Polynomial template

[Rubén Campos]

I've trying to implement polynomials of arbitrary order as a C++ template,
as shown here:

template <unsigned long int N>
class Polynomial
{
public:
Polynomial ();
~Polynomial ();

float getCoefficient (unsigned long int
const index);
void setCoefficient (unsigned long int const
index, float const value);

float evaluate (float const x);

Polynomial <N-1> derive ();
Polynomial <N+1> integrate ();

private:
float mCoefficients[N+1];
};

As could be expected, I've found problems with the extreme order
polynomials, that is, trying to derive a polynomial of 0 order (in fact, a
real number) or trying to integrate a polynomial of maximum order ((2^N) -
1).

So the question is, how can I deal with extreme order polynomials? It's
possible to provide different declarations (not only definitions) to
derive() and integrate()? Should I detect those illegal attempts and break
it with exception throwing?

Thank you

 

[Martin Eisenberg]

I've trying to implement polynomials of arbitrary order as a C++
template, as shown here:

template <unsigned long int N>
class Polynomial
{
public:
Polynomial ();
~Polynomial ();

float getCoefficient (unsigned long int const index);
void setCoefficient (unsigned long int const index, float const value);

float evaluate (float const x);

Polynomial <N-1> derive ();
Polynomial <N+1> integrate ();

private:
float mCoefficients[N+1];
};

As could be expected, I've found problems with the extreme order
polynomials, that is, trying to derive a polynomial of 0 order
(in fact, a real number) or trying to integrate a polynomial of
maximum order ((2^N) - 1).

So the question is, how can I deal with extreme order
polynomials? It's possible to provide different declarations
(not only definitions) to derive() and integrate()? Should I
detect those illegal attempts and break it with exception
throwing?

You could specialize Polynomial, but that would mean a lot of
duplication, so you might prefer to make derive and integrate
overloaded free functions.

#include <limits>
#include <stdexcept>

template <unsigned long int N>
Polynomial <N-1> derive(Polynomial <N> const & poly)
{ /* ... */ }

Polynomial <0> derive(Polynomial <0> const &)
{ return Polynomial <0> (); }
// I assume a fresh polynomial is identically zero.

template <unsigned long int N>
Polynomial <N+1> integrate(Polynomial <N> const & poly)
{ /* ... */ }

void integrate(Polynomial<std::numeric_limits<
unsigned long int>::max()> const &)
{ throw std:ut_of_range("Polynomial order too large"); }


Martin