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|
// file kernel/x/c/root.c: pth-root of extensible integers
/*-----------------------------------------------------------------------+
| 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. |
+-----------------------------------------------------------------------+
| |
| Racine p-me |
| |
+-----------------------------------------------------------------------*/
/*
entre :
a = entier extensible
_b = NULL ou pointeur sur un entier extensible
p = entier > 0
mode = 0,1 ou 2
sortie :
si mode & 3 = 0: b <- floor(a^(1/p))
si mode & 3 = 1: b <- floor(a^(1/p)+1/2)
si mode & 3 = 2: b <- ceil(a^(1/p))
si mode & 3 = 1: b <- ceil(a^(1/p)-1/2) (= floor(a^(1/p)+1/2))
si _b != NULL, *_b <- b
retourne b
erreurs :
NEGATIVE_EXPONENT si p <= 0
NEGATIVE_BASE si a < 0 et p est pair
*/
xint xx(private_root)(xint *_b, xint a, long p, long mode) {
long la = xx_lg(a), sa = xx_sgn(a), lb, q,r, exact;
chiffre *aa;
int free_a;
xint b;
xx_push_roots_2(a,_b);
#ifdef caml_api
#define a __lr.a
#define _b __lr._b
#endif
/* contrle les arguments */
if (p <= 0) xx(failwith)(NEGATIVE_EXPONENT);
if ((sa) && (!(p&1))) xx(failwith)(NEGATIVE_BASE);
/* cas a = 0 ou p = 1 */
if (la == 0) {
b = xx(enlarge)(_b,0);
b->hd = 0;
xx_update_and_return(_b,b);
}
if (p == 1) {
b = xx(enlarge)(_b,la);
if (a != b) {xn(move)(a->val,la,b->val); b->hd = a->hd;}
xx_update_and_return(_b,b);
}
/* mode = 1 ou 3 -> calcule floor((2^p|a|)^(1/p)) */
if (mode & 1) {
/* aa <- 2^p*|a| */
q = p/HW; r = p & (HW-1);
aa = xn(alloc)(la+q+1);
xn(clear)(aa,q);
aa[la+q] = xn(shift_up)(a->val,la,aa+q,r);
for (la += q+1; aa[la-1] == 0; la--);
free_a = 1;
/* b->val <- floor( (floor((2^p|a|)^(1/p))+1)/2 ) */
lb = (la+p-1)/p + 1;
b = xx(enlarge)(_b,lb);
xn(root)(aa,la,b->val,p);
b->val[lb-1] = xn(inc1)(b->val,lb-1);
xn(shift_down)(b->val,lb,b->val,1);
}
/* mode = 0 ou 2 -> calcule floor(|a|^(1/p)) */
else {
/* b->val = floor(|a|^(1/p)) */
lb = (la+p-1)/p;
b = xx(enlarge)(_b,lb+1);
if (a == b) {
aa = xn(alloc)(la);
xn(move)(a->val,la,aa);
free_a = 1;
} else {aa = a->val; free_a = 0;}
exact = xn(root)(aa,la,b->val,p);
/* si la racine n'est pas entire, incrmente b si a < 0 en mode 0
ou a > 0 en mode 2 */
if (sa) mode ^= 2;
if ((!exact) && (mode & 2)) {b->val[lb] = xn(inc1)(b->val,lb); lb++;}
}
/* sgn(b) = sgn(a) */
xx(make_head)(b,lb,sa);
if (free_a) xn(free)(aa);
xx_update_and_return(_b,b);
#undef a
#undef _b
}
#if defined(caml_api) || defined(ocaml_api)
xint xx(root) ( xint *_b, xint a, long p) {return xx(private_root)(_b, a,Long_val(p),0);}
xint xx(groot) (value mode, xint *_b, xint a, long p) {return xx(private_root)(_b, a,Long_val(p),Round_val(mode));}
xint xx(f_root) ( xint a, long p) {return xx(private_root)(xx_null,a,Long_val(p),0);}
xint xx(f_groot)(value mode, xint a, long p) {return xx(private_root)(xx_null,a,Long_val(p),Round_val(mode));}
#endif /* api */
|
