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);
}
static GEN
Z2XQ_invnorm_pcyc(GEN a, GEN T, long e)
{
GEN q = int2n(e);
GEN z = ZpXQ_norm_pcyc(a, T, q, gen_2);
return Fp_inv(z, q);
}
static trace_data *
init_trace(trace_data *T, GEN S, nflift_t *L, GEN q)
{
long e = gexpo(S), i,j, l,h;
GEN qgood, S1, invd;
if (e < 0) return NULL; /* S = 0 */
qgood = int2n(e - 32); /* single precision check */
if (cmpii(qgood, q) > 0) q = qgood;
S1 = gdivround(S, q);
if (gcmp0(S1)) return NULL;
invd = ginv(itor(L->den, DEFAULTPREC));
T->dPinvS = gmul(L->iprk, S);
l = lg(S);
h = lg(T->dPinvS[1]);
T->PinvSdbl = (double**)cgetg(l, t_MAT);
init_dalloc();
for (j = 1; j < l; j++)
{
double *t = dalloc(h * sizeof(double));
GEN c = gel(T->dPinvS,j);
pari_sp av = avma;
T->PinvSdbl[j] = t;
for (i=1; i < h; i++) t[i] = rtodbl(mpmul(invd, gel(c,i)));
avma = av;
}
T->d = L->den;
T->P1 = gdivround(L->prk, q);
T->S1 = S1; return T;
}
static GEN _frob_lin(void *E, GEN F, GEN x2, long N)
{
GEN T = gel(F,3);
GEN q = int2n(N);
GEN y2 = Z2XQ_frob(x2, T, q);
GEN lin = ZX_add(ZX_mul(gel(F,1), y2), ZX_mul(gel(F,2), x2));
(void) E;
return FpX_rem(ZX_remi2n(lin, N), T, q);
}
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;
}
GEN
gcdii(GEN a, GEN b)
{
long v, w;
pari_sp av;
GEN t;
switch (absi_cmp(a,b))
{
case 0: return absi(a);
case -1: swap(a,b);
}
if (!signe(b)) return absi(a);
/* here |a|>|b|>0. Try single precision first */
if (lgefint(a)==3)
return igcduu((ulong)a[2], (ulong)b[2]);
if (lgefint(b)==3)
{
ulong u = resiu(a,(ulong)b[2]);
if (!u) return absi(b);
return igcduu((ulong)b[2], u);
}
/* larger than gcd: "avma=av" gerepile (erasing t) is valid */
av = avma; (void)new_chunk(lgefint(b)+1); /* HACK */
t = remii(a,b);
if (!signe(t)) { avma=av; return absi(b); }
a = b; b = t;
v = vali(a); a = shifti(a,-v); setabssign(a);
w = vali(b); b = shifti(b,-w); setabssign(b);
if (w < v) v = w;
switch(absi_cmp(a,b))
{
case 0: avma=av; a=shifti(a,v); return a;
case -1: swap(a,b);
}
if (is_pm1(b)) { avma=av; return int2n(v); }
{
/* general case */
/*This serve two purposes: 1) mpn_gcd destroy its input and need an extra
* limb 2) this allows us to use icopy instead of gerepile later. NOTE: we
* must put u before d else the final icopy could fail.
*/
GEN res= cgeti(lgefint(a)+1);
GEN ca = icopy_ef(a,lgefint(a)+1);
GEN cb = icopy_ef(b,lgefint(b)+1);
long l = mpn_gcd(LIMBS(res), LIMBS(ca), NLIMBS(ca), LIMBS(cb), NLIMBS(cb));
res[1] = evalsigne(1)|evallgefint(l+2);
avma=av;
return shifti(res,v);
}
}
/* Assume a = 1 [4] */
static GEN
Z2XQ_invnorm(GEN a, GEN T, long e)
{
pari_timer ti;
GEN pe = int2n(e), s;
if (degpol(a)==0)
return Fp_inv(Fp_powu(gel(a,2), get_FpX_degree(T), pe), pe);
if (DEBUGLEVEL>=3) timer_start(&ti);
s = ZpXQ_log(a, T, gen_2, e);
if (DEBUGLEVEL>=3) timer_printf(&ti,"Z2XQ_log");
s = Fp_neg(FpXQ_trace(s, T, pe), pe);
if (DEBUGLEVEL>=3) timer_printf(&ti,"FpXQ_trace");
s = modii(gel(Qp_exp(cvtop(s, gen_2, e-2)),4),pe);
if (DEBUGLEVEL>=3) timer_printf(&ti,"Qp_exp");
return s;
}
static GEN
nf_LLL_cmbf(nfcmbf_t *T, GEN p, long k, long rec)
{
nflift_t *L = T->L;
GEN pk = L->pk, PRK = L->prk, PRKinv = L->iprk, GSmin = L->GSmin;
GEN Tpk = L->Tpk;
GEN famod = T->fact, nf = T->nf, ZC = T->ZC, Br = T->Br;
GEN Pbase = T->polbase, P = T->pol, dn = T->dn;
GEN nfT = gel(nf,1);
GEN Btra;
long dnf = degpol(nfT), dP = degpol(P);
double BitPerFactor = 0.5; /* nb bits / modular factor */
long i, C, tmax, n0;
GEN lP, Bnorm, Tra, T2, TT, CM_L, m, list, ZERO;
double Bhigh;
pari_sp av, av2, lim;
long ti_LLL = 0, ti_CF = 0;
pari_timer ti2, TI;
lP = absi(leading_term(P));
if (is_pm1(lP)) lP = NULL;
