/*
* All or portions of this file Copyright (c) Amazon.com, Inc. or its affiliates or
* its licensors.
*
* For complete copyright and license terms please see the LICENSE at the root of this
* distribution (the "License"). All use of this software is governed by the License,
* or, if provided, by the license below or the license accompanying this file. Do not
* remove or modify any license notices. This file is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
*/
// Original file Copyright Crytek GMBH or its affiliates, used under license.

#ifndef CRYINCLUDE_CRYPHYSICS_POLYNOMIAL_H
#define CRYINCLUDE_CRYPHYSICS_POLYNOMIAL_H
#pragma once

#if ENABLE_CRY_PHYSICS

template<class ftype, int degree>
class polynomial_tpl
{
public:
    explicit polynomial_tpl() { denom = (ftype)1; };
    explicit polynomial_tpl(ftype op) { zero(); data[degree] = op; }
    ILINE polynomial_tpl& zero()
    {
        for (int i = 0; i <= degree; i++)
        {
            data[i] = 0;
        }
        denom = (ftype)1;
        return *this;
    }
    polynomial_tpl(const polynomial_tpl<ftype, degree>& src) { *this = src; }
    polynomial_tpl& operator=(const polynomial_tpl<ftype, degree>& src)
    {
        denom = src.denom;
        for (int i = 0; i <= degree; i++)
        {
            data[i] = src.data[i];
        }
        return *this;
    }
    template<int degree1>
    ILINE polynomial_tpl& operator=(const polynomial_tpl<ftype, degree1>& src)
    {
        int i;
        denom = src.denom;
        for (i = 0; i <= min(degree, degree1); i++)
        {
            data[i] = src.data[i];
        }
        for (; i < degree; i++)
        {
            data[i] = 0;
        }
        return *this;
    }
    ILINE polynomial_tpl& set(ftype* pdata)
    {
        for (int i = 0; i <= degree; i++)
        {
            data[degree - i] = pdata[i];
        }
        return *this;
    }

    ILINE ftype& operator[](int idx) { return data[idx]; }

    void calc_deriviative(polynomial_tpl<ftype, degree>& deriv, int curdegree = degree) const;

    ILINE polynomial_tpl& fixsign()
    {
        ftype sg = sgnnz(denom);
        denom *= sg;
        for (int i = 0; i <= degree; i++)
        {
            data[i] *= sg;
        }
        return *this;
    }

    int findroots(ftype start, ftype end, ftype* proots, int nIters = 20, int curdegree = degree, bool noDegreeCheck = false) const;
    int nroots(ftype start, ftype end) const;

    ILINE ftype eval(ftype x) const
    {
        ftype res = 0;
        for (int i = degree; i >= 0; i--)
        {
            res = res * x + data[i];
        }
        return res;
    }
    ILINE ftype eval(ftype x, int subdegree) const
    {
        ftype res = data[subdegree];
        for (int i = subdegree - 1; i >= 0; i--)
        {
            res = res * x + data[i];
        }
        return res;
    }

    ILINE polynomial_tpl& operator+=(ftype op) { data[0] += op * denom; return *this; }
    ILINE polynomial_tpl& operator-=(ftype op) { data[0] -= op * denom; return *this; }
    ILINE polynomial_tpl operator*(ftype op) const
    {
        polynomial_tpl<ftype, degree> res;
        res.denom = denom;
        for (int i = 0; i <= degree; i++)
        {
            res.data[i] = data[i] * op;
        }
        return res;
    }
    ILINE polynomial_tpl& operator*=(ftype op)
    {
        for (int i = 0; i <= degree; i++)
        {
            data[i] *= op;
        }
        return *this;
    }
    ILINE polynomial_tpl operator/(ftype op) const
    {
        polynomial_tpl<ftype, degree> res = *this;
        res.denom = denom * op;
        return res;
    }
    ILINE polynomial_tpl& operator/=(ftype op) { denom *= op;   return *this; }

