/*
 * Copyright (C) 2015  Pascal Giorgi
 *
 * Written by Pascal Giorgi   <pascal.giorgi@lirmm.fr>
 *
 * ========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_matpoly_mult_ftt_recint_INL
#define __LINBOX_matpoly_mult_ftt_recint_INL

#include <givaro/zring.h>
#include <recint/rint.h>
#include "linbox/ring/modular.h"
#include "linbox/randiter/random-fftprime.h"
#include "linbox/randiter/random-prime.h"
#include <fflas-ffpack/field/rns-double.h>
#define MB(x) ((x)/(double)(1<<20))
#ifndef MEMINFO
#define MEMINFO ""
#endif

#ifdef LOW_MEMORY_PMBASIS
#define MEMFACTOR 4
#define CRT_SIZE 3
#endif

namespace LinBox{

	/***************************************************
	 **** Polynomial Matrix Multiplication over Z[x] ***
	 ***************************************************/
	template<size_t K >
	class PolynomialMatrixFFTMulDomain<Givaro::ZRing<RecInt::ruint<K> > > {
	public:
		typedef Givaro::ZRing<RecInt::ruint<K> >   IntField;
		typedef RecInt::ruint<K>    Element;
		//typedef Givaro::Modular<uint32_t>     ModField;
		typedef Givaro::Modular<double>         ModField;
		typedef PolynomialMatrix<PMType::polfirst,PMStorage::plain,ModField> MatrixP_F; // Polynomial matrix stored as a matrix of polynomials
		typedef PolynomialMatrix<PMType::polfirst,PMStorage::plain,IntField> MatrixP_I; // Polynomial matrix stored as a matrix of polynomials

	private:
		const IntField     *_field;
		integer           _maxnorm;

		template<typename PMatrix1>
		size_t logmax(const PMatrix1& A) const {
			return size_t(1)<<K;
		}

	public:


		inline const IntField & field() const { return *_field; }


		PolynomialMatrixFFTMulDomain (const IntField &F, const integer maxnorm=0) :
			_field(&F), _maxnorm(maxnorm) {}

		template<typename PMatrix1, typename PMatrix2, typename PMatrix3>
		void mul (PMatrix1 &c, const PMatrix2 &a, const PMatrix3 &b, size_t max_rowdeg=0) const {
			//compute a bound on the entry of the input matrix a and b
			FFT_PROFILE_START(2);
			integer maxA,maxB;
			maxA=maxB=_maxnorm;			
			if (_maxnorm==0){
				maxA=1;maxA<<=uint64_t(logmax(a));
				maxB=1;maxB<<=uint64_t(logmax(b));
			}
			integer bound=maxA*maxB*uint64_t(a.coldim())*uint64_t(std::min(a.size(),b.size()));
			if (_maxnorm==0) bound*=2; //seems to compute over Z, need to double to handle possible negative value
			FFT_PROFILING(2,"max norm computation");

			mul_crtla(c,a,b,maxA,maxB,bound, max_rowdeg);
		}
    

		template<typename PMatrix1, typename PMatrix2, typename PMatrix3>
		void midproduct (PMatrix1 &c, const PMatrix2 &a, const PMatrix3 &b,
						 bool smallLeft=true, size_t n0=0, size_t n1=0) const {
			//compute a bound on the entry of the input matrix a and b
			FFT_PROFILE_START(2);
			integer maxA,maxB;
			maxA=maxB=_maxnorm;
			if (_maxnorm==0){
				maxA=1;maxA<<=uint64_t(logmax(a));
				maxB=1;maxB<<=uint64_t(logmax(b));
			}
			integer bound=maxA*maxB*integer((uint64_t)a.coldim());
			if (_maxnorm==0) bound*=2; //seems to compute over Z, need to double to handle possible negative value
			if (smallLeft)
				bound*= (uint64_t)a.size();
			else
				bound*= (uint64_t)b.size();

