GEN
bezout(GEN a, GEN b, GEN *pu, GEN *pv)
{
GEN t,u,u1,v,v1,d,d1,q,r;
GEN *pt;
pari_sp av, av1;
long s, sa, sb;
ulong g;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
s = abscmpii(a,b);
if (s < 0)
{
t=b; b=a; a=t;
pt=pu; pu=pv; pv=pt;
}
/* now |a| >= |b| */
sa = signe(a); sb = signe(b);
if (!sb)
{
if (pv) *pv = gen_0;
switch(sa)
{
case 0: if (pu) *pu = gen_0; return gen_0;
case 1: if (pu) *pu = gen_1; return icopy(a);
case -1: if (pu) *pu = gen_m1; return(negi(a));
}
}
if (s == 0) /* |a| == |b| != 0 */
{
if (pu) *pu = gen_0;
if (sb > 0)
{ if (pv) *pv = gen_1; return icopy(b); }
else
{ if (pv) *pv = gen_m1; return(negi(b)); }
}
/* now |a| > |b| > 0 */
if (lgefint(a) == 3) /* single-word affair */
{
g = xxgcduu(uel(a,2), uel(b,2), 0, &xu, &xu1, &xv, &xv1, &s);
sa = s > 0 ? sa : -sa;
sb = s > 0 ? -sb : sb;
if (pu)
{
if (xu == 0) *pu = gen_0; /* can happen when b divides a */
else if (xu == 1) *pu = sa < 0 ? gen_m1 : gen_1;
else if (xu == 2) *pu = sa < 0 ? gen_m2 : gen_2;
else
{
*pu = cgeti(3);
(*pu)[1] = evalsigne(sa)|evallgefint(3);
(*pu)[2] = xu;
}
}
if (pv)
{
if (xv == 1) *pv = sb < 0 ? gen_m1 : gen_1;
else if (xv == 2) *pv = sb < 0 ? gen_m2 : gen_2;
else
{
*pv = cgeti(3);
(*pv)[1] = evalsigne(sb)|evallgefint(3);
(*pv)[2] = xv;
}
}
if (g == 1) return gen_1;
else if (g == 2) return gen_2;
else return utoipos(g);
}
/* general case */
av = avma;
(void)new_chunk(lgefint(b) + (lgefint(a)<<1)); /* room for u,v,gcd */
/* if a is significantly larger than b, calling lgcdii() is not the best
* way to start -- reduce a mod b first
*/
if (lgefint(a) > lgefint(b))
{
d = absi(b), q = dvmdii(absi(a), d, &d1);
if (!signe(d1)) /* a == qb */
{
avma = av;
if (pu) *pu = gen_0;
if (pv) *pv = sb < 0 ? gen_m1 : gen_1;
return (icopy(d));
}
else
{
u = gen_0;
u1 = v = gen_1;
v1 = negi(q);
}
/* if this results in lgefint(d) == 3, will fall past main loop */
}
else
{
d = absi(a); d1 = absi(b);
u = v1 = gen_1; u1 = v = gen_0;
}
av1 = avma;
/* main loop is almost identical to that of invmod() */
while (lgefint(d) > 3 && signe(d1))
{
lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, ULONG_MAX);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
if ((lhmres == 1) || (lhmres == -1))
{
if (xv1 == 1)
{
r = subii(d,d1); d=d1; d1=r;
a = subii(u,u1); u=u1; u1=a;
a = subii(v,v1); v=v1; v1=a;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
a = subii(u, mului(xv1,u1)); u=u1; u1=a;
a = subii(v, mului(xv1,v1)); v=v1; v1=a;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
a = subii(muliu(u,xu), muliu(u1,xv));
u1 = subii(muliu(u,xu1), muliu(u1,xv1)); u = a;
a = subii(muliu(v,xu), muliu(v1,xv));
v1 = subii(muliu(v,xu1), muliu(v1,xv1)); v = a;
if (lhmres&1) { togglesign(d); togglesign(u); togglesign(v); }
else { togglesign(d1); togglesign(u1); togglesign(v1); }
}
}
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
a = subii(u,mulii(q,u1));
u=u1; u1=a;
a = subii(v,mulii(q,v1));
v=v1; v1=a;
d=d1; d1=r;
}
if (gc_needed(av,1))
{
if(DEBUGMEM>1) pari_warn(warnmem,"bezout");
gerepileall(av1,6, &d,&d1,&u,&u1,&v,&v1);
}
} /* end while */
/* Postprocessing - final sprint */
if (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3, and
* gcd(d,d1) is nonzero and fits into one word
*/
g = xxgcduu(uel(d,2), uel(d1,2), 0, &xu, &xu1, &xv, &xv1, &s);
u = subii(muliu(u,xu), muliu(u1, xv));
v = subii(muliu(v,xu), muliu(v1, xv));
if (s < 0) { sa = -sa; sb = -sb; }
avma = av;
if (pu) *pu = sa < 0 ? negi(u) : icopy(u);
if (pv) *pv = sb < 0 ? negi(v) : icopy(v);
if (g == 1) return gen_1;
else if (g == 2) return gen_2;
else return utoipos(g);
}
/* get here when the final sprint was skipped (d1 was zero already).