    ILINE polynomial_tpl<ftype, degree*2> sqr() const { return *this * *this; }

    ftype denom;
    ftype data[degree + 1];
};

template <class ftype>
struct tagPolyE
{
    inline static ftype polye() {return (ftype)1E-10; }
};

template<>
inline float tagPolyE<float>::polye() {return 1e-6f; }

template <class ftype>
inline ftype polye() { return tagPolyE<ftype>::polye(); }

// Don't use this macro; use AZStd::max instead. This is only here to make the template const arguments below readable
// and because Visual Studio 2013 doesn't have a const_expr version of std::max
#define deprecated_degmax(degree1, degree2) (((degree1) > (degree2)) ? (degree1) : (degree2))

template<class ftype, int degree>
ILINE polynomial_tpl<ftype, degree> operator+(const polynomial_tpl<ftype, degree>& pn, ftype op)
{
    polynomial_tpl<ftype, degree> res = pn;
    res.data[0] += op * res.denom;
    return res;
}
template<class ftype, int degree>
ILINE polynomial_tpl<ftype, degree> operator-(const polynomial_tpl<ftype, degree>& pn, ftype op)
{
    polynomial_tpl<ftype, degree> res = pn;
    res.data[0] -= op * res.denom;
    return res;
}

template<class ftype, int degree>
ILINE polynomial_tpl<ftype, degree> operator+(ftype op, const polynomial_tpl<ftype, degree>& pn)
{
    polynomial_tpl<ftype, degree> res = pn;
    res.data[0] += op * res.denom;
    return res;
}
template<class ftype, int degree>
ILINE polynomial_tpl<ftype, degree> operator-(ftype op, const polynomial_tpl<ftype, degree>& pn)
{
    polynomial_tpl<ftype, degree> res = pn;
    res.data[0] -= op * res.denom;
    for (int i = 0; i <= degree; i++)
    {
        res.data[i] = -res.data[i];
    }
    return res;
}
template<class ftype, int degree>
polynomial_tpl<ftype, degree*2> ILINE psqr(const polynomial_tpl<ftype, degree>& op) { return op * op; }

template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> operator+(const polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
{
    polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> res;
    int i;
    NO_BUFFER_OVERRUN
    for (i = 0; i <= min(degree1, degree2); i++)
    {
        res.data[i] = op1.data[i] * op2.denom + op2.data[i] * op1.denom;
    }
    for (; i <= degree1; i++)
    {
        res.data[i] = op1.data[i] * op2.denom;
    }
    for (; i <= degree2; i++)
    {
        res.data[i] = op2.data[i] * op1.denom;
    }
    res.denom = op1.denom * op2.denom;
    return res;
}
template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> operator-(const polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
{
    polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> res;
    int i;
    for (i = 0; i <= min(degree1, degree2); i++)
    {
        res.data[i] = op1.data[i] * op2.denom - op2.data[i] * op1.denom;
    }
    for (; i <= degree1; i++)
    {
        res.data[i] = op1.data[i] * op2.denom;
    }
    for (; i <= degree2; i++)
    {
        res.data[i] = op2.data[i] * op1.denom;
    }
    res.denom = op1.denom * op2.denom;
    return res;
}

template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, degree1>& operator+=(polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
{
    for (int i = 0; i < min(degree1, degree2); i++)
    {
        op1.data[i] = op1.data[i] * op2.denom + op2.data[i] * op1.denom;
    }
    op1.denom *= op2.denom;
    return op1;
}
template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, degree1>& operator-=(polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
{
    for (int i = 0; i < min(degree1, degree2); i++)
    {
        op1.data[i] = op1.data[i] * op2.denom - op2.data[i] * op1.denom;
    }
    op1.denom *= op2.denom;
    return op1;
}