			FFT_PROFILING(2,"max norm computation");

			midproduct_crtla(c,a,b,maxA,maxB,bound,smallLeft, n0,n1);
		}


    
		// WARNING: Polynomial Matrix should stored as matrix of polynomial with integer coefficient
		// outputsize -> its the size of the output if known in advance and less than a.size()+b.size()-1
		template< typename PMatrix1,typename PMatrix2, typename PMatrix3>
		void mul_crtla(PMatrix1 &c, const PMatrix2 &a, const PMatrix3 &b,
					   const integer& maxA, const integer& maxB, const integer& bound, size_t max_rowdeg=0) const {
			//std::cout<<"MUL CRT LA STARTING: "<<STR_MEMINFO<<std::endl;      
			FFT_PROFILE_START(2);
			linbox_check(a.coldim() == b.rowdim());
			size_t m = a.rowdim();
			size_t k = a.coldim();
			size_t n = b.coldim();
			size_t s= a.size()+b.size()-1; // MUST BE CHANGED TO the 0-rowdeg of (a.b)
			if (max_rowdeg!=0) s = max_rowdeg+1;
			c.resize(s);
			size_t lpts=0;
			size_t pts  = 1; while (pts < s) { pts= pts<<1; ++lpts; }

			//std::cout<<"MULCRT_LA: "<<c.size()<<" -> "<<a.size()<<"x"<<b.size()<<" (nb pts=2^"<<lpts<<")\n";
      
			// compute max prime value for FFLAS      
			//uint64_t prime_max=std::sqrt( (1ULL<<53) /k)+1;
			uint64_t prime_max=maxFFTPrimeValue(k,pts); // CAREFUL: only for Modular<double>
      
			std::vector<integer> bas;
			getFFTPrime(prime_max,lpts,bound,bas,k,s);
      
			std::vector<double> basis(bas.size());
			std::copy(bas.begin(),bas.end(),basis.begin());
			FFPACK::rns_double RNS(basis);
			size_t num_primes = RNS._size;
#ifdef FFT_PROFILER
			//double tMul=0.,tCopy=0;;
			if (FFT_PROF_LEVEL<3){
				std::cout << "number of FFT primes :" << num_primes << std::endl;
				std::cout << "max prime            : "<<prime_max<<" ("<<integer(prime_max).bitsize()<<")"<<std::endl;
				std::cout << "bitsize of the output: "<<bound.bitsize()
						  <<"( "<< RNS._M.bitsize()<<" )"<<std::endl;
				std::cout <<" +++++++++++++++++++++++++++++++"<<std::endl;
			}
#endif
			FFT_PROFILING(2,"init of CRT approach");
			// reduce t_a and t_b modulo each FFT primes
			size_t n_ta=m*k*a.size(), n_tb=k*n*b.size();      
			std::vector<MatrixP_F*> c_i (num_primes);

#ifndef LOW_MEMORY_PMBASIS 
			ADD_MEM(8*(n_ta+n_tb)*num_primes);      
			double* t_a_mod= new double[n_ta*num_primes];
			double* t_b_mod= new double[n_tb*num_primes];
			RNS.init(1, n_ta, t_a_mod, n_ta, a.getPointer(), n_ta, maxA);
			RNS.init(1, n_tb, t_b_mod, n_tb, b.getPointer(), n_tb, maxB);
			FFT_PROFILING(2,"reduction mod pi of input matrices");
      
			FFT_PROFILE_START(2);
			for (size_t l=0;l<num_primes;l++)
				{
					//FFT_PROFILE_START;
					ModField f(RNS._basis[l]);
					MatrixP_F a_i (f, m, k, pts);
					MatrixP_F b_i (f, k, n, pts);
		 
					c_i[l] = new MatrixP_F(f, m, n, pts);
					// copy reduced data
					for (size_t i=0;i<m*k;i++)
						for (size_t j=0;j<a.size();j++)
							a_i.ref(i,j)=t_a_mod[l*n_ta+j+i*a.size()];
					for (size_t i=0;i<k*n;i++)
						for (size_t j=0;j<b.size();j++)
							b_i.ref(i,j)=t_b_mod[l*n_tb+j+i*b.size()];	
					PolynomialMatrixThreePrimesFFTMulDomain<ModField> fftdomain (f);
					integer bound=integer(RNS._basis[l]-1)*integer(RNS._basis[l]-1)
						*integer((uint64_t) k)*integer((uint64_t)std::min(a.size(),b.size()));
#ifdef CHECK_MATPOL_MUL
					Matrixp_F copy_a_i(f, m, k, pts),copy_b_i(f, k, n, pts);
					copy_a_i.copy(a_i);
					copy_b_i.copy(b_i);
#endif		 
					fftdomain.mul_fft(lpts, *c_i[l], a_i, b_i, bound);
#ifdef CHECK_MATPOL_MUL
					std::cerr<<"(3 primes CRT) - ";
					check_mul(*c_i[l], copy_a_i, copy_b_i,s);
#endif

