bairstow.hpp

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#pragma once
 
#include <utility>
#include <vector>
 
#include "matrix2.hpp"
#include "vector2.hpp"
// #include "vector2_ref.hpp"
 
using Vec2 = ginger::Vector2<double>;
using Mat2 = ginger::Matrix2<Vec2>;
using Vec2Ref = ginger::Vector2<double&>;
 
namespace ginger {
    class Options;
}
 
extern auto horner_ref(std::vector<double>& coeffs, std::vector<Vec2Ref>& vcoeffs,
                       std::size_t degree, const Vec2& vr) -> Vec2Ref;
 
extern auto bairstow(const std::vector<double>& coeffs, Vec2& vr, const ginger::Options& options)
    -> std::pair<unsigned int, bool>;
 
inline auto makeadjoint_ref(const Vec2& vr, const Vec2Ref& vp) -> Mat2 {
    auto p = vp.x();
    auto s = vp.y();
    return {Vec2{s, -p}, Vec2{-p * vr.y(), p * vr.x() + s}};
}
 
inline auto delta_ref(const Vec2Ref& vA, const Vec2& vr, const Vec2Ref& vp) -> Vec2 {
    const auto mp = makeadjoint_ref(vr, vp);  // 2 mul's
    return mp.mdot(vA) / mp.det();            // 6 mul's + 2 div's
}