int
fmpcb_poly_contains_fmpq_poly(const fmpcb_poly_t poly1, const fmpq_poly_t poly2)
{
long i;
fmpq_t t;
if (poly2->length > poly1->length)
return 0;
fmpq_init(t);
for (i = 0; i < poly2->length; i++)
{
fmpq_poly_get_coeff_fmpq(t, poly2, i);
if (!fmpcb_contains_fmpq(poly1->coeffs + i, t))
{
fmpq_clear(t);
return 0;
}
}
fmpq_clear(t);
for (i = poly2->length; i < poly1->length; i++)
if (!fmpcb_contains_zero(poly1->coeffs + i))
return 0;
return 1;
}
dgsl_rot_mp_t *dgsl_rot_mp_init(const long n, const fmpz_poly_t B, mpfr_t sigma, fmpq_poly_t c, const dgsl_alg_t algorithm, const oz_flag_t flags) {
assert(mpfr_cmp_ui(sigma, 0) > 0);
dgsl_rot_mp_t *self = (dgsl_rot_mp_t*)calloc(1, sizeof(dgsl_rot_mp_t));
if(!self) dgs_die("out of memory");
dgsl_alg_t alg = algorithm;
self->n = n;
self->prec = mpfr_get_prec(sigma);
fmpz_poly_init(self->B);
fmpz_poly_set(self->B, B);
if(fmpz_poly_length(self->B) > n)
dgs_die("polynomial is longer than length n");
else
fmpz_poly_realloc(self->B, n);
fmpz_poly_init(self->c_z);
fmpq_poly_init(self->c);
mpfr_init2(self->sigma, self->prec);
mpfr_set(self->sigma, sigma, MPFR_RNDN);
if (alg == DGSL_DETECT) {
if (fmpz_poly_is_one(self->B) && (c && fmpq_poly_is_zero(c))) {
alg = DGSL_IDENTITY;
} else if (c && fmpq_poly_is_zero(c))
alg = DGSL_INLATTICE;
else
alg = DGSL_COSET; //TODO: we could test for lattice membership here
}
size_t tau = 3;
if (2*ceil(sqrt(log2((double)n))) > tau)
tau = 2*ceil(sqrt(log2((double)n)));
switch(alg) {
case DGSL_IDENTITY: {
self->D = (dgs_disc_gauss_mp_t**)calloc(1, sizeof(dgs_disc_gauss_mp_t*));
mpfr_t c_;
mpfr_init2(c_, self->prec);
mpfr_set_d(c_, 0.0, MPFR_RNDN);
self->D[0] = dgs_disc_gauss_mp_init(self->sigma, c_, tau, DGS_DISC_GAUSS_DEFAULT);
self->call = dgsl_rot_mp_call_identity;
mpfr_clear(c_);
break;
}
case DGSL_GPV_INLATTICE: {
self->D = (dgs_disc_gauss_mp_t**)calloc(n, sizeof(dgs_disc_gauss_mp_t*));
if (c && !fmpq_poly_is_zero(c)) {
fmpq_t c_i;
fmpq_init(c_i);
for(int i=0; i<n; i++) {
fmpq_poly_get_coeff_fmpq(c_i, c, i);
fmpz_poly_set_coeff_fmpz(self->c_z, i, fmpq_numref(c_i));
}
fmpq_clear(c_i);
}
mpfr_mat_t G;
mpfr_mat_init(G, n, n, self->prec);
mpfr_mat_set_fmpz_poly(G, B);
mpfr_mat_gso(G, MPFR_RNDN);
mpfr_t sigma_;
mpfr_init2(sigma_, self->prec);
mpfr_t norm;
mpfr_init2(norm, self->prec);
mpfr_t c_;
