void fmpz_poly_revert_series_lagrange(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n) { fmpz *Qcopy; int Qalloc; slong Qlen = Q->length; if (Qlen < 2 || !fmpz_is_zero(Q->coeffs) || !fmpz_is_pm1(Q->coeffs + 1)) { flint_printf("Exception (fmpz_poly_revert_series_lagrange). Input must have \n" "zero constant term and +1 or -1 as coefficient of x^1.\n"); abort(); } if (Qlen >= n) { Qcopy = Q->coeffs; Qalloc = 0; } else { slong i; Qcopy = (fmpz *) flint_malloc(n * sizeof(fmpz)); for (i = 0; i < Qlen; i++) Qcopy[i] = Q->coeffs[i]; for ( ; i < n; i++) Qcopy[i] = 0; Qalloc = 1; } if (Qinv != Q) { fmpz_poly_fit_length(Qinv, n); _fmpz_poly_revert_series_lagrange(Qinv->coeffs, Qcopy, n); } else { fmpz_poly_t t; fmpz_poly_init2(t, n); _fmpz_poly_revert_series_lagrange(t->coeffs, Qcopy, n); fmpz_poly_swap(Qinv, t); fmpz_poly_clear(t); } _fmpz_poly_set_length(Qinv, n); _fmpz_poly_normalise(Qinv); if (Qalloc) flint_free(Qcopy); }
void _fmpz_poly_revert_series_newton(fmpz * Qinv, const fmpz * Q, long n) { if (n <= 2) { _fmpz_vec_set(Qinv, Q, n); return; } else { long *a, i, k; fmpz *T, *U, *V; T = _fmpz_vec_init(n); U = _fmpz_vec_init(n); V = _fmpz_vec_init(n); k = n; for (i = 1; (1L << i) < k; i++); a = (long *) flint_malloc(i * sizeof(long)); a[i = 0] = k; while (k >= FLINT_REVERSE_NEWTON_CUTOFF) a[++i] = (k = (k + 1) / 2); _fmpz_poly_revert_series_lagrange(Qinv, Q, k); _fmpz_vec_zero(Qinv + k, n - k); for (i--; i >= 0; i--) { k = a[i]; _fmpz_poly_compose_series(T, Q, k, Qinv, k, k); _fmpz_poly_derivative(U, T, k); fmpz_zero(U + k - 1); fmpz_zero(T + 1); _fmpz_poly_div_series(V, T, U, k); _fmpz_poly_derivative(T, Qinv, k); _fmpz_poly_mullow(U, V, k, T, k, k); _fmpz_vec_sub(Qinv, Qinv, U, k); } flint_free(a); _fmpz_vec_clear(T, n); _fmpz_vec_clear(U, n); _fmpz_vec_clear(V, n); } }