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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