ceph/src/boost/libs/numeric/interval/include/boost/numeric/interval/detail/division.hpp

   1 /* Boost interval/detail/division.hpp file
   2  *
   3  * Copyright 2003 Guillaume Melquiond, Sylvain Pion
   4  *
   5  * Distributed under the Boost Software License, Version 1.0.
   6  * (See accompanying file LICENSE_1_0.txt or
   7  * copy at http://www.boost.org/LICENSE_1_0.txt)
   8  */
   9
  10 #ifndef BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
  11 #define BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
  12
  13 #include <boost/numeric/interval/detail/interval_prototype.hpp>
  14 #include <boost/numeric/interval/detail/bugs.hpp>
  15 #include <boost/numeric/interval/detail/test_input.hpp>
  16 #include <boost/numeric/interval/rounded_arith.hpp>
  17 #include <algorithm>
  18
  19 namespace boost {
  20 namespace numeric {
  21 namespace interval_lib {
  22 namespace detail {
  23
  24 template<class T, class Policies> inline
  25 interval<T, Policies> div_non_zero(const interval<T, Policies>& x,
  26                                    const interval<T, Policies>& y)
  27 {
  28   // assert(!in_zero(y));
  29   typename Policies::rounding rnd;
  30   typedef interval<T, Policies> I;
  31   const T& xl = x.lower();
  32   const T& xu = x.upper();
  33   const T& yl = y.lower();
  34   const T& yu = y.upper();
  35   if (::boost::numeric::interval_lib::user::is_neg(xu))
  36     if (::boost::numeric::interval_lib::user::is_neg(yu))
  37       return I(rnd.div_down(xu, yl), rnd.div_up(xl, yu), true);
  38     else
  39       return I(rnd.div_down(xl, yl), rnd.div_up(xu, yu), true);
  40   else if (::boost::numeric::interval_lib::user::is_neg(xl))
  41     if (::boost::numeric::interval_lib::user::is_neg(yu))
  42       return I(rnd.div_down(xu, yu), rnd.div_up(xl, yu), true);
  43     else
  44       return I(rnd.div_down(xl, yl), rnd.div_up(xu, yl), true);
  45   else
  46     if (::boost::numeric::interval_lib::user::is_neg(yu))
  47       return I(rnd.div_down(xu, yu), rnd.div_up(xl, yl), true);
  48     else
  49       return I(rnd.div_down(xl, yu), rnd.div_up(xu, yl), true);
  50 }
  51
  52 template<class T, class Policies> inline
  53 interval<T, Policies> div_non_zero(const T& x, const interval<T, Policies>& y)
  54 {
  55   // assert(!in_zero(y));
  56   typename Policies::rounding rnd;
  57   typedef interval<T, Policies> I;
  58   const T& yl = y.lower();
  59   const T& yu = y.upper();
  60   if (::boost::numeric::interval_lib::user::is_neg(x))
  61     return I(rnd.div_down(x, yl), rnd.div_up(x, yu), true);
  62   else
  63     return I(rnd.div_down(x, yu), rnd.div_up(x, yl), true);
  64 }
  65
  66 template<class T, class Policies> inline
  67 interval<T, Policies> div_positive(const interval<T, Policies>& x, const T& yu)
  68 {
  69   // assert(::boost::numeric::interval_lib::user::is_pos(yu));
  70   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
  71       ::boost::numeric::interval_lib::user::is_zero(x.upper()))
  72     return x;
  73   typename Policies::rounding rnd;
  74   typedef interval<T, Policies> I;
  75   const T& xl = x.lower();
  76   const T& xu = x.upper();
  77   typedef typename Policies::checking checking;
  78   if (::boost::numeric::interval_lib::user::is_neg(xu))
  79     return I(checking::neg_inf(), rnd.div_up(xu, yu), true);
  80   else if (::boost::numeric::interval_lib::user::is_neg(xl))
  81     return I(checking::neg_inf(), checking::pos_inf(), true);
  82   else
  83     return I(rnd.div_down(xl, yu), checking::pos_inf(), true);
  84 }
  85
  86 template<class T, class Policies> inline
  87 interval<T, Policies> div_positive(const T& x, const T& yu)
  88 {
  89   // assert(::boost::numeric::interval_lib::user::is_pos(yu));
  90   typedef interval<T, Policies> I;
  91   if (::boost::numeric::interval_lib::user::is_zero(x))
  92     return I(static_cast<T>(0), static_cast<T>(0), true);
  93   typename Policies::rounding rnd;
  94   typedef typename Policies::checking checking;
  95   if (::boost::numeric::interval_lib::user::is_neg(x))
  96     return I(checking::neg_inf(), rnd.div_up(x, yu), true);
  97   else
  98     return I(rnd.div_down(x, yu), checking::pos_inf(), true);
