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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/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/bound_between_1.h $ // $Id: include/CGAL/Algebraic_kernel_d/bound_between_1.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // // Author(s) : Michael Kerber // // ============================================================================ #ifndef CGAL_BOUND_BETWEEN_1_H #define CGAL_BOUND_BETWEEN_1_H 1 #include #include #include #include #include #include #include #include #include #include #include #include namespace CGAL { namespace internal { /*! \brief tries to find a SIMPLE rational q with aq * is a power of two, and is not too big. There is no guarantee to find * the rational value between a and b of minimal * bit size. */ template 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::Compose compose; typedef typename CGAL::Get_arithmetic_kernel::Arithmetic_kernel AK; typedef typename AK::Bigfloat_interval Bigfloat_interval; typedef typename CGAL::Bigfloat_interval_traits ::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::Get_mantissa mantissa; typename CGAL::internal::Float_traits::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) { 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