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// file kernel/n/h/moddiv.h: division/square root with modular remainder
/*-----------------------------------------------------------------------+
| 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. |
+-----------------------------------------------------------------------+
| |
| Division et racine carre avec reste modulaire |
| |
+-----------------------------------------------------------------------*/
/* ---------------------------------------- Division avec ou sans reste
entre :
a = naturel de longueur lc+lb
b = naturel de longueur lb
c = naturel de longueur lc
rem = 0 ou 1 ou 2
contraintes :
lb >= 2, lc > 0, le bit de poids fort de b est non nul,
a < BASE^lc*b
a,b,c non confondus
sortie si rem = 0 :
a <- ind.
c <- approx(a/b) avec -ceil(log_2(lb))*BASE^(lb-1) < a - b*c < b
sortie si rem = 1 :
a <- a mod b
c <- floor(a/b)
sortie si rem = 2 :
a <- ind.
c <- approx(a/b) avec -ceil(log_2(lb))*BASE^(lb-1) < a - b*c < b
et c = floor(a/b) si c[0] = 0
*/
void xn(moddiv)(chiffre *a, long lc, chiffre *b, long lb, chiffre *c, int rem);
/* ---------------------------------------- Racine carre
entre :
a = naturel de longueur la
b = naturel de longueur la/2
contraintes :
la > 0, la pair, BASE/16 <= a[la-1] < BASE/4
a,b non confondus
sortie :
b <- 2*floor(sqrt(a))
a <- a - b^2/4
*/
void xn(modsqrt)(chiffre *a, long la, chiffre *b);
|