  99 }
 100
 101 template<class T, class Policies> inline
 102 interval<T, Policies> div_negative(const interval<T, Policies>& x, const T& yl)
 103 {
 104   // assert(::boost::numeric::interval_lib::user::is_neg(yl));
 105   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
 106       ::boost::numeric::interval_lib::user::is_zero(x.upper()))
 107     return x;
 108   typename Policies::rounding rnd;
 109   typedef interval<T, Policies> I;
 110   const T& xl = x.lower();
 111   const T& xu = x.upper();
 112   typedef typename Policies::checking checking;
 113   if (::boost::numeric::interval_lib::user::is_neg(xu))
 114     return I(rnd.div_down(xu, yl), checking::pos_inf(), true);
 115   else if (::boost::numeric::interval_lib::user::is_neg(xl))
 116     return I(checking::neg_inf(), checking::pos_inf(), true);
 117   else
 118     return I(checking::neg_inf(), rnd.div_up(xl, yl), true);
 119 }
 120
 121 template<class T, class Policies> inline
 122 interval<T, Policies> div_negative(const T& x, const T& yl)
 123 {
 124   // assert(::boost::numeric::interval_lib::user::is_neg(yl));
 125   typedef interval<T, Policies> I;
 126   if (::boost::numeric::interval_lib::user::is_zero(x))
 127     return I(static_cast<T>(0), static_cast<T>(0), true);
 128   typename Policies::rounding rnd;
 129   typedef typename Policies::checking checking;
 130   if (::boost::numeric::interval_lib::user::is_neg(x))
 131     return I(rnd.div_down(x, yl), checking::pos_inf(), true);
 132   else
 133     return I(checking::neg_inf(), rnd.div_up(x, yl), true);
 134 }
 135
 136 template<class T, class Policies> inline
 137 interval<T, Policies> div_zero(const interval<T, Policies>& x)
 138 {
 139   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
 140       ::boost::numeric::interval_lib::user::is_zero(x.upper()))
 141     return x;
 142   else return interval<T, Policies>::whole();
 143 }
 144
 145 template<class T, class Policies> inline
 146 interval<T, Policies> div_zero(const T& x)
 147 {
 148   if (::boost::numeric::interval_lib::user::is_zero(x))
 149     return interval<T, Policies>(static_cast<T>(0), static_cast<T>(0), true);
 150   else return interval<T, Policies>::whole();
 151 }
 152
 153 template<class T, class Policies> inline
 154 interval<T, Policies> div_zero_part1(const interval<T, Policies>& x,
 155                                      const interval<T, Policies>& y, bool& b)
 156 {
 157   // assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()));
 158   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) && ::boost::numeric::interval_lib::user::is_zero(x.upper()))
 159     { b = false; return x; }
 160   typename Policies::rounding rnd;
 161   typedef interval<T, Policies> I;
 162   const T& xl = x.lower();
 163   const T& xu = x.upper();
 164   const T& yl = y.lower();
 165   const T& yu = y.upper();
 166   typedef typename Policies::checking checking;
 167   if (::boost::numeric::interval_lib::user::is_neg(xu))
 168     { b = true;  return I(checking::neg_inf(), rnd.div_up(xu, yu), true); }
 169   else if (::boost::numeric::interval_lib::user::is_neg(xl))
 170     { b = false; return I(checking::neg_inf(), checking::pos_inf(), true); }
 171   else
 172     { b = true;  return I(checking::neg_inf(), rnd.div_up(xl, yl), true); }
 173 }
 174
 175 template<class T, class Policies> inline
 176 interval<T, Policies> div_zero_part2(const interval<T, Policies>& x,
 177                                      const interval<T, Policies>& y)
 178 {
 179   // assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()) && (div_zero_part1(x, y, b), b));
 180   typename Policies::rounding rnd;
 181   typedef interval<T, Policies> I;
 182   typedef typename Policies::checking checking;
 183   if (::boost::numeric::interval_lib::user::is_neg(x.upper()))
 184     return I(rnd.div_down(x.upper(), y.lower()), checking::pos_inf(), true);
 185   else
 186     return I(rnd.div_down(x.lower(), y.upper()), checking::pos_inf(), true);
 187 }
 188
 189 } // namespace detail
 190 } // namespace interval_lib
 191 } // namespace numeric
 192 } // namespace boost
 193
 194 #endif // BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP