// Copyright (c) 1997  ETH Zurich (Switzerland).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.2-beta1/Bounding_volumes/include/CGAL/Min_sphere_of_spheres_d/Min_sphere_of_spheres_d_pair.h $
// $Id: include/CGAL/Min_sphere_of_spheres_d/Min_sphere_of_spheres_d_pair.h 431cfb5357d $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Kaspar Fischer


#ifndef CGAL_MINIBALL_PAIR
#define CGAL_MINIBALL_PAIR

#include <CGAL/license/Bounding_volumes.h>


namespace CGAL_MINIBALL_NAMESPACE {

  namespace Min_sphere_of_spheres_d_impl {

    static const double Min_float = 1.0e-120;

    // a bunch of float/double constants that are used as tolerance in the
    // template code of the package.
    // "The stuff we're talking about only kicks in when floating-point
    // arithmetic is being used, and here double is surely a reasonable
    // default."
    // An old code contained functions instead of the following types and
    // it work for exact type (for example, Gmpq) due to the fact that
    // they are convertible to double.
    // This is indeed the least invasive fix dropint the function that were
    // defined here and cause linkage bug.
    // You can still have a behavior of instantiating only if a type
    // is convertibale to double (by using type_traits together with _if)
    // but until "the whole design should be overhauled at some point"
    // this is fine.
    template <typename FT>
      struct SqrOfEps
      {
          // That constant is embedded in an inline static function, to
          // workaround a bug of g++>=4.1
          //   https://gcc.gnu.org/bugzilla/show_bug.cgi?id=36912
          // g++ does not like const floating expression when -frounding-math
          // is used.
          static double result() {
              return 1.0e-32;
          }
      };

    template <>
      struct SqrOfEps<float>
      {
          // That constant is embedded in an inline static function, to
          // workaround a bug of g++>=4.1
          //   https://gcc.gnu.org/bugzilla/show_bug.cgi?id=36912
          // g++ does not like const floating expression when -frounding-math
          // is used.
          static float result() {
              return  1.0e-14f;
          }
      };

    template <typename FT>
      struct Tol
      {
        // That constant is embedded in an inline static function, to
        // workaround a bug of g++>=4.1
        //   https://gcc.gnu.org/bugzilla/show_bug.cgi?id=36912
        // g++ does not like const floating expression when -frounding-math
        // is used.
        static double result() {
          return 1.0 + 1.0e-16; // 1.0e-16 = Eps_double
        }
      };

    template <>
      struct Tol<float>
      {
        // That constant is embedded in an inline static function, to
        // workaround a bug of g++>=4.1
        //   https://gcc.gnu.org/bugzilla/show_bug.cgi?id=36912
        // g++ does not like const floating expression when -frounding-math
        // is used.
        static float result() {
          return 1.0f + 1.0e-7f; // 1.0e-7f = Eps_float;
        }
      };
  }

  template<typename FT>
  inline FT sqr(const FT& x) {
    return x*x;
  }

  // We do not use std::inner_product() because in our case the number n
  // of operands is known.  An optimizing compiler like GCC thus unrolls
  // the following loop.  The same holds for copy_n().
  template<int N,typename T,
           typename InputIterator1,typename InputIterator2,
           typename BinaryOperation1,typename BinaryOperation2>
  inline T
  inner_product_n(InputIterator1 first1,InputIterator2 first2,T init,
                  BinaryOperation1 op1,BinaryOperation2 op2) {
    for (int i=0; i<N; ++i, ++first1, ++first2)
      init = op1(init,op2(*first1,*first2));
    return init;
  }

  template<int N,typename InputIterator,typename OutputIterator>
  inline void copy_n(InputIterator first,OutputIterator result) {
    for (int i=0; i<N; ++i, ++first, ++result)
      *result = *first;
  }

  inline bool is_approximate(const Tag_false /* is_exact*/) {
    return true;
  }

  inline bool is_approximate(const Tag_true /* is_exact */) {
    return false;
  }

  template<typename FT>
  class Pair : public std::pair<FT,FT> {
  private:
    typedef std::pair<FT,FT> Base;

  public: // construction:
    Pair() : Base() {}

    Pair(const FT& a,const FT& b) : Base(a,b) {}

    Pair(int i) : Base(i,0) {}

    Pair& operator=(const FT& x) {
      this->first  = x;
      this->second = 0;
      return *this;
    }

  public:  // arithmetic and comparison:
    inline Pair operator+(const Pair& a) const {
      return Pair(this->first+a.first,this->second+a.second);
    }

    inline Pair operator-(const Pair& a) const {
      return Pair(this->first-a.first,this->second-a.second);
    }

    inline Pair operator-(const FT& a) const {
      return Pair(this->first-a,this->second);
    }

    inline Pair operator*(const FT& a) const {
      return Pair(this->first*a,this->second*a);
    }

    inline Pair operator/(const FT& a) const {
      CGAL_MINIBALL_ASSERT(a != FT(0));
      return Pair(this->first/a,this->second/a);
    }

    inline Pair& operator+=(const Pair& p) {
      this->first  += p.first;
      this->second += p.second;
      return *this;
    }

    inline Pair& operator-=(const Pair& p) {
      this->first  -= p.first;
      this->second -= p.second;
      return *this;
    }

    inline bool operator!=(const Pair& p) const {
      return this->first!=p.first || this->second!=p.second;
    }
  };

  template<typename FT>
  inline Pair<FT> operator+(const FT& a,const Pair<FT>& p) {
    return Pair<FT>(a+p.first,p.second);
  }

  template<typename FT>
  inline Pair<FT> operator-(const FT& a,const Pair<FT>& p) {
    return Pair<FT>(a-p.first,-p.second);
  }

  template<typename FT>
  inline bool is_neg(const FT& p,const FT&) {
    return p < 0;
  }

  template<typename FT>
  inline bool is_neg(const Pair<FT> p,const FT& d) {
    const bool aneg = p.first<FT(0), bneg = p.second<FT(0);

    if (aneg && bneg)
      return true;
    if (!aneg && !bneg)
      return false;

    // So what remains are the cases (i) a<0,b>=0 and (ii) a>=0,b<0:
    //   (i)  We need to test b*sqrt(d)<-a with b,-a>=0.
    //   (ii) We need to test a<(-b)*sqrt(d) with a,-b>=0.
    // Hence:
    const FT x = sqr(p.second)*d, y = sqr(p.first);
    return aneg? x<y : y<x;
  }

  template<typename FT>
  inline bool is_zero(const Pair<FT> p,const FT& d) {
    if (d != FT(0))
      // check whether the sides of a=-b*sqrt(d) (*)
      // have different signs:
      if ((p.first>FT(0)) ^ (p.second<FT(0)))
        return false;

    // Here we have either:
    //   (i)   d=0, or
    //   (ii)  a>0,b<0,d!=0, or
    //   (iii) a<=0,b>=0,d!=0
    // Hence both sides of (*) are either positive or negative.
    return sqr(p.first) == sqr(p.second)*d;
  }

  template<typename FT>
  inline bool is_neg_or_zero(const FT& p, const FT&) {
    return p <= 0;
  }

  template<typename FT>
  inline bool is_neg_or_zero(const Pair<FT> p,const FT& d) {
    return is_neg(p,d) || is_zero(p,d);
  }

} // namespace CGAL_MINIBALL_NAMESPACE

#endif // CGAL_MINIBALL_PAIR
