1 /*
2 Copyright (C) 2010 Sebastian Pancratz
3 Copyright (C) 2011-2014 Fredrik Johansson
4
5 This file is part of FLINT.
6
7 FLINT is free software: you can redistribute it and/or modify it under
8 the terms of the GNU Lesser General Public License (LGPL) as published
9 by the Free Software Foundation; either version 2.1 of the License, or
10 (at your option) any later version. See <https://www.gnu.org/licenses/>.
11 */
12
13 #include "fmpz_poly.h"
14
15 #define FLINT_REVERSE_NEWTON_CUTOFF 10
16
17 void
_fmpz_poly_revert_series_newton(fmpz * Qinv,const fmpz * Q,slong Qlen,slong n)18 _fmpz_poly_revert_series_newton(fmpz * Qinv,
19 const fmpz * Q, slong Qlen, slong n)
20 {
21 fmpz *T, *U, *V;
22 slong alloc = 3 * n;
23
24 if (n <= 2)
25 {
26 _fmpz_vec_set(Qinv, Q, n);
27 return;
28 }
29
30 T = _fmpz_vec_init(alloc);
31 U = T + n;
32 V = U + n;
33
34 FLINT_NEWTON_INIT(FLINT_REVERSE_NEWTON_CUTOFF, n)
35
36 FLINT_NEWTON_BASECASE(k)
37 _fmpz_poly_revert_series_lagrange(Qinv, Q, Qlen, k);
38 _fmpz_vec_zero(Qinv + k, n - k);
39 FLINT_NEWTON_END_BASECASE
40
41 FLINT_NEWTON_LOOP(FLINT_UNUSED(k0), k)
42 _fmpz_poly_compose_series(T, Q, FLINT_MIN(Qlen, k), Qinv, k, k);
43 _fmpz_poly_derivative(U, T, k); fmpz_zero(U + k - 1);
44 fmpz_zero(T + 1);
45 _fmpz_poly_div_series(V, T, k, U, k, k);
46 _fmpz_poly_derivative(T, Qinv, k);
47 _fmpz_poly_mullow(U, V, k, T, k, k);
48 _fmpz_vec_sub(Qinv, Qinv, U, k);
49 FLINT_NEWTON_END_LOOP
50
51 FLINT_NEWTON_END
52
53 _fmpz_vec_clear(T, alloc);
54 }
55
56 void
fmpz_poly_revert_series_newton(fmpz_poly_t Qinv,const fmpz_poly_t Q,slong n)57 fmpz_poly_revert_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n)
58 {
59 slong Qlen = Q->length;
60
61 if (Qlen < 2 || !fmpz_is_zero(Q->coeffs) || !fmpz_is_pm1(Q->coeffs + 1))
62 {
63 flint_printf("Exception (fmpz_poly_revert_series_newton). Input must have \n"
64 "zero constant term and +1 or -1 as coefficient of x^1\n.");
65 flint_abort();
66 }
67
68 if (Qinv != Q)
69 {
70 fmpz_poly_fit_length(Qinv, n);
71 _fmpz_poly_revert_series_newton(Qinv->coeffs, Q->coeffs, Qlen, n);
72 }
73 else
74 {
75 fmpz_poly_t t;
76 fmpz_poly_init2(t, n);
77 _fmpz_poly_revert_series_newton(t->coeffs, Q->coeffs, Qlen, n);
78 fmpz_poly_swap(Qinv, t);
79 fmpz_poly_clear(t);
80 }
81
82 _fmpz_poly_set_length(Qinv, n);
83 _fmpz_poly_normalise(Qinv);
84 }
85