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https://github.com/vale981/arb
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70 lines
2.1 KiB
C
70 lines
2.1 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT 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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FLINT 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 FLINT; 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) 2012 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_exp_series(arb_poly_t z, const arb_poly_t x, long n)
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{
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long a[FLINT_BITS];
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long i;
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arb_poly_t t;
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if (z == x)
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{
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arb_poly_t t;
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arb_poly_init(t, arb_poly_prec(x));
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arb_poly_set(t, x);
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arb_poly_exp_series(z, t, n);
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arb_poly_clear(t);
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return;
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}
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a[i = 0] = n;
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while (n >= 2)
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a[++i] = (n = (n + 1) / 2);
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arb_poly_init(t, arb_poly_prec(z));
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/* first coefficient (assuming input zero, todo: general case) */
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arb_poly_set_si(z, 1);
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fmpz_mul_2exp(arb_poly_coeffs(z), arb_poly_coeffs(z), arb_poly_prec(z));
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fmpz_set_si(arb_poly_expref(z), -arb_poly_prec(z));
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fmpz_zero(arb_poly_radref(z));
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/* Newton iteration */
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for (i--; i >= 0; i--)
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{
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n = a[i];
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arb_poly_log_series(t, z, n);
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arb_poly_neg(t, t);
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arb_poly_add(t, t, x);
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arb_poly_mullow(t, z, t, n);
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arb_poly_add(z, z, t);
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}
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arb_poly_clear(t);
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}
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