/* return the factorization of the square-free polynomial x.
The coeffs of x are in Z_nf and its leading term is a rational integer.
deg(x) > 1, deg(nfpol) > 1
If fl = 1, return only the roots of x in nf
If fl = 2, as fl=1 if pol splits, [] otherwise */
static GEN
nfsqff(GEN nf, GEN pol, long fl)
{
long n, nbf, dpol = degpol(pol);
GEN pr, C0, polbase, init_fa = NULL;
GEN N2, rep, polmod, polred, lt, nfpol = gel(nf,1);
nfcmbf_t T;
nflift_t L;
pari_timer ti, ti_tot;
if (DEBUGLEVEL>2) { TIMERstart(&ti); TIMERstart(&ti_tot); }
n = degpol(nfpol);
polbase = unifpol(nf, pol, t_COL);
if (typ(polbase) != t_POL) pari_err(typeer, "nfsqff");
polmod = lift_intern( unifpol(nf, pol, t_POLMOD) );
if (dpol == 1) return mkvec(QXQX_normalize(polmod, nfpol));
/* heuristic */
if (dpol*3 < n)
{
GEN z, t;
long i;
if (DEBUGLEVEL>2) fprintferr("Using Trager's method\n");
z = (GEN)polfnf(polmod, nfpol)[1];
if (fl) {
long l = lg(z);
for (i = 1; i < l; i++)
{
t = gel(z,i); if (degpol(t) > 1) break;
gel(z,i) = gneg(gdiv(gel(t,2), gel(t,3)));
}
setlg(z, i);
if (fl == 2 && i != l) return cgetg(1,t_VEC);
}
return z;
}
nbf = nf_pick_prime(5, nf, polbase, fl, <, &init_fa, &pr, &L.Tp);
if (fl == 2 && nbf < dpol) return cgetg(1,t_VEC);
if (nbf <= 1)
{
if (!fl) return mkvec(QXQX_normalize(polmod, nfpol)); /* irreducible */
if (!nbf) return cgetg(1,t_VEC); /* no root */
}
if (DEBUGLEVEL>2) {
msgTIMER(&ti, "choice of a prime ideal");
fprintferr("Prime ideal chosen: %Z\n", pr);
}
pol = simplify_i(lift(polmod));
L.tozk = gel(nf,8);
L.topow= Q_remove_denom(gel(nf,7), &L.topowden);
T.ZC = L2_bound(nf, L.tozk, &(T.dn));
T.Br = nf_root_bounds(pol, nf); if (lt) T.Br = gmul(T.Br, lt);
if (fl) C0 = normlp(T.Br, 2, n);
else C0 = nf_factor_bound(nf, polbase); /* bound for T_2(Q_i), Q | P */
T.bound = mulrr(T.ZC, C0); /* bound for |Q_i|^2 in Z^n on chosen Z-basis */
N2 = mulsr(dpol*dpol, normlp(T.Br, 4, n)); /* bound for T_2(lt * S_2) */
T.BS_2 = mulrr(T.ZC, N2); /* bound for |S_2|^2 on chosen Z-basis */
if (DEBUGLEVEL>2) {
msgTIMER(&ti, "bound computation");
fprintferr(" 1) T_2 bound for %s: %Z\n", fl?"root":"factor", C0);
fprintferr(" 2) Conversion from T_2 --> | |^2 bound : %Z\n", T.ZC);
fprintferr(" 3) Final bound: %Z\n", T.bound);
}
L.p = gel(pr,1);
if (L.Tp && degpol(L.Tp) == 1) L.Tp = NULL;
bestlift_init(0, nf, pr, T.bound, &L);
if (DEBUGLEVEL>2) TIMERstart(&ti);
polred = ZqX_normalize(polbase, lt, &L); /* monic */
if (fl) {
GEN z = nf_DDF_roots(pol, polred, nfpol, lt, init_fa, nbf, fl, &L);
if (lg(z) == 1) return cgetg(1, t_VEC);
return z;
}
{
pari_sp av = avma;
if (L.Tp)
rep = FqX_split_all(init_fa, L.Tp, L.p);
else
{
long d;
rep = cgetg(dpol + 1, t_VEC); gel(rep,1) = FpX_red(polred,L.p);
d = FpX_split_Berlekamp((GEN*)(rep + 1), L.p);
setlg(rep, d + 1);
}
T.fact = gerepilecopy(av, sort_vecpol(rep, &cmp_pol));
}
if (DEBUGLEVEL>2) msgTIMER(&ti, "splitting mod %Z", pr);
T.pr = pr;
T.L = &L;
T.polbase = polbase;
T.pol = pol;
T.nf = nf;
T.hint = 1; /* useless */
rep = nf_combine_factors(&T, polred, L.p, L.k, dpol-1);
if (DEBUGLEVEL>2)
fprintferr("Total Time: %ld\n===========\n", TIMER(&ti_tot));
return rep;
}
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;
}
/* 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;
}
/*
* shine_iteration_loop:
* ------------------
*/
void shine_iteration_loop(shine_global_config *config)
{
shine_psy_xmin_t l3_xmin;
gr_info *cod_info;
int max_bits;
int ch, gr, i;
int *ix;
for(ch=config->wave.channels; ch--; )
{
for(gr=0; gr<config->mpeg.granules_per_frame; gr++)
{
/* setup pointers */
ix = config->l3_enc[ch][gr];
config->l3loop.xr = config->mdct_freq[ch][gr];
/* Precalculate the square, abs, and maximum,
* for use later on.
