mirror of
https://github.com/vale981/arb
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103 lines
2.8 KiB
C
103 lines
2.8 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2013 Fredrik Johansson
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******************************************************************************/
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#include "acb_poly.h"
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#define TAN_NEWTON_CUTOFF 20
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void
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_acb_poly_tan_series(acb_ptr g,
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acb_srcptr h, long hlen, long len, long prec)
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{
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hlen = FLINT_MIN(hlen, len);
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if (hlen == 1)
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{
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acb_tan(g, h, prec);
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_acb_vec_zero(g + 1, len - 1);
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}
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else if (len == 2)
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{
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acb_t t;
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acb_init(t);
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acb_tan(g, h, prec);
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acb_mul(t, g, g, prec);
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acb_add_ui(t, t, 1, prec);
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acb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */
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acb_clear(t);
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}
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else
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{
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acb_ptr t, u;
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t = _acb_vec_init(2 * len);
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u = t + len;
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NEWTON_INIT(TAN_NEWTON_CUTOFF, len)
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NEWTON_BASECASE(n)
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_acb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec);
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_acb_poly_div_series(g, t, n, u, n, n, prec);
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NEWTON_END_BASECASE
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NEWTON_LOOP(m, n)
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_acb_poly_mullow(u, g, m, g, m, n, prec);
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acb_add_ui(u, u, 1, prec);
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_acb_poly_atan_series(t, g, m, n, prec);
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_acb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec);
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_acb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec);
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NEWTON_END_LOOP
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NEWTON_END
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_acb_vec_clear(t, 2 * len);
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}
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}
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void
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acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, long n, long prec)
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{
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if (h->length == 0 || n == 0)
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{
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acb_poly_zero(g);
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return;
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}
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if (g == h)
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{
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acb_poly_t t;
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acb_poly_init(t);
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acb_poly_tan_series(t, h, n, prec);
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acb_poly_swap(g, t);
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acb_poly_clear(t);
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return;
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}
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acb_poly_fit_length(g, n);
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_acb_poly_tan_series(g->coeffs, h->coeffs, h->length, n, prec);
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_acb_poly_set_length(g, n);
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_acb_poly_normalise(g);
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}
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