/usr/include/CGAL/Root_of_traits.h is in libcgal-dev 4.2-5ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 | // Copyright (c) 2005,2006 INRIA Sophia-Antipolis (France)
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Sylvain Pion, Monique Teillaud, Athanasios Kakargias, Michael Hemmer
#ifndef CGAL_ROOT_OF_TRAITS_H
#define CGAL_ROOT_OF_TRAITS_H
#include <CGAL/number_type_basic.h>
#include <CGAL/Get_arithmetic_kernel.h>
#include <CGAL/Sqrt_extension.h>
#include <CGAL/Quotient.h>
#include <boost/mpl/has_xxx.hpp>
namespace CGAL {
template < typename NT >
struct Root_of_traits;
template < class NT >
inline
typename Root_of_traits< NT >::Root_of_2
make_root_of_2(const NT &a, const NT &b, const NT &c)
{
typename Root_of_traits<NT>::Make_root_of_2 make_root_of_2;
return make_root_of_2(a,b,c);
}
template < class NT >
inline
typename Root_of_traits< NT >::Root_of_2
make_root_of_2(const NT &a, const NT &b, const NT &c,const bool smaller)
{
typename Root_of_traits<NT>::Make_root_of_2 make_root_of_2;
return make_root_of_2(a,b,c,smaller);
}
template < class NT >
inline
typename Root_of_traits< NT >::Root_of_2
make_sqrt(const NT &a)
{
typename Root_of_traits<NT>::Make_sqrt make_sqrt;
return make_sqrt(a);
}
template < class NT , class OutputIterator>
inline
OutputIterator
compute_roots_of_2(const NT &a_, const NT &b_, const NT &c_, OutputIterator oit)
{
typedef typename Root_of_traits<NT>::Root_of_1 Root_of_1;
typedef typename Root_of_traits<NT>::Root_of_2 Root_of_2;
typename CGAL::Coercion_traits<Root_of_1,NT>::Cast cast;
Root_of_1 a(cast(a_)), b(cast(b_)), c(cast(c_));
if ( a != 0 ) {
Root_of_1 a0_ (-b/(2*a));
Root_of_1 root_(CGAL_NTS square(a0_) - c/a);
switch(CGAL::sign(root_)){
case CGAL::NEGATIVE: return oit;
case CGAL::ZERO: *oit++ = Root_of_2(a0_); return oit;
default:
// two roots
*oit++ = make_root_of_2(a0_,Root_of_1(-1),root_);
*oit++ = make_root_of_2(a0_,Root_of_1( 1),root_);
return oit;
}
}
else {
*oit++ = -c/b; return oit;
}
}
namespace internal {
BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(Has_typedef_Arithmetic_kernel,Arithmetic_kernel,false)
template <class NT,bool has_AK=Has_typedef_Arithmetic_kernel<Get_arithmetic_kernel<NT> >::value>
struct Get_rational_type{
typedef Quotient<NT> type;
};
template <class NT>
struct Get_rational_type<NT,true>{
typedef typename Get_arithmetic_kernel<NT>::Arithmetic_kernel::Rational type;
};
//Default or not a field.
//If no specialization of Get_arithmetic_kernel is available, a field type compatible with NT
//is made using CGAL::Quotient
template < typename NT, class Algebraic_category>
struct Root_of_traits_helper{
// typedef Quotient<NT> Root_of_1;
typedef typename Get_rational_type<NT>::type Root_of_1;
typedef CGAL::Sqrt_extension<Root_of_1,Root_of_1,::CGAL::Tag_true,::CGAL::Tag_true> Root_of_2;
// typedef CGAL::Root_of_2<NT> Root_of_2;
struct Make_root_of_2{
typedef Root_of_2 result_type;
Root_of_2 operator()(const NT& a, const NT& b, const NT& c) const {
return Root_of_2(a,b,c);
}
Root_of_2 operator()(const NT& a, const NT& b, const NT& c, bool s) const {
return Root_of_2(a,b,c,s);
}
Root_of_2 operator()(const Root_of_1& a,
const Root_of_1& b,
const Root_of_1& c) const {
return Root_of_2(a,b,c);
}
Root_of_2 operator()(const Root_of_1& a,
const Root_of_1& b,
const Root_of_1& c,
bool s) const {
return Root_of_2(a,b,c,s);
}
};
private:
typedef CGAL::Algebraic_structure_traits<Root_of_2> AST;
public:
typedef typename AST::Square Square;
typedef typename AST::Inverse Inverse;
struct Make_sqrt {
typedef Root_of_2 result_type;
Root_of_2 operator()(const NT& x) const {
return Root_of_2(x,true);
}
};
};
template < typename FT>
struct Root_of_traits_helper < FT, Field_tag >
{
typedef FT Root_of_1;
private:
typedef Fraction_traits<FT> FrT;
// Field must be a Type (Decomposable)
// We have the typedef as VC10 fails with
// static_assert(FrT::Is_fraction::value)
