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// $Source: /var/lib/cvs/Givaro/src/library/poly1/givpoly1kara.inl,v $
// Copyright(c)'1994-2011 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
// Authors: J-G Dumas
// $Id: givpoly1kara.inl,v 1.3 2011-11-08 10:38:00 jgdumas Exp $
// ==========================================================================
#ifndef __GIVARO_poly1_kara_INL
#define __GIVARO_poly1_kara_INL
namespace Givaro {
#ifndef KARA_THRESHOLD
#define KARA_THRESHOLD 50
#endif
#ifndef SQR_THRESHOLD
#define SQR_THRESHOLD 50
#endif
#ifndef GIVMIN
#define GIVMIN(a,b) ((a)<(b)?(a):(b))
#endif
// forces standard multiplication
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::stdmul( Rep& R, const Rep& P, const Rep& Q ) const
{
const size_t sP = P.size();
const size_t sQ = Q.size();
if ((sQ ==0) || (sP ==0)) { R.reallocate(0); return R; }
const size_t sR = sP+sQ-1;
if (sR != R.size() ) R.reallocate(sR);
stdmul(R, R.begin(), R.end(),
P, P.begin(), P.end(),
Q, Q.begin(), Q.end());
return setdegree(R);
}
// forces FIRST recursive level with Karatsuba multiplication
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::karamul( Rep& R, const Rep& P, const Rep& Q ) const
{
const size_t sP = P.size();
const size_t sQ = Q.size();
if ((sQ ==0) || (sP ==0)) { R.reallocate(0); return R; }
const size_t sR = sP+sQ-1;
if (sR != R.size()) R.reallocate(sR);
karamul(R, R.begin(), R.end(),
P, P.begin(), P.end(),
Q, Q.begin(), Q.end());
return setdegree(R);
}
// Generic mul with choices between standard and Karatsuba multiplication
// Multiplies between the iterator bounds.
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::mul(
Rep& R, const RepIterator Rbeg, const RepIterator Rend,
const Rep& P, const RepConstIterator Pbeg, const RepConstIterator Pend,
const Rep& Q, const RepConstIterator Qbeg, const RepConstIterator Qend ) const {
if ( ( (Pend-Pbeg)> KARA_THRESHOLD ) &&
( (Qend-Qbeg)> KARA_THRESHOLD) )
return karamul(R, Rbeg, Rend,
P, Pbeg, Pend,
Q, Qbeg, Qend);
else
return stdmul(R, Rbeg, Rend,
P, Pbeg, Pend,
Q, Qbeg, Qend);
}
// Generic sqr with choices between standard and recursive multiplication
// Multiplies between the iterator bounds.
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::sqr(
Rep& R, const RepIterator Rbeg, const RepIterator Rend,
const Rep& P, const RepConstIterator Pbeg, const RepConstIterator Pend) const {
Type_t two; _domain.init(two);
_domain.add(two, _domain.one, _domain.one);
if ( (Pend-Pbeg)> SQR_THRESHOLD )
return sqrrec(R, Rbeg, Rend,
P, Pbeg, Pend,
two);
else
return stdsqr(R, Rbeg, Rend,
P, Pbeg, Pend,
two);
}
// Standard multiplication between iterator bounds
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::stdmul(
Rep& R, const RepIterator Rbeg, const RepIterator Rend,
const Rep& P, const RepConstIterator Pbeg, const RepConstIterator Pend,
const Rep& Q, const RepConstIterator Qbeg, const RepConstIterator Qend ) const {
RepConstIterator ai=Pbeg,bi=Qbeg;
RepIterator ri=Rbeg, rig=Rbeg;
if (_domain.isZero(*ai))
for(;bi!=Qend;++bi,++ri)
*ri = _domain.zero;
else
for(;bi!=Qend;++bi,++ri)
if (_domain.isZero(*bi))
*ri = _domain.zero;
else
_domain.mul(*ri,*ai,*bi);
for(;ri!=Rend;++ri)
*ri = _domain.zero;
for(++ai,++rig;ai!=Pend;++ai,++rig)
if (! _domain.isZero(*ai))
for(ri=rig,bi=Qbeg;bi!=Qend;++bi,++ri)
_domain.axpyin(*ri,*ai,*bi);
return R;
}
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::karamul( Rep& R, const RepIterator Rbeg, const RepIterator Rend, const Rep& P, const RepConstIterator Pbeg, const RepConstIterator Pend, const Rep& Q, const RepConstIterator Qbeg, const RepConstIterator Qend ) const
{
// Initialize R to zero
for(RepIterator ri=Rbeg; ri!= Rend; ++ri) _domain.assign(*ri,_domain.zero);
const size_t halfP = (size_t) ((Pend-Pbeg)>>1);