n0 = lg(famod) - 1;
/* Lattice: (S PRK), small vector (vS vP). To find k bound for the image,
* write S = S1 q + S0, P = P1 q + P0
* |S1 vS + P1 vP|^2 <= Bhigh for all (vS,vP) assoc. to true factors */
Btra = mulrr(ZC, mulsr(dP*dP, normlp(Br, 2, dnf)));
Bhigh = get_Bhigh(n0, dnf);
C = (long)ceil(sqrt(Bhigh/n0)) + 1; /* C^2 n0 ~ Bhigh */
Bnorm = dbltor( n0 * C * C + Bhigh );
ZERO = zeromat(n0, dnf);
av = avma; lim = stack_lim(av, 1);
TT = cgetg(n0+1, t_VEC);
Tra = cgetg(n0+1, t_MAT);
for (i=1; i<=n0; i++) TT[i] = 0;
CM_L = gscalsmat(C, n0);
/* tmax = current number of traces used (and computed so far) */
for(tmax = 0;; tmax++)
{
long a, b, bmin, bgood, delta, tnew = tmax + 1, r = lg(CM_L)-1;
GEN oldCM_L, M_L, q, S1, P1, VV;
int first = 1;
/* bound for f . S_k(genuine factor) = ZC * bound for T_2(S_tnew) */
Btra = mulrr(ZC, mulsr(dP*dP, normlp(Br, 2*tnew, dnf)));
bmin = logint(ceil_safe(sqrtr(Btra)), gen_2, NULL);
if (DEBUGLEVEL>2)
fprintferr("\nLLL_cmbf: %ld potential factors (tmax = %ld, bmin = %ld)\n",
r, tmax, bmin);
/* compute Newton sums (possibly relifting first) */
if (gcmp(GSmin, Btra) < 0)
{
nflift_t L1;
GEN polred;
bestlift_init(k<<1, nf, T->pr, Btra, &L1);
polred = ZqX_normalize(Pbase, lP, &L1);
k = L1.k;
pk = L1.pk;
PRK = L1.prk;
PRKinv = L1.iprk;
GSmin = L1.GSmin;
Tpk = L1.Tpk;
famod = hensel_lift_fact(polred, famod, Tpk, p, pk, k);
for (i=1; i<=n0; i++) TT[i] = 0;
}
for (i=1; i<=n0; i++)
{
GEN h, lPpow = lP? gpowgs(lP, tnew): NULL;
GEN z = polsym_gen(gel(famod,i), gel(TT,i), tnew, Tpk, pk);
gel(TT,i) = z;
h = gel(z,tnew+1);
/* make Newton sums integral */
lPpow = mul_content(lPpow, dn);
if (lPpow) h = FpX_red(gmul(h,lPpow), pk);
gel(Tra,i) = nf_bestlift(h, NULL, L); /* S_tnew(famod) */
}
/* compute truncation parameter */
if (DEBUGLEVEL>2) { TIMERstart(&ti2); TIMERstart(&TI); }
oldCM_L = CM_L;
av2 = avma;
b = delta = 0; /* -Wall */
AGAIN:
M_L = Q_div_to_int(CM_L, utoipos(C));
VV = get_V(Tra, M_L, PRK, PRKinv, pk, &a);
if (first)
{ /* initialize lattice, using few p-adic digits for traces */
bgood = (long)(a - max(32, BitPerFactor * r));
b = max(bmin, bgood);
delta = a - b;
}
else
{ /* add more p-adic digits and continue reduction */
if (a < b) b = a;
b = max(b-delta, bmin);
if (b - delta/2 < bmin) b = bmin; /* near there. Go all the way */
}
/* restart with truncated entries */
q = int2n(b);
P1 = gdivround(PRK, q);
S1 = gdivround(Tra, q);
T2 = gsub(gmul(S1, M_L), gmul(P1, VV));
m = vconcat( CM_L, T2 );
if (first)
{
first = 0;
m = shallowconcat( m, vconcat(ZERO, P1) );
/* [ C M_L 0 ]
* m = [ ] square matrix
* [ T2' PRK ] T2' = Tra * M_L truncated
*/
}
CM_L = LLL_check_progress(Bnorm, n0, m, b == bmin, /*dbg:*/ &ti_LLL);
if (DEBUGLEVEL>2)
fprintferr("LLL_cmbf: (a,b) =%4ld,%4ld; r =%3ld -->%3ld, time = %ld\n",
a,b, lg(m)-1, CM_L? lg(CM_L)-1: 1, TIMER(&TI));
if (!CM_L) { list = mkcol(QXQX_normalize(P,nfT)); break; }
if (b > bmin)
{
CM_L = gerepilecopy(av2, CM_L);
goto AGAIN;
}
if (DEBUGLEVEL>2) msgTIMER(&ti2, "for this trace");
i = lg(CM_L) - 1;
if (i == r && gequal(CM_L, oldCM_L))
{
CM_L = oldCM_L;
avma = av2; continue;
}
if (i <= r && i*rec < n0)
{
pari_timer ti;
if (DEBUGLEVEL>2) TIMERstart(&ti);
list = nf_chk_factors(T, P, Q_div_to_int(CM_L,utoipos(C)), famod, pk);
if (DEBUGLEVEL>2) ti_CF += TIMER(&ti);
if (list) break;
CM_L = gerepilecopy(av2, CM_L);
}
if (low_stack(lim, stack_lim(av,1)))
{
if(DEBUGMEM>1) pari_warn(warnmem,"nf_LLL_cmbf");
gerepileall(av, Tpk? 9: 8,
&CM_L,&TT,&Tra,&famod,&pk,&GSmin,&PRK,&PRKinv,&Tpk);
}
}
if (DEBUGLEVEL>2)
fprintferr("* Time LLL: %ld\n* Time Check Factor: %ld\n",ti_LLL,ti_CF);
return list;
}
