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700 lines
26 KiB
C++
700 lines
26 KiB
C++
/*
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* Copyright (c) Contributors to the Open 3D Engine Project
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*
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* SPDX-License-Identifier: Apache-2.0 OR MIT
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*
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*/
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// Copied utils functions from CryPhysics that are used by non-physics systems
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// This functions will be eventually removed, DO *NOT* use these functions
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// TO-DO: Re-implement users using new code
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// LY-109806
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#pragma once
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#include "Cry_Math.h"
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namespace LegacyCryPhysicsUtils
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{
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namespace polynomial_tpl_IMPL
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{
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template<class ftype, int degree>
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class polynomial_tpl
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{
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public:
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explicit polynomial_tpl() { denom = (ftype)1; };
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explicit polynomial_tpl(ftype op) { zero(); data[degree] = op; }
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AZ_FORCE_INLINE polynomial_tpl& zero()
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{
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for (int i = 0; i <= degree; i++)
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{
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data[i] = 0;
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}
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denom = (ftype)1;
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return *this;
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}
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polynomial_tpl(const polynomial_tpl<ftype, degree>& src) { *this = src; }
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polynomial_tpl& operator=(const polynomial_tpl<ftype, degree>& src)
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{
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denom = src.denom;
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for (int i = 0; i <= degree; i++)
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{
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data[i] = src.data[i];
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}
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return *this;
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}
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template<int degree1>
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AZ_FORCE_INLINE polynomial_tpl& operator=(const polynomial_tpl<ftype, degree1>& src)
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{
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int i;
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denom = src.denom;
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for (i = 0; i <= min(degree, degree1); i++)
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{
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data[i] = src.data[i];
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}
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for (; i < degree; i++)
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{
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data[i] = 0;
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}
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return *this;
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}
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AZ_FORCE_INLINE polynomial_tpl& set(ftype* pdata)
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{
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for (int i = 0; i <= degree; i++)
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{
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data[degree - i] = pdata[i];
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}
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return *this;
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}
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AZ_FORCE_INLINE ftype& operator[](int idx) { return data[idx]; }
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void calc_deriviative(polynomial_tpl<ftype, degree>& deriv, int curdegree = degree) const;
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AZ_FORCE_INLINE polynomial_tpl& fixsign()
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{
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ftype sg = sgnnz(denom);
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denom *= sg;
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for (int i = 0; i <= degree; i++)
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{
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data[i] *= sg;
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}
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return *this;
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}
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int findroots(ftype start, ftype end, ftype* proots, int nIters = 20, int curdegree = degree, bool noDegreeCheck = false) const;
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int nroots(ftype start, ftype end) const;
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AZ_FORCE_INLINE ftype eval(ftype x) const
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{
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ftype res = 0;
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for (int i = degree; i >= 0; i--)
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{
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res = res * x + data[i];
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}
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return res;
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}
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AZ_FORCE_INLINE ftype eval(ftype x, int subdegree) const
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{
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ftype res = data[subdegree];
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for (int i = subdegree - 1; i >= 0; i--)
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{
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res = res * x + data[i];
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}
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return res;
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}
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AZ_FORCE_INLINE polynomial_tpl& operator+=(ftype op) { data[0] += op * denom; return *this; }
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AZ_FORCE_INLINE polynomial_tpl& operator-=(ftype op) { data[0] -= op * denom; return *this; }
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AZ_FORCE_INLINE polynomial_tpl operator*(ftype op) const
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{
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polynomial_tpl<ftype, degree> res;
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res.denom = denom;
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for (int i = 0; i <= degree; i++)
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{
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res.data[i] = data[i] * op;
