553 lines
19 KiB
C
553 lines
19 KiB
C
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// Copyright (c) 2006-2008 Max-Planck-Institute Saarbruecken (Germany).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Michael Hemmer <hemmer@mpi-inf.mpg.de>
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//============================================================================
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#ifndef CGAL_CORE_BIGFLOAT_H
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#define CGAL_CORE_BIGFLOAT_H
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#include <CGAL/basic.h>
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#include <CGAL/number_type_basic.h>
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#include <CGAL/CORE/BigFloat.h>
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#include <CGAL/CORE_coercion_traits.h>
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#include <CGAL/Interval_traits.h>
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#include <CGAL/Bigfloat_interval_traits.h>
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namespace CGAL {
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// ######### Interval_traits
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template<>
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class Interval_traits<CORE::BigFloat>
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: public internal::Interval_traits_base<CORE::BigFloat>{
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typedef CORE::BigFloat Interval;
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public:
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typedef Interval_traits<CORE::BigFloat> Self;
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typedef CORE::BigFloat Type;
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typedef CORE::BigFloat Bound;
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typedef CGAL::Tag_true Is_interval;
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typedef CGAL::Tag_true Is_bigfloat_interval;
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struct Lower :public CGAL::cpp98::unary_function<Interval,Bound>{
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Bound operator() ( Interval x ) const {
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CORE::BigFloat result = ::CORE::BigFloat(x.m()-x.err(),0,x.exp());
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CGAL_postcondition(result <= x);
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return result;
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}
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};
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struct Upper :public CGAL::cpp98::unary_function<Interval,Bound>{
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Bound operator() ( Interval x ) const {
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CORE::BigFloat result = ::CORE::BigFloat(x.m()+x.err(),0,x.exp());
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CGAL_postcondition(result >= x);
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return result;
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}
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};
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struct Width :public CGAL::cpp98::unary_function<Interval,Bound>{
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Bound operator() ( Interval x ) const {
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unsigned long err = 2*x.err();
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return Bound(CORE::BigInt(err),0,x.exp());
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}
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};
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struct Median :public CGAL::cpp98::unary_function<Interval,Bound>{
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Bound operator() ( Interval x ) const {
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return Bound(x.m(),0,x.exp());
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}
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};
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struct Norm :public CGAL::cpp98::unary_function<Interval,Bound>{
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Bound operator() ( Interval x ) const {
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BOOST_USING_STD_MAX();
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return max BOOST_PREVENT_MACRO_SUBSTITUTION (Upper()(x).abs(),Lower()(x).abs());
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}
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};
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struct Zero_in :public CGAL::cpp98::unary_function<Interval,bool>{
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bool operator() ( Interval x ) const {
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return x.isZeroIn();
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}
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};
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struct In :public CGAL::cpp98::binary_function<Bound,Interval,bool>{
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bool operator()( Bound x, const Interval& a ) const {
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CGAL_precondition(CGAL::singleton(x));
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return (Lower()(a) <= x && x <= Upper()(a));
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}
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};
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struct Equal :public CGAL::cpp98::binary_function<Interval,Interval,bool>{
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bool operator()( const Interval& a, const Interval& b ) const {
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return (Upper()(a) == Upper()(b) && Lower()(a) == Lower()(b));
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}
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};
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struct Subset :public CGAL::cpp98::binary_function<Interval,Interval,bool>{
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bool operator()( const Interval& a, const Interval& b ) const {
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return Lower()(b) <= Lower()(a) && Upper()(a) <= Upper()(b);
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}
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};
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struct Proper_subset :public CGAL::cpp98::binary_function<Interval,Interval,bool>{
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bool operator()( const Interval& a, const Interval& b ) const {
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return Subset()(a,b) && (!Equal()(a,b));
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}
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};
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struct Intersection :public CGAL::cpp98::binary_function<Interval,Interval,Interval>{
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Interval operator()( const Interval& a, const Interval& b ) const {
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BOOST_USING_STD_MAX();
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BOOST_USING_STD_MIN();
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// std::cout <<"a= (" << a.m() << "+-" << a.err() << ")*2^" << a.exp() << std::endl;
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Bound l(max BOOST_PREVENT_MACRO_SUBSTITUTION (Lower()(a),Lower()(b)));
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Bound u(min BOOST_PREVENT_MACRO_SUBSTITUTION (Upper()(a),Upper()(b)));
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if(u < l ) throw Exception_intersection_is_empty();
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return Construct()(l,u);
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}
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};
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struct Overlap :public CGAL::cpp98::binary_function<Interval,Interval,bool>{
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bool operator() ( Interval x, Interval y ) const {
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Self::Zero_in Zero_in;
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bool result = Zero_in(x-y);
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return result;
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}
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};
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struct Hull :public CGAL::cpp98::binary_function<Interval,Interval,Interval>{
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// for debugging
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/* void print_bf(CORE::BigFloat bf, std::string s) const {
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std::cout << s << ".m()=" << bf.m() << ","
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<< s << ".err()=" << bf.err() << ","
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<< s << ".exp()=" << bf.exp() << ","
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<< "td=" << bf << std::endl;
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}
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*/
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Interval operator() ( Interval x, Interval y ) const {
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BOOST_USING_STD_MAX();
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BOOST_USING_STD_MIN();
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#if 0
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// this is not possible since CORE::centerize has a bug.
