/* Copyright (C) 2011 Fredrik Johansson This file is part of FLINT. FLINT is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. See . */ #include #include "flint.h" #include "fmpz.h" #include "fmpz_poly.h" #include "fmpz_mat.h" #include "ulong_extras.h" void _fmpz_poly_compose_series_brent_kung(fmpz * res, const fmpz * poly1, slong len1, const fmpz * poly2, slong len2, slong n) { fmpz_mat_t A, B, C; fmpz *t, *h; slong i, m; if (n == 1) { fmpz_set(res, poly1); return; } m = n_sqrt(n) + 1; fmpz_mat_init(A, m, n); fmpz_mat_init(B, m, m); fmpz_mat_init(C, m, n); h = _fmpz_vec_init(n); t = _fmpz_vec_init(n); /* Set rows of B to the segments of poly1 */ for (i = 0; i < len1 / m; i++) _fmpz_vec_set(B->rows[i], poly1 + i*m, m); _fmpz_vec_set(B->rows[i], poly1 + i*m, len1 % m); /* Set rows of A to powers of poly2 */ fmpz_one(A->rows[0]); _fmpz_vec_set(A->rows[1], poly2, len2); for (i = 2; i < m; i++) _fmpz_poly_mullow(A->rows[i], A->rows[i-1], n, poly2, len2, n); fmpz_mat_mul(C, B, A); /* Evaluate block composition using the Horner scheme */ _fmpz_vec_set(res, C->rows[m - 1], n); _fmpz_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n); for (i = m - 2; i >= 0; i--) { _fmpz_poly_mullow(t, res, n, h, n, n); _fmpz_poly_add(res, t, n, C->rows[i], n); } _fmpz_vec_clear(h, n); _fmpz_vec_clear(t, n); fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(C); } void fmpz_poly_compose_series_brent_kung(fmpz_poly_t res, const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !fmpz_is_zero(poly2->coeffs)) { flint_printf("Exception (fmpz_poly_compose_series_brent_kung). Inner \n" "polynomial must have zero constant term.\n"); flint_abort(); } if (len1 == 0 || n == 0) { fmpz_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { fmpz_poly_set_fmpz(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { fmpz_poly_fit_length(res, lenr); _fmpz_poly_compose_series_brent_kung(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr); _fmpz_poly_set_length(res, lenr); _fmpz_poly_normalise(res); } else { fmpz_poly_t t; fmpz_poly_init2(t, lenr); _fmpz_poly_compose_series_brent_kung(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr); _fmpz_poly_set_length(t, lenr); _fmpz_poly_normalise(t); fmpz_poly_swap(res, t); fmpz_poly_clear(t); } }