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}
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return res;
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}
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AZ_FORCE_INLINE polynomial_tpl& operator*=(ftype op)
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{
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for (int i = 0; i <= degree; i++)
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{
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data[i] *= op;
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}
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return *this;
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}
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AZ_FORCE_INLINE polynomial_tpl operator/(ftype op) const
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{
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polynomial_tpl<ftype, degree> res = *this;
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res.denom = denom * op;
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return res;
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}
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AZ_FORCE_INLINE polynomial_tpl& operator/=(ftype op) { denom *= op; return *this; }
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree * 2> sqr() const { return *this * *this; }
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ftype denom;
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ftype data[degree + 1];
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};
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template <class ftype>
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struct tagPolyE
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{
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inline static ftype polye() { return (ftype)1E-10; }
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};
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template<>
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inline float tagPolyE<float>::polye() { return 1e-6f; }
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template <class ftype>
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inline ftype polye() { return tagPolyE<ftype>::polye(); }
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// Don't use this macro; use AZStd::max instead. This is only here to make the template const arguments below readable
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// and because Visual Studio 2013 doesn't have a const_expr version of std::max
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#define deprecated_degmax(degree1, degree2) (((degree1) > (degree2)) ? (degree1) : (degree2))
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template<class ftype, int degree>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree> operator+(const polynomial_tpl<ftype, degree>& pn, ftype op)
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{
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polynomial_tpl<ftype, degree> res = pn;
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res.data[0] += op * res.denom;
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return res;
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}
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template<class ftype, int degree>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree> operator-(const polynomial_tpl<ftype, degree>& pn, ftype op)
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{
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polynomial_tpl<ftype, degree> res = pn;
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res.data[0] -= op * res.denom;
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return res;
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}
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template<class ftype, int degree>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree> operator+(ftype op, const polynomial_tpl<ftype, degree>& pn)
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{
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polynomial_tpl<ftype, degree> res = pn;
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res.data[0] += op * res.denom;
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return res;
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}
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template<class ftype, int degree>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree> operator-(ftype op, const polynomial_tpl<ftype, degree>& pn)
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{
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polynomial_tpl<ftype, degree> res = pn;
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res.data[0] -= op * res.denom;
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for (int i = 0; i <= degree; i++)
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{
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res.data[i] = -res.data[i];
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}
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return res;
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}
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template<class ftype, int degree>
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polynomial_tpl<ftype, degree * 2> AZ_FORCE_INLINE psqr(const polynomial_tpl<ftype, degree>& op) { return op * op; }
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> operator+(const polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
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{
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polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> res;
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int i;
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for (i = 0; i <= min(degree1, degree2); i++)
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{
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res.data[i] = op1.data[i] * op2.denom + op2.data[i] * op1.denom;
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}
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for (; i <= degree1; i++)
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{
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res.data[i] = op1.data[i] * op2.denom;
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}
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for (; i <= degree2; i++)
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{
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res.data[i] = op2.data[i] * op1.denom;
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}
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res.denom = op1.denom * op2.denom;
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return res;
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}
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> operator-(const polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
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{
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polynomial_tpl<ftype, deprecated_degmax(degree1, degree2)> res;
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int i;
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for (i = 0; i <= min(degree1, degree2); i++)
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{
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res.data[i] = op1.data[i] * op2.denom - op2.data[i] * op1.denom;
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}
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for (; i <= degree1; i++)
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{
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res.data[i] = op1.data[i] * op2.denom;
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}
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for (; i <= degree2; i++)
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{