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Interval result = CORE::centerize(x,y);
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#else
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//print_bf(x,"x");
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//print_bf(y,"y");
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CORE::BigFloat result;
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// Unfortunately, CORE::centerize(x,y) has bugs.
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if ((x.m() == y.m()) && (x.err() == y.err()) && (x.exp() == y.exp())) {
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return x;
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}
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CORE::BigFloat lower = min BOOST_PREVENT_MACRO_SUBSTITUTION (CGAL::lower(x), CGAL::lower(y));
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CORE::BigFloat upper = max BOOST_PREVENT_MACRO_SUBSTITUTION (CGAL::upper(x), CGAL::upper(y));
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CORE::BigFloat mid = (lower + upper)/2;
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//print_bf(lower,"lower");
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//print_bf(upper,"upper");
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//print_bf(mid,"mid");
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// Now we have to compute the error. The problem is that .err() is just a long
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CORE::BigFloat err = (upper - lower)/CORE::BigFloat(2);
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//print_bf(err,"err");
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//std::cout << "lower " << lower << std::endl;
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//std::cout << "upper " << upper << std::endl;
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//std::cout << "mid " << mid << std::endl;
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//std::cout << "err I " << err << std::endl;
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// shift such that err.m()+err.err() fits into long
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int digits_long = std::numeric_limits<long>::digits;
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if(::CORE::bitLength(err.m()+err.err()) >= digits_long){
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long shift = ::CORE::bitLength(err.m()) - digits_long + 1 ;
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//std::cout << "shift " << shift<< std::endl;
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long new_err = ((err.m()+err.err()) >> shift).longValue()+1;
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err = CORE::BigFloat(0,new_err,0) * CORE::BigFloat::exp2(err.exp()*CORE::CHUNK_BIT+shift);
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}else{
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err = CORE::BigFloat(0,err.m().longValue()+err.err(),err.exp());
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}
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//print_bf(err,"new_err");
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// TODO: This is a workaround for a bug in operator+
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// of CORE::Bigfloat. If the exponent difference is too big,
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// this might cause problems, since the error is a long
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if(mid.exp() > err.exp()) {
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long mid_err = mid.err();
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CORE::BigInt mid_m = mid.m();
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mid_err = mid_err << (mid.exp()-err.exp())*CORE::CHUNK_BIT;
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mid_m = mid_m << (mid.exp()-err.exp())*CORE::CHUNK_BIT;
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mid = CORE::BigFloat(mid_m,mid_err,err.exp());
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//print_bf(mid,"corr_mid");
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}
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//print_bf(result,"result");
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result = mid + err;
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#endif
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CGAL_postcondition(
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CGAL::lower(result)
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<= min BOOST_PREVENT_MACRO_SUBSTITUTION (CGAL::lower(x), CGAL::lower(y)));
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CGAL_postcondition(
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CGAL::upper(result)
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>= max BOOST_PREVENT_MACRO_SUBSTITUTION (CGAL::upper(x), CGAL::upper(y)));
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return result ;
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}
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};
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struct Singleton :public CGAL::cpp98::unary_function<Interval,bool> {
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bool operator() ( Interval x ) const {
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return (x.err() == 0);
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}
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};
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struct Construct :public CGAL::cpp98::binary_function<Bound,Bound,Interval>{
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Interval operator()( const Bound& l,const Bound& r) const {
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CGAL_precondition( l < r );
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return Hull()(l,r);
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}
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};
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};
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// ########### Bigfloat_interval_traits
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// template<typename BFI> long relative_precision(BFI bfi);
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namespace internal{
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CORE::BigFloat
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inline