mpfr_init2(c_, self->prec);
mpfr_set_d(c_, 0.0, MPFR_RNDN);
for(long i=0; i<n; i++) {
_mpfr_vec_2norm(norm, G->rows[i], n, MPFR_RNDN);
assert(mpfr_cmp_d(norm, 0.0) > 0);
mpfr_div(sigma_, self->sigma, norm, MPFR_RNDN);
assert(mpfr_cmp_d(sigma_, 0.0) > 0);
self->D[i] = dgs_disc_gauss_mp_init(sigma_, c_, tau, DGS_DISC_GAUSS_DEFAULT);
}
mpfr_clear(sigma_);
mpfr_clear(norm);
mpfr_clear(c_);
mpfr_mat_clear(G);
self->call = dgsl_rot_mp_call_gpv_inlattice;
break;
}
case DGSL_INLATTICE: {
fmpq_poly_init(self->sigma_sqrt);
long r= 2*ceil(sqrt(log(n)));
fmpq_poly_t Bq; fmpq_poly_init(Bq);
fmpq_poly_set_fmpz_poly(Bq, self->B);
fmpq_poly_oz_invert_approx(self->B_inv, Bq, n, self->prec, flags);
fmpq_poly_clear(Bq);
_dgsl_rot_mp_sqrt_sigma_2(self->sigma_sqrt, self->B, sigma, r, n, self->prec, flags);
mpfr_init2(self->r_f, self->prec);
mpfr_set_ui(self->r_f, r, MPFR_RNDN);
self->call = dgsl_rot_mp_call_inlattice;
break;
}
case DGSL_COSET:
dgs_die("not implemented");
default:
dgs_die("not implemented");
}
return self;
}
int fmpq_poly_oz_sqrt_approx_pade(fmpq_poly_t f_sqrt, const fmpq_poly_t f, const long n, const int p, const mpfr_prec_t prec, const mpfr_prec_t bound, oz_flag_t flags, const fmpq_poly_t init) {
fmpq_poly_t y; fmpq_poly_init(y);
fmpq_poly_t y_next; fmpq_poly_init(y_next);
fmpq_poly_t z; fmpq_poly_init(z);
fmpq_poly_t z_next; fmpq_poly_init(z_next);
mpfr_t norm; mpfr_init2(norm, prec);
mpfr_t prev_norm; mpfr_init2(prev_norm, prec);
mpfr_t log_f; mpfr_init2(log_f, prec);
if (init) {
// z = y/x
fmpq_poly_set(y, init);
_fmpq_poly_oz_invert_approx(z, f, n, prec);
fmpq_poly_oz_mul(z, z, y, n);
} else {
fmpq_poly_set(y, f);
fmpq_poly_set_coeff_si(z, 0, 1);
}
fmpq_t *xi = (fmpq_t*)calloc(p, sizeof(fmpq_t));
fmpq_t *a2 = (fmpq_t*)calloc(p, sizeof(fmpq_t));
fmpq_t *c = (fmpq_t*)calloc(p, sizeof(fmpq_t));
fmpq_poly_t *t_ = (fmpq_poly_t*)calloc(p, sizeof(fmpq_poly_t));
fmpq_poly_t *s_ = (fmpq_poly_t*)calloc(p, sizeof(fmpq_poly_t));
mpfr_t pi; mpfr_init2(pi, 4*prec);
mpfr_const_pi(pi, MPFR_RNDN);
#pragma omp parallel for
for(int i=0; i<p; i++) {
mpfr_t xi_r; mpfr_init2(xi_r, 4*prec);
mpfr_t a2_r; mpfr_init2(a2_r, 4*prec);
/* ζ_i = 1/2 * (1 + cos( (2·i -1)·π/(2·p) )) */
mpfr_set_si(xi_r, 2*i+1, MPFR_RNDN);
mpfr_mul(xi_r, xi_r, pi, MPFR_RNDN);
mpfr_div_si(xi_r, xi_r, 2*p, MPFR_RNDN);
