static GEN
F2xq_elltrace_Harley(GEN a6, GEN T2)
{
pari_sp ltop = avma;
pari_timer ti;
GEN T, sqx;
GEN x, x2, t;
long n = F2x_degree(T2), N = ((n + 1)>>1) + 2;
long ispcyc;
if (n==1) return gen_m1;
if (n==2) return F2x_degree(a6) ? gen_1 : stoi(-3);
if (n==3) return F2x_degree(a6) ? (F2xq_trace(a6,T2) ? stoi(-3): gen_1)
: stoi(5);
timer_start(&ti);
sqx = mkvec2(F2xq_sqrt(polx_F2x(T2[1]),T2), T2);
if (DEBUGLEVEL>1) timer_printf(&ti,"Sqrtx");
ispcyc = zx_is_pcyc(F2x_to_Flx(T2));
T = ispcyc? F2x_to_ZX(T2): F2x_canonlift(T2, N-2);
if (DEBUGLEVEL>1) timer_printf(&ti,"Teich");
T = FpX_get_red(T, int2n(N));
if (DEBUGLEVEL>1) timer_printf(&ti,"Barrett");
x = solve_AGM_eqn(F2x_to_ZX(a6), N-2, T, sqx);
if (DEBUGLEVEL>1) timer_printf(&ti,"Lift");
x2 = ZX_Z_add_shallow(ZX_shifti(x,2), gen_1);
t = (ispcyc? Z2XQ_invnorm_pcyc: Z2XQ_invnorm)(x2, T, N);
if (DEBUGLEVEL>1) timer_printf(&ti,"Norm");
if (cmpii(sqri(t), int2n(n + 2)) > 0)
t = subii(t, int2n(N));
return gerepileuptoint(ltop, t);
}
/* x t_POL, n > 0. Return x mod polcyclo(2^n) = (x^(2^(n-1)) + 1). IN PLACE */
static GEN
red_cyclo2n_ip(GEN x, long n)
{
long i, pow2 = 1L<<(n-1);
for (i = lg(x)-1; i>pow2+1; i--)
if (signe(gel(x,i))) gel(x,i-pow2) = subii(gel(x,i-pow2), gel(x,i));
return normalizepol_lg(x, i+1);
}
GEN
F2xq_ellcard(GEN a, GEN a6, GEN T)
{
pari_sp av = avma;
long n = F2x_degree(T);
GEN q = int2u(n), c;
if (typ(a)==t_VECSMALL)
{
GEN t = F2xq_elltrace_Harley(a6, T);
c = addii(q, F2xq_trace(a,T) ? addui(1,t): subui(1,t));
} else if (n==1)
{
long a4i = lgpol(gel(a,2)), a6i = lgpol(a6);
return utoi(a4i? (a6i? 1: 5): 3);
}
else if (n==2)
{
GEN a3 = gel(a,1), a4 = gel(a,2), x = polx_F2x(T[1]), x1 = pol1_F2x(T[1]);
GEN a613 = F2xq_mul(F2x_add(x1, a6),a3,T), a43= F2xq_mul(a4,a3,T);
long f0= F2xq_trace(F2xq_mul(a6,a3,T),T);
long f1= F2xq_trace(F2x_add(a43,a613),T);
long f2= F2xq_trace(F2x_add(F2xq_mul(a43,x,T),a613),T);
long f3= F2xq_trace(F2x_add(F2xq_mul(a43,F2x_add(x,x1),T),a613),T);
c = utoi(9-2*(f0+f1+f2+f3));
}
else
{
struct _F2xqE e;
long m = (n+1)>>1;
GEN q1 = addis(q, 1);
GEN v = n==4 ? mkvec4s(13,17,21,25)
: odd(n) ? mkvec3(subii(q1,int2u(m)),q1,addii(q1,int2u(m))):
mkvec5(subii(q1,int2u(m+1)),subii(q1,int2u(m)),q1,
addii(q1,int2u(m)),addii(q1,int2u(m+1)));
e.a2=a; e.a6=a6; e.T=T;
c = gen_select_order(v,(void*)&e, &F2xqE_group);
if (n==4 && equaliu(c, 21)) /* Ambiguous case */
{
GEN d = F2xq_powu(polx_F2x(T[1]),3,T), a3 = gel(a,1);
e.a6 = F2x_add(a6,F2xq_mul(d,F2xq_sqr(a3,T),T)); /* twist */
c = subui(34, gen_select_order(mkvec2s(13,25),(void*)&e, &F2xqE_group));