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round(const CORE::BigFloat& x, long rel_prec = CORE::get_static_defRelPrec().toLong() ){
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CGAL_postcondition(rel_prec >= 0);
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// since there is not rel prec defined if Zero_in(x)
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if (x.isZeroIn()) return x;
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// if (CGAL::get_significant_bits(x) <= rel_prec) return x;
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// if 1
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// CORE::BigFloat xr;
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// xr.approx(x,rel_prec,1024);
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// typedef CORE::BigFloat BF;
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// else
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typedef CORE::BigFloat BF;
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BF xr;
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CORE::BigInt m = x.m();
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long err = x.err();
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long exp = x.exp();
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// std::cout <<"(" << m << "+-" <<err << ")*2^"<<(CORE::CHUNK_BIT*exp) << std::endl;
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// if (err != 0)
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// std::cout <<"current prec: " << CGAL::relative_precision(x) << std::endl;
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// else
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// std::cout <<"current prec: " << " SINGLETON " << std::endl;
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// std::cout <<"desired prec: " << rel_prec << std::endl;
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// std::cout <<"bitLength: " << CORE::bitLength(m) << std::endl;
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// long shift = ::CORE::bitLength(m) - rel_prec - 1;
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long shift ;
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if (err == 0)
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shift = ::CORE::bitLength(m) - rel_prec - 3;
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else
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shift = CGAL::relative_precision(x) - rel_prec -1;
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if( shift > 0 ){
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m >>= shift ;
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err >>= shift;
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xr = BF(m,err+1,0)*BF::exp2(exp*CORE::CHUNK_BIT+shift);
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}else{ // noting to do
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xr = x;
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}
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// std::cout <<"(" <<m << "+-" <<err+1 << ")*2^"<<(CORE::CHUNK_BIT*exp) << std::endl;
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// if (xr.err() != 0)
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// std::cout <<"current prec: " << CGAL::relative_precision(xr) << std::endl;
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// else
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// std::cout <<"current prec: " << " SINGLETON "<< std::endl;
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// std::cout <<"desired prec: " << rel_prec << std::endl;
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// endif
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CGAL_postcondition(singleton(xr) || CGAL::relative_precision(xr) - rel_prec >= 0);
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CGAL_postcondition(singleton(xr) || CGAL::relative_precision(xr) - rel_prec <= 32);
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CGAL_postcondition(BF(xr.m()-xr.err(),0,xr.exp()) <= BF(x.m()-x.err(),0,x.exp()));
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CGAL_postcondition(BF(xr.m()+xr.err(),0,xr.exp()) >= BF(x.m()+x.err(),0,x.exp()));
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return xr;
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}
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}
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template<> class Bigfloat_interval_traits<CORE::BigFloat>
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:public Interval_traits<CORE::BigFloat>
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{
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typedef CORE::BigFloat NT;
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typedef CORE::BigFloat BF;
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public:
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typedef Bigfloat_interval_traits<NT> Self;
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struct Relative_precision {
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// type for the \c AdaptableUnaryFunction concept.
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typedef NT argument_type;
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// type for the \c AdaptableUnaryFunction concept.
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typedef long result_type;
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long operator()( NT x) const {
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CGAL_precondition(!Singleton()(x));
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CGAL_precondition(!CGAL::zero_in(x));
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x = x.abs();
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NT w = Width()(x);
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w /= ::CORE::BigFloat(x.m()-x.err(),0,x.exp());
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w = w.abs();
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return -(CORE::ceilLg(w.m()+w.err())+w.exp()*CORE::CHUNK_BIT);
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}
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};
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struct Set_precision {
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// type for the \c AdaptableUnaryFunction concept.
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typedef long argument_type;
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// type for the \c AdaptableUnaryFunction concept.