				}      
			FFT_PROFILING(2,"FFTprime mult+copying");
			DEL_MEM(8*(n_ta+n_tb)*num_primes);
			delete[] t_a_mod;
			delete[] t_b_mod;
#else
			size_t CRT_NBPRIME=CRT_SIZE;
			ADD_MEM(8*(n_ta+n_tb)*CRT_NBPRIME);
			double* t_a_mod= new double[n_ta*CRT_NBPRIME];
			double* t_b_mod= new double[n_tb*CRT_NBPRIME];
      
			for(size_t loop=0;loop<num_primes;loop+=CRT_NBPRIME){	
				// create chunk of RNS
				size_t rns_chunk=std::min(CRT_NBPRIME,num_primes-loop); // nbr of primes in the current smallRNS basis
				std::vector<double> smallBasis(rns_chunk);
				std::copy(basis.begin()+loop,basis.begin()+loop+rns_chunk,smallBasis.begin());
				FFPACK::rns_double smallRNS(smallBasis);
				smallRNS.precompute_cst(RNS._ldm);	
				smallRNS.init(1, n_ta, t_a_mod, n_ta, a.getPointer(), n_ta, maxA);
				smallRNS.init(1, n_tb, t_b_mod, n_tb, b.getPointer(), n_tb, maxB);
				FFT_PROFILING(2,"reduction mod pi of input matrices");
				for (size_t l=0;l<rns_chunk;l++)
					{
						ModField f(smallRNS._basis[l]);
						MatrixP_F a_i (f, m, k, pts);
						MatrixP_F b_i (f, k, n, pts);	
						c_i[loop+l] = new MatrixP_F(f, m, n, pts);
						// copy reduced data
						for (size_t i=0;i<m*k;i++)
							for (size_t j=0;j<a.size();j++)
								a_i.ref(i,j)=t_a_mod[l*n_ta+j+i*a.size()];
						for (size_t i=0;i<k*n;i++)
							for (size_t j=0;j<b.size();j++)
								b_i.ref(i,j)=t_b_mod[l*n_tb+j+i*b.size()];	
	    
						PolynomialMatrixThreePrimesFFTMulDomain<ModField> fftdomain (f);
						integer bound=integer(smallRNS._basis[l]-1)*integer(smallRNS._basis[l]-1)
							*integer((int64_t)k)*integer((uint64_t)std::min(a.size(),b.size()));

#ifdef CHECK_MATPOL_MUL
						MatrixP_F copy_a_i(f, m, k, pts),copy_b_i(f, k, n, pts);
						copy_a_i.copy(a_i);
						copy_b_i.copy(b_i);
#endif		 
						fftdomain.mul_fft(lpts, *c_i[loop+l], a_i, b_i, bound);
#ifdef CHECK_MATPOL_MUL
						std::cerr<<"(3 prime -CRT) - ";
						check_mul(*c_i[loop+l], copy_a_i, copy_b_i,s);
#endif	    
					}      
				FFT_PROFILING(2,"FFTprime mult+copying");
			} // end of loop for memory saving
			DEL_MEM(8*(n_ta+n_tb)*CRT_NBPRIME);
			delete[] t_a_mod;
			delete[] t_b_mod;
#endif
      
			if (false && num_primes < 2) {
				FFT_PROFILE_START(2);	
				//c.copy(*c_i[0],0,s-1);
			} else {
				FFT_PROFILE_START(2);

#ifndef LOW_MEMORY_PMBASIS
				// construct contiguous storage for c_i
				size_t n_tc=m*n*s;
				ADD_MEM(8*n_tc*num_primes);
				double *t_c_mod = new double[n_tc*num_primes];
				//std::cout<<"RNS OUT ALLOC done: "<<STR_MEMINFO<<std::endl;      
				for (size_t l=0;l<num_primes;l++){
					for (size_t i=0;i<m*n;i++)
						for (size_t j=0;j<s;j++)
							t_c_mod[l*n_tc + (j+i*s)]= c_i[l]->get(i,j);
					delete c_i[l];
				}
				FFT_PROFILING(2,"linearization of results mod pi");

