FindRoot.h

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// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)
// SPDX-FileCopyrightText: 2021 Jorrit Rouwe
// SPDX-License-Identifier: MIT
 
#pragma once
 
JPH_NAMESPACE_BEGIN
 
template <typename T>
inline int FindRoot(const T inA, const T inB, const T inC, T &outX1, T &outX2)
{
    // Check if this is a linear equation
    if (inA == T(0))
    {
        // Check if this is a constant equation
        if (inB == T(0))
        {
            if (inC == T(0))
            {
                outX1 = outX2 = 0.0f;
                return 1; // Actually infinitely many solutions
            }
 
            return 0;
        }
 
        // Linear equation with 1 solution
        outX1 = outX2 = -inC / inB;
        return 1;
    }
 
    // See Numerical Recipes in C, Chapter 5.6 Quadratic and Cubic Equations
    T det = DifferenceOfProducts(inB, inB, T(4) * inA, inC);
    if (det < T(0))
        return 0;
    T q = (inB + Sign(inB) * Sqrt(det)) / T(-2);
    outX1 = q / inA;
    if (q == T(0))
    {
        outX2 = outX1;
        return 1;
    }
    outX2 = inC / q;
    return 2;
}
 
JPH_NAMESPACE_END