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typedef long result_type;
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long operator() ( long prec ) const {
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long result = ::CORE::get_static_defRelPrec().toLong();
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::CORE::get_static_defRelPrec() = prec;
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::CORE::get_static_defBFdivRelPrec() = prec;
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return result;
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}
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};
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struct Get_precision {
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|
|
// type for the \c AdaptableGenerator concept.
|
||
|
|
typedef long result_type;
|
||
|
|
|
||
|
|
long operator() () const {
|
||
|
|
return ::CORE::get_static_defRelPrec().toLong();
|
||
|
|
}
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
//
|
||
|
|
// Algebraic structure traits
|
||
|
|
//
|
||
|
|
template <> class Algebraic_structure_traits< CORE::BigFloat >
|
||
|
|
: public Algebraic_structure_traits_base< CORE::BigFloat,
|
||
|
|
Field_with_kth_root_tag > {
|
||
|
|
public:
|
||
|
|
typedef Tag_false Is_exact;
|
||
|
|
typedef Tag_true Is_numerical_sensitive;
|
||
|
|
|
||
|
|
class Sqrt
|
||
|
|
: public CGAL::cpp98::unary_function< Type, Type > {
|
||
|
|
public:
|
||
|
|
Type operator()( const Type& x ) const {
|
||
|
|
// What I want is a sqrt computed with
|
||
|
|
// ::CORE::get_static_defRelPrec() bits.
|
||
|
|
// And not ::CORE::defBFsqrtAbsPrec as CORE does.
|
||
|
|
|
||
|
|
CGAL_precondition(::CORE::get_static_defRelPrec().toLong() > 0);
|
||
|
|
CGAL_precondition(x > 0);
|
||
|
|
|
||
|
|
Type a = CGAL::internal::round(
|
||
|
|
x, ::CORE::get_static_defRelPrec().toLong()*2);
|
||
|
|
CGAL_postcondition(a > 0);
|
||
|
|
|
||
|
|
Type tmp1 = CORE::BigFloat(
|
||
|
|
a.m(),0,0).sqrt(::CORE::get_static_defRelPrec().toLong());
|
||
|
|
Type err =
|
||
|
|
Type(0,long(std::sqrt(double(a.err()))),0)
|
||
|
|
* CORE::BigFloat::exp2(a.exp()*7);
|
||
|
|
Type result = tmp1*CORE::BigFloat::exp2(a.exp()*7) + err;
|
||
|
|
|
||
|
|
CGAL_postcondition(result >= 0);
|
||
|
|
CGAL_postcondition(CGAL::lower(result*result) <= CGAL::lower(x));
|
||
|
|
CGAL_postcondition(CGAL::upper(result*result) >= CGAL::upper(x));
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
class Kth_root
|
||
|
|
: public CGAL::cpp98::binary_function<int, Type, Type> {
|
||
|
|
public:
|
||
|
|
Type operator()( int k,
|
||
|
|
const Type& x) const {
|
||
|
|
CGAL_precondition_msg( k > 0, "'k' must be positive for k-th roots");
|
||
|
|
// CORE::radical isn't implemented for negative values of x, so we
|
||
|
|
// have to handle this case separately
|
||
|
|
if( x < 0 && k%2 != 0) {
|
||
|
|
return Type(-CORE::radical( -x, k ) );
|
||
|
|
}
|
||
|
|
|
||
|
|
return Type( CORE::radical( x, k ) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
//
|
||
|
|
// Real embeddable traits
|
||
|
|
//
|
||
|
|
template <> class Real_embeddable_traits< CORE::BigFloat >
|
||
|
|
: public INTERN_RET::Real_embeddable_traits_base< CORE::BigFloat , CGAL::Tag_true > {
|
||
|
|
public:
|
||
|
|
class Abs
|
||
|
|
: public CGAL::cpp98::unary_function< Type, Type > {
|
||
|
|
public:
|
||
|
|
Type operator()( const Type& x ) const {
|
||
|
|
Type result;
|
||
|
|
|
||
|
|
if(x.isZeroIn()){
|
||
|
|
CORE::BigInt m;
|
||
|
|
if(x.m() < 0 ){
|
||
|
|
m = -(x.m()-x.err());
|
||
|
|