				// reconstruct the result in C
				RNS.convert(1,n_tc,0,c.getWritePointer(),n_tc, t_c_mod, n_tc, _maxnorm);
				//std::cout<<"RNS OUT COMP done: "<<STR_MEMINFO<<std::endl;      
				DEL_MEM(8*n_tc*num_primes);
				delete[] t_c_mod;
#else
				size_t s_small= s/MEMFACTOR; 
				size_t s_last = s- s_small*(MEMFACTOR-1);
				size_t n_tc_small= m*n*s_small;
				size_t n_tc_last = m*n*s_last;
				{
					ADD_MEM(8*n_tc_small*num_primes);
					//std::cout<<"RNS OUT ALLOC done: "<<STR_MEMINFO<<std::endl;      
					double *t_c_mod = new double[n_tc_small*num_primes];
					for (size_t memiter=0;memiter<MEMFACTOR-1;memiter++){	 
						for (size_t l=0;l<num_primes;l++){
							for (size_t i=0;i<m*n;i++)
								for (size_t j=0;j<s_small;j++)
									t_c_mod[l*n_tc_small + (j+i*s_small)]= c_i[l]->get(i,memiter*s_small+j);
						}	
						// reconstruct the result in C
						RNS.convert(m*n,s_small,0,c.getWritePointer()+memiter*s_small,s, t_c_mod, n_tc_small, _maxnorm);
						//std::cout<<"RNS OUT COMP done: "<<STR_MEMINFO<<std::endl;      
					}
					DEL_MEM(8*n_tc_small*num_primes);
					delete[] t_c_mod;
				}	
				{
					ADD_MEM(8*n_tc_last*num_primes);
					double *t_c_mod = new double[n_tc_last*num_primes];
					// perform the last step
					for (size_t l=0;l<num_primes;l++){
						for (size_t i=0;i<m*n;i++)
							for (size_t j=0;j<s_last;j++)
								t_c_mod[l*n_tc_last + (j+i*s_last)]= c_i[l]->get(i,(MEMFACTOR-1)*s_small+j);
						delete c_i[l];
					}	  
					// reconstruct the result in C
					RNS.convert(m*n,s_last,0,c.getWritePointer()+(MEMFACTOR-1)*s_small,s, t_c_mod, n_tc_last, _maxnorm);
					DEL_MEM(8*n_tc_last*num_primes);
					delete[] t_c_mod;
				}
	
#endif
			}
      
			//      std::cout<<"c"<<":="<<c<<";\n";
			FFT_PROFILING(2,"k prime reconstruction");
			// std::cout<<"CC:="<<c<<std::endl;
			// std::cout<<"<-----------------: "<<std::endl;;
		}
    

		// WARNING: Polynomial Matrix should stored as matrix of polynomial with integer coefficient 
		template< typename PMatrix1,typename PMatrix2, typename PMatrix3>
		void midproduct_crtla(PMatrix1 &c, const PMatrix2 &a, const PMatrix3 &b,
							  const integer& maxA, const integer& maxB, const integer& bound,
							  bool smallLeft=true, size_t n0=0, size_t n1=0) const {
			// void midproduct_crtla(MatrixP_I &c, const MatrixP_I &a, const MatrixP_I &b,
			// 			  const integer& maxA, const integer& maxB, const integer& bound,
			// 			  bool smallLeft=true, size_t n0=0, size_t n1=0) {
			FFT_PROFILE_START(2);
			linbox_check(a.coldim() == b.rowdim());
			size_t m = a.rowdim();
			size_t k = a.coldim();
			size_t n = b.coldim();
			size_t hdeg = (n0==0?c.size():n0);
			size_t deg  = (n1==0?2*hdeg-1:n1);
			linbox_check(c.size()>=deg-hdeg);

			if (smallLeft){
				linbox_check(b.size()<hdeg+deg);
			}
			else
				linbox_check(a.size()<hdeg+deg);
      