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res.data[i] = op2.data[i] * op1.denom;
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}
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res.denom = op1.denom * op2.denom;
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return res;
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}
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree1>& operator+=(polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
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{
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for (int i = 0; i < min(degree1, degree2); i++)
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{
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op1.data[i] = op1.data[i] * op2.denom + op2.data[i] * op1.denom;
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}
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op1.denom *= op2.denom;
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return op1;
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}
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree1>& operator-=(polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
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{
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for (int i = 0; i < min(degree1, degree2); i++)
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{
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op1.data[i] = op1.data[i] * op2.denom - op2.data[i] * op1.denom;
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}
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op1.denom *= op2.denom;
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return op1;
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}
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree1 + degree2> operator*(const polynomial_tpl<ftype, degree1>& op1, const polynomial_tpl<ftype, degree2>& op2)
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{
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polynomial_tpl<ftype, degree1 + degree2> res;
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res.zero();
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int j;
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switch (degree1)
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{
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case 8:
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for (j = 0; j <= degree2; j++)
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{
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res.data[8 + j] += op1.data[8] * op2.data[j];
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}
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case 7:
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for (j = 0; j <= degree2; j++)
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{
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res.data[7 + j] += op1.data[7] * op2.data[j];
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}
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case 6:
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for (j = 0; j <= degree2; j++)
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{
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res.data[6 + j] += op1.data[6] * op2.data[j];
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}
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case 5:
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for (j = 0; j <= degree2; j++)
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{
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res.data[5 + j] += op1.data[5] * op2.data[j];
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}
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case 4:
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for (j = 0; j <= degree2; j++)
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{
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res.data[4 + j] += op1.data[4] * op2.data[j];
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}
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case 3:
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for (j = 0; j <= degree2; j++)
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{
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res.data[3 + j] += op1.data[3] * op2.data[j];
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}
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case 2:
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for (j = 0; j <= degree2; j++)
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{
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res.data[2 + j] += op1.data[2] * op2.data[j];
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}
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case 1:
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for (j = 0; j <= degree2; j++)
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{
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res.data[1 + j] += op1.data[1] * op2.data[j];
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}
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case 0:
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for (j = 0; j <= degree2; j++)
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{
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res.data[0 + j] += op1.data[0] * op2.data[j];
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}
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}
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res.denom = op1.denom * op2.denom;
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return res;
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}
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template <class ftype>
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AZ_FORCE_INLINE void polynomial_divide(const polynomial_tpl<ftype, 8>& num, const polynomial_tpl<ftype, 8>& den, polynomial_tpl<ftype, 8>& quot,
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polynomial_tpl<ftype, 8>& rem, int degree1, int degree2)
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{
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int i, j, k, l;
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ftype maxel;
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for (i = 0; i <= degree1; i++)
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{
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rem.data[i] = num.data[i];
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}
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for (i = 0; i <= degree1 - degree2; i++)
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{
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quot.data[i] = 0;
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}
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for (i = 1, maxel = fabs_tpl(num.data[0]); i <= degree1; i++)
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{
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maxel = max(maxel, num.data[i]);
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}
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for (maxel *= polye<ftype>(); degree1 >= 0 && fabs_tpl(num.data[degree1]) < maxel; degree1--)
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{
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;
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}
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for (i = 1, maxel = fabs_tpl(den.data[0]); i <= degree2; i++)
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{
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maxel = max(maxel, den.data[i]);
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}
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for (maxel *= polye<ftype>(); degree2 >= 0 && fabs_tpl(den.data[degree2]) < maxel; degree2--)
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{
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;
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}