}else{
|
||
|
|
m = x.m()+x.err();
|
||
|
|
}
|
||
|
|
if(m % 2 == 1) m += 1;
|
||
|
|
|
||
|
|
Type upper(m,0,x.exp());
|
||
|
|
result = CORE::centerize(CORE::BigFloat(0),upper);
|
||
|
|
|
||
|
|
CGAL_postcondition(result.m()-result.err() <= 0);
|
||
|
|
if(result.m()-result.err() != 0){
|
||
|
|
result = this->operator()(result);
|
||
|
|
}
|
||
|
|
CGAL_postcondition(result.m()-result.err() == 0);
|
||
|
|
}else{
|
||
|
|
result = CORE::abs(x);
|
||
|
|
}
|
||
|
|
CGAL_postcondition(result.m()-result.err() >= 0);
|
||
|
|
CGAL_postcondition(Type(result.m()+result.err(),0,result.exp())
|
||
|
|
>= Type(x.m()+x.err(),0,x.exp()));
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
class Sgn
|
||
|
|
: public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > {
|
||
|
|
public:
|
||
|
|
::CGAL::Sign operator()( const Type& x ) const {
|
||
|
|
::CGAL::Sign result = sign( x.sign());
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
class Compare
|
||
|
|
: public CGAL::cpp98::binary_function< Type, Type,
|
||
|
|
Comparison_result > {
|
||
|
|
public:
|
||
|
|
Comparison_result operator()( const Type& x,
|
||
|
|
const Type& y ) const {
|
||
|
|
return (Comparison_result) sign( (x-y).sign());
|
||
|
|
}
|
||
|
|
CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT( Type,
|
||
|
|
Comparison_result )
|
||
|
|
};
|
||
|
|
|
||
|
|
class To_double
|
||
|
|
: public CGAL::cpp98::unary_function< Type, double > {
|
||
|
|
public:
|
||
|
|
double operator()( const Type& x ) const {
|
||
|
|
// this call is required to get reasonable values for the double
|
||
|
|
// approximation
|
||
|
|
return x.doubleValue();
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
class To_interval
|
||
|
|
: public CGAL::cpp98::unary_function< Type, std::pair< double, double > > {
|
||
|
|
public:
|
||
|
|
std::pair<double, double> operator()( const Type& x ) const {
|
||
|
|
|
||
|
|
double lb,ub;
|
||
|
|
|
||
|
|
Type x_lower = CGAL::lower(CGAL::internal::round(CGAL::lower(x),50));
|
||
|
|
Type x_upper = CGAL::upper(CGAL::internal::round(CGAL::upper(x),50));
|
||
|
|
|
||
|
|
// since matissa has 50 bits only, conversion to double is exact
|
||
|
|
lb = x_lower.doubleValue();
|
||
|
|
CGAL_postcondition(lb == x_lower);
|
||
|
|
ub = x_upper.doubleValue();
|
||
|
|
CGAL_postcondition(ub == x_upper);
|
||
|
|
|
||
|
|
std::pair<double, double> result(lb,ub);
|
||
|
|
CGAL_postcondition( result.first <= CORE::Expr(CGAL::lower(x)));
|
||
|
|
CGAL_postcondition( result.second >= CORE::Expr(CGAL::upper(x)));
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
//since types are included by CORE_coercion_traits.h:
|
||
|
|
#include <CGAL/CORE_Expr.h>
|
||
|
|
#include <CGAL/CORE_BigInt.h>
|
||
|
|
#include <CGAL/CORE_BigRat.h>
|
||
|
|
#include <CGAL/CORE_BigFloat.h>
|
||
|
|
#include <CGAL/CORE_arithmetic_kernel.h>
|
||
|
|
|
||
|
|
namespace Eigen {
|
||
|
|
template<class> struct NumTraits;
|
||
|
|
template<> struct NumTraits<CORE::BigFloat>
|
||
|
|
{
|
||
|
|
typedef CORE::BigFloat Real;
|
||
|
|
typedef CORE::BigFloat NonInteger;
|
||
|
|
typedef CORE::BigFloat Nested;
|
||
|
|
typedef CORE::BigFloat Literal;
|
||
|
|
|
||
|
|
static inline Real epsilon() { return 0; }
|
||
|
|
static inline Real dummy_precision() { return 0; }
|
||
|
|
|
||
|
|
enum {
|
||
|
|
IsInteger = 0,
|
||
|
|
IsSigned = 1,
|
||
|
|
IsComplex = 0,
|
||
|
|
RequireInitialization = 1,
|
||
|
|
ReadCost = 6,
|
||
|
|
AddCost = 60,
|
||
|
|
MulCost = 60
|
||
|
|
};
|
||
|
|
};
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif // CGAL_CORE_BIGFLOAT_H
|