template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, degree1 + degree2> operator*(const polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
{
    INDEX_NOT_OUT_OF_RANGE
    polynomial_tpl<ftype, degree1 + degree2> res;
    res.zero();
    int j;
    switch (degree1)
    {
    case 8:
        for (j = 0; j <= degree2; j++)
        {
            res.data[8 + j] += op1.data[8] * op2.data[j];
        }
    case 7:
        for (j = 0; j <= degree2; j++)
        {
            res.data[7 + j] += op1.data[7] * op2.data[j];
        }
    case 6:
        for (j = 0; j <= degree2; j++)
        {
            res.data[6 + j] += op1.data[6] * op2.data[j];
        }
    case 5:
        for (j = 0; j <= degree2; j++)
        {
            res.data[5 + j] += op1.data[5] * op2.data[j];
        }
    case 4:
        for (j = 0; j <= degree2; j++)
        {
            res.data[4 + j] += op1.data[4] * op2.data[j];
        }
    case 3:
        for (j = 0; j <= degree2; j++)
        {
            res.data[3 + j] += op1.data[3] * op2.data[j];
        }
    case 2:
        for (j = 0; j <= degree2; j++)
        {
            res.data[2 + j] += op1.data[2] * op2.data[j];
        }
    case 1:
        for (j = 0; j <= degree2; j++)
        {
            res.data[1 + j] += op1.data[1] * op2.data[j];
        }
    case 0:
        for (j = 0; j <= degree2; j++)
        {
            res.data[0 + j] += op1.data[0] * op2.data[j];
        }
    }
    res.denom = op1.denom * op2.denom;
    return res;
}


template <class ftype>
ILINE void polynomial_divide(const polynomial_tpl<ftype, 8>& num, const polynomial_tpl<ftype, 8>& den, polynomial_tpl<ftype, 8>& quot,
    polynomial_tpl<ftype, 8>& rem, int degree1, int degree2)
{
    int i, j, k, l;
    ftype maxel;
    for (i = 0; i <= degree1; i++)
    {
        rem.data[i] = num.data[i];
    }
    for (i = 0; i <= degree1 - degree2; i++)
    {
        quot.data[i] = 0;
    }
    for (i = 1, maxel = fabs_tpl(num.data[0]); i <= degree1; i++)
    {
        maxel = max(maxel, num.data[i]);
    }
    for (maxel *= polye<ftype>(); degree1 >= 0 && fabs_tpl(num.data[degree1]) < maxel; degree1--)
    {
        ;
    }
    for (i = 1, maxel = fabs_tpl(den.data[0]); i <= degree2; i++)
    {
        maxel = max(maxel, den.data[i]);
    }
    for (maxel *= polye<ftype>(); degree2 >= 0 && fabs_tpl(den.data[degree2]) < maxel; degree2--)
    {
        ;
    }
    rem.denom = num.denom;
    quot.denom = (ftype)1;
    if (degree1 < 0 || degree2 < 0)
    {
        return;
    }

    for (k = degree1 - degree2, l = degree1; l >= degree2; l--, k--)
    {
        quot.data[k] = rem.data[l] * den.denom;
        quot.denom *= den.data[degree2];
        for (i = degree1 - degree2; i > k; i--)
        {
            quot.data[i] *= den.data[degree2];
        }
        for (i = degree2 - 1, j = l - 1; i >= 0; i--, j--)
        {
            rem.data[j] = rem.data[j] * den.data[degree2] - den.data[i] * rem.data[l];
        }
        for (; j >= 0; j--)
        {
            rem.data[j] *= den.data[degree2];
        }
        rem.denom *= den.data[degree2];
    }
}

