calculate polynomial with coefficients as abstract class Number - c++

Question

I am struggling with adding operations of classes Natural, Rational, Complex that represent appropriate math objects. I need that to calculate polynomial in x.
All classes inherit abstract class Number. Having all coefficients in an array of Numbers I want to calculate the polynomial. To do so I need operation of multiplying by double (x is double). x gets transformed into Rational and multiplied. This works fine. My problem is how to add classes of abstract type Number?
I can't make it work. All I get is never ending recursion in Number::add(Number) (it invokes itself instead of invoking others methods for types Natural, Rational, Complex).
#include
#include
#include
#include
#include
#include
#include
using namespace std;
class Natural;class Rational;class Complex;
class Number {
public:
virtual string toString() const = 0;
virtual Number *operator*(const Rational) const = 0;
virtual Number *add(const Natural*) const = 0;
virtual Number *add(const Rational*) const = 0;
virtual Number *add(const Complex*) const = 0;
virtual Number *add(const Number *n) const {
n->add(this);
}
};
class Natural : public Number {
friend class Complex;
int n;
public:
Natural(const Natural &s) {
n = s.n;
}
Natural(int number) : n(number) {}
string toString() const {
stringstream ss;
ss << n;
return ss.str();
}
operator Rational() const;
operator Complex() const;
operator int() const {
return n;
}
Number *operator*(const Rational r) const;
Number *add(const Natural* number) const {
return new Natural(n + number->n);
}
Number *add(const Rational*) const;
Number *add(const Complex*) const;
};
class Rational : public Number {
friend class Natural;
int numerator, denominator;
void divideByGCD() {
int a = numerator, b = denominator;
//cout << a << ' ' << b << ' ';
if(a < b) {
int temp = a;
a = b;
b = temp;
}
while (b > 0) {
int r = a % b;
a = b; b = r;
//cout << r << endl;
}
numerator /= a;
denominator /= a;
//cout << a << endl;
}
public:
Rational() {}
Rational(const Rational &s) {
numerator = s.numerator;
denominator = s.denominator;
}
Rational(int n, int d) {
if(d == 0) throw new runtime_error("denominator equals 0");
if(d < 0) {
numerator = -n;
denominator = -d;
} else {
numerator = n;
denominator = d;
}
divideByGCD();
}
Rational(double d) {
int i = 0, mul = 1;
int r = d-floor(d);;
while(r!=0) {
i++; mul *= 10;
r = 10*r-floor(10*r);
}
numerator = (int)mul*d;
denominator = mul;
divideByGCD();
}
string toString() const {
stringstream ss;
ss << numerator;
if(denominator > 1) ss << '/' << denominator;
return ss.str();
}
operator const Complex() const;
operator const double() const {
return (double)numerator/denominator;
}
Number *operator*(const Rational r) const {
return new Rational(numerator*r.numerator, denominator*r.denominator);
}
Number *add(const Rational* r) const {
return new Rational(numerator*r->denominator+r->numerator*denominator, denominator*r->denominator);
}
Number *add(const Natural*) const;
Number *add(const Complex*) const;
};
class Complex : public Number {
friend class Rational;
double real, imaginary;
static const double radius = 10;
public:
Complex() {}
Complex(const Complex &s) {
real = s.real;
imaginary = s.imaginary;
}
Complex(const double r, const double im) : real(r), imaginary(im) {}
string toString() const {
stringstream ss;
ss << real;
if(imaginary != 0) ss << '+' << imaginary << 'i';
return ss.str();
}
Number *operator*(const Rational r) const;
Number *add(const Complex* c) const {
return new Complex(real + c->real, imaginary + c->imaginary);
}
Number *add(const Natural*) const;
Number *add(const Rational*) const;
};
Natural::operator Rational() const {
return Rational(n,1);
}
Natural::operator Complex() const {
return Complex(n, 0);
}
Rational::operator const Complex() const {
return Complex((double)numerator/denominator, 0);
}
Number *Natural::operator*(const Rational r) const {
return new Rational(n*r.numerator, r.denominator);
}
Number *Complex::operator*(const Rational r) const {
return new Complex(real*(double)r, imaginary*(double)r);
}
Number *Natural::add(const Rational *r) const {
if(r->denominator == 1) return new Natural(n+r->numerator);
else return new Rational(n*r->denominator,r->denominator);
}
Number *Natural::add(const Complex *c) const {
return c->add(this);
}
Number *Rational::add(const Natural *n) const {
return n->add(this);
}
Number *Rational::add(const Complex *c) const {
return new Complex(c->real+(double)*this, c->imaginary);
}
Number *Complex::add(const Natural *number) const {
return new Complex(real+number->n, imaginary);
}
Number *Complex::add(const Rational *r) const {
return r->add(this);
}
Number *poly(double x, Number *a[], unsigned int size) {
if(size == 1) return a[0];
else return a[0]->add((*poly(x, a+1, size-1))*Rational(x));
}
int main() {
cout << (Natural(5)*(Rational)2.0)->toString() << endl;
Number *coefs[] = {new Natural(5), new Natural(6)};
cout << poly(2, coefs, 2) << endl;
}
How should I fix Number::add(Number) so that while invoking add on object of type Number program itself figure out which of virtual method add to choose?

Answer 1

This is known as multi-dispatch. Here are some links to look at
Multiple_dispatch
best multimethods implementation

Answer 2

I think the problem is:
virtual Number *add(const Number *n) const {
n->add(this);
}
If you multiply a Rational by a Natural that is stored in a Number *, it can't polymorphicly upcast the Number * to a Natural *. I agree w/g-makulik in that references/values make a lot more sense here, as you are leaking memory all over the place. Remove support for Number + Number. Also, if I add a Natural and a Rational together, I get a Number * back, but what kind of number is it? I think the architecture needs a bit more thought; I might get rid of the base class pure virtual methods entirely (except maybe toString). For example:
class Number
{
public:
virtual string toString() = 0;
};
class Rational : public Number
{
string toString() {...}
// forget 'add', use operators
Rational operator+(const Rational & _rhs) const {Rational ret; ...; return ret;}
Rational & operator+=(const Rational & _rhs) const {...; return *this;}
...
}
Edit
For a quick fix, I think you just need to get rid of virtual Number *operator*(const Rational) const = 0;, and replace it with a version for each sub-class (e.x., Rational * operator*(const Natural) const)
Or, add an enumerated member variable to Number to keep track of the type:
enum Type { NATURAL, RATIONAL, ...}
Type mType;
or use RTTI, such that you can selectively choose the right add method in Number::add:
Number * add(Number * _rhs)
{
if(_rhs->mType == RATIONAL)
return this->add((Rational *)_rhs);
...
}
it looks kinda sloppy, but it will work

Answer 3

it looks like Visitor pattern is what I've been looking for. I wanted to have functions accept and visit in the same class. I believe my mistake was to give them the same name.