* Now the matrix is final, and d contains the gcd.
*/
avma = av;
if (pu) *pu = sa < 0 ? negi(u) : icopy(u);
if (pv) *pv = sb < 0 ? negi(v) : icopy(v);
return icopy(d);
}
int
invmod(GEN a, GEN b, GEN *res)
#endif
{
GEN v,v1,d,d1,q,r;
pari_sp av, av1, lim;
long s;
ulong g;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if (typ(a) != t_INT || typ(b) != t_INT) pari_err(arither1);
if (!signe(b)) { *res=absi(a); return 0; }
av = avma;
if (lgefint(b) == 3) /* single-word affair */
{
ulong d1 = umodiu(a, (ulong)(b[2]));
if (d1 == 0)
{
if (b[2] == 1L)
{ *res = gen_0; return 1; }
else
{ *res = absi(b); return 0; }
}
g = xgcduu((ulong)(b[2]), d1, 1, &xv, &xv1, &s);
#ifdef DEBUG_LEHMER
fprintferr(" <- %lu,%lu\n", (ulong)(b[2]), (ulong)(d1[2]));
fprintferr(" -> %lu,%ld,%lu; %lx\n", g,s,xv1,avma);
#endif
avma = av;
if (g != 1UL) { *res = utoipos(g); return 0; }
xv = xv1 % (ulong)(b[2]); if (s < 0) xv = ((ulong)(b[2])) - xv;
*res = utoipos(xv); return 1;
}
(void)new_chunk(lgefint(b));
d = absi(b); d1 = modii(a,d);
v=gen_0; v1=gen_1; /* general case */
#ifdef DEBUG_LEHMER
fprintferr("INVERT: -------------------------\n");
output(d1);
#endif
av1 = avma; lim = stack_lim(av,1);
while (lgefint(d) > 3 && signe(d1))
{
#ifdef DEBUG_LEHMER
fprintferr("Calling Lehmer:\n");
#endif
lhmres = lgcdii((ulong*)d, (ulong*)d1, &xu, &xu1, &xv, &xv1, MAXULONG);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
#ifdef DEBUG_LEHMER
fprintferr("Lehmer returned %d [%lu,%lu;%lu,%lu].\n",
lhmres, xu, xu1, xv, xv1);
#endif
if ((lhmres == 1) || (lhmres == -1))
{
if (xv1 == 1)
{
r = subii(d,d1); d=d1; d1=r;
a = subii(v,v1); v=v1; v1=a;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
a = subii(v, mului(xv1,v1)); v=v1; v1=a;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
a = subii(muliu(v,xu), muliu(v1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
v1 = subii(muliu(v,xu1), muliu(v1,xv1)); v = a;
if (lhmres&1)
{
setsigne(d,-signe(d));
setsigne(v,-signe(v));
}
else
{
if (signe(d1)) { setsigne(d1,-signe(d1)); }
setsigne(v1,-signe(v1));
}
}
}
#ifdef DEBUG_LEHMER
else
fprintferr("Lehmer returned 0.\n");
output(d); output(d1); output(v); output(v1);
sleep(1);
#endif
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
a = subii(v,mulii(q,v1));
v=v1; v1=a;
d=d1; d1=r;
}
if (low_stack(lim, stack_lim(av,1)))
{
GEN *gptr[4]; gptr[0]=&d; gptr[1]=&d1; gptr[2]=&v; gptr[3]=&v1;
if(DEBUGMEM>1) pari_warn(warnmem,"invmod");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint */
if (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3, and
* gcd(d,d1) is nonzero and fits into one word
*/
g = xxgcduu((ulong)d[2], (ulong)d1[2], 1, &xu, &xu1, &xv, &xv1, &s);
#ifdef DEBUG_LEHMER
output(d);output(d1);output(v);output(v1);
fprintferr(" <- %lu,%lu\n", (ulong)d[2], (ulong)d1[2]);
fprintferr(" -> %lu,%ld,%lu; %lx\n", g,s,xv1,avma);
#endif
if (g != 1UL) { avma = av; *res = utoipos(g); return 0; }
/* (From the xgcduu() blurb:)
* For finishing the multiword modinv, we now have to multiply the
* returned matrix (with properly adjusted signs) onto the values
* v' and v1' previously obtained from the multiword division steps.
* Actually, it is sufficient to take the scalar product of [v',v1']
* with [u1,-v1], and change the sign if s==1.
*/
v = subii(muliu(v,xu1),muliu(v1,xv1));
if (s > 0) setsigne(v,-signe(v));
avma = av; *res = modii(v,b);
#ifdef DEBUG_LEHMER
output(*res); fprintfderr("============================Done.\n");
sleep(1);
#endif
return 1;
}
/* get here when the final sprint was skipped (d1 was zero already) */
avma = av;
if (!equalii(d,gen_1)) { *res = icopy(d); return 0; }
*res = modii(v,b);
#ifdef DEBUG_LEHMER
output(*res); fprintferr("============================Done.\n");
sleep(1);
#endif
return 1;
}
