mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
94 lines
2.3 KiB
C
94 lines
2.3 KiB
C
/*
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Copyright (C) 2017 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_poly.h"
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void
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_acb_poly_log1p_series(acb_ptr res, acb_srcptr f, slong flen, slong n, slong prec)
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{
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acb_t a;
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flen = FLINT_MIN(flen, n);
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acb_init(a);
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acb_log1p(a, f, prec);
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if (flen == 1)
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{
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_acb_vec_zero(res + 1, n - 1);
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}
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else if (n == 2)
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{
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acb_add_ui(res, f + 0, 1, prec);
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acb_div(res + 1, f + 1, res + 0, prec);
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}
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else if (_acb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
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{
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slong i, j, d = flen - 1;
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acb_add_ui(res, f + 0, 1, prec);
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for (i = 1, j = d; j < n; j += d, i++)
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{
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if (i == 1)
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acb_div(res + j, f + d, res, prec);
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else
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acb_mul(res + j, res + j - d, res + d, prec);
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_acb_vec_zero(res + j - d + 1, flen - 2);
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}
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_acb_vec_zero(res + j - d + 1, n - (j - d + 1));
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for (i = 2, j = 2 * d; j < n; j += d, i++)
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acb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
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}
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else
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{
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acb_ptr f_diff, f_inv;
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slong alloc;
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alloc = n + flen;
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f_inv = _acb_vec_init(alloc);
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f_diff = f_inv + n;
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acb_add_ui(f_diff, f, 1, prec);
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_acb_vec_set(f_diff + 1, f + 1, flen - 1);
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_acb_poly_inv_series(f_inv, f_diff, flen, n, prec);
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_acb_poly_derivative(f_diff, f, flen, prec);
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_acb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
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_acb_poly_integral(res, res, n, prec);
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_acb_vec_clear(f_inv, alloc);
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}
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acb_swap(res, a);
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acb_clear(a);
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}
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void
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acb_poly_log1p_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec)
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{
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slong flen = f->length;
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if (flen == 0 || n == 0)
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{
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acb_poly_zero(res);
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return;
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}
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if (flen == 1 /*&& !acb_contains_si(f->coeffs, -1)*/)
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n = 1;
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acb_poly_fit_length(res, n);
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_acb_poly_log1p_series(res->coeffs, f->coeffs, flen, n, prec);
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_acb_poly_set_length(res, n);
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_acb_poly_normalise(res);
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}
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