}
}
return gerepileuptoint(av, c);
}
/* return d = gcd(a,b), sets u, v such that au + bv = gcd(a,b) */
GEN
extgcd(GEN A, GEN B, GEN *U, GEN *V)
{
pari_sp av = avma;
GEN ux = gen_1, vx = gen_0, a = A, b = B;
if (typ(a) != t_INT) pari_err_TYPE("extgcd",a);
if (typ(b) != t_INT) pari_err_TYPE("extgcd",b);
if (signe(a) < 0) { a = negi(a); ux = negi(ux); }
while (!gequal0(b))
{
GEN r, q = dvmdii(a, b, &r), v = vx;
vx = subii(ux, mulii(q, vx));
ux = v; a = b; b = r;
}
*U = ux;
*V = diviiexact( subii(a, mulii(A,ux)), B );
gerepileall(av, 3, &a, U, V); return a;
}
/* pol^2 mod (x^2+1,N) */
static GEN
sqrmod4(GEN pol, Red *R)
{
GEN a,b,A,B;
long lv = lg(pol);
if (lv==2) return pol;
if (lv==3) return sqrconst(pol, R);
a = gel(pol,3);
b = gel(pol,2);
A = centermodii(mulii(a, shifti(b,1)), R->N, R->N2);
B = centermodii(mulii(subii(b,a),addii(b,a)), R->N, R->N2);
return makepoldeg1(A,B);
}
/* T mod polcyclo(p), assume deg(T) < 2p */
static GEN
red_cyclop(GEN T, long p)
{
long i, d;
GEN y, z;
d = degpol(T) - p; /* < p */
if (d <= -2) return T;
/* reduce mod (x^p - 1) */
y = ZX_mod_Xnm1(T, p);
z = y+2;
/* reduce mod x^(p-1) + ... + 1 */
d = p-1;
if (degpol(y) == d)
for (i=0; i<d; i++) gel(z,i) = subii(gel(z,i), gel(z,d));
return normalizepol_lg(y, d+2);
}
/* pol^2 mod (polcyclo(5),N) */
static GEN
sqrmod5(GEN pol, Red *R)
{
GEN c2,b,c,d,A,B,C,D;
long lv = lg(pol);
if (lv==2) return pol;
if (lv==3) return sqrconst(pol, R);
c = gel(pol,3); c2 = shifti(c,1);
d = gel(pol,2);
if (lv==4)
{
A = sqri(d);
B = mulii(c2, d);
C = sqri(c);
A = centermodii(A, R->N, R->N2);
B = centermodii(B, R->N, R->N2);
C = centermodii(C, R->N, R->N2); return mkpoln(3,A,B,C);
}
b = gel(pol,4);
if (lv==5)
{
A = mulii(b, subii(c2,b));
B = addii(sqri(c), mulii(b, subii(shifti(d,1),b)));
C = subii(mulii(c2,d), sqri(b));
D = mulii(subii(d,b), addii(d,b));
}
else
{ /* lv == 6 */
GEN a = gel(pol,5), a2 = shifti(a,1);
/* 2a(d - c) + b(2c - b) */
A = addii(mulii(a2, subii(d,c)), mulii(b, subii(c2,b)));
/* c(c - 2a) + b(2d - b) */
B = addii(mulii(c, subii(c,a2)), mulii(b, subii(shifti(d,1),b)));
/* (a-b)(a+b) + 2c(d - a) */
C = addii(mulii(subii(a,b),addii(a,b)), mulii(c2,subii(d,a)));
/* 2a(b - c) + (d-b)(d+b) */
D = addii(mulii(a2, subii(b,c)), mulii(subii(d,b), addii(d,b)));
}
A = centermodii(A, R->N, R->N2);
B = centermodii(B, R->N, R->N2);
C = centermodii(C, R->N, R->N2);
D = centermodii(D, R->N, R->N2); return mkpoln(4,A,B,C,D);
}
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
