text: // Geometric Tools LLC, Redmond WA 98052
  // Copyright (c) 1998-2015
  // 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: 1.0.1 (2014/12/13)
  
  #pragma once
  
  #include <gte/GteConstants.h>
  #include <cmath>
  
  // Approximations to acos(x) of the form f(x) = sqrt(1-x)*p(x)
  // where the polynomial p(x) of degree D minimizes the quantity
  // maximum{|acos(x)/sqrt(1-x) - p(x)| : x in [0,1]} over all
  // polynomials of degree D.
  
  namespace gte
  {
  
  template <typename Real>
  class ACosEstimate
  {
  public:
      // The input constraint is x in [0,1].  For example,
      //   float x; // in [0,1]
      //   float result = ACosEstimate<float>::Degree<3>(x);
      template <int D>
      inline static Real Degree(Real x);
  
  private:
      // Metaprogramming and private implementation to allow specialization of
      // a template member function.
      template <int D> struct degree {};
      inline static Real Evaluate(degree<1>, Real x);
      inline static Real Evaluate(degree<2>, Real x);
      inline static Real Evaluate(degree<3>, Real x);
      inline static Real Evaluate(degree<4>, Real x);
      inline static Real Evaluate(degree<5>, Real x);
      inline static Real Evaluate(degree<6>, Real x);
      inline static Real Evaluate(degree<7>, Real x);
      inline static Real Evaluate(degree<8>, Real x);
  };
  
  //----------------------------------------------------------------------------
  template <typename Real>
  template <int D>
  inline Real ACosEstimate<Real>::Degree(Real x)
  {
      return Evaluate(degree<D>(), x);
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<1>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG1_C1;
      poly = (Real)GTE_C_ACOS_DEG1_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<2>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG2_C2;
      poly = (Real)GTE_C_ACOS_DEG2_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG2_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<3>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG3_C3;
      poly = (Real)GTE_C_ACOS_DEG3_C2 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG3_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG3_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<4>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG4_C4;
      poly = (Real)GTE_C_ACOS_DEG4_C3 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG4_C2 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG4_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG4_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<5>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG5_C5;
      poly = (Real)GTE_C_ACOS_DEG5_C4 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG5_C3 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG5_C2 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG5_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG5_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<6>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG6_C6;
      poly = (Real)GTE_C_ACOS_DEG6_C5 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG6_C4 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG6_C3 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG6_C2 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG6_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG6_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<7>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG7_C7;
      poly = (Real)GTE_C_ACOS_DEG7_C6 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG7_C5 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG7_C4 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG7_C3 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG7_C2 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG7_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG7_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  template <typename Real>
  inline Real ACosEstimate<Real>::Evaluate(degree<8>, Real x)
  {
      Real poly;
      poly = (Real)GTE_C_ACOS_DEG8_C8;
      poly = (Real)GTE_C_ACOS_DEG8_C7 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C6 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C5 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C4 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C3 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C2 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C1 + poly * x;
      poly = (Real)GTE_C_ACOS_DEG8_C0 + poly * x;
      poly = poly * sqrt((Real)1 - x);
      return poly;
  }
  //----------------------------------------------------------------------------
  
  }
  