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rem.denom = num.denom;
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quot.denom = (ftype)1;
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if (degree1 < 0 || degree2 < 0)
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{
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return;
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}
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for (k = degree1 - degree2, l = degree1; l >= degree2; l--, k--)
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{
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quot.data[k] = rem.data[l] * den.denom;
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quot.denom *= den.data[degree2];
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for (i = degree1 - degree2; i > k; i--)
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{
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quot.data[i] *= den.data[degree2];
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}
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for (i = degree2 - 1, j = l - 1; i >= 0; i--, j--)
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{
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rem.data[j] = rem.data[j] * den.data[degree2] - den.data[i] * rem.data[l];
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}
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for (; j >= 0; j--)
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{
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rem.data[j] *= den.data[degree2];
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}
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rem.denom *= den.data[degree2];
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}
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}
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree1 - degree2> operator/(const polynomial_tpl<ftype, degree1>& num, const polynomial_tpl<ftype, degree2>& den)
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{
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polynomial_tpl<ftype, degree1 - degree2> quot;
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polynomial_tpl<ftype, degree1> rem;
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polynomial_divide((polynomial_tpl<ftype, 8>&)num, (polynomial_tpl<ftype, 8>&)den, (polynomial_tpl<ftype, 8>&)quot,
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(polynomial_tpl<ftype, 8>&)rem, degree1, degree2);
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return quot;
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}
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template <class ftype, int degree1, int degree2>
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AZ_FORCE_INLINE polynomial_tpl<ftype, degree2 - 1> operator%(const polynomial_tpl<ftype, degree1>& num, const polynomial_tpl<ftype, degree2>& den)
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{
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polynomial_tpl<ftype, degree1 - degree2> quot;
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polynomial_tpl<ftype, degree1> rem;
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polynomial_divide((polynomial_tpl<ftype, 8>&)num, (polynomial_tpl<ftype, 8>&)den, (polynomial_tpl<ftype, 8>&)quot,
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(polynomial_tpl<ftype, 8>&)rem, degree1, degree2);
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return (polynomial_tpl<ftype, degree2 - 1>&)rem;
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}
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template <class ftype, int degree>
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AZ_FORCE_INLINE void polynomial_tpl<ftype, degree>::calc_deriviative(polynomial_tpl<ftype, degree>& deriv, int curdegree) const
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{
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for (int i = 0; i < curdegree; i++)
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{
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deriv.data[i] = data[i + 1] * (i + 1);
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}
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deriv.denom = denom;
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}
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template<typename to_t, typename from_t>
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to_t* convert_type(from_t* input)
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{
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typedef union
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{
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to_t* to;
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from_t* from;
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} convert_union;
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convert_union u;
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u.from = input;
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return u.to;
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}
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template <class ftype, int degree>
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AZ_FORCE_INLINE int polynomial_tpl<ftype, degree>::nroots(ftype start, ftype end) const
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{
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polynomial_tpl<ftype, degree> f[degree + 1];
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int i, j, sg_a, sg_b;
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ftype val, prevval;
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calc_deriviative(f[0]);
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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]),
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*convert_type<polynomial_tpl<ftype, 8> >(&f[1]), degree, degree - 1);
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f[1].denom = -f[1].denom;
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for (i = 2; i < degree; i++)
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{
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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]),
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*convert_type<polynomial_tpl<ftype, 8> >(&f[i]), degree + 1 - i, degree - i);
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f[i].denom = -f[i].denom;
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if (fabs_tpl(f[i].denom) > (ftype)1E10)
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{
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for (j = 0; j <= degree - 1 - i; j++)
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{
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f[i].data[j] *= (ftype)1E-10;
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}
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f[i].denom *= (ftype)1E-10;
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}
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}
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prevval = eval(start) * denom;
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for (i = sg_a = 0; i < degree; i++, prevval = val)
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{
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val = f[i].eval(start, degree - 1 - i) * f[i].denom;
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sg_a += isneg(val * prevval);
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}
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prevval = eval(end) * denom;
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for (i = sg_b = 0; i < degree; i++, prevval = val)
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{
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val = f[i].eval(end, degree - 1 - i) * f[i].denom;
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sg_b += isneg(val * prevval);
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}