*/
for (i=GRANULE_SIZE, config->l3loop.xrmax=0; i--;)
{
config->l3loop.xrsq[i] = mulsr(config->l3loop.xr[i],config->l3loop.xr[i]);
config->l3loop.xrabs[i] = labs(config->l3loop.xr[i]);
if(config->l3loop.xrabs[i]>config->l3loop.xrmax)
config->l3loop.xrmax=config->l3loop.xrabs[i];
}
cod_info = (gr_info *) &(config->side_info.gr[gr].ch[ch]);
cod_info->sfb_lmax = SFB_LMAX - 1; /* gr_deco */
calc_xmin(&config->ratio, cod_info, &l3_xmin, gr, ch );
if ( config->mpeg.version == MPEG_I )
calc_scfsi(&l3_xmin,ch,gr,config);
/* calculation of number of available bit( per granule ) */
max_bits = shine_max_reservoir_bits(&config->pe[ch][gr],config);
/* reset of iteration variables */
memset(config->scalefactor.l[gr][ch],0,sizeof(config->scalefactor.l[gr][ch]));
memset(config->scalefactor.s[gr][ch],0,sizeof(config->scalefactor.s[gr][ch]));
for ( i=4; i--; )
cod_info->slen[i] = 0;
cod_info->part2_3_length = 0;
cod_info->big_values = 0;
cod_info->count1 = 0;
cod_info->scalefac_compress = 0;
cod_info->table_select[0] = 0;
cod_info->table_select[1] = 0;
cod_info->table_select[2] = 0;
cod_info->region0_count = 0;
cod_info->region1_count = 0;
cod_info->part2_length = 0;
cod_info->preflag = 0;
cod_info->scalefac_scale = 0;
cod_info->count1table_select= 0;
/* all spectral values zero ? */
if(config->l3loop.xrmax)
cod_info->part2_3_length = shine_outer_loop(max_bits,&l3_xmin,ix,
gr,ch,config);
shine_ResvAdjust(cod_info, config );
cod_info->global_gain = cod_info->quantizerStepSize+210;
} /* for gr */
} /* for ch */
shine_ResvFrameEnd(config);
}
/*
* L3_iteration_loop:
* ------------------
*/
void L3_iteration_loop(struct config_t *cfg, double pe[][2],
long mdct_freq_org[2][2][samp_per_frame2],
L3_psy_ratio_t *ratio,
L3_side_info_t *side_info,
int l3_enc[2][2][samp_per_frame2],
int mean_bits,
L3_scalefac_t *scalefactor)
{
L3_psy_xmin_t l3_xmin;
gr_info *cod_info;
int *main_data_begin;
int max_bits;
int ch, gr, i;
static int firstcall = 1;
int *ix;
main_data_begin = &side_info->main_data_begin;
if ( firstcall )
{
*main_data_begin = 0;
firstcall=0;
}
scalefac_band_long = &sfBandIndex[cfg->mpeg.samplerate_index + (cfg->mpeg.type * 3)].l[0];
for(ch=cfg->wave.channels; ch--; )
{
for(gr=0; gr<2; gr++)
{
/* setup pointers */
ix = l3_enc[gr][ch];
xr = mdct_freq_org[gr][ch];
/* Precalculate the square, abs, and maximum,
* for use later on.
*/
for (i=samp_per_frame2, xrmax=0; i--;)
{
xrsq[i] = mulsr(xr[i],xr[i]);
xrabs[i] = labs(xr[i]);
if(xrabs[i]>xrmax)
xrmax=xrabs[i];
}
cod_info = (gr_info *) &(side_info->gr[gr].ch[ch]);
cod_info->sfb_lmax = SFB_LMAX - 1; /* gr_deco */
calc_xmin(ratio, cod_info, &l3_xmin, gr, ch );
calc_scfsi(side_info,&l3_xmin,ch,gr);
/* calculation of number of available bit( per granule ) */
max_bits = ResvMaxBits(cfg, side_info,&pe[gr][ch],mean_bits);
/* reset of iteration variables */
memset(scalefactor->l[gr][ch],0,22);
memset(scalefactor->s[gr][ch],0,14);
for ( i=4; i--; )
cod_info->slen[i] = 0;
cod_info->part2_3_length = 0;
cod_info->big_values = 0;
cod_info->count1 = 0;
cod_info->scalefac_compress = 0;
cod_info->table_select[0] = 0;
cod_info->table_select[1] = 0;
cod_info->table_select[2] = 0;
cod_info->region0_count = 0;
cod_info->region1_count = 0;
cod_info->part2_length = 0;
cod_info->preflag = 0;
cod_info->scalefac_scale = 0;
cod_info->count1table_select= 0;
/* all spectral values zero ? */
if(xrmax)
cod_info->part2_3_length = outer_loop(max_bits,&l3_xmin,ix,
scalefactor,
gr,ch,side_info );
ResvAdjust(cfg, cod_info, side_info, mean_bits );
cod_info->global_gain = cod_info->quantizerStepSize+210;
} /* for gr */
} /* for ch */
ResvFrameEnd(cfg, side_info,mean_bits);
}
