/usr/include/givaro/givpoly1kara.inl is in libgivaro-dev 3.2.13-1.2.
This file is owned by root:root, with mode 0o644.
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// $Source: /var/lib/cvs/Givaro/src/library/poly1/givpoly1kara.inl,v $
// Copyright(c)'94-97 by Givaro Team
// see the copyright file.
// Authors: T. Gautier
// $Id: givpoly1kara.inl,v 1.1.1.1 2004/05/12 16:08:24 jgdumas Exp $
// ==========================================================================
// Description: To be rewrite using Array0 and subarray0 or generator!!!
#define KARA_THRESHOLD 10
template<class T>
void Poly1<T>::stdmul(Array0<T>& R,
const Array0<T>& P, const Array0<T>& Q,
Degree tP, Degree tQ)
{
int i,j ;
for (i=0 ; i <= tP+tQ ; i++) R[i] = T(zero) ;
for (i=0 ; i <= tP ; i++)
for (j=0 ; j <= tQ ; j++)
R[i+j] += P[i]*Q[j] ;
}
// Tailles requises par les entrees.
// P : polynome de degre tP
// Q : " " tQ
// R : " " tP+tQ
// Tmp1 : " " 2*([1+max(tP,tQ)] div 2)
// Tmp2 : " " ([1+max(tP,tQ)] div 2)
// Au sein de l'algo :
// P0 : " " k <= tP
// P1 : " " tP - k <= k
// Q0 : " " k <= tQ
// Q1 : " " tQ - k <= k
template<class T>
void Poly1<T>::karatsuba(Array0<T>& P, const Array0<T>& Q,
Array0<T>& R, Array0<T>& Tmp1,
Degree tP, Degree tQ)
{
if ((tP <=KARA_THRESHOLD) || (tQ <=KARA_THRESHOLD))
{
Poly1<T>::stdmul(P, Q, R, tP, tQ) ;
return ;
}
Degree k ;
if (tQ <= tP)
{
int i ;
k = tP/2 ;
if (tQ <= k)
{
//cout << "heheh : tP:" << tP << " tQ: " << tQ << endl ;
Poly1<T>::karatsuba(P, Q, R, Tmp1, k, tQ) ;
Poly1<T>::karatsuba(P+k+1, Q, Tmp1, P, tP-k-1, tQ) ;
for (i=0 ; i <= tP+tQ-k-1 ; i++) R[i+k+1] += Tmp1[i] ;
return ;
}
// Debut des tableaux :
T* R00 = R ;
T* R01 = R + k + 1 ;
T* R0 = R ;
T* R1 = R + 2*k + 2 ;
T* P0 = P ;
T* P1 = P + k+1 ;
const T* Q0 = Q ;
const T* Q1 = Q + k+1 ;
// P1-P0 -> R00
for (i=0 ; i < tP-k ; i++) R00[i] = P1[i] - P0[i] ;
for (i=tP-k ; i <= k ; i++) R00[i] = -P0[i] ;
// Q0-Q1 -> R01, degQ0 = k > degQ1 = tQ-k
for (i=0 ; i < tQ-k ; i++) R01[i] = Q0[i] - Q1[i] ;
for (i=tQ-k ; i <= k ; i++) R01[i] = Q0[i] ;
// Recursive calls
_karatsuba(R00, R01, Tmp1, R1, k, k) ;
_karatsuba(P0, Q0, R0, R1, k, k) ;
_karatsuba(P1, Q1, R1, P0, tP-k-1, tQ-k-1) ;
// Merge des termes
// Correction des termes du milieu:
for (i=0 ; i <=2*k ; i++) Tmp1[i] += R0[i] ;
for (i=0 ; i <=tP+tQ-2*k-2 ; i++) Tmp1[i] += R1[i] ;
// Mis a jour du resultat
R[2*k+1] = T(zero) ;
for (i=0 ; i <=2*k ; i++) R[i+k+1] += Tmp1[i] ;
}
else
{
int i ;
k = tQ/2 ;
if (tP <= k)
{
//cout << "heheh : tP:" << tP << " tQ: " << tQ << endl ;
_karatsuba(P, Q, R, Tmp1, tP, k) ;
_karatsuba(P, Q+k+1, Tmp1, P, tP, tQ-k-1) ;
for (i=0 ; i <= tP+tQ-k-1 ; i++) R[i+k+1] += Tmp1[i] ;
return ;
}
// Debut des tableaux :
T* R00 = R ;
T* R01 = R + k + 1 ;
T* R0 = R ;
T* R1 = R + 2*k + 2 ;
T* P0 = P ;
T* P1 = P + k+1 ;
const T* Q0 = Q ;
const T* Q1 = Q + k+1 ;
// P1-P0 -> R00
for (i=0 ; i < tP-k ; i++) R00[i] = P1[i] - P0[i] ;
for (i=tP-k ; i <= k ; i++) R00[i] = -P0[i] ;
// Q0-Q1 -> R01, degQ0 = k > degQ1 = tQ-k
for (i=0 ; i < tQ-k ; i++) R01[i] = Q0[i] - Q1[i] ;
for (i=tQ-k ; i <= k ; i++) R01[i] = Q0[i] ;
// Recursive calls
_karatsuba(R00, R01, Tmp1, R1, k, k) ;
_karatsuba(P0, Q0, R0, R1, k, k) ;
_karatsuba(P1, Q1, R1, P0, tP-k-1, tQ-k-1) ;
// Merge des termes
// Correction des termes du milieu:
for (i=0 ; i <=2*k ; i++) Tmp1[i] += R0[i] ;
for (i=0 ; i <=tP+tQ-2*k-2 ; i++) Tmp1[i] += R1[i] ;
// Mis a jour du resultat
R[2*k+1] = T(zero) ;
for (i=0 ; i <=2*k ; i++) R[i+k+1] += Tmp1[i] ;
}
}
template<class T>
const Poly1<T> Karatsuba(const Poly1<T>& P, const Poly1<T>& Q)
{
Degree degP = P.degree() ;
Degree degQ = Q.degree() ;
T* Res = new T[degP+degQ+1];
T* PP = new T[degP+1];
T* Tmp1, *Tmp2 ;
if (degQ <= degP)
{
Tmp1 = new T[degP+1];
// Tmp2 = new T[degP+1];
}
else
{
Tmp1 = new T[degQ+1];
// Tmp2 = new T[degQ+1];
}
int i ;
for (i=0 ; i<= degQ+degP ; i++) Res[i] = T(zero) ;
for (i=0 ; i<= degP ; i++) PP[i] = P[i] ;
_karatsuba(PP, Q.baseptr(), Res, Tmp1, degP, degQ) ;
Poly1<T> PRes(P.variable(), degP+degQ, Res) ;
delete [] Tmp1 ; delete [] PP ; delete [] Res ;
return PRes ;
}
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