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);
}
int
main(void)
{
GEN M,N1,N2, F1,F2,D;
struct pari_thread pth[MAXTHREADS];
int numth = omp_get_max_threads(), i;
/* Initialise the main PARI stack and global objects (gen_0, etc.) */
pari_init(4000000,500000);
if (numth > MAXTHREADS)
{
numth = MAXTHREADS;
omp_set_num_threads(numth);
}
/* Compute in the main PARI stack */
N1 = addis(int2n(256), 1); /* 2^256 + 1 */
N2 = subis(int2n(193), 1); /* 2^193 - 1 */
M = mathilbert(80);
/*Allocate pari thread structures */
for (i = 1; i < numth; i++) pari_thread_alloc(&pth[i],4000000,NULL);
#pragma omp parallel
{
int this_th = omp_get_thread_num();
if (this_th) (void)pari_thread_start(&pth[this_th]);
#pragma omp sections
{
#pragma omp section
{
F1 = factor(N1);
}
#pragma omp section
{
F2 = factor(N2);
}
#pragma omp section
{
D = det(M);
}
} /* omp sections */
if (this_th) pari_thread_close();
} /* omp parallel */
pari_printf("F1=%Ps\nF2=%Ps\nlog(D)=%Ps\n", F1, F2, glog(D,3));
for (i = 1; i < numth; i++) pari_thread_free(&pth[i]);
return 0;
}
// Digit reversal
GEN
rev(GEN n, long B)
{
pari_sp av = avma;
if (typ(n) != t_INT)
pari_err_TYPE("rev", n);
GEN m = modis(n, B);
n = divis(n, B);
pari_sp btop = avma, st_lim = stack_lim(btop, 1);
while (signe(n)) {
m = addis(mulis(m, B), smodis(n, B));
n = divis(n, B);
if (low_stack(st_lim, stack_lim(btop, 1)))
gerepileall(btop, 2, &m, &n);
}
m = gerepilecopy(av, m);
return m;
}
GEN gadd1e(GEN *x)
{
*x=typ(*x)==t_INT?addis(*x,1):gaddgs(*x,1);
return *x;
}
void PPCAssembler::lis(RegGPR rd, S16 simm) { addis(rd, r0, simm); }
/* d = requested degree for subfield. Return DATA, valid for given pol, S and d
* If DATA != NULL, translate pol [ --> pol(X+1) ] and update DATA
* 1: polynomial pol
* 2: p^e (for Hensel lifts) such that p^e > max(M),
* 3: Hensel lift to precision p^e of DATA[4]
* 4: roots of pol in F_(p^S->lcm),
* 5: number of polynomial changes (translations)
* 6: Bezout coefficients associated to the S->ff[i]
* 7: Hadamard bound for coefficients of h(x) such that g o h = 0 mod pol.
* 8: bound M for polynomials defining subfields x PD->den
* 9: *[i] = interpolation polynomial for S->ff[i] [= 1 on the first root
S->firstroot[i], 0 on the others] */
static void
compute_data(blockdata *B)
{
GEN ffL, roo, pe, p1, p2, fk, fhk, MM, maxroot, pol;
primedata *S = B->S;
GEN p = S->p, T = S->T, ff = S->ff, DATA = B->DATA;
long i, j, l, e, N, lff = lg(ff);
if (DEBUGLEVEL>1) fprintferr("Entering compute_data()\n\n");
pol = B->PD->pol; N = degpol(pol);
roo = B->PD->roo;
if (DATA) /* update (translate) an existing DATA */
{
GEN Xm1 = gsub(pol_x[varn(pol)], gen_1);
GEN TR = addis(gel(DATA,5), 1);
GEN mTR = negi(TR), interp, bezoutC;
gel(DATA,5) = TR;
pol = translate_pol(gel(DATA,1), gen_m1);
l = lg(roo); p1 = cgetg(l, t_VEC);
for (i=1; i<l; i++) gel(p1,i) = gadd(TR, gel(roo,i));
roo = p1;
fk = gel(DATA,4); l = lg(fk);
for (i=1; i<l; i++) gel(fk,i) = gsub(Xm1, gel(fk,i));
bezoutC = gel(DATA,6); l = lg(bezoutC);
interp = gel(DATA,9);
for (i=1; i<l; i++)
{
if (degpol(interp[i]) > 0) /* do not turn pol_1[0] into gen_1 */
{
p1 = translate_pol(gel(interp,i), gen_m1);
gel(interp,i) = FpXX_red(p1, p);
}
if (degpol(bezoutC[i]) > 0)
{
p1 = translate_pol(gel(bezoutC,i), gen_m1);
gel(bezoutC,i) = FpXX_red(p1, p);
}
}
ff = cgetg(lff, t_VEC); /* copy, don't overwrite! */
for (i=1; i<lff; i++)
gel(ff,i) = FpX_red(translate_pol((GEN)S->ff[i], mTR), p);
}
else
{
DATA = cgetg(10,t_VEC);
fk = S->fk;
gel(DATA,5) = gen_0;
gel(DATA,6) = shallowcopy(S->bezoutC);
gel(DATA,9) = shallowcopy(S->interp);
}
gel(DATA,1) = pol;
MM = gmul2n(bound_for_coeff(B->d, roo, &maxroot), 1);
gel(DATA,8) = MM;
e = logint(shifti(vecmax(MM),20), p, &pe); /* overlift 2^20 [for d-1 test] */
gel(DATA,2) = pe;
gel(DATA,4) = roots_from_deg1(fk);
/* compute fhk = hensel_lift_fact(pol,fk,T,p,pe,e) in 2 steps
* 1) lift in Zp to precision p^e */
ffL = hensel_lift_fact(pol, ff, NULL, p, pe, e);
fhk = NULL;
for (l=i=1; i<lff; i++)
{ /* 2) lift factorization of ff[i] in Qp[X] / T */
GEN F, L = gel(ffL,i);
long di = degpol(L);
F = cgetg(di+1, t_VEC);
for (j=1; j<=di; j++) F[j] = fk[l++];
L = hensel_lift_fact(L, F, T, p, pe, e);
fhk = fhk? shallowconcat(fhk, L): L;
}
gel(DATA,3) = roots_from_deg1(fhk);
p1 = mulsr(N, gsqrt(gpowgs(utoipos(N-1),N-1),DEFAULTPREC));
p2 = gpowgs(maxroot, B->size + N*(N-1)/2);
p1 = gdiv(gmul(p1,p2), gsqrt(B->PD->dis,DEFAULTPREC));
gel(DATA,7) = mulii(shifti(ceil_safe(p1), 1), B->PD->den);
if (DEBUGLEVEL>1) {
fprintferr("f = %Z\n",DATA[1]);
fprintferr("p = %Z, lift to p^%ld\n", p, e);
fprintferr("2 * Hadamard bound * ind = %Z\n",DATA[7]);
fprintferr("2 * M = %Z\n",DATA[8]);
}
if (B->DATA) {
DATA = gclone(DATA);
if (isclone(B->DATA)) gunclone(B->DATA);
}
B->DATA = DATA;
}
