/* linbox/blackbox/classic-rational-reconstruction.h
 * Copyright (C) 2009 Anna Marszalek
 *
 * Written by Anna Marszalek <aniau@astronet.pl>
 *
 * ========LICENCE========
 * This file is part of the library LinBox.
 *
  * LinBox is free software: 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 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 * ========LICENCE========
 */


#ifndef __LINBOX_classic_reconstruction_H
#define __LINBOX_classic_reconstruction_H

#include <iostream>

#include "linbox/algorithms/rational-reconstruction-base.h"

namespace LinBox
{

	/*
	 * implements classic rational reconstruction by extended euclidean algorithm,
	 * Wang's bounds [Wang 1981] are used as default
	 */

	template <class Ring>
	class ClassicRationalReconstruction: public RReconstructionBase<Ring> {
	protected:
		const bool _reduce;
		const bool _recursive;
	public:
		const Ring _intRing;
		typedef typename Ring::Element Element;

		ClassicRationalReconstruction(const Ring& Z, const bool reduce = true, const bool recursive = false) :
			RReconstructionBase<Ring>(Z),
			_reduce(reduce), _recursive (recursive), _intRing(Z)
		{}

		ClassicRationalReconstruction<Ring> (const ClassicRationalReconstruction<Ring>& RR):
			RReconstructionBase<Ring>(RR._intRing),
			_reduce(RR._reduce), _recursive(RR._recursive), _intRing(RR._intRing)
		{}

		~ClassicRationalReconstruction() {}

		//Wang method
		bool reconstructRational(Element& a, Element& b, const Element& x, const Element& m) const
		{
			Element a_bound; _intRing.sqrt(a_bound, m/2);
			bool res = reconstructRational(a,b,x,m,a_bound);
			res = res && (b <= a_bound);
			return res;
		}

		bool reconstructRational(Element& a, Element& b, const Element& x, const Element& m, const Element& a_bound) const{
			bool res=false;

			if (x == 0) {
				a = 0;
				b = 1;
			}
			else {
				res = ratrecon(a,b,x,m,a_bound);
				if (_recursive) {
					for(Element newbound = a_bound + 1; (!res) && (newbound<x) ; ++newbound)
						res = ratrecon(a,b,x,m,newbound);
				}
			}
			if (!res) {
				a = x> m/2? x-m: x;
				b = 1;
				if (a > 0) res = (a < a_bound);
				else res = (-a < a_bound);
			}

			return res;
		}


	protected:

		bool ratrecon(Element& a,Element& b,const Element& x,const Element& m,const Element& a_bound) const
		{

			Element  r0, t0, q, u;
			r0=m;
			t0=0;
			a=x;
			b=1;
			//Element s0,s1; s0=1,s1=0;//test time gcdex;
			while(a>=a_bound)
				//while (t0 <= b_bound)
			{

				q = r0;
				_intRing.divin(q,a);        // r0/num
				//++this->C.div_counter;

				u = a;
				a = r0;
				r0 = u;	// r0 <-- num

				_intRing.maxpyin(a,u,q); // num <-- r0-q*num
				//++this->C.mul_counter;
				//if (a == 0) return false;

				u = b;
				b = t0;
				t0 = u;	// t0 <-- den

				_intRing.maxpyin(b,u,q); // den <-- t0-q*den
				//++this->C.mul_counter;

				//u = s1;
				//s1 = s0;
				//s0 = u;

				//_intRing.maxpyin(s0,u,q);
				//++this->C.mul_counter;

			}

			//if (den < 0) {
			//	_intRing.negin(num);
			//      _intRing.negin(den);
			//}

			if ((a>0) && (_reduce)) {

				// [GG, MCA, 1999] Theorem 5.26
				// (ii)
				Element gg;
				//++this->C.gcd_counter;
				if (_intRing.gcd(gg,a,b) != 1) {

					Element ganum, gar2;
					for( q = 1, ganum = r0-a, gar2 = r0 ; (ganum >= a_bound) || (gar2<a_bound); ++q ) {
						ganum -= a;
						gar2 -= a;
					}

					//_intRing.maxpyin(r0,q,a);
					r0 = ganum;
					_intRing.maxpyin(t0,q,b);
					//++this->C.mul_counter;++this->C.mul_counter;
					if (t0 < 0) {
						a = -r0;
						b = -t0;
					}
					else {
						a = r0;
						b = t0;
					}

