int dgsl_rot_mp_call_recenter_fmpq_poly(fmpz_poly_t rop, const dgsl_rot_mp_t *self, const fmpq_poly_t c, gmp_randstate_t state) { fmpq_poly_t x; fmpq_poly_init(x); fmpq_poly_sample_D1(x, self->n, self->prec, state); fmpq_poly_oz_mul(x, self->sigma_sqrt, x, self->n); fmpq_poly_neg(x, x); // we sample with centre c/g fmpq_poly_t t; fmpq_poly_init(t); fmpq_poly_oz_mul(t, c, self->B_inv, self->n); fmpq_poly_add(x, t, x); // (c+x2) fmpq_poly_clear(t); fmpz_poly_disc_gauss_rounding(rop, x, self->r_f, state); fmpz_poly_oz_mul(rop, self->B, rop, self->n); fmpq_poly_clear(x); return 0; }
int _dgsl_rot_mp_call_inlattice_multiplier(fmpz_poly_t rop, const dgsl_rot_mp_t *self, gmp_randstate_t state) { const long n = self->n; fmpq_poly_t x; fmpq_poly_init(x); fmpq_poly_sample_D1(x, n, self->prec, state); fmpq_poly_oz_mul(x, self->sigma_sqrt, x, self->n); fmpq_poly_neg(x, x);; fmpz_poly_disc_gauss_rounding(rop, x, self->r_f, state); fmpz_poly_neg(rop, rop);; fmpq_poly_clear(x); return 0; }
int dgsl_rot_mp_call_plus1(fmpz_poly_t rop, const dgsl_rot_mp_t *self, gmp_randstate_t state) { const long n = self->n; fmpq_poly_t x; fmpq_poly_init(x); fmpq_poly_sample_D1(x, n, self->prec, state); fmpq_poly_oz_mul(x, self->sigma_sqrt, x, self->n); fmpq_poly_neg(x, x); // (-x2) // we sample with centre c = -1/g fmpq_poly_sub(x, x, self->B_inv); // (c+x2) fmpz_poly_disc_gauss_rounding(rop, x, self->r_f, state); fmpz_poly_neg(rop, rop); fmpz_poly_oz_mul(rop, self->B, rop, self->n); fmpz_add_ui(rop->coeffs, rop->coeffs, 1); fmpq_poly_clear(x); return 0; }
static int _fmpq_poly_oz_sqrt_approx_break(mpfr_t norm, const fmpq_poly_t f_sqrt, const fmpq_poly_t f, const long n, const mpfr_prec_t bound, const mpfr_prec_t prec) { fmpq_poly_t f_approx; fmpq_poly_init(f_approx); fmpq_poly_oz_mul(f_approx, f_sqrt, f_sqrt, n); fmpq_poly_sub(f_approx, f_approx, f); fmpq_poly_2norm_mpfr(norm, f_approx, MPFR_RNDN); mpfr_t f_norm; mpfr_init2(f_norm, prec); fmpq_poly_2norm_mpfr(f_norm, f, MPFR_RNDN); mpfr_div(norm, norm, f_norm, MPFR_RNDN); int r = 0; if(mpfr_cmp_si_2exp(norm, 1, -bound) < 0) r = 1; mpfr_clear(f_norm); fmpq_poly_clear(f_approx); return r; }
void _dgsl_rot_mp_sqrt_sigma_2(fmpq_poly_t rop, const fmpz_poly_t g, const mpfr_t sigma, const int r, const long n, const mpfr_prec_t prec, const oz_flag_t flags) { fmpq_poly_zero(rop); fmpq_t r_q2; fmpq_init(r_q2); fmpq_set_si(r_q2, r, 1); fmpq_mul(r_q2, r_q2, r_q2); fmpq_neg(r_q2, r_q2); fmpq_poly_set_coeff_fmpq(rop, 0, r_q2); fmpq_clear(r_q2); fmpq_poly_t g_q; fmpq_poly_init(g_q); fmpq_poly_set_fmpz_poly(g_q, g); fmpq_poly_t ng; fmpq_poly_init(ng); fmpq_poly_oz_invert_approx(ng, g_q, n, prec, flags); fmpq_poly_t ngt; fmpq_poly_init(ngt); fmpq_poly_oz_conjugate(ngt, ng, n); fmpq_poly_t nggt; fmpq_poly_init(nggt); fmpq_poly_oz_mul(nggt, ng, ngt, n); /** We compute sqrt(g^-T · g^-1) to use it as the starting point for convergence on sqrt(σ^2 · g^-T · g^-1 - r^2) below. We can compute the former with less precision than the latter */ mpfr_t norm; mpfr_init2(norm, prec); fmpz_poly_eucl_norm_mpfr(norm, g, MPFR_RNDN); double p = mpfr_get_d(norm, MPFR_RNDN); /** |g^-1| ~= 1/|g| |g^-T| ~= |g^-1| |g^-1·g^-T| ~= sqrt(n)·|g^-T|·|g^-1| */ fmpq_poly_t sqrt_start; fmpq_poly_init(sqrt_start); p = log2(n) + 4*log2(p); int fail = -1; while (fail) { p = 2*p; if (fail<0) fail = fmpq_poly_oz_sqrt_approx_db(sqrt_start, nggt, n, p, prec/2, flags, NULL); else fail = fmpq_poly_oz_sqrt_approx_db(sqrt_start, nggt, n, p, prec/2, flags, sqrt_start); if(fail) fprintf(stderr, "FAILED for precision %7.1f with code (%d), doubling precision.\n", p, fail); } fmpq_t sigma2; fmpq_init(sigma2); fmpq_set_mpfr(sigma2, sigma, MPFR_RNDN); fmpq_poly_scalar_mul_fmpq(sqrt_start, sqrt_start, sigma2); fmpq_mul(sigma2, sigma2, sigma2); fmpq_poly_scalar_mul_fmpq(nggt, nggt, sigma2); fmpq_clear(sigma2); fmpq_poly_add(rop, rop, nggt); p = p + 2*log2(mpfr_get_d(sigma, MPFR_RNDN)); fmpq_poly_oz_sqrt_approx_babylonian(rop, rop, n, p, prec, flags, sqrt_start); mpfr_clear(norm); fmpq_poly_clear(g_q); fmpq_poly_clear(ng); fmpq_poly_clear(ngt); fmpq_poly_clear(nggt); fmpq_poly_clear(sqrt_start); }
int fmpq_poly_oz_sqrt_approx_babylonian(fmpq_poly_t f_sqrt, const fmpq_poly_t f, const long n, 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); mpfr_t norm; mpfr_init2(norm, prec); mpfr_t prev_norm; mpfr_init2(prev_norm, prec); if (init) { fmpq_poly_set(y, init); } else { fmpq_poly_set(y, f); } mpfr_t log_f; mpfr_init2(log_f, prec); uint64_t t = oz_walltime(0); int r = 0; for(long k=0; ; k++) { _fmpq_poly_oz_invert_approx(y_next, y, n, prec); fmpq_poly_oz_mul(y_next, f, y_next, n); fmpq_poly_add(y_next, y_next, y); fmpq_poly_scalar_div_si(y_next, y_next, 2); fmpq_poly_set(y, y_next); r = _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(r) { r = 0; break; } if (k>0 && mpfr_cmp_ui_2exp(norm, 1, bound) >= 0) { /* something went really wrong */ r = -1; break; } mpfr_div_ui(prev_norm, prev_norm, 2, MPFR_RNDN); 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); } 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); return r; }
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; }