template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, degree1 - degree2> operator/(const polynomial_tpl<ftype, degree1>& num, const polynomial_tpl<ftype, degree2>& den)
{
    polynomial_tpl<ftype, degree1 - degree2> quot;
    polynomial_tpl<ftype, degree1> rem;
    polynomial_divide((polynomial_tpl<ftype, 8>&)num, (polynomial_tpl<ftype, 8>&)den, (polynomial_tpl<ftype, 8>&)quot,
        (polynomial_tpl<ftype, 8>&)rem, degree1, degree2);
    return quot;
}
template <class ftype, int degree1, int degree2>
ILINE polynomial_tpl<ftype, degree2 - 1> operator%(const polynomial_tpl<ftype, degree1>& num, const polynomial_tpl<ftype, degree2>& den)
{
    polynomial_tpl<ftype, degree1 - degree2> quot;
    polynomial_tpl<ftype, degree1> rem;
    polynomial_divide((polynomial_tpl<ftype, 8>&)num, (polynomial_tpl<ftype, 8>&)den, (polynomial_tpl<ftype, 8>&)quot,
        (polynomial_tpl<ftype, 8>&)rem, degree1, degree2);
    return (polynomial_tpl<ftype, degree2 - 1>&)rem;
}

template <class ftype, int degree>
ILINE void polynomial_tpl<ftype, degree>::calc_deriviative(polynomial_tpl<ftype, degree>& deriv, int curdegree) const
{
    for (int i = 0; i < curdegree; i++)
    {
        deriv.data[i] = data[i + 1] * (i + 1);
    }
    deriv.denom = denom;
}

template<typename to_t, typename from_t>
to_t* convert_type(from_t* input)
{
    typedef union
    {
        to_t* to;
        from_t* from;
    } convert_union;
    convert_union u;
    u.from = input;
    return u.to;
}

template <class ftype, int degree>
ILINE int polynomial_tpl<ftype, degree>::nroots(ftype start, ftype end) const
{
    polynomial_tpl<ftype, degree> f[degree + 1];
    int i, j, sg_a, sg_b;
    ftype val, prevval;

    calc_deriviative(f[0]);
    polynomial_divide(*convert_type<polynomial_tpl<ftype, 8> >(this), *convert_type< polynomial_tpl<ftype, 8> >(&f[0]), *convert_type<polynomial_tpl<ftype, 8> >(&f[degree]),
        *convert_type<polynomial_tpl<ftype, 8> >(&f[1]), degree, degree - 1);
    f[1].denom = -f[1].denom;
    for (i = 2; i < degree; i++)
    {
        polynomial_divide(*convert_type<polynomial_tpl<ftype, 8> >(&f[i - 2]), *convert_type<polynomial_tpl<ftype, 8> >(&f[i - 1]), *convert_type<polynomial_tpl<ftype, 8> >(&f[degree]),
            *convert_type<polynomial_tpl<ftype, 8> >(&f[i]), degree + 1 - i, degree - i);
        f[i].denom = -f[i].denom;
        if (fabs_tpl(f[i].denom) > (ftype)1E10)
        {
            for (j = 0; j <= degree - 1 - i; j++)
            {
                f[i].data[j] *= (ftype)1E-10;
            }
            f[i].denom *= (ftype)1E-10;
        }
    }

    prevval = eval(start) * denom;
    for (i = sg_a = 0; i < degree; i++, prevval = val)
    {
        val = f[i].eval(start, degree - 1 - i) * f[i].denom;
        sg_a += isneg(val * prevval);
    }

    prevval = eval(end) * denom;
    for (i = sg_b = 0; i < degree; i++, prevval = val)
    {
        val = f[i].eval(end, degree - 1 - i) * f[i].denom;
        sg_b += isneg(val * prevval);
    }

    return fabs_tpl(sg_a - sg_b);
}

template<class ftype>
ILINE ftype cubert_tpl(ftype x) { return fabs_tpl(x) > (ftype)1E-20 ? exp_tpl(log_tpl(fabs_tpl(x)) * (ftype)(1.0 / 3)) * sgnnz(x) : x; }
template<class ftype>
ILINE ftype pow_tpl(ftype x, ftype pow) { return fabs_tpl(x) > (ftype)1E-20 ? exp_tpl(log_tpl(fabs_tpl(x)) * pow) * sgnnz(x) : x; }
template<class ftype>
ILINE void swap(ftype* ptr, int i, int j) { ftype t = ptr[i]; ptr[i] = ptr[j]; ptr[j] = t; }