mpfr_cos(xi_r, xi_r, MPFR_RNDN);
mpfr_add_si(xi_r, xi_r, 1, MPFR_RNDN);
mpfr_div_si(xi_r, xi_r, 2, MPFR_RNDN);
/* α_i^2 = 1/ζ_i -1 */
mpfr_set_si(a2_r, 1, MPFR_RNDN);
mpfr_div(a2_r, a2_r, xi_r, MPFR_RNDN);
mpfr_sub_si(a2_r, a2_r, 1, MPFR_RNDN);
fmpq_init(xi[i]);
fmpq_init(a2[i]);
fmpq_set_mpfr(xi[i], xi_r, MPFR_RNDN);
fmpq_set_mpfr(a2[i], a2_r, MPFR_RNDN);
fmpq_init(c[i]);
fmpq_poly_init(t_[i]);
fmpq_poly_init(s_[i]);
mpfr_clear(xi_r);
mpfr_clear(a2_r);
}
mpfr_clear(pi);
uint64_t t = oz_walltime(0);
int r = 0;
int cont = 1;
for(long k=0; cont; k++) {
if (k == 0 || mpfr_cmp_ui(prev_norm, 1) > 0)
_fmpq_poly_oz_sqrt_approx_scale(y, z, n, prec);
/* T = sum([1/xi[i] * ~(Z*Y + a2[i]) for i in range(p)]) */
#pragma omp parallel for
for(int i=0; i<p; i++) {
fmpq_poly_oz_mul(t_[i], z, y, n);
fmpq_poly_get_coeff_fmpq(c[i], t_[i], 0);
fmpq_add(c[i], c[i], a2[i]);
fmpq_poly_set_coeff_fmpq(t_[i], 0, c[i]);
fmpq_poly_scalar_mul_fmpq(t_[i], t_[i], xi[i]);
_fmpq_poly_oz_invert_approx(s_[i], t_[i], n, prec);
}
for(int i=1; i<p; i++)
fmpq_poly_add(s_[0], s_[0], s_[i]);
#pragma omp parallel sections
{
#pragma omp section
{
fmpq_poly_oz_mul(y_next, y, s_[0], n);
fmpq_poly_scalar_div_si(y_next, y_next, p);
fmpq_poly_set(y, y_next);
}
#pragma omp section
{
fmpq_poly_oz_mul(z_next, z, s_[0], n);
fmpq_poly_scalar_div_si(z_next, z_next, p);
fmpq_poly_set(z, z_next);
}
}
cont = !_fmpq_poly_oz_sqrt_approx_break(norm, y, f, n, bound, prec);
if(flags & OZ_VERBOSE) {
mpfr_log2(log_f, norm, MPFR_RNDN);
mpfr_fprintf(stderr, "Computing sqrt(Σ):: k: %4d, Δ=|sqrt(Σ)^2-Σ|: %7.2Rf", k, log_f);
fprintf(stderr, " <? %4ld, ", -bound);
fprintf(stderr, "t: %8.2fs\n", oz_seconds(oz_walltime(t)));
fflush(0);
}
if (cont) {
if (k>0 && mpfr_cmp_ui_2exp(norm, 1, bound) >= 0) {
/* something went really wrong */
r = -1;
break;
}
if (k>0 && mpfr_cmp(norm, prev_norm) >= 0) {
/* we don't converge any more */
r = 1;
break;
}
mpfr_set(prev_norm, norm, MPFR_RNDN);
}
}
for(int i=0; i<p; i++) {
fmpq_clear(xi[i]);
fmpq_clear(a2[i]);
fmpq_clear(c[i]);
fmpq_poly_clear(t_[i]);
fmpq_poly_clear(s_[i]);
}
free(xi);
free(a2);
free(c);
free(t_);
free(s_);
mpfr_clear(log_f);
fmpq_poly_set(f_sqrt, y);
mpfr_clear(norm);
mpfr_clear(prev_norm);
fmpq_poly_clear(y_next);
fmpq_poly_clear(y);
fmpq_poly_clear(z_next);
fmpq_poly_clear(z);
return r;
}