mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
84 lines
2.3 KiB
C
84 lines
2.3 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 "arb_poly.h"
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void
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_arb_poly_asin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
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{
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arb_t c;
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arb_init(c);
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arb_asin(c, h, prec);
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hlen = FLINT_MIN(hlen, n);
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if (hlen == 1)
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{
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_arb_vec_zero(g + 1, n - 1);
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}
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else
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{
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arb_ptr t, u;
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slong ulen;
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t = _arb_vec_init(n);
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u = _arb_vec_init(n);
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/* asin(h(x)) = integral(h'(x)/sqrt(1-h(x)^2)) */
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ulen = FLINT_MIN(n, 2 * hlen - 1);
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_arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
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arb_sub_ui(u, u, 1, prec);
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_arb_vec_neg(u, u, ulen);
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_arb_poly_rsqrt_series(t, u, ulen, n, prec);
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_arb_poly_derivative(u, h, hlen, prec);
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_arb_poly_mullow(g, t, n, u, hlen - 1, n, prec);
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_arb_poly_integral(g, g, n, prec);
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_arb_vec_clear(t, n);
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_arb_vec_clear(u, n);
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}
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arb_swap(g, c);
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arb_clear(c);
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}
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void
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arb_poly_asin_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
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{
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slong hlen = h->length;
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if (hlen == 0 || n == 0)
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{
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arb_poly_zero(g);
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return;
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}
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arb_poly_fit_length(g, n);
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_arb_poly_asin_series(g->coeffs, h->coeffs, hlen, n, prec);
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_arb_poly_set_length(g, n);
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_arb_poly_normalise(g);
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}
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