template <class ftype, int maxdegree>
int polynomial_tpl<ftype, maxdegree>::findroots(ftype start, ftype end, ftype* proots, int nIters, int degree, bool noDegreeCheck) const
{
    int i, j, nRoots = 0;
    ftype maxel;
    if (!noDegreeCheck)
    {
        for (i = 1, maxel = fabs_tpl(data[0]); i <= degree; i++)
        {
            maxel = max(maxel, data[i]);
        }
        for (maxel *= polye<ftype>(); degree > 0 && fabs_tpl(data[degree]) <= maxel; degree--)
        {
            ;
        }
    }

    if (degree == 1)
    {
        proots[0] = data[0] / data[1];
        nRoots = 1;
    }
    else if (degree == 2)
    {
        ftype a, b, c, d, bound[2], sg;

        a = data[2];
        b = data[1];
        c = data[0];
        d = aznumeric_cast<ftype>(sgnnz(a));
        a *= d;
        b *= d;
        c *= d;
        d = b * b - a * c * 4;
        bound[0] = start * a * 2 + b;
        bound[1] = end * a * 2 + b;
        sg = aznumeric_cast<ftype>((sgnnz(bound[0] * bound[1]) + 1) >> 1);
        bound[0] *= bound[0];
        bound[1] *= bound[1];
        bound[isneg(fabs_tpl(bound[1]) - fabs_tpl(bound[0]))] *= sg;

        if (isnonneg(d) & inrange(d, bound[0], bound[1]))
        {
            d = sqrt_tpl(d);
            a = (ftype)0.5 / a;
            proots[nRoots] = (-b - d) * a;
            nRoots += inrange(proots[nRoots], start, end);
            proots[nRoots] = (-b + d) * a;
            nRoots += inrange(proots[nRoots], start, end);
        }
    }
    else if (degree == 3)
    {
        ftype t, a, b, c, a3, p, q, Q, Qr, Ar, Ai, phi;

        t = (ftype)1.0 / data[3];
        a = data[2] * t;
        b = data[1] * t;
        c = data[0] * t;
        a3 = a * (ftype)(1.0 / 3);
        p = b - a * a3;
        q = (a3 * b - c) * (ftype)0.5 - cube(a3);
        Q = cube(p * (ftype)(1.0 / 3)) + q * q;
        Qr = sqrt_tpl(fabs_tpl(Q));

        if (Q > 0)
        {
            proots[0] = cubert_tpl(q + Qr) + cubert_tpl(q - Qr) - a3;
            nRoots = 1;
        }
        else
        {
            phi = atan2_tpl(Qr, q) * (ftype)(1.0 / 3);
            t = pow_tpl(Qr * Qr + q * q, (ftype)(1.0 / 6));
            Ar = t * cos_tpl(phi);
            Ai = t * sin_tpl(phi);
            proots[0] = 2 * Ar - a3;
            proots[1] = aznumeric_cast<ftype>(-Ar + Ai * sqrt3 - a3);
            proots[2] = aznumeric_cast<ftype>(-Ar - Ai * sqrt3 - a3);
            i = idxmax3(proots);
            swap(proots, i, 2);
            i = isneg(proots[0] - proots[1]);
            swap(proots, i, 1);
            nRoots = 3;
        }
    }
    else if (degree == 4)
    {
        ftype t, a3, a2, a1, a0, y, R, D, E, subroots[3];
        const ftype e = (ftype)1E-9;

        INDEX_NOT_OUT_OF_RANGE
            t = (ftype)1.0 / data[4];
        a3 = data[3] * t;
        a2 = data[2] * t;
        a1 = data[1] * t;
        a0 = data[0] * t;
        polynomial_tpl<ftype, 3> p3aux;
        ftype kp3aux[] = { 1, -a2, a1 * a3 - 4 * a0, 4 * a2 * a0 - a1 * a1 - a3 * a3 * a0 };
        p3aux.set(kp3aux);
        if (!p3aux.findroots((ftype) - 1E20, (ftype)1E20, subroots))
        {
            return 0;
        }
        R = a3 * a3 * (ftype)0.25 - a2 + (y = subroots[0]);

