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// Copyright (c) 2006-2009 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/bound_between_1.h $
// $Id: include/CGAL/Algebraic_kernel_d/bound_between_1.h 08b27d3db14 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
//
// Author(s) : Michael Kerber <mkerber@mpi-inf.mpg.de>
//
// ============================================================================
#ifndef CGAL_BOUND_BETWEEN_1_H
#define CGAL_BOUND_BETWEEN_1_H 1
#include <iterator>
#include <CGAL/basic.h>
#include <CGAL/Algebraic_kernel_d/enums.h>
#include <CGAL/Arithmetic_kernel.h>
#include <CGAL/Algebraic_kernel_d/Float_traits.h>
#include <CGAL/convert_to_bfi.h>
#include <CGAL/Algebraic_kernel_d/Real_embeddable_extension.h>
#include <CGAL/Polynomial_traits_d.h>
#include <CGAL/Algebraic_kernel_d/Bitstream_coefficient_kernel.h>
#include <CGAL/Bigfloat_interval_traits.h>
#include <boost/numeric/interval.hpp>
#include <CGAL/Coercion_traits.h>
namespace CGAL {
namespace internal {
/*! \brief tries to find a SIMPLE rational q with a<q<b.
*
* In this context, simple means that the denominator of <tt>q</tt>
* is a power of two, and is not too big. There is no guarantee to find
* the rational value between <tt>a</tt> and <tt>b</tt> of minimal
* bit size.
*/
template<typename Algebraic_real>
typename Algebraic_real::Rational
simple_bound_between(const Algebraic_real& a,
const Algebraic_real&b) {
//srb.start();
typedef typename Algebraic_real::Rational Rational;
typename CGAL::Fraction_traits<Rational>::Compose compose;
typedef typename
CGAL::Get_arithmetic_kernel<Rational>::Arithmetic_kernel AK;
typedef typename AK::Bigfloat_interval Bigfloat_interval;
typedef typename CGAL::Bigfloat_interval_traits<Bigfloat_interval>
::Bound Bigfloat;
typedef typename AK::Integer Integer;
long old_prec = CGAL::get_precision(Bigfloat_interval());
CGAL_assertion(a!=b);
if(a>b) {
return simple_bound_between(b,a);
}
//std::cout << "Intermediate1: " << CGAL::to_double(a) << " " << CGAL::to_double(b) << std::endl;
/*
* First, refine a and b until their isolating intervals are disjoint
* Therefore, the bigger interval is refined in each substep
*/
//srb_a.start();
if(a.high() >= b.low()) {
Rational size_a=a.high()-a.low(),
size_b=b.high() - b.low();
while(a.high() >= b.low()) {
if(size_a < size_b) {
b.refine();
size_b=b.high() - b.low();
} else {
a.refine();
size_a=a.high()-a.low();
}
}
}
//srb_a.stop();
//srb_b.start();
Bigfloat x=CGAL::upper(CGAL::convert_to_bfi(a.high()));
Bigfloat y=CGAL::lower(CGAL::convert_to_bfi(b.low()));
if(x>=y) {
Rational size_a=a.high() - a.low(),
size_b=b.high() - b.low(),
size_max = size_a>size_b ? size_a : size_b,
size_int = b.low()-a.high();
while(x>=y) {
//std::cout << "x and y: " << x << " and " << y << std::endl;
//std::cout << "sizes: " << CGAL::to_double(size_int) << " " << CGAL::to_double(size_max) << std::endl;
if(size_int>size_max) {
CGAL::set_precision(Bigfloat_interval(),
2*CGAL::get_precision(Bigfloat_interval()));
x=CGAL::upper(CGAL::convert_to_bfi(a.high()));
y=CGAL::lower(CGAL::convert_to_bfi(b.low()));
} else {
if(size_a < size_b) {
b.refine();
size_b=b.high() - b.low();
y=CGAL::lower(CGAL::convert_to_bfi(b.low()));
} else {
a.refine();
size_a=a.high()-a.low();
x=CGAL::upper(CGAL::convert_to_bfi(a.high()));
}
size_max = size_a>size_b ? size_a : size_b;
size_int = b.low()-a.high();
}
}
}
CGAL_assertion(x<y);
//srb_b.stop();
//std::cout << "Intermediate2: " << x << " " << y << std::endl;
typename CGAL::internal::Float_traits<Bigfloat>::Get_mantissa mantissa;
typename CGAL::internal::Float_traits<Bigfloat>::Get_exponent exponent;
