GteExpEstimate.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

#include <Mathematics/GteExp2Estimate.h>

// Minimax polynomial approximations to 2^x.  The polynomial p(x) of
// degree D minimizes the quantity maximum{|2^x - p(x)| : x in [0,1]}
// over all polynomials of degree D.  The natural exponential is
// computed using exp(x) = 2^{x log(2)}, where log(2) is the natural
// logarithm of 2.

namespace gte
{

template <typename Real>
class ExpEstimate
{
public:
    // The input constraint is x in [0,1].  For example,
    //   float x; // in [0,1]
    //   float result = ExpEstimate<float>::Degree<3>(x);
    template <int D>
    inline static Real Degree(Real x);

    // The input x can be any real number.  Range reduction is used to
    // generate a value y in [0,1], call Degree(y), and combine the output
    // with the proper exponent to obtain the approximation.  For example,
    //   float x;  // x >= 0
    //   float result = ExpEstimate<float>::DegreeRR<3>(x);
    template <int D>
    inline static Real DegreeRR(Real x);
};


template <typename Real>
template <int D>
inline Real ExpEstimate<Real>::Degree(Real x)
{
    return Exp2Estimate<Real>::Degree<D>((Real)GTE_C_LN_2 * x);
}

template <typename Real>
template <int D>
inline Real ExpEstimate<Real>::DegreeRR(Real x)
{
    return Exp2Estimate<Real>::DegreeRR<D>((Real)GTE_C_LN_2 * x);
}


}