Complex number prints wierd

[Protoman]

I'm trying to print a complex number and i get this as output: Phi:
(1.618034,0.000000).
What does it mean? How do I get it to print normally? Here's the code:

----------fib.hpp-------------
#ifndef FIB_HPP
#define FIB_HPP
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <complex>
using namespace std;

namespace
{
template <long N>
class Fib
{
public:
static const long double val=Fib<N-2>::val+Fib<N-1>::val;
};

template<>
class Fib<2>
{
public:
static const long double val=1;
};

template<>
class Fib<1>
{
public:
static const long double val=1;
};

const complex<long double> phi= Fib<32>::val/Fib<31>::val;
}
#endif
--------------------------

------Main.cpp------
#include "fib.hpp"

int main()
{
cout << "Phi: " << fixed << phi << endl;
system("PAUSE");
return 0;
}

 

[Kai-Uwe Bux]

I'm trying to print a complex number and i get this as output: Phi:
(1.618034,0.000000).
What does it mean?

It means that your complex number has a real part of 1.618034 and an
imaginary part of 0.0.

How do I get it to print normally?

This is the way complex numbers print *normally*. What did you expect?


[code snipped]


Best

Kai-Uwe Bux

 

[Protoman]

OK. Is this a fast way to get fibonacci numbers?

 

[Chris Goller]

You are calculating the fibonacci of 32 and 31 at compile time. So,
when the program runs, it doesn't have to calculate the sequence.

 

[Protoman]

Is there anyway I can make it faster? Do you know if there's a name for
what I'm doing for Fib?

 

[Greg]

You are calculating the fibonacci of 32 and 31 at compile time. So,
when the program runs, it doesn't have to calculate the sequence.

There is no such thing as the Fibonacci of a number.

Granted, there is 32nd and 31st Fibonacci number, but this program is
certainly not calculating either of them. Nor is it successfully
calculating the golden mean.

This program is simply dividing the sum of all integers from 1 to 32 by
the sum of all integers from 1 to 31.

Greg

 

[Kai-Uwe Bux]

There is no such thing as the Fibonacci of a number.

Granted, there is 32nd and 31st Fibonacci number, but this program is
certainly not calculating either of them. Nor is it successfully
calculating the golden mean.

Your assesment is a little off, at least if you are referring to the program
in the original post: if the program compiled, it would compute Fibonacci
numbers and the golden mean; the problem with the code is that it uses
in-place initialization for non-integral types. Here is a version that
compiles. The algorithm is completely unchanged.

#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <complex>
using namespace std;

template <long N>
class Fib
{
public:
static const unsigned long val=Fib<N-2>::val+Fib<N-1>::val;
};

template<>
class Fib<2>
{
public:
static const unsigned long val=1;
};

template<>
class Fib<1>
{
public:
static const unsigned long val=1;
};

const double phi= double(Fib<32>::val)/double(Fib<31>::val);

int main()
{
cout << "Phi: " << fixed << phi << endl;
return 0;
}

Guess what it prints:

Phi: 1.618034

That passes for an approximation of the golden mean. Moreover, you can print
the first few terms of the sequence:

#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <complex>
using namespace std;

template <long N>
class Fib
{
public:
static const unsigned long val=Fib<N-2>::val+Fib<N-1>::val;
};

template<>
class Fib<2>
{
public:
static const unsigned long val=1;
};

template<>
class Fib<1>
{
public:
static const unsigned long val=1;
};

const double phi= double(Fib<32>::val)/double(Fib<31>::val);

int main()
{
cout << Fib<1>::val << " "
<< Fib<2>::val << " "
<< Fib<3>::val << " "
<< Fib<4>::val << " "
<< Fib<5>::val << " "
<< Fib<6>::val << " "
<< Fib<7>::val << "\n";
return 0;
}


And that prints:

1 1 2 3 5 8 13

Looks like Fibonacci numbers to me.


Also, it is actually clear from the code that the program computes the
Fibonacci sequence.

This program is simply dividing the sum of all integers from 1 to 32 by
the sum of all integers from 1 to 31.

No it does not. The sum of all integers from 1 to 32 is 16*31. The sum of
all integers from 1 to 31 is 15*31. The quotient is 16/15.



Best

Kai-Uwe Bux

 

[Protoman]

So, how does the compiler execute the metaprogram?

 

[Karl Heinz Buchegger]

So, how does the compiler execute the metaprogram?

Well. If *you* were the compiler. What would *you* need to
do in order to create an executable program.
(Actually: A surprisingly large number of so called 'clever'
programming is just an adoption of what people do in real
life. So if you direct your thinking into 'What would I do
if all I have is paper and pencil?' is surprisingly often
an excellent tool in understanding what is going on.)

The compiler comes to compiling:

const complex<long double> phi= Fib<32>::val/Fib<31>::val;

This is a declaration of a complex<double> variable called phi.
The variable is initialized with the value of
Fib<32>::val/Fib<31>::val

For this the compiler needs to know
Fib<32>::val
and Fib<31>::val

Fib<32> is the instantiation of a template. Thus the compiler
looks up the Fib template and substitutes 32 for N

template <long N>
class Fib
{
public:
static const long double val=Fib<N-2>::val+Fib<N-1>::val;
};

becomes

class Fib
{
public:
static const long double val=Fib<30>::val+Fib<31>::val;
};

In order to make this compilable the compiler has to come up with
the initial value for val. For this it has to evaluate the initialization
part:

Fib<30>::val+Fib<31>::val

Again: The compiler is looking for an instantiation of Fib<30> and since
there is none it creates one, substituting 30 for N

class Fib
{
public:
static const long double val=Fib<28>::val+Fib<29>::val;
};

Part of compiling that one, makes the compiler look for an instatiation
of Fib<28>. Since there is none, the compiler creates one, using 28 for N

class Fib
{
public:
static const long double val=Fib<26>::val+Fib<27>::val;
};

And so on, and so on.
Finally the compiler will have the request to intialize one of the
generated classes with:

class Fib
{
public:
static const long double val=Fib<1>::val+Fib<2>::val;
};

Looking for Fib<1> the compiler figures out, that the programmer specified
that one:

template<>
class Fib<1>
{
public:
static const long double val=1;
};

so it doesn't need to create one on its own. Same for Fib<2>.

Since those 2 classes are 'complete' the compiler now can use
them to continue working on

class Fib
{
public:
static const long double val=Fib<1>::val+Fib<2>::val;
};

(which was the template instatiation for Fib<3>).
Fib<1>::val is known, it equals 1.
Fib<2>::val is known, it equals 1
Thus the initialization value for Fib<3>::val thus must be 2

Having this value, the compiler can continue on finishing
Fib<4> and so on, and so on, until finally Fib<32>::val can
be calculated by the compiler.
Now the whole story starts again for Fib<31>.

If both values Fib<32>::val and Fib<31>::val are known to the
copmiler, it can easily calculate Fib<32>::val / Fib<31>::val
and assign that value to phi.


However why one would want to do all of that with complex numbers
is bejond my imagination.

 

[Protoman]

So that's how metaprogramming works. Thanks!!!