an
overloading based approach, which works around the problem without
needing to change the call syntax:

template <unsigned int N>
struct UnsignedInt
{
static unsigned int const value = N;
};

template <typename T>
class Math
{
public:
template <unsigned int iterations>
static T SqrtApprox(cons t T x, const T guess,
UnsignedInt<ite rations>* = 0)
{
return SqrtApprox(
x,
T(0.5f) * (guess + (x/guess)),
(UnsignedInt<it erations - 1>*)0
);
}

private:
static T SqrtApprox(cons t T x, const T guess, UnsignedInt<0>* )
{
return guess;
}
};

#include <iostream>

int main()
{
std::cout << Math<double>::S qrtApprox<10>(9 .5, 3.1) << '\n';
}

There may be other workarounds too.

Indeed :) the following uses a separate template class to delegate work
into. Funny ... my compiler gives me an internal error with this. :)

template <unsigned n>
struct SqrtApproxImpl {
template <typename T>
static T eval(const T x, const T guess)
{return SqrtApproxImpl< n-1>::eval(x, T(0.5f) * (guess + (x/guess)));}
};

template <>
struct SqrtApproxImpl< 0> {
template <typename T>
static T eval(const T x, const T guess)
{return guess;}
};

template <typename T>
struct Math {
template <unsigned n>
static T SqrtApprox(cons t T x, const T guess)
{ return SqrtApproxImpl< n>::eval(x, guess); }
};

#include <iostream>

int main()
{
std::cout << Math<double>::S qrtApprox<10>(9 .5, 3.1) << std::endl;
return 0;
}