ratlift(GEN x, GEN m, GEN *a, GEN *b, GEN amax, GEN bmax)
{
GEN d,d1,v,v1,q,r;
pari_sp av = avma, av1, lim;
long lb,lr,lbb,lbr,s,s0;
ulong vmax;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if ((typ(x) | typ(m) | typ(amax) | typ(bmax)) != t_INT) pari_err(arither1);
if (signe(bmax) <= 0)
pari_err(talker, "ratlift: bmax must be > 0, found\n\tbmax=%Z\n", bmax);
if (signe(amax) < 0)
pari_err(talker, "ratilft: amax must be >= 0, found\n\tamax=%Z\n", amax);
/* check 2*amax*bmax < m */
if (cmpii(shifti(mulii(amax, bmax), 1), m) >= 0)
pari_err(talker, "ratlift: must have 2*amax*bmax < m, found\n\tamax=%Z\n\tbmax=%Z\n\tm=%Z\n", amax,bmax,m);
/* we _could_ silently replace x with modii(x,m) instead of the following,
* but let's leave this up to the caller
*/
avma = av; s = signe(x);
if (s < 0 || cmpii(x,m) >= 0)
pari_err(talker, "ratlift: must have 0 <= x < m, found\n\tx=%Z\n\tm=%Z\n", x,m);
/* special cases x=0 and/or amax=0 */
if (s == 0)
{
if (a != NULL) *a = gen_0;
if (b != NULL) *b = gen_1;
return 1;
}
else if (signe(amax)==0)
return 0;
/* assert: m > x > 0, amax > 0 */
/* check here whether a=x, b=1 is a solution */
if (cmpii(x,amax) <= 0)
{
if (a != NULL) *a = icopy(x);
if (b != NULL) *b = gen_1;
return 1;
}
/* There is no special case for single-word numbers since this is
* mainly meant to be used with large moduli.
*/
(void)new_chunk(lgefint(bmax) + lgefint(amax)); /* room for a,b */
d = m; d1 = x;
v = gen_0; v1 = gen_1;
/* assert d1 > amax, v1 <= bmax here */
lb = lgefint(bmax);
lbb = bfffo(*int_MSW(bmax));
s = 1;
av1 = avma; lim = stack_lim(av, 1);
/* general case: Euclidean division chain starting with m div x, and
* with bounds on the sequence of convergents' denoms v_j.
* Just to be different from what invmod and bezout are doing, we work
* here with the all-nonnegative matrices [u,u1;v,v1]=prod_j([0,1;1,q_j]).
* Loop invariants:
* (a) (sign)*[-v,v1]*x = [d,d1] (mod m) (componentwise)
* (sign initially +1, changes with each Euclidean step)
* so [a,b] will be obtained in the form [-+d,v] or [+-d1,v1];
* this congruence is a consequence of
* (b) [x,m]~ = [u,u1;v,v1]*[d1,d]~,
* where u,u1 is the usual numerator sequence starting with 1,0
* instead of 0,1 (just multiply the eqn on the left by the inverse
* matrix, which is det*[v1,-u1;-v,u], where "det" is the same as the
* "(sign)" in (a)). From m = v*d1 + v1*d and
* (c) d > d1 >= 0, 0 <= v < v1,
* we have d >= m/(2*v1), so while v1 remains smaller than m/(2*amax),
* the pair [-(sign)*d,v] satisfies (1) but violates (2) (d > amax).
