JUCE/modules/juce_dsp/maths/juce_Polynomial.h

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  ==============================================================================
*/

namespace juce::dsp
{

/**
    A class representing a polynomial

    @tags{DSP}
*/
template <typename FloatingType>
class Polynomial
{
public:
    //==============================================================================
    /** Creates a new polynomial which will always evaluate to zero. */
    Polynomial()
    {
        coeffs.add (0);
    }

    /** Creates a new polynomial with given coefficients.

        @param numCoefficients The number of coefficients stored in coefficients.
                               This is also the order of the returned polynomial.
        @param coefficients    The coefficients which will be used by the newly
                               created polynomial. The Polynomial class will keep
                               a private copy of the coefficients.
    */
    Polynomial (const FloatingType* coefficients, int numCoefficients)
        : coeffs (coefficients, numCoefficients)
    {
        jassert (! coeffs.isEmpty());
    }

    /** Creates a copy of another polynomial. */
    Polynomial (const Polynomial&) = default;

    /** Creates a copy of another polynomial. */
    Polynomial (Polynomial&&) = default;

    /** Creates a copy of another polynomial. */
    Polynomial& operator= (const Polynomial&) = default;

    /** Creates a copy of another polynomial. */
    Polynomial& operator= (Polynomial&&) = default;

    /** Creates a new polynomial with coefficients by a C++11 initializer list.
        This function can be used in the following way:
        Polynomial<float> p ({0.5f, -0.3f, 0.2f});
    */
    template <typename... Values>
    Polynomial (Values... items)  : coeffs (items...)
    {
        jassert (! coeffs.isEmpty());
    }

    //==============================================================================
    /** Returns a single coefficient of the receiver for reading */
    FloatingType operator[] (int index) const noexcept              { return coeffs.getUnchecked (index); }

    /** Returns a single coefficient of the receiver for modifying. */
    FloatingType& operator[] (int index) noexcept                   { return coeffs.getReference (index); }

    /** Evaluates the value of the polynomial at a single point x. */
    FloatingType operator() (FloatingType x) const noexcept
    {
        // Horner's method
        FloatingType y (0);

        for (int i = coeffs.size(); --i >= 0;)
            y = (x * y) + coeffs.getUnchecked (i);

        return y;
    }

    /** Returns the order of the polynomial. */
    int getOrder() noexcept
    {
        return coeffs.size() - 1;
    }

    //==============================================================================
    /** Returns the polynomial with all its coefficients multiplied with a gain factor */
    Polynomial<FloatingType> withGain (double gain) const
    {
        auto result = *this;

        for (auto& c : result.coeffs)
            c *= gain;

        return result;
    }

    /** Returns the sum of this polynomial with another */
    Polynomial<FloatingType> getSumWith (const Polynomial<FloatingType>& other) const
    {
        if (coeffs.size() < other.coeffs.size())
            return other.getSumWith (*this);

        auto result = *this;

        for (int i = 0; i < other.coeffs.size(); ++i)
            result[i] += other[i];

        return result;
    }

    /** computes the product of two polynomials and return the result */
    Polynomial<FloatingType> getProductWith (const Polynomial<FloatingType>& other) const
    {
        Polynomial<FloatingType> result;
        result.coeffs.clearQuick();

        auto N1 = coeffs.size();
        auto N2 = other.coeffs.size();
        auto Nmax = jmax (N1, N2);

        auto N = N1 + N2 - 1;

        for (int i = 0; i < N; ++i)
        {
            FloatingType value (0);

            for (int j = 0; j < Nmax; ++j)
                if (j >= 0 && j < N1 && i - j >= 0 && i - j < N2)
                    value = value + (*this)[j] * other[i - j];

            result.coeffs.add (value);
        }

        return result;
    }

private:
    //==============================================================================
    Array<FloatingType> coeffs;

    JUCE_LEAK_DETECTOR (Polynomial)
};

} // namespace juce::dsp