					//                                if (t0 > m/k) {
					if (abs((double)b) > (double)m/(double)a_bound) {
						if (!_recursive) {
							std::cerr
							<< "*** Error *** No rational reconstruction of "
							<< x
							<< " modulo "
							<< m
							<< " with denominator <= "
							<< (m/a_bound)
							<< std::endl;
						}
						return false;
					}
					if (_intRing.gcd(gg,a,b) != 1) {
						if (!_recursive)
							std::cerr
							<< "*** Error *** There exists no rational reconstruction of "
							<< x
							<< " modulo "
							<< m
							<< " with |numerator| < "
							<< a_bound
							<< std::endl
							<< "*** Error *** But "
							<< a
							<< " = "
							<< b
							<< " * "
							<< x
							<< " modulo "
							<< m
							<< std::endl;
						return false;
					}
				}
				}
				// (i)
				if (b < 0) {
					_intRing.negin(a);
					_intRing.negin(b);
				}

				// std::cerr << "RatRecon End " << num << "/" << den << std::endl;
				return true;
			}
		};

		/*
		 * implements classic rational reconstruction by extended euclidean algorithm,
		 * reconstructed pair corresponds to the maximal (or large enough) quotient, see MQRR Alg. of Monagan [Monagan2004] is used
		 */

		template <class Ring>
		class ClassicMaxQRationalReconstruction:public ClassicRationalReconstruction<Ring> {
		public:
			const Ring _intRing;
			typedef typename Ring::Element Element;

			ClassicMaxQRationalReconstruction(const Ring& Z, const bool reduce = true, const bool recursive = false) :
				ClassicRationalReconstruction<Ring>(Z,reduce,recursive), _intRing(Z)
		       	{}

			ClassicMaxQRationalReconstruction(const ClassicMaxQRationalReconstruction<Ring>& RR) :
				ClassicRationalReconstruction<Ring>(RR), _intRing(RR._intRing)
			{}

			~ClassicMaxQRationalReconstruction() {}

			bool reconstructRational(Element& a, Element& b, const Element& x, const Element& m) const
			{
				bool res = maxEEA(a,b,x,m);
				return res;
			}

			bool reconstructRational(Element& a, Element& b, const Element& x, const Element& m, const Element& a_bound) const{
				bool res= false;
				return res = ClassicRationalReconstruction<Ring>::reconstructRational(a,b,x,m,a_bound);
			}

		protected:
			bool maxEEA(Element& a, Element& b, const Element& x, const Element& m) const{

				Element qmax = 0, amax=x, bmax =1;

				Element  r0, t0, q, u;
				r0=m;
				t0=0;
				a=x;
				b=1;
				//Element s0,s; s0=1,s=0;//test time gcdex;

				Element T = m.bitsize();
				int c = 5;	//should be changed here to enhance probability of correctness

				while((a>0) && (r0.bitsize() > T.bitsize() + c))
				{
					q = r0;
					_intRing.divin(q,a);        // r0/num
					//++this->C.div_counter;
					if (q > qmax) {
						amax = a;
						bmax = b;
						qmax = q;
						if (qmax.bitsize() > T.bitsize() + c) break;
					}

					u = a;
					a = r0;
					r0 = u;	// r0 <-- num

					_intRing.maxpyin(a,u,q); // num <-- r0-q*num
					//++this->C.mul_counter;
					//if (a == 0) return false;

					u = b;
					b = t0;
					t0 = u;	// t0 <-- den

					_intRing.maxpyin(b,u,q); // den <-- t0-q*den
					//++this->C.mul_counter;
				}

				a = amax;
				b = bmax;

				if (b < 0) {
					_intRing.negin(a);
					_intRing.negin(b);
				}

				Element gg;
				_intRing.gcd(gg,a,b);
				//++this->C.gcd_counter;

				//if (q > T)
				//Element T = m.bitsize();
				//int c = 20;
				//T=0;c=0;
				if (qmax.bitsize() > T.bitsize() + c) {
					return true;
				}
				else return false;

				//if (gg > 1) return false;
				//else return true;
			}
		};

	}
#endif //__LINBOX_classic_reconstruction_H

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