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|
// file kernel/x/c/gcd.c: 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 |
| |
+-----------------------------------------------------------------------*/
/* +--------------------------------------+
| Dveloppement en fraction continue |
+--------------------------------------+ */
/*
entre :
a,b = entiers extensibles
_d,_u,_v,_p,_q = NULL ou pointeurs vers des entiers extensibles
mode = long
sortie :
calcule d,u,v,p,q tels que :
u*a - v*b = d = pgcd positif(a,b)
p*b = q*a = ppcm(a,b) avec le signe de a*b
p*u - q*v = 1
pour x = d,u,v,p,q : si _x != NULL, *_x <- x
valeur de retour : c_api ml_api
si mode & 3 = 0 : NULL unit
si mode & 3 = 1 : d d
si mode & 3 = 2 : NULL (d,u,v)
si mode & 3 = 3 : NULL (d,u,v,p,q)
erreur :
MULTIPLE_RESULT si (_d,_u,_v,_p,_q) contient deux pointeurs non nuls gaux
*/
#if defined(c_api)
xint
#elif defined(caml_api) || defined(ocaml_api)
value
#endif
xx(private_cfrac)(xint *_d, xint *_u, xint *_v, xint *_p, xint *_q,
xint a, xint b, long mode) {
long la = xx_lg(a), lb = xx_lg(b);
long sa = xx_sgn(a), sb = xx_sgn(b);
int ok, want_d, want_u, want_v, want_p, want_q, want_uvpq;
chiffre *_x[6], un[1];
long i,su,_l[6];
xx_push_roots_75(_d,_u,_v,_p,_q,a,b,d,u,v,p,q);
#ifdef caml_api
#define _d __lr._d
#define _u __lr._u
#define _v __lr._v
#define _p __lr._p
#define _q __lr._q
#define a __lr.a
#define b __lr.b
#define d __lr.d
#define u __lr.u
#define v __lr.v
#define p __lr.p
#define q __lr.q
#endif
/* vrifie que les pointeurs non nuls sont distincts */
ok = 1;
if (_d != xx_null) ok &= ((_d != _u) && (_d != _v) && (_d != _p) && (_d != _q));
if (_u != xx_null) ok &= ((_u != _v) && (_u != _p) && (_u != _q));
if (_v != xx_null) ok &= ((_v != _p) && (_v != _q));
if (_p != xx_null) ok &= (_p != _q);
if (!ok) xx(failwith)(MULTIPLE_RESULT);
/* rsultats calculer */
#if defined(c_api)
want_d = ((_d != xx_null) || (mode & 3) == 1);
want_u = (_u != xx_null);
want_v = (_v != xx_null);
want_p = (_p != xx_null);
want_q = (_q != xx_null);
#elif defined(caml_api) || defined(ocaml_api)
switch(mode & 3) {
case 0: want_d = 1;
want_u = want_v = (_u != xx_null);
want_p = want_q = (_p != xx_null);
break;
case 1: want_d = 1; want_u = want_v = want_p = want_q = 0; break;
case 2: want_d = want_u = want_v = 1; want_p = want_q = 0; break;
default:want_d = want_u = want_v = want_p = want_q = 1; break;
}
#endif
want_uvpq = want_u|want_v|want_p|want_q;
/* constitue le 6-uplet de calcul */
_x[0] = xn(alloc)(3*(la+lb)); /* a */
_x[1] = _x[0] + la; /* b */
_x[2] = _x[1] + lb; /* p */
_x[3] = _x[2] + la; /* s */
_x[4] = _x[3] + lb; /* q */
_x[5] = _x[4] + la; /* r */
xn(move)(a->val,la,_x[0]); _l[0] = la;
xn(move)(b->val,lb,_x[1]); _l[1] = lb;
/* dcompose a/b en fraction continue */
if ((la) && (lb)) xn(lehmer)(_x,_l, want_uvpq);
else {un[0] = 1; _x[2] = _x[3] = un; _l[2] = _l[3] = 1; _l[4] = _l[5] = 0;}
/* fixe les signes et recopie les rsultats demands
[x2 x4] [d] [|a|]
si x1 = 0 : [x5 x3] * [0] = [|b|] -> |u| = x3, |v| = x4, |p| = x2, |q| = x5
signes : sa sb u v p q -> su = sp = sa, sv = sq = sb
+ + + + + +
+ - + - + -
- + - + - +
- - - - - -
[x2 x4] [0] [|a|]
si x0 = 0 : [x5 x3] * [d] = [|b|] -> |u| = x5, |v| = x2, |p| = x4, |q| = x3
signes : sa sb u v p q -> -su = sp = sa, -sv = sq = sb
+ + - - + +
+ - - + + -
- + + - - +
- - + + - -
*/
if (_l[1] == 0) {i=0; su=0;} else {i=1; su=SIGN_m;}
#define store(var,index,sgn) \
if (want_##var) do { \
var = xx(enlarge)(_##var,_l[index]); \
xn(move)(_x[index],_l[index],var->val); \
var->hd = (_l[index]) ? _l[index]|(sgn) : 0; \
xx(update)(_##var,var); \
} while(0)
store(d, i, 0);
store(u, 3+2*i, su^sa);
store(v, 4-2*i, su^sb);
store(p, 2+2*i, sa);
store(q, 5-2*i, sb);
xn(free)(_x[0]);
#undef store
/* valeur de retour */
#if defined(c_api)
return d;
#elif defined(caml_api) || defined(ocaml_api)
{ xint *res;
switch(mode & 3) {
case 0: res = (xint *)Val_unit; break;
case 1: res = (xint *)d; break;
case 2: res = (xint *)alloc_tuple(3);
res[0] = d;
res[1] = u;
res[2] = v;
break;
default:res = (xint *)alloc_tuple(5);
res[0] = d;
res[1] = u;
res[2] = v;
res[3] = p;
res[4] = q;
break;
}
xx_pop_roots();
return (value)res;
}
#endif
#undef _d
#undef _u
#undef _v
#undef _p
#undef _q
#undef a
#undef b
#undef d
#undef u
#undef v
#undef p
#undef q
}
#if defined(caml_api) || defined(ocaml_api)
/* fonctions spcialises */
value xx(gcd)(xint *_d, xint a, xint b) {
return xx(private_cfrac)(_d,xx_null,xx_null,xx_null,xx_null,a,b,0);
}
value xx(gcd_ex)(xint *_d, xint *_u, xint *_v, xint a, xint b) {
return xx(private_cfrac)(_d,_u,_v,xx_null,xx_null,a,b,0);
}
value xx(cfrac)(xint *_d, xint *_u, xint *_v, xint *_p, xint *_q, xint a, xint b) {
return xx(private_cfrac)(_d,_u,_v,_p,_q,a,b,0);
}
value xx(cfrac_bytecode)(xint **v, int argn) {
return xx(private_cfrac)(v[0],v[1],v[2],v[3],v[4],(xint)v[5],(xint)v[6],0);
}
value xx(f_gcd)(xint a, xint b) {
return xx(private_cfrac)(xx_null,xx_null,xx_null,xx_null,xx_null,a,b,1);
}
value xx(f_gcd_ex)(xint a, xint b) {
return xx(private_cfrac)(xx_null,xx_null,xx_null,xx_null,xx_null,a,b,2);
}
value xx(f_cfrac)(xint a, xint b) {
return xx(private_cfrac)(xx_null,xx_null,xx_null,xx_null,xx_null,a,b,3);
}
#endif
|