// std::cout << CGAL::to_double(x) << " < " << CGAL::to_double(y) << std::endl;
Integer x_m = mantissa(x), y_m=mantissa(y);
long x_e = exponent(x), y_e = exponent(y);
//std::cout << "Floats1: " << x_m << " " << x_e << " and " << y_m << " " << y_e << std::endl;
if (((x_m > 0) && (y_m < 0)) || ((x_m < 0) && (y_m > 0))) {
//srb.stop();
return Rational(0);
}
bool negative=false;
if(x_m<=0 && y_m <=0) {
x_m=-x_m;
y_m=-y_m;
std::swap(x_m,y_m);
std::swap(x_e,y_e);
negative=true;
}
// Now, we have that (x_m,x_e) represents a number smaller than (y_m,y_e)
//srb_c.start();
//std::cout << "Floats2: " << x_m << " " << x_e << " and " << y_m << " " << y_e << std::endl;
// As long as the mantissa is even, simplify
while(x_m != 0 && (x_m & 1)==0 ) {
x_m=x_m >> 1;
x_e++;
}
while(y_m != 0 && (y_m & 1)==0 ) {
y_m=y_m >> 1;
y_e++;
}
//srb_c.stop();
//std::cout << "Floats3: " << x_m << " " << x_e << " and " << y_m << " " << y_e << std::endl;
// Bring both numbers to a common exponent
//srb_d.start();
long min_e = x_e < y_e ? x_e : y_e;
while(x_e > min_e) {
x_m=x_m << 1;
x_e--;
}
while(y_e > min_e) {
y_m=y_m << 1;
y_e--;
}
//srb_d.stop();
CGAL_assertion(y_e==x_e && x_e==min_e);
CGAL_assertion(x_m < y_m);
//std::cout << "Floats4: " << x_m << " " << x_e << " and " << y_m << " " << y_e << std::endl;
// Avoid mantissas to have difference one
if(y_m-x_m==Integer(1)) {
x_m=x_m << 1;
y_m=y_m << 1;
x_e--;
y_e--;
min_e--;
}
//std::cout << "Floats5: " << x_m << " " << x_e << " and " << y_m << " " << y_e << std::endl;
Integer final_mantissa(0);
//srb_e.start();
long x_log = x_m==Integer(0) ? -1 : CGAL::internal::floor_log2_abs(x_m),
y_log = y_m==Integer(0) ? -1 : CGAL::internal::floor_log2_abs(y_m),
old_log = y_log;
//std::cout << x_log << " < " << y_log << std::endl;
while(x_log==y_log) {
//std::cout << "here" << std::endl;
while(old_log > y_log) {
final_mantissa = final_mantissa << 1;
old_log--;
}
CGAL_assertion((x_m & ((Integer(1) << x_log) - 1)) == x_m - CGAL::ipower(Integer(2),x_log));
x_m = x_m & ((Integer(1) << x_log) - 1); // x_m - CGAL::ipower(Integer(2),x_log);
y_m = y_m & ((Integer(1) << y_log) - 1); // y_m - CGAL::ipower(Integer(2),y_log);
final_mantissa++;
old_log=y_log;
x_log = x_m==0 ? -1 : CGAL::internal::floor_log2_abs(x_m);
y_log = y_m==0 ? -1 : CGAL::internal::floor_log2_abs(y_m);
}
//srb_e.stop();
// Now, x_log != y_log, in fact, y_log is greater
CGAL_assertion(x_log<y_log);
//srb_f.start();
while(old_log > y_log) {
final_mantissa = final_mantissa << 1;
old_log--;
}
if((y_m & ((Integer(1) << y_log) - 1 ))==0) { // y_m - CGAL::ipower(Integer(2),y_log)==0) {
// Now, the constructed value would be equal to
while(y_log!=0 && x_log==y_log-1) {
final_mantissa = final_mantissa << 1;
final_mantissa++;
y_log--;
x_m = x_m==0 ? 0 : Integer(x_m & ((Integer(1) << x_log) - 1)); //x_m - CGAL::ipower(Integer(2),x_log);
x_log = x_m==0 ? -1 : CGAL::internal::floor_log2_abs(x_m);
}
final_mantissa = final_mantissa << 1;
final_mantissa++;
y_log--;
} else {
final_mantissa++;
}
//srb_f.stop();
min_e += y_log;
Rational rat_between;
//std::cout << "Min_e: " << min_e << std::endl;
if(min_e > 0) {
rat_between = compose(final_mantissa << min_e,
Integer(1));
} else {
rat_between = compose(final_mantissa, Integer(1) << -min_e);
}
if(negative) {
rat_between = -rat_between;
}
//std::cout << "Result: " << a.high() << " " << rat_between << " " << b.low() << std::endl;
CGAL_assertion(a.high() < rat_between);
CGAL_assertion(b.low() > rat_between);
CGAL::set_precision(Bigfloat_interval(),old_prec);
//srb.stop();
return rat_between;
}
} // namespace internal
} //namespace CGAL
#endif // CGAL_BOUND_BETWEEN_1_H
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