			//linbox_check(2*c.size()-1 == b.size());
			//size_t deg= b.size()+1;
			//size_t hdeg= deg/2;
			size_t lpts=0;
			size_t pts  = 1; while (pts < deg) { pts= pts<<1; ++lpts; }

			// compute max prime value for FFLAS
			uint64_t prime_max= std::sqrt( (1ULL<<53) / k)+1;
			std::vector<integer> bas;
			getFFTPrime(prime_max,lpts,bound,bas,k,deg);
      
			std::vector<double> basis(bas.size());
			std::copy(bas.begin(),bas.end(),basis.begin());
			FFPACK::rns_double RNS(basis);
			size_t num_primes = RNS._size;
#ifdef FFT_PROFILER
			double tMul=0.,tCopy=0;;
			if (FFT_PROF_LEVEL<3){
				std::cout << "number of FFT primes :" << num_primes << std::endl;
				std::cout << "max prime            : "<<prime_max<<" ("<<integer(prime_max).bitsize()<<")"<<std::endl;
				std::cout << "bitsize of the output: "<<bound.bitsize()
						  <<"( "<< RNS._M.bitsize()<<" )"<<std::endl;
				std::cout <<" +++++++++++++++++++++++++++++++"<<std::endl;
			}
#endif
			FFT_PROFILING(2,"init of CRT approach");

			size_t n_ta=m*k*a.size(), n_tb=k*n*b.size();
			std::vector<MatrixP_F*> c_i (num_primes);
      
#ifndef LOW_MEMORY_PMBASIS 
			// reduce t_a and t_b modulo each FFT primes
			ADD_MEM(8*(n_ta+n_tb)*num_primes);
			double* t_a_mod= new double[n_ta*num_primes];
			double* t_b_mod= new double[n_tb*num_primes];

			RNS.init(1, n_ta, t_a_mod, n_ta, a.getPointer(), n_ta, maxA);
			RNS.init(1, n_tb, t_b_mod, n_tb, b.getPointer(), n_tb, maxB);
			FFT_PROFILING(2,"reduction mod pi of input matrices");
      


			for (size_t l=0;l<num_primes;l++){
				FFT_PROFILE_START(2);
				ModField f(RNS._basis[l]);
				MatrixP_F a_i (f, m, k, pts);
				MatrixP_F b_i (f, k, n, pts);
				c_i[l] = new MatrixP_F(f, m, n, pts);
				// copy reduced data and reversed when necessary according to midproduct algo
				//std::cout<<"hdeg-size: "<<hdeg<<" <-> "<<a.size()<<std::endl;
				for (size_t i=0;i<m*k;i++)
					for (size_t j=0;j<a.size();j++)
						if (smallLeft)
							a_i.ref(i,hdeg-1-j)=t_a_mod[l*n_ta+j+i*a.size()];
						else
							a_i.ref(i,j)=t_a_mod[l*n_ta+j+i*a.size()];
				for (size_t i=0;i<k*n;i++)
					for (size_t j=0;j<b.size();j++)
						if (smallLeft)
							b_i.ref(i,j)=t_b_mod[l*n_tb+j+i*b.size()];
						else
							b_i.ref(i,hdeg-1-j)=t_b_mod[l*n_tb+j+i*b.size()];
				FFT_PROFILE_GET(2,tCopy);
	
				PolynomialMatrixThreePrimesFFTMulDomain<ModField> fftdomain (f);       
				integer bound2=integer(RNS._basis[l]-1)*integer(RNS._basis[l]-1)
					*integer((uint64_t)a.coldim())*integer((uint64_t)std::min(a.size(),b.size()));
	