const size_t halfQ = (size_t) ((Qend-Qbeg)>>1);
const size_t half = GIVMIN(halfP, halfQ);
const size_t halfR = half<<1;
const RepConstIterator Pmid=Pbeg+(ssize_t)half; // cut P in halves
const RepConstIterator Qmid=Qbeg+(ssize_t)half; // cut Q in halves
const RepIterator Rmid=Rbeg+(ssize_t)halfR; // cut R in halves
mul(R, Rbeg, Rmid, // Recursive dynamic choice
P, Pbeg, Pmid,
Q, Qbeg, Qmid); // PlQl in first storage part of R
mul(R, Rmid, Rend, // Recursive dynamic choice
P, Pmid, Pend,
Q, Qmid, Qend); // PhQh in second storage part of R
Rep PHPL;
for(RepConstIterator PHi=Pmid; PHi!=Pend; ++PHi)
PHPL.push_back(*PHi);
subin(PHPL, PHPL.begin(), P, Pbeg, Pmid); // Ph - Pl
setdegree(PHPL);
Rep QHQL;
for(RepConstIterator QHi=Qmid; QHi!=Qend; ++QHi)
QHQL.push_back(*QHi);
subin(QHQL, QHQL.begin(), Q, Qbeg, Qmid); // Qh - Ql
setdegree(QHQL);
Rep M;
mul(M, // Recursive dynamic choice
PHPL,
QHQL); // (Ph-Pl)(Qh-Ql)
setdegree(M);
subin(M, M.begin(), M.end(), R, Rbeg, Rmid);// -= PlQl
setdegree(M);
subin(M, M.begin(), M.end(), R, Rmid, Rend);// -= PhQh
setdegree(M);
RepIterator ri=Rbeg+(ssize_t)half;
RepConstIterator mi=M.begin(); // update R with mid product
for( ; mi != M.end(); ++ri, ++mi) _domain.subin(*ri, *mi);
return R;
}
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::sqrrec( Rep& R, const RepIterator Rbeg, const RepIterator Rend, const Rep& P, const RepConstIterator Pbeg, const RepConstIterator Pend, const Type_t& two) const
{
// Initialize R to zero
for(RepIterator ri=Rbeg; ri!= Rend; ++ri) _domain.assign(*ri,_domain.zero);
const size_t half = (size_t) ((Pend-Pbeg)>>1);
const size_t halfR = (half<<1);
const RepConstIterator Pmid=Pbeg+(ssize_t)half; // cut P in halves
const RepIterator Rmid=Rbeg+(ssize_t)halfR; // cut R in halves
sqr(R, Rbeg, Rmid-1, // Recursive dynamic choice
P, Pbeg, Pmid); // Pl^2 in first storage part of R
sqr(R, Rmid, Rend, // Recursive dynamic choice
P, Pmid, Pend); // Ph^2 in second storage part of R
Rep M(P.size());
mul(M, M.begin(), M.end(), // Recursive dynamic choice
P, Pbeg, Pmid,
P, Pmid, Pend);
setdegree(M);
this->mulin(M,two);
RepIterator ri=Rbeg+(ssize_t)half;
RepConstIterator mi=M.begin(); // update R with mid product
for( ; mi != M.end(); ++ri, ++mi) _domain.addin(*ri, *mi);
return R;
}
// Standard square
template <class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::stdsqr(
Rep& R, const RepIterator Rbeg, const RepIterator Rend,
const Rep& P, const RepConstIterator Pbeg, const RepConstIterator Pend,
const Type_t& two) const {
_domain.mul(*Rbeg, *Pbeg, *Pbeg);
RepIterator rit(Rbeg);
RepConstIterator pit=Pbeg;
for(++rit,++pit; rit != Rend; ++pit, ++rit) {
_domain.assign(*rit,_domain.zero);
RepConstIterator backpit=pit, forpit=pit;
for(--backpit ; forpit != Pend; --backpit, ++forpit) {
_domain.axpyin(*rit, *backpit, *forpit);
if (backpit == Pbeg) break;
}
_domain.mulin(*rit, two);
++rit;
_domain.assign(*rit,_domain.zero);
backpit=pit, forpit=pit;
for(--backpit,++forpit; forpit != Pend; --backpit, ++forpit)
{
_domain.axpyin(*rit, *backpit, *forpit);
if (backpit == Pbeg) break;
}
_domain.mulin(*rit, two);
_domain.axpyin(*rit, *pit, *pit);
}
// for(size_t i=0; i<dR; ++i) {
// // even coefficients
// _domain.assign(R[i],_domain.zero);
// size_t iot(i>>1);
// size_t firstj( i>dP ? i-dP : 0);
// for(size_t j=firstj; j<iot; ++j)
// _domain.axpyin(R[i], P[j], P[i-j]);
// _domain.mulin(R[i], two);
// _domain.axpyin(R[i],P[iot],P[iot]);
// // odd coefficients
// ++i; ++iot;
// _domain.assign(R[i],_domain.zero);
// firstj = i>dP ? i-dP : 0;
// for(size_t j=firstj; j<iot; ++j) {
// _domain.axpyin(R[i], P[j], P[i-j]);
// }
// _domain.mulin(R[i], two);
// }
// _domain.mul(R[dR],P[dP],P[dP]);
return R;
}
}
#endif // __GIVARO_poly1_kara_INL
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