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