 
#ifdef CHECK_MATPOL_MIDP
				MatrixP_F copy_a_i(f, m, k, a.size()),copy_b_i(f, k, n, b.size());
				//copy_a_i.copy(a_i);
				//copy_b_i.copy(b_i);
				for (size_t i=0;i<m*k;i++)
					for (size_t j=0;j<a.size();j++)
						copy_a_i.ref(i,j)=t_a_mod[l*n_ta+j+i*a.size()];
				for (size_t i=0;i<k*n;i++)
					for (size_t j=0;j<b.size();j++)
						copy_b_i.ref(i,j)=t_b_mod[l*n_tb+j+i*b.size()];	
#endif		 
				fftdomain.midproduct_fft(lpts, *(c_i[l]), a_i, b_i, bound2, smallLeft);
#ifdef CHECK_MATPOL_MIDP
				std::cerr<<"(3 prime -CRT) - ";
				check_midproduct(*c_i[l], copy_a_i, copy_b_i,smallLeft,n0,n1,c.size());
#endif	          
				FFT_PROFILE_GET(2,tMul);
			}      
			DEL_MEM(8*(n_ta+n_tb)*num_primes);
			delete[] t_a_mod;
			delete[] t_b_mod;
#else
			// loop for memory saving
			size_t CRT_NBPRIME=CRT_SIZE;
			ADD_MEM(8*(n_ta+n_tb)*CRT_NBPRIME);
			double* t_a_mod= new double[n_ta*CRT_NBPRIME];
			double* t_b_mod= new double[n_tb*CRT_NBPRIME];
            
			for(size_t loop=0;loop<num_primes;loop+=CRT_NBPRIME){	
				// create chunk of RNS
				size_t rns_chunk=std::min(CRT_NBPRIME,num_primes-loop); // nbr of primes in the current smallRNS basis
				std::vector<double> smallBasis(rns_chunk);
				std::copy(basis.begin()+loop,basis.begin()+loop+rns_chunk,smallBasis.begin());
				FFPACK::rns_double smallRNS(smallBasis);
				smallRNS.precompute_cst(RNS._ldm);
				smallRNS.init(1, n_ta, t_a_mod, n_ta, a.getPointer(), n_ta, maxA);
				smallRNS.init(1, n_tb, t_b_mod, n_tb, b.getPointer(), n_tb, maxB);
				FFT_PROFILING(2,"reduction mod pi of input matrices");

				for (size_t l=0;l<rns_chunk;l++)
					{	    
						//FFT_PROFILE_START;
						//std::cout<<"prime: "<<(long)smallRNS._basis[l]<<std::endl;
						ModField f(smallRNS._basis[l]);
						MatrixP_F a_i (f, m, k, pts);
						MatrixP_F b_i (f, k, n, pts);	
						c_i[loop+l] = new MatrixP_F(f, m, n, pts);


						integer bound2=integer(smallRNS._basis[l]-1)*integer(smallRNS._basis[l]-1)
							*integer((uint64_t)a.coldim())*integer((uint64_t)std::min(a.size(),b.size()));

						// copy reduced data
						for (size_t i=0;i<m*k;i++)
							for (size_t j=0;j<a.size();j++)
								if (smallLeft)
									a_i.ref(i,hdeg-1-j)=t_a_mod[l*n_ta+j+i*a.size()];
								else
									a_i.ref(i,j)=t_a_mod[l*n_ta+j+i*a.size()];
						for (size_t i=0;i<k*n;i++)
							for (size_t j=0;j<b.size();j++)
								if (smallLeft)
									b_i.ref(i,j)=t_b_mod[l*n_tb+j+i*b.size()];
								else
									b_i.ref(i,hdeg-1-j)=t_b_mod[l*n_tb+j+i*b.size()];
						FFT_PROFILE_GET(2,tCopy);

						PolynomialMatrixThreePrimesFFTMulDomain<ModField> fftdomain (f);
	    
#ifdef CHECK_MATPOL_MIDP
						MatrixP_F copy_a_i(f, m, k, a.size()),copy_b_i(f, k, n, b.size());
						//copy_a_i.copy(a_i);
						//copy_b_i.copy(b_i);
						for (size_t i=0;i<m*k;i++)
							for (size_t j=0;j<a.size();j++)
								copy_a_i.ref(i,j)=t_a_mod[l*n_ta+j+i*a.size()];
						for (size_t i=0;i<k*n;i++)
							for (size_t j=0;j<b.size();j++)
								copy_b_i.ref(i,j)=t_b_mod[l*n_tb+j+i*b.size()];	    
#endif		 
						fftdomain.midproduct_fft(lpts, *(c_i[loop+l]), a_i, b_i,bound2, smallLeft);	    
#ifdef CHECK_MATPOL_MIDP
						std::cerr<<"(3 prime -CRT) - ";
						check_midproduct(*c_i[loop+l], copy_a_i, copy_b_i,smallLeft,n0,n1,c.size());
#endif	    	    
						FFT_PROFILE_GET(2,tMul);

