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// file kernel/n/h/gcd.h: greatest common divisor
/*-----------------------------------------------------------------------+
| Copyright 2005-2006, Michel Quercia (michel.quercia@prepas.org) |
| |
| This file is part of Numerix. Numerix 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. |
| |
| The Numerix 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 the GNU MP Library; see the file COPYING. If not, |
| write to the Free Software Foundation, Inc., 59 Temple Place - |
| Suite 330, Boston, MA 02111-1307, USA. |
+-----------------------------------------------------------------------+
| |
| PGCD |
| |
+-----------------------------------------------------------------------*/
/*
entre :
_v = tableau de pointeurs vers 6 naturels a,b,p,s,q,r
_l = tableau de 6 longueurs la,lb,lp,lq,lr,ls
mode = 0,1,2
contraintes :
la > 0, lb > 0, a[la-1] > 0, b[lb-1] > 0
capacit(p) >= la, capacit(q) >= la,
capacit(r) >= lb, capacit(s) >= lb.
dveloppe en fraction continue la fraction a/b (mode = 0 ou 1)
ou les fractions a/(b+1) et (a+1)/b tant que les quotients sont
gaux et la prcision des nombres rsiduels est suffisante (mode = 2).
dans les trois mode, calcule des entiers naturels p',q',r',s',a',b' tels que
a = p'*a' + q'*b'
b = r'*a' + s'*b'
p'*s' - q'*r' = 1
avec a' = 0 ou b' = 0 (mode 0 ou 1)
a' >= q' et b' >= r' (mode 2)
sortie si mode = 0 :
a,b <- a',b', met jour les longueurs
p,q,r,s <- ind.
sortie si mode = 1 ou 2 :
a,b,p,s,q,r <- a',b',p',s',q',r', met jour les longueurs
remarque :
en mode 2 on progresse d'au moins une tape (= un chiffre dans la
premire division) si et seulement si a <> b.
*/
void xn(gcd_n2)(chiffre **_v, long *_l, int mode);
void xn(lehmer)(chiffre **_v, long *_l, int mode);
|