* Conversely, v1 > bmax indicates that no further solutions will be
* forthcoming; [-(sign)*d,v] will be the last, and first, candidate.
* Thus there's at most one point in the chain division where a solution
* can live: v < bmax, v1 >= m/(2*amax) > bmax, and this is acceptable
* iff in fact d <= amax (e.g. m=221, x=34 or 35, amax=bmax=10 fail on
* this count while x=32,33,36,37 succeed). However, a division may leave
* a zero residue before we ever reach this point (consider m=210, x=35,
* amax=bmax=10), and our caller may find that gcd(d,v) > 1 (numerous
* examples -- keep m=210 and consider any of x=29,31,32,33,34,36,37,38,
* 39,40,41).
* Furthermore, at the start of the loop body we have in fact
* (c') 0 <= v < v1 <= bmax, d > d1 > amax >= 0,
* (and are never done already).
*
* Main loop is similar to those of invmod() and bezout(), except for
* having to determine appropriate vmax bounds, and checking termination
* conditions. The signe(d1) condition is only for paranoia
*/
while (lgefint(d) > 3 && signe(d1))
{
/* determine vmax for lgcdii so as to ensure v won't overshoot.
* If v+v1 > bmax, the next step would take v1 beyond the limit, so
* since [+-d1,v1] is not a solution, we give up. Otherwise if v+v1
* is way shorter than bmax, use vmax=MAXULUNG. Otherwise, set vmax
* to a crude lower approximation of bmax/(v+v1), or to 1, which will
* allow the inner loop to do one step
*/
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG;
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1);
/* the latter is pessimistic but faster than a division */
}
/* do a Lehmer-Jebelean round */
lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, vmax);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
if ((lhmres == 1) || (lhmres == -1))
{
s = -s;
if (xv1 == 1)
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (lhmres&1)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1))
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done. Assert v <= bmax here. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise
* proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* lhmres != 0 */
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
d=d1; d1=r;
r = addii(v,mulii(q,v1));
v=v1; v1=r;
s = -s;
/* check whether we are done now. Since we weren't before the div, it
* suffices to examine v1 and d1 -- the new d (former d1) cannot cut it
*/
if (cmpii(v1,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (cmpii(d1,amax) <= 0) /* done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
}
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,"ratlift");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint. Since we usually underestimate vmax,
* this function needs a loop here instead of a simple conditional.
* Note we can only get here when amax fits into one word (which will
* typically not be the case!). The condition is bogus -- d1 is never
* zero at the start of the loop. There will be at most a few iterations,
* so we don't bother collecting garbage
*/
while (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3.
* Moreover, we aren't done already, or we would have returned by now.
* Recompute vmax...
*/
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: d,d1=%Z,%Z\n", d, d1);
fprintferr("rl-fs: v,v1=%Z,%Z\n", v, v1);
#endif
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG; /* (cannot in fact happen) */
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1); /* as above */
}
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: vmax=%lu\n", vmax);
#endif
/* single-word "Lehmer", discarding the gcd or whatever it returns */
(void)rgcduu((ulong)*int_MSW(d), (ulong)*int_MSW(d1), vmax, &xu, &xu1, &xv, &xv1, &s0);
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: [%lu,%lu; %lu,%lu] %s\n",
xu, xu1, xv, xv1,
s0 < 0 ? "-" : "+");
#endif
if (xv1 == 1) /* avoid multiplications */
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
s = -s;
}
else if (xu == 0) /* and xv==1, xu1==1, xv1 > 1 */
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
s = -s;
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (s0 < 0)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1)) /* sic: might vanish now */
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done, as above. Assert v <= bmax. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* while */
/* get here when we have run into d1 == 0 before returning... in fact,
* this cannot happen.
*/
pari_err(talker, "ratlift failed to catch d1 == 0\n");
/* NOTREACHED */
return 0;
}
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;
}