typedef typename FrT::Is_fraction ISF;
CGAL_static_assertion((ISF::value));
typedef typename FrT::Numerator_type RT;
typedef typename FrT::Decompose Decompose;
public:
typedef CGAL::Sqrt_extension<Root_of_1,Root_of_1,::CGAL::Tag_true,::CGAL::Tag_true> Root_of_2;
struct Make_root_of_2{
typedef Root_of_2 result_type;
Root_of_2
operator()(const FT& a, const FT& b, const FT& c) const {
return Root_of_2(a,b,c);
}
Root_of_2
operator()(const FT& a, const FT& b, const FT& c, bool smaller) const {
Decompose decompose;
RT a_num,b_num,c_num;
RT a_den,b_den,c_den; // Denomiantor same as RT
decompose(a,a_num,a_den);
decompose(b,b_num,b_den);
decompose(c,c_num,c_den);
RT a_ = a_num * b_den * c_den;
RT b_ = b_num * a_den * c_den;
RT c_ = c_num * a_den * b_den;
return make_root_of_2(a_,b_,c_,smaller);
}
};
private:
typedef CGAL::Algebraic_structure_traits<Root_of_2> AST;
public:
typedef typename AST::Square Square;
typedef typename AST::Inverse Inverse;
struct Make_sqrt{
typedef Root_of_2 result_type;
Root_of_2 operator()(const FT& x) const {
return Root_of_2( FT(0),FT(1),x);
}
};
};
template < typename NT >
struct Root_of_traits_helper < NT, Field_with_sqrt_tag >
{
typedef NT Root_of_1;
typedef NT Root_of_2;
struct Make_root_of_2{
typedef NT result_type;
// just a copy, not sure about the semantic of smaller
NT operator()(const NT& a, const NT& b, const NT& c, bool smaller) const {
// former make_root_of_2_sqrt()
CGAL_assertion( a != 0 );
NT discriminant = CGAL_NTS square(b) - a*c*4;
CGAL_assertion( discriminant >= 0 );
NT d = CGAL_NTS sqrt(discriminant);
if ((smaller && a>0) || (!smaller && a<0))
d = -d;
return (d-b)/(a*2);
}
// it's so easy
NT operator()(const NT& a, const NT& b, const NT& c) const {
return a + b * CGAL_NTS sqrt(c) ;
}
};
private:
typedef CGAL::Algebraic_structure_traits<Root_of_2> AST;
public:
typedef typename AST::Square Square;
typedef typename AST::Inverse Inverse;
struct Make_sqrt{
typedef Root_of_2 result_type;
Root_of_2 operator()(const NT& x) const {
return CGAL::sqrt(x);
}
};
};
template < typename NT >
struct Root_of_traits_helper < NT, Field_with_kth_root_tag >
:public Root_of_traits_helper < NT, Field_with_sqrt_tag>{};
template < typename NT >
struct Root_of_traits_helper < NT, Field_with_root_of_tag >
:public Root_of_traits_helper < NT, Field_with_sqrt_tag>{};
} // namespace internal
// Default Traits class for NT types
template < typename NT >
struct Root_of_traits
: public internal::Root_of_traits_helper<NT,
typename Algebraic_structure_traits<NT>::Algebraic_category> {
typedef internal::Root_of_traits_helper<NT,
typename Algebraic_structure_traits<NT>::Algebraic_category> Base;
typedef typename Base::Root_of_1 RootOf_1;
typedef typename Base::Root_of_2 RootOf_2;
};
template <bool B>
struct Root_of_traits<Interval_nt<B> >{
typedef Interval_nt<B> Root_of_1;
typedef Interval_nt<B> Root_of_2;
typedef Root_of_1 RootOf_1;
typedef Root_of_2 RootOf_2;
struct Make_root_of_2{
typedef Interval_nt<B> result_type;
// just a copy, not sure about the semantic of smaller
Interval_nt<B> operator()(const Interval_nt<B>& a, const Interval_nt<B>& b, const Interval_nt<B>& c, bool smaller) const {
// former make_root_of_2_sqrt()
if (CGAL::possibly(a==0))
return Interval_nt<B>::largest();
Interval_nt<B> discriminant = CGAL_NTS square(b) - a*c*4;
CGAL_assertion(discriminant >= 0);
Interval_nt<B> d = CGAL_NTS sqrt(discriminant);
if ((smaller && a>0) || (!smaller && a<0))
d = -d;
return (d-b)/(a*2);
}
// it's so easy
Interval_nt<B> operator()(const Interval_nt<B>& a, const Interval_nt<B>& b, const Interval_nt<B>& c) const {
return a + b * CGAL_NTS sqrt(c) ;
}
};
private:
typedef CGAL::Algebraic_structure_traits<Interval_nt<B> > AST;
public:
typedef typename AST::Square Square;
typedef typename AST::Inverse Inverse;
typedef typename AST::Sqrt Make_sqrt;
};
} //namespace CGAL
#include <CGAL/Root_of_traits_specializations.h>
#endif // CGAL_ROOT_OF_TRAITS_H
|