int main() { setbuf(stdout, NULL); SetSeed(ZZ(0)); for (long l = 256; l <= 16384; l *= 2) { // for (long n = 256; n <= 16384; n *= 2) { for (long idx = 0; idx < 13; idx ++) { long n = 256*(1L << idx/2); if (idx & 1) n += n/2; SetSeed((ZZ(l) << 64) + ZZ(n)); ZZ p; RandomLen(p, l); if (!IsOdd(p)) p++; ZZ_p::init(p); ZZ_pX a, c, f; random(a, n); random(f, n); SetCoeff(f, n); ZZ_pXModulus F(f); double t; SqrMod(c, a, F); long iter = 1; do { t = GetTime(); for (long i = 0; i < iter; i++) SqrMod(c, a, F); t = GetTime() - t; iter *= 2; } while (t < 3); iter /= 2; t = GetTime(); for (long i = 0; i < iter; i++) SqrMod(c, a, F); t = GetTime()-t; double NTLTime = t; FlintZZ_pX f_a(a), f_c, f_f(f), f_finv; fmpz_mod_poly_reverse(f_finv.value, f_f.value, f_f.value->length); fmpz_mod_poly_inv_series_newton(f_finv.value, f_finv.value, f_f.value->length); fmpz_mod_poly_mulmod_preinv(f_c.value, f_a.value, f_a.value, f_f.value, f_finv.value); t = GetTime(); for (long i = 0; i < iter; i++) fmpz_mod_poly_mulmod_preinv(f_c.value, f_a.value, f_a.value, f_f.value, f_finv.value); t = GetTime()-t; double FlintTime = t; printf("%8.2f", FlintTime/NTLTime); } printf("\n"); } }
int fmpz_mod_poly_is_irreducible_ddf(const fmpz_mod_poly_t poly) { fmpz_mod_poly_t f, v, vinv, reducedH0, tmp; fmpz_mod_poly_t *h, *H, *I; slong i, j, l, m, n, d; fmpz_t p; double beta; int result = 1; n = fmpz_mod_poly_degree(poly); if (n < 2) return 1; if (!fmpz_mod_poly_is_squarefree(poly)) return 0; beta = 0.5 * (1. - (log(2) / log(n))); l = ceil(pow(n, beta)); m = ceil(0.5 * n / l); /* initialization */ fmpz_init(p); fmpz_set(p, &poly->p); fmpz_mod_poly_init(f, p); fmpz_mod_poly_init(v, p); fmpz_mod_poly_init(vinv, p); fmpz_mod_poly_init(reducedH0, p); fmpz_mod_poly_init(tmp, p); if (!(h = flint_malloc((2 * m + l + 1) * sizeof(fmpz_mod_poly_struct)))) { flint_printf("Exception (fmpz_mod_poly_is_irreducible_ddf): \n"); flint_printf("Not enough memory.\n"); abort(); } H = h + (l + 1); I = H + m; for (i = 0; i < l + 1; i++) fmpz_mod_poly_init(h[i], p); for (i = 0; i < m; i++) { fmpz_mod_poly_init(H[i], p); fmpz_mod_poly_init(I[i], p); } fmpz_mod_poly_make_monic(v, poly); fmpz_mod_poly_reverse (vinv, v, v->length); fmpz_mod_poly_inv_series_newton (vinv, vinv, v->length); /* compute baby steps: h[i]=x^{p^i}mod v */ fmpz_mod_poly_set_coeff_ui(h[0], 1, 1); for (i = 1; i < l + 1; i++) fmpz_mod_poly_powmod_fmpz_binexp_preinv(h[i], h[i - 1], p, v, vinv); /* compute coarse distinct-degree factorisation */ fmpz_mod_poly_set(H[0], h[l]); fmpz_mod_poly_set(reducedH0, H[0]); d = 1; for (j = 0; j < m; j++) { /* compute giant steps: H[i]=x^{p^(li)}mod v */ if (j > 0) { fmpz_mod_poly_rem (reducedH0, reducedH0, v); fmpz_mod_poly_rem (tmp, H[j-1], v); fmpz_mod_poly_compose_mod_brent_kung_preinv(H[j], tmp, reducedH0, v, vinv); } /* compute interval polynomials */ fmpz_mod_poly_set_coeff_ui(I[j], 0, 1); for (i = l - 1; (i >= 0) && (2*d <= v->length - 1); i--, d++) { fmpz_mod_poly_rem(tmp, h[i], v); fmpz_mod_poly_sub(tmp, H[j], tmp); fmpz_mod_poly_mulmod_preinv (I[j], tmp, I[j], v, vinv); } /* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */ /* F_j is stored on the place of I_j */ fmpz_mod_poly_gcd(I[j], v, I[j]); if (I[j]->length > 1) { result = 0; break; } } fmpz_clear(p); fmpz_mod_poly_clear(f); fmpz_mod_poly_clear(reducedH0); fmpz_mod_poly_clear(v); fmpz_mod_poly_clear(vinv); fmpz_mod_poly_clear(tmp); for (i = 0; i < l + 1; i++) fmpz_mod_poly_clear(h[i]); for (i = 0; i < m; i++) { fmpz_mod_poly_clear(H[i]); fmpz_mod_poly_clear(I[i]); } flint_free(h); return result; }