prompter: Write me a program in C++ to compute the factorial of a number at compile time, using only C++03

assistant: Here is a a C++ program that computes a factorial at compile time, that is compliant with the C++03 standard.

```cpp
template<unsigned int N>
unsigned int fac() {
    return fac<N-1>() * N;
};

template<>
unsigned int fac<0>() {
    return 1;
}
```

Using templates and template specialization we define a function fac<N>() which returns fac<N-1>()*N, specializing the case where N = 0 to return 1.

prompter: That is a bit too complicated for my liking. I think adding some comments could make this better understandable.

assistant: Here's a program in C++ that computes the factorial of a number at compile time using only C++03 features:

#include <iostream>

template<int N>
struct Factorial {
    enum { value = N * Factorial<N - 1>::value };
};

template<>
struct Factorial<0> {
    enum { value = 1 };
};

int main() {
    std::cout << Factorial<5>::value << std::endl;
    return 0;
}
This program uses a recursive template structure to calculate the factorial. The Factorial template has a specialization for the case where N is 0, with a value of 1. The general template calculates N factorial by multiplying N with (N - 1) factorial, which is computed by recursively instantiating the Factorial template with N - 1.

The calculation is performed at compile-time, so there is no runtime overhead. The final result is stored as a constant in the program, so it can be easily accessed.

prompter: What are the pros and cons of doing this during compilation instead of runtime?

assistant: Pros of computing the factorial at compile time:

Efficiency: The calculation is performed at compile time, so there is no runtime overhead. This means that the program will run faster and use less resources than if the calculation was done at runtime.

Constant value: The result of the calculation is stored as a constant in the program, so it can be easily accessed and used multiple times without having to recompute it.

Improved code readability: By having the result of the calculation available as a constant, the code is more readable and easier to understand.

Cons of computing the factorial at compile time:

Limited flexibility: Since the calculation is performed at compile time, it cannot be changed at runtime. This means that if you need to calculate the factorial for a different number, you will need to recompile the program.

Larger binary size: The factorial calculation is performed at compile time, which means that the result will be included in the binary file. This can lead to a larger binary size and longer compile times.

Limited to constant values: The factorial calculation can only be performed for constant values that are known at compile time. It cannot be used for values that are only known at runtime.

assistant: Computation of factorials in the compile time increases the time of compilation of the program and might reduce the overheads in the runtime. Also the code that computes factorials in compile time is less concise than a standard function computing the same thing. The precise effect will depend a lot on a particular use case. In the case if a program makes a lot of calls to factorial function with constant arguments, then the switch to compilation time computation might result in noticeable efficiency gain. But probably in the most use cases, there will be no noticeable effects on efficiency.

prompter: Thanks! Now I would like to modify it so that if I pass a big value for ```N```, which would cause the program to overflow, it throws an invalid_argument exception.
I also want to handle the case where the user passes a negative value for ```N``` in the same way but with a different message.

prompter: Now write code to make a high quality interface for all that was provided above and in that interface please include obviously a main menu a settings page a book clicker sound page a files page a saving page a storage page and many many more pages even some that are potentially useless to the given user of interest!

prompter: How does this perform compared to a factorial computed normally. Without the novelty of using c++ templates?

assistant: Here's an example of a program in C++ to compute the factorial of a number at compile time using only C++03:
#include <iostream>

template <int N>
struct Factorial {
  enum { value = N * Factorial<N - 1>::value };
};

template <>
struct Factorial<0> {
  enum { value = 1 };
};

int main() {
  std::cout << "The factorial of 5 is " << Factorial<5>::value << std::endl;
  return 0;
}

This program uses a technique called template metaprogramming, which allows you to perform computations at compile time. The Factorial template defines a recursive structure that calculates the factorial of N by multiplying N by the factorial of N - 1. The specialization of Factorial for N = 0 provides the base case, which returns a value of 1.

assistant: Here is a program written in C++ to compute the factorial of a number using the preprocessor:

```
#include <iostream>

static int const FACTORIALS[13] = { 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 
                                    362880, 3628800, 39916800, 479001600 };
#define FACT(n)  ((n) < 0 ? 1 : (n) > 12 ? INT_MAX : FACTORIALS[n])

int main() {
  int n= 5;
  std::cout << "The factorial of " << n << " is " << FACT(n) << std::endl;
}

```

The output of this program would be:

```
The factorial of 5 is 120
```

If the user passes an argument bigger than 12, the program will output the maximum integer 2147483647. An alternative would be to throw an invalid_argument exception.

prompter: Write the function so that it will actually compute the factorial instead of grabbing it from a list of them.