					}      
				FFT_PROFILING(2,"FFTprime mult+copying");
				//FFT_PROFILE(2,"copying linear reduced matrix",tCopy);
				//FFT_PROFILE(2,"FFTprime multiplication",tMul);

			} // end of loop for memory saving
			DEL_MEM(8*(n_ta+n_tb)*CRT_NBPRIME);
			delete[] t_a_mod;
			delete[] t_b_mod;

#endif




			FFT_PROFILE(2,"copying linear reduced matrix",tCopy);
			FFT_PROFILE(2,"FFTprime multiplication",tMul);

			if (num_primes < 2) {
				FFT_PROFILE_START(2);
				c.copy(*(c_i[0]),0,c.size()-1);
			} else {
				FFT_PROFILE_START(2);

				size_t s=c.size();
#ifndef LOW_MEMORY_PMBASIS
				// construct contiguous storage for c_i
				size_t n_tc=m*n*s;
				ADD_MEM(8*n_tc*num_primes);
				double *t_c_mod = new double[n_tc*num_primes];
				for (size_t l=0;l<num_primes;l++){
					for (size_t i=0;i<m*n;i++)
						for (size_t j=0;j<s;j++)
							t_c_mod[l*n_tc + (j+i*s)]= c_i[l]->get(i,j);
					delete c_i[l];
				}
				FFT_PROFILING(2,"linearization of results mod pi");

				// reconstruct the result in C
				RNS.convert(1,n_tc,0,c.getWritePointer(),n_tc, t_c_mod, n_tc, _maxnorm);
				DEL_MEM(8*n_tc*num_primes);
				delete[] t_c_mod;
#else
				size_t s_small= s/MEMFACTOR;
				size_t s_last = s- s_small*(MEMFACTOR-1);
				size_t n_tc_small= m*n*s_small;
				size_t n_tc_last = m*n*s_last;
				{
					ADD_MEM(8*n_tc_small*num_primes);
					double *t_c_mod = new double[n_tc_small*num_primes];
					for (size_t memiter=0;memiter<MEMFACTOR-1;memiter++){	 
						for (size_t l=0;l<num_primes;l++){
							for (size_t i=0;i<m*n;i++)
								for (size_t j=0;j<s_small;j++)
									t_c_mod[l*n_tc_small + (j+i*s_small)]= c_i[l]->get(i,memiter*s_small+j);
						}	
						// reconstruct the result in C
						RNS.convert(m*n,s_small,0,c.getWritePointer()+memiter*s_small,s, t_c_mod, n_tc_small, _maxnorm);
					}
					DEL_MEM(8*n_tc_small*num_primes);
					delete[] t_c_mod;
				}	
				{
					ADD_MEM(8*n_tc_last*num_primes);
					double *t_c_mod = new double[n_tc_last*num_primes];
					// perform the last step
					for (size_t l=0;l<num_primes;l++){
						for (size_t i=0;i<m*n;i++)
							for (size_t j=0;j<s_last;j++)
								t_c_mod[l*n_tc_last + (j+i*s_last)]= c_i[l]->get(i,(MEMFACTOR-1)*s_small+j);
						delete c_i[l];
					}	  
					// reconstruct the result in C
					RNS.convert(m*n,s_last,0,c.getWritePointer()+(MEMFACTOR-1)*s_small,s, t_c_mod, n_tc_last, _maxnorm);
					DEL_MEM(8*n_tc_last*num_primes);
					delete[] t_c_mod;
				}
	
#endif
			}
		}
      
	};


	/***************************************************************************
	 **** Polynomial Matrix Multiplication over Fp[x], with p multiprecision ***
	 ***************************************************************************/
	template <size_t K, size_t L>
	class PolynomialMatrixFFTMulDomain<Givaro::Modular<RecInt::ruint<K>,RecInt::ruint<L> > > {
	public:
		typedef Givaro::Modular<RecInt::ruint<K>,RecInt::ruint<L> >       Field;
		typedef typename Field::Element     Element;
		typedef Givaro::ZRing<RecInt::ruint<L>>  IntField;