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return fabs_tpl(sg_a - sg_b);
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}
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template<class ftype>
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AZ_FORCE_INLINE 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; }
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template<class ftype>
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AZ_FORCE_INLINE 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; }
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template<class ftype>
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AZ_FORCE_INLINE void swap(ftype* ptr, int i, int j) { ftype t = ptr[i]; ptr[i] = ptr[j]; ptr[j] = t; }
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template <class ftype, int maxdegree>
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int polynomial_tpl<ftype, maxdegree>::findroots(ftype start, ftype end, ftype* proots, [[maybe_unused]] int nIters, int degree, bool noDegreeCheck) const
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{
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AZ_UNUSED(nIters);
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int i, j, nRoots = 0;
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ftype maxel;
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if (!noDegreeCheck)
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{
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for (i = 1, maxel = fabs_tpl(data[0]); i <= degree; i++)
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{
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maxel = max(maxel, data[i]);
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}
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for (maxel *= polye<ftype>(); degree > 0 && fabs_tpl(data[degree]) <= maxel; degree--)
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{
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;
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}
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}
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if constexpr (maxdegree >= 1)
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{
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if (degree == 1)
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{
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proots[0] = data[0] / data[1];
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nRoots = 1;
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}
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}
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if constexpr (maxdegree >= 2)
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{
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if (degree == 2)
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{
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ftype a, b, c, d, bound[2], sg;
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a = data[2];
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b = data[1];
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c = data[0];
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d = aznumeric_cast<ftype>(sgnnz(a));
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a *= d;
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b *= d;
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c *= d;
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d = b * b - a * c * 4;
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bound[0] = start * a * 2 + b;
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bound[1] = end * a * 2 + b;
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sg = aznumeric_cast<ftype>((sgnnz(bound[0] * bound[1]) + 1) >> 1);
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bound[0] *= bound[0];
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bound[1] *= bound[1];
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bound[isneg(fabs_tpl(bound[1]) - fabs_tpl(bound[0]))] *= sg;
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if (isnonneg(d) & inrange(d, bound[0], bound[1]))
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{
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d = sqrt_tpl(d);
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a = (ftype)0.5 / a;
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proots[nRoots] = (-b - d) * a;
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nRoots += inrange(proots[nRoots], start, end);
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proots[nRoots] = (-b + d) * a;
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nRoots += inrange(proots[nRoots], start, end);
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}
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}
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}
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if constexpr (maxdegree >= 3)
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{
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if (degree == 3)
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{
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ftype t, a, b, c, a3, p, q, Q, Qr, Ar, Ai, phi;
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|
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t = (ftype)1.0 / data[3];
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a = data[2] * t;
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b = data[1] * t;
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c = data[0] * t;
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a3 = a * (ftype)(1.0 / 3);
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p = b - a * a3;
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q = (a3 * b - c) * (ftype)0.5 - cube(a3);
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Q = cube(p * (ftype)(1.0 / 3)) + q * q;
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Qr = sqrt_tpl(fabs_tpl(Q));
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|
|
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if (Q > 0)
|
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{
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proots[0] = cubert_tpl(q + Qr) + cubert_tpl(q - Qr) - a3;
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nRoots = 1;
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|
}
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else
|
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{
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|
phi = atan2_tpl(Qr, q) * (ftype)(1.0 / 3);
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t = pow_tpl(Qr * Qr + q * q, (ftype)(1.0 / 6));
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Ar = t * cos_tpl(phi);
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Ai = t * sin_tpl(phi);
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proots[0] = 2 * Ar - a3;
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proots[1] = aznumeric_cast<ftype>(-Ar + Ai * sqrt3 - a3);
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proots[2] = aznumeric_cast<ftype>(-Ar - Ai * sqrt3 - a3);
|
|
i = idxmax3(proots);
|
|
swap(proots, i, 2);
|
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i = isneg(proots[0] - proots[1]);
|
|
swap(proots, i, 1);
|
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nRoots = 3;
|
|
}
|
|
}
|
|
}
|
|
|
|
if constexpr (maxdegree >= 4)
|
|
{
|
|
if (degree == 4)
|
|
{
|
|
ftype t, a3, a2, a1, a0, y, R, D, E, subroots[3];
|
|
const ftype e = (ftype)1E-9;
|
|
|
|
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);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if constexpr (maxdegree > 4)
|
|
{
|
|
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;
|
|
}
|
|
} // namespace polynomial_tpl_IMPL
|
|
template<class ftype, int degree>
|
|
using polynomial_tpl = polynomial_tpl_IMPL::polynomial_tpl<ftype, degree>;
|
|
|
|
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;
|
|
} // namespace LegacyCryPhysicsUtils
|