        if (R > -e)
        {
            if (R < e)
            {
                D = E = a3 * a3 * (ftype)(3.0 / 4) - 2 * a2;
                t = y * y - 4 * a0;
                if (t < -e)
                {
                    return 0;
                }
                t = 2 * sqrt_tpl(max((ftype)0, t));
            }
            else
            {
                R = sqrt_tpl(max((ftype)0, R));
                D = E = a3 * a3 * (ftype)(3.0 / 4) - R * R - 2 * a2;
                t = (4 * a3 * a2 - 8 * a1 - a3 * a3 * a3) / R * (ftype)0.25;
            }
            if (D + t > -e)
            {
                D = sqrt_tpl(max((ftype)0, D + t));
                proots[nRoots++] = a3 * (ftype) - 0.25 + (R - D) * (ftype)0.5;
                proots[nRoots++] = a3 * (ftype) - 0.25 + (R + D) * (ftype)0.5;
            }
            if (E - t > -e)
            {
                E = sqrt_tpl(max((ftype)0, E - t));
                proots[nRoots++] = a3 * (ftype) - 0.25 - (R + E) * (ftype)0.5;
                proots[nRoots++] = a3 * (ftype) - 0.25 - (R - E) * (ftype)0.5;
            }
            if (nRoots == 4)
            {
                i = idxmax3(proots);
                if (proots[3] < proots[i])
                {
                    swap(proots, i, 3);
                }
                i = idxmax3(proots);
                swap(proots, i, 2);
                i = isneg(proots[0] - proots[1]);
                swap(proots, i, 1);
            }
        }
    }
    else if (degree > 4)
    {
        ftype roots[maxdegree + 1], prevroot, val, prevval[2], curval, bound[2], middle;
        polynomial_tpl<ftype, maxdegree> deriv;
        int nExtremes, iter, iBound;
        calc_deriviative(deriv);

        // find a subset of deriviative extremes between start and end
        for (nExtremes = deriv.findroots(start, end, roots + 1, nIters, degree - 1) + 1; nExtremes > 1 && roots[nExtremes - 1] > end; nExtremes--)
        {
            ;
        }
        for (i = 1; i < nExtremes && roots[i] < start; i++)
        {
            ;
        }
        roots[i - 1] = start;
        PREFAST_ASSUME(nExtremes < maxdegree + 1);
        roots[nExtremes++] = end;

        for (prevroot = start, prevval[0] = eval(start, degree), nRoots = 0; i < nExtremes; prevval[0] = val, prevroot = roots[i++])
        {
            val = eval(roots[i], degree);
            if (val * prevval[0] < 0)
            {
                // we have exactly one root between prevroot and roots[i]
                bound[0] = prevroot;
                bound[1] = roots[i];
                iter = 0;
                do
                {
                    middle = (bound[0] + bound[1]) * (ftype)0.5;
                    curval = eval(middle, degree);
                    iBound = isneg(prevval[0] * curval);
                    bound[iBound] = middle;
                    prevval[iBound] = curval;
                } while (++iter < nIters);
                proots[nRoots++] = middle;
            }
        }
    }

    for (i = 0; i < nRoots && proots[i] < start; i++)
    {
        ;
    }
    for (; nRoots > i && proots[nRoots - 1] > end; nRoots--)
    {
        ;
    }
    for (j = i; j < nRoots; j++)
    {
        proots[j - i] = proots[j];
    }

    return nRoots - i;
}

typedef polynomial_tpl<real, 3> P3;
typedef polynomial_tpl<real, 2> P2;
typedef polynomial_tpl<real, 1> P1;
typedef polynomial_tpl<float, 3> P3f;
typedef polynomial_tpl<float, 2> P2f;
typedef polynomial_tpl<float, 1> P1f;

#endif // ENABLE_CRY_PHYSICS

#endif // CRYINCLUDE_CRYPHYSICS_POLYNOMIAL_H