		// Polynomial matrix stored as a polynomial of matrix
		typedef PolynomialMatrix<PMType::polfirst,PMStorage::plain,Field> MatrixP_F;
		// Polynomial matrix stored as a polynomial of matrix
		typedef PolynomialMatrix<PMType::polfirst,PMStorage::plain,IntField> MatrixP_I;

	private:
		const Field            *_field;  // Read only
		RecInt::ruint<K>         _p;
    
	public:
		inline const Field & field() const { return *_field; }
    
		PolynomialMatrixFFTMulDomain(const Field &F) : _field(&F) {
			_p=field().cardinality();
		}

		template<typename Matrix1, typename Matrix2, typename Matrix3>
		void mul (Matrix1 &c, const Matrix2 &a, const Matrix3 &b, size_t max_rowdeg=0) const {
			FFT_PROFILE_START(2);
			MatrixP_F a2(field(),a.rowdim(),a.coldim(),a.size());
			MatrixP_F b2(field(),b.rowdim(),b.coldim(),b.size());
			MatrixP_F c2(field(),c.rowdim(),c.coldim(),c.size());
			a2.copy(a,0,a.size()-1);
			b2.copy(b,0,b.size()-1);
			FFT_PROFILING(2,"converting rep of input");
			mul(c2,a2,b2, max_rowdeg);
			FFT_PROFILE_START(2);
			c.copy(c2,0,c.size()-1);
			FFT_PROFILING(2,"converting rep of output");

		}
    
		// Matrix with polynomials  
		void mul (MatrixP_F &c, const MatrixP_F &a, const MatrixP_F &b, size_t max_rowdeg=0) const {
			FFT_PROFILE_START(2);
			IntField Z;
			Givaro::Integer pp(_p);
			//std::cerr<<"FFT RECINT MUL 1: "<<c.size()<<" -> "<<a.size()<<"x"<<b.size()<<"  "<<STR_MEMINFO<<MEMINFO<<std::endl;
			PolynomialMatrixFFTMulDomain<IntField> Zmul(Z,pp);
			integer bound=pp*pp*integer((uint64_t)a.coldim())*integer((uint64_t)std::min(a.size(),b.size()));
			Zmul.mul_crtla(c,a,b,_p,_p,bound, max_rowdeg);
			//std::cerr<<"FFT RECINT MUL 2: "<<c.size()<<" -- "<<STR_MEMINFO<<MEMINFO<<std::endl;
      
			FFT_PROFILING(2,"reduction mod p of output");
		}



		template<typename Matrix1, typename Matrix2, typename Matrix3>
		void midproduct (Matrix1 &c, const Matrix2 &a, const Matrix3 &b,
						 bool smallLeft=true, size_t n0=0, size_t n1=0) const {

			MatrixP_F a2(field(),a.rowdim(),a.coldim(),a.size());
			MatrixP_F b2(field(),b.rowdim(),b.coldim(),b.size());
			a2.copy(a,0,a.size()-1);
			b2.copy(b,0,b.size()-1);
			MatrixP_F c2(field(),c.rowdim(),c.coldim(),c.size());
			midproduct(c2,a2,b2,smallLeft,n0,n1);
			c.copy(c2,0,c.size()-1);
		} 

		void midproduct (MatrixP_F &c, const MatrixP_F &a, const MatrixP_F &b,
						 bool smallLeft=true, size_t n0=0, size_t n1=0) const {
			FFT_PROFILE_START(2);
			IntField Z;
			Givaro::Integer pp(_p);
			PolynomialMatrixFFTMulDomain<IntField> Zmul(Z,pp);
			//MatrixP_I c2(Zmul,c.rowdim(),c.coldim(),c.size());
			//Zmul.midproduct(c2,a,b,smallLeft,n0,n1);
			Zmul.midproduct(c,a,b,smallLeft,n0,n1);
      
			// reduce the result mod p
			// FFT_PROFILE_START(2);
			// for (size_t i=0;i<c.rowdim()*c.coldim();i++)
			// 	for (size_t j=0;j<c.size();j++)
			// 	  c.ref(i,j)=integer(c2.ref(i,j))%pp;
			FFT_PROFILING(2,"reduction mod p of output");
		}
	};

  







} // end of namespace LinBox

#endif // __LINBOX_matpoly_mult